Effect of Intraplant Insect Movement onEconomic Thresholds

c W HOY C E McCULLOCH2 A J SAWYER3A M SHELTON ANDC A SHOEMAKER

Department of Entomology Cornell UniversityNew York State Agricultural Experiment Station

Geneva New York 14456

EnvironEntomol19(5) 1578-1596 (1990)ABSTRACT Asimulation model wasconstructed to examine the effects of intraplant spatialdynamics of the lepidopteran pest complex of cabbage on direct damage to the marketableparts of the plant Diurnal fluctuations in microclimate for different parts of the crop canopywere simulated with sine functions Larval development rates for each specieswere simulatedwith logisticfunctions of temperature the development processwith time-varying distributeddelays and feeding rates with exponential functions of temperature and larval age Larvaltransition probabilities within the crop canopy were modeled with either constants or definiteintegrals of the Beta probability density function the shape parameters of which weremodeled as functions of temperature The model provided a good fit to data on changes inintraplant distribution of these larvae and intraplant distribution of feeding damage Eval-uation of model predictions suggeststhat a threshold population density used for managementdecisions should not be static but should be a complex function of species larval agedistribution and forecast temperatures A model like the one presented here could serve asthat complex function

KEY WORDS Insecta simulation model pest management

CURRENTLYmany pest management programs relyon economic thresholds to determine when pestpopulations must be reduced to prevent econom-ically important damage to a crop The economicthreshold is a simple model which predicts that acertain amount of damage to the marketable partsof the crop will occur within a given period oftime Economic thresholds developed in the past(Stern 1973 Poston et al 1983 Pedigo et al 1986Onstad 1987) however did not take into accountthe spatial structure of multiple pests and theirinjury within the crop canopy We hypothesize thatintraplant movement of insect pests profoundly af-fects the amount of damage they cause on themarketable parts of their host plant Herein wedescribe the construction and analysis of a simu-lation model we have used to explore the influenceof intraplant spatial dynamics of insect pests ondamage to the marketable parts of a crop Newtechniques were developed to model intraplantmovement as a function of microclimatic condi-tions within the crop canopy Spatial dynamics ofsome species are influenced by the host plant (Hoy

I To whomreprintrequestsshouldbe addressedCurrentad-dressDepartmentof EntomologyOhioAgriculturalResearchand DevelopmentCenterThe OhioStateUniversityWoosterOhio44691-6900

bullBiometricsUnitCornellUniversityIthacaNY14853USDA-ARSPlantProtectionResearchUnitUSPlantSoil

amp NutritionLaboratoryIthacaNY14853bullDepartmentofCivilandEnvironmentalEngineeringCornell

UniversityIthacaNY14853

amp Shelton 1987) and this interaction was also cap-tured in the models mathematical form

The system we studied includes fresh marketcabbage and its lepidopteran pest complex dia-mondback moth Plutella xylostella L cabbagelooper Trichoplusia ni (Hubner) and importedcabbageworm Artogeia rapae L The larvae ofeach pest damage the crop by chewing holes in theleaves The marketable parts of the cabbage cropthe head and four surrounding wrapper leaves andthe unmarketable parts the remaining frame leavesare vulnerable to this feeding damage Thereforethe leaves that are fed upon marketable or un-marketable largely determine the economic im-portance of the damage

Threshold population densities have been eval-uated and used to manage cabbage lepidopteranpests The thresholds proposed for fresh marketcabbage and for most crops have typically beenestablished by treating research plots at differentpopulation densities to estimate the maximum pop-ulation density at which 5 (or some other arbi-trary percentage) of cabbage heads will be ren-dered unmarketable They are often called actionthresholds because the required economic analysisfor a true economic threshold is usually impossibleto perform In practice however even the damageresulting from using a given action threshold canvary considerably Leibee et al (1984) tested sev-eral thresholds as well as weekly insecticide appli-cations and found that all treatment regimes gavesatisfactory results in two locations while only the

OO46-225X901578-1596$02000 copy 1990 EntomologicalSocietyof America

October 1990 HoY ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1579

weekly application provided gt95 marketableheads (rated according to Greene et al 1969) attwo other locations A threshold of one new feedinghole per plant based on the results of Chalfant etal (1979) yielded results as poor as 396 mar-ketable heads in a subsequent test (Workman et al1980) Other examples in which results of usingeither calendar schedules or proposed thresholdsvary in different locations or at different times havebeen reported as well (Sears et al 1983 Shelton etal 1983 Morisak et al 1984 Kirby amp Slosser 1984Cartwright et al 1987) These varying results implythat growers require a more reliable means of pre-dicting damage to their crop

We have proceeded by first validating our mod-el comparing predictions with observed data todetermine whether the predictions are accurateenough to be useful for our analysis Second wehave examined our more complex models predic-tions of damage resulting from a static thresholdpopulation density when factors affecting intra-plant spatial dynamics are varied Results suggestthat a useful model that predicts damage to themarketable parts of cabbage plants must incorpo-rate intra plant spatial dynamics of the lepidopteranpest complex Finally to gain insight into the po-tential for use of our model as a management toolwe analyzed the sensitivity of model predictions tochanges in the values of parameters and variablesinput by the user Before discussing these analyseswe describe the model and how parameters wereestimated

Model Description

Simulation modeling involves forecasting changesin the value of state variables which represent thestate of a system over time The system describedby this model includes populations of P xylostellaA rapae and T ni a cabbage crop and the in-fluence of weather conditions The cabbage cropis assumed to consist of mature or nearly mature(growth stage 8 or 9 Andaloro et al 1983b) plantsof uniform size State variables in the model are

Nkj(t) the average number N per plant of larvaeof species s and age subclass k on stratum jat time t (in days)

where

s = 1 2 3 representing P xylostella A rapaeand T ni respectively

k 1 2 20 representing subclasses in thedevelopment model and approximate agegroups

j 1 2 5 representing the head four sur-rounding wrapper leaves upper frame leavesmid frame leaves and lower frame leaves re-spectively

Thus the entire crop is represented by five verticalstrata and the entire population of each species is

represented by an average number and age struc-ture per plant on each of the five strata Althoughdistribution of larvae and their damage betweenplants is quite important it goes beyond the scopeof this study An auxiliary variable

Ej = average accumulated area offeeding (cm2) on stratum j

is calculated to estimate damage to the cropBelow we describe how the state variables change

as larval development and movement are simulat-ed and how the auxiliary variable is calculated asthe state variables change We have observed thatmortality due to naturally occurring agents over a7-d period in commercial cabbage fields is eithernegligible or too rare to be a useful addition to themodel Diurnal temperature fluctuations in eachof the different plant strata are incorporated asexternal variables A list of variables with defini-tions and parameter estimates is given in Table 1Inputs each of the submodels and output are de-scribed below for the model when run on a Macin-tosh computer (Apple Computer Cupertino Cal-if)Model Inputs Initial values for the state vari-

ables and the microclimate sub model must be inputby the user These include a weather forecast highand low temperatures and hours of sunshine forthe next 7 d and the average number per plant ofeach species on each stratum obtained by samplinga cabbage field Initial age distribution is estab-lished for A rapae and T ni by providing separateaverages for eggs small (first and second instars)and large (third fourth and fifth instars) larvaeThe initial age distribution is further defined byidentifying the proportion of larvae over the entireplant estimated to be in each of the five instarsThese initial values of state variables are input in-teractively in the screen depicted in Fig I (theweather forecast is input similarly)Microclimate A cabbage plant offers insects a

variety of microhabitats from exposed and sunnyleaves to leaves in almost perpetual shade there-fore temperature is modeled separately for eachof the plant strata Temperature (0C) in each stra-tum j at a given time t (days) tempj(t) is modeledwith sine functions to simulate diurnal fluctuationin temperature according to

tempt) = avtempt) + ampj(t)sine(t271) (1)

where

avtempj(t) the days average ambient air tem-perature in stratum j[=(maximum temperature + mini-mum temperature)2]

ampj(t) half of the days temperature rangein stratum j[=(maximum temperature - mini-mum temperature)2]

t is updated in increments of 002 d

1580 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

Table 1 List of variables used in a model to predict feeding damage by Lepidoptera on cabbage For parametervalues eSlimaled from our dala estimates (and standard errors in parentheses) are given

Variable Definition Type (or used Estimated valueto calculate)

Nkit) Average number N per plant of larvae of species s in State f(time rates)age subclass k on stratum j at time t (in days)

Eit) Average accumulated area of feeding (cm2) on stratum Auxiliary f(time rates)j at time t

temPI(t) Temperature in stratum j at time t (C) Exogenous f(time forecast)avtemPI(t) Days average temperature in stratum j at time t eC) Exogenous From weather forecastamPit) - days range in temperature in stratum j (C) Exogenous From weather forecastmlj m2j Constants to calculate ampj(t) as a function of amps(t) Exogenous j = 1 06658 (0089) 0

and forecasted hours of sunshine j = 2 (interpolated)j = 3 07634 (0487)00968 (0057)j = 4 (interpolated)j= 5 00

DELit) Development time (days) for the larval period of Rate f(temPI(t))species s in stratum j

C Maximum developmental rate for species s Rate P xylostella 01429middot[1 + eXP(gls + g20T)] A rapae 00909

T nt 01120Topt Temperature for maximum development rate (C) Rate 33C for all speciesgls820 Empirically estimated constants for development rate Rate A rapae 30707 (0201) -01624 (0012)

equations P xylostella 32317 (0118)-01458 (0007)

T nt 42059 (0130) -01884 (0008)DEL Relative dispersion in development time for species s Rate P xylostella 40

T A rapae 30T nt 50

Fs Proportional shift in substages of the distributed delay Rate P xylostella 05model of development A rapae 025

T nt 06U(t) Indicator variable in distributed delay Rate f(F DEL)FPDkj(t) Area of leaf (mm2) consumed per larva of species s in Rate f(temperature age)

age subclass k per day on stratum j at time this hz hJs Empirically estimated constants to calculate leaf area Rate P xylostella -23055 (108)

consumed per day as a function of temperature and 05273 (0108) -00117 (0003)larval age A rapite 36466 (125) 03183 (0124)

-00068 (0003)T nt 25730 (0968) 04072 (0097)

-00071 (0002) bullP4t) Transition probabilities for species s at time t from Rate For P xylostella

stratum t to stratum j [75~ 00 0]125 75 125 0 0o 125 75 125 0o 0 125 75 125o 0 0 2 8

For A rapae

[ 20 00]28 0 0 02 5 3 0 01 5 3 1 01 4 3 1 1

For T nt f(avgj(t))CI C2d] Constants (c] dl) and coefficients of temperature (C2 Rate See Hoy et al (1989)

d2 d2) for estimating shape parameters of Beta proba-bility density functions according to temperature

ajk bjk Shape parameters for the Beta pdfs described above Rate fCc] C2d] d2 avgj(t))(used to calculate transition probabilities for T nt)

Thus to simulate different microclimates in thedifferent strata we require a separate temperatureaverage and range for each of the strata Theseaverages and ranges were simulated by a simplemodel based on energy balance relationships in acrop canopy

Average temperature in each stratum is modeledas the forecast average ambient air temperaturemultiplied by a constant The constant for the lowerframe leaves was estimated as 10 (ie the tem-perature in the shaded lower frame is close to the

temperature that would be measured in a standardweather recording shelter) The constants for thehead and upper frame were modeled as the av-erage ratio of temperature measurements (de-scribed below) in those strata to measurements tak-en in the lower frame (103 104 105 1025 forthe head wrapper upper frame and midframeleaves respectively) For the wrapper leaves andmidframe leaves (j = 2 and 4) where temperaturemeasurements were not available average tem-perature is estimated by linear interpolation be-

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1581

r- bullbullbull File

iOEdit

Inputs

Fill in the bOXl8with the nquirld numblu

I~~li~~Cli~~II~~Itjinlr~degr~li~cr~8Ii~~81APIo~ J J) ) j j jj~

DB leW eL

Hledm~ 811 I[JCJ 8~11 I[]wrepPlrl 0 II 0 I 0 II 0 II 0 I 0 II 0 I

Uppn I 0 II 0 I =0=11 0 II 0 I 0 II 0 Il1id I 0 II 0 I =0 11 0 II 025 I 0 II 120 I

Lo~rl 0 II 0 1_0 ---II 0 II 100 I 002 II 030 I( RUN ) ( STRRT OUER

tt ------

Fig 1 Computer screen displaying the interactive input table for initializing a model to predict feeding damageby Lepidoptera on cabbage

tween averages for the other strata (j = 1 3 and35 respectively)

Like average temperature the temperature rangeis assumed to be the same in the lower frame leavesas in the forecast for ambient conditions Aroundthe cabbage head the observed temperature rangewas consistently narrower than it was under thelower frame leaves The head has considerable massand moderates the temperature around it There-fore the temperature range in stratum 1 the headis modeled as a proportion of the range in the lowerframe The temperature range in the upper frameis modeled as the range in the lower frame plus aneffect of sunshine

amp3(t) = amp5(t) + m3 + m2) (forecasted hours of

sunshine on day t) (2)

where ml and m2 are empirically estimated con-stants The upper frame leaves absorb radiant heatenergy from sunlight resulting in higher daytimetemperatures than on the lower leaves they radiateheat more easily at night than the lower leavesbecause they are exposed to the sky resulting inlower night temperatures in this part of the canopy

Measurements were not available for the tem-perature range in the wrapper and midframe leavesTemperature ranges in these strata were modeledsimilarly to the upper frame leaves but the effect

of sunshine was reduced to two-thirds that of theupper frame for the wrapper leaves and one-thirdthat of the upper frame for the midframe leavesbecause these strata receive less sunlight

To estimate the differences in average temper-ature and amplitude between strata temperaturewas monitored on the undersides of the leaves inthree of the strata (the head upper frame leavesand lower frame leaves) from 13 August to 23October 1986 in research plots in Geneva N Y asdescribed in Hoy et al (1989) Hourly temperatureaverages from 2-min samples were recorded Dailytotal solar radiation and ambient air temperatureswere measured at the New York State AgriculturalExperiment Station weather station Geneva NYDaily total solar radiation (caljcm) was dividedby an estimate of average solar radiation per hourfor Geneva N Y during the time the measure-ments were taken to approximate hours of sun-shine Estimated coefficients for the regression de-scribed above and for each of the constants aregiven in Table 1 (SAS Institute 1982) Quadraticand higher order polynomial coefficients for solarradiation were not significantly different from zero(P = 01228 n = 43) indicating that the relation-ship could be described as linear T-statistics onslope coefficients in these regression analyses alsoindicated that the linear effects of solar radiationon amplitude in the upper frame leaves were sig-

1582 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

(3)

Fig 2 Calculated development times for P xylo-stella A rapae and T ni larvae on cabbage (solidlines)compared with development times previously reportedin the literature at specific temperatures

30

A rapaebull Chenamp Su1982bull Smithamp Smilowitz1976o Tatchell1981o Theunissenet al198511 Given1944bull Richards1940bull Harcourt1955

P xylosteJao Hardy1938bull Chenamp Su1978o Miner194711 Yamadaamp Kawasaki1983

20

Tni+ Shoreyet al1962(males)bull Shoreyet al1962(females)o Jackson1969[] Tobaat al197311 Boldtat al1975bull Butleretal1975bull Chenamp Su1982

o

Temperature (Oe)

o

o10

20

40

80

60

10

20

30

40

10

20

30

Ulgtctl0-Q)

Ei=EQ)

EaoQ)gtQ)Cl

algorithm shifts a proportion of the contents of eachsubclass to the next subclass at certain time stepsThe number of time steps before each shift occursand the proportion of the contents of each subclassshifted are determined by the average develop-ment time or delay and the estimated dispersionin development times The controlled dispersionmodel was used because fewer subclasses were re-quired to represent the observed distribution ofdevelopment times adequately (with 20 subclasses

whereDELj(t) average development time (days) for

the larval period in species s on stra-tum j at time t

C (maximum development rate)(l +eBb + R2s Top

Top temperature at which maximum de-velopment rate occurs

Tj(t) temperature on stratum j at time tif tempj(t) 5 Top2 Top - tempj(t) if tempj(t) gt Top

gt g2gt empirically estimated constants forspecies s

This model was used because it fits developmentrate data for T ni well (Butler et a1 1976) and itcould easily be fit to data for the other species usingstandard nonlinear regression packages Becausethe relationship between temperature and devel-opment time of P xylostella and A rapae is qual-itatively similar to that of T ni the function abovewas expected to provide a good fit to the data forthese species as well The gls and g2gt from equation3 were estimated by nonlinear regression (SASInstitute 1982) with the Marquardt computationmethod from data collected by AMS and P BBaker (unpublished data) (Table 1) Minimum de-velopment times (days) for each species were es-timated from data in the literature to be 8 d forP xylostella 12 d for A rapae and 9 d for T niall at 33degC The inverse of these minimum devel-opment times was used to approximate each of theC (equation 3) in the estimations

Development times calculated using the algo-rithm with parameters calculated from AMS andP B Bakers data were very similar to those re-ported in the literature for A rapae and T niwhereas development times for P xylostella wereslightly longer than those previously reported (Fig2) The parameter estimates obtained from AMSand P B Bakers unpublished data were used be-cause the food source in their study excised cab-bage leaves was most similar to the food source ofthe population being modeled Because food sourcecan affect larval development rate (Shorey et a11962 Jones amp Ives 1979 Wolfson 1982) use ofthese data rather than data from the literatureshould provide more accurate results

Dispersion in development times was simulatedby a time-varying distributed delay (Manetsch 1976)with controlled dispersion (Goudriaan 1973) This

nificant (P lt 005 n = 43) In addition the effectof solar radiation on temperatures in the head wasnot significant (P = 02733 n = 43)

Development Rates Average larval develop-ment rates are calculated as a function of temper-ature for each species according to the algorithmproposed by Stinner et al (1974)

1 CDELt) (1 + egh+8r(I))

October 1990 Hoy ET ALINTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1583

where

Nkt + At) = Nkt(t) + U(t)Fmiddot[Nlk_Jlt) - Nkt)] (4)

feeding area (mm2) per day perlarva of species s in subclass k onstratum j at time tdays average temperature instratum j at time taverage proportion of larval de-velopment completed by sub-class k

(2~- 0)empirical constants for species s

avtempt)

where

1If each subclass is assumed to represent 20 of a

larvas development time average feeding rate foreach subclass in the distributed delay is calculated

(k 1) at the midpoint of the class agek = 20 - 40 ill

Equation (6) Thus accumulated feeding in cm2 issummed over all age classes of all species and all

instars) and large (third fourth and fifth instars)larvae on a given stratum We typically observeconsiderable overlap in P xylostella life stages inthe field Therefore the initial number of P xy-lostella on each stratum is evenly divided amongthe 20 delay subclasses that represent this speciesand only forecast total numbers of P xylostellalarvae are reported

Feeding Rates Accumulated feeding by eachspecies on each stratum is calculated as a functionof temperature and larval age The larvae of eachspecies tend to eat very little until the final instarswhen feeding rates increase dramatically (Chen ampSu 1978 1982) An exponential model is used toensure that the predicted feeding rate is positiveand to provide a qualitatively good fit Plots of In(feeding aread) against proportion of develop-ment time completed at three temperatures ap-peared linear with intercept close to zero and slopedependent on temperature Tatchell (1981) studiedconsumption by A rapae at lower temperaturesand found that total consumption (leaf area in cm2)

increased between 13 and 19degC then decreasedbetween 19 and 24degCj Boldt et a1(1975) found thatT ni consumption increased from 20 to 25degC andthen decreased between 25 and 30degC These studiesand the plots described above indicate that theeffects of temperature on feeding rates are not lin-ear rather they are greater at intermediate tem-peratures and less at low and high temperaturesWe describe this effect of temperature on feedingrate by defining the slope in a regression of In(feeding aread) predicted by larval age as a qua-dratic function of temperature Feeding rate perlarva per day as a function of temperature and ageof the larva can then be expressed as an exponentialfunction

(5)

F

U(t)

M(t)

5(t) 1 - 20DEV(t) the proportion of each

Sj

subclass shiftedthe standard deviation of developmenttimes for species s1 for M(t) = 123 o otherwise At

~ F DELi(r) 20

At 002 dr = At 2At 3M

52-- - was found to be fairly constant for eachDEVspeci~s over three temperatures (AMS and P BBaker unpublished data) so F was assumed to bea constant (Table 1) When programmed U(t) actsas an indicator for the shift of contents from eachsubclass to the next subclass and F gives the pro-portion of each subclass shifted

The subclasses are used to approximate larvalage groups which are required to calculate age-specific feeding rates and to assign an age to thelarvae that move between strata Larvae on dif-ferent strata develop at different rates because ofdifferent temperaturesj therefore larvae that movebetween strata must be placed in the appropriateage group at the new location (technically thesubclasses refer to relative maturity rather thanchronological age)

The average number of a given instar per plantis divided evenly among delay subclasses desig-nated to represent that instar as follows k = 1-34-6 7-10 11-15 16-20 for A rapae instars onethrough five and k = 1-3 4-6 7-9 10-14 15-20for T ni instars one through five The number ofsubclasses used to represent each instar for a givenspecies was based on estimates of the proportionof total larval development time spent in each in-star (AMS and P B Baker unpublished data)For example if approximately one-fourth of thelarval period is spent in the last instar the last instarwould be represented by one-fourth of the sub-classes the last five Summing over the appropriatesubclasses gives the number of individuals in a giv-en instar at a given time In practice instar des-ignations are used only for initialization and re-porting forecast numbers of small (first and second

for each species the output was similar to a delaywithout controlled dispersion using approximatelytwice the number of subclasses and twice theamount of computing time)

Programming the distributed delay with con-trolled dispersion yields the following differenceequation for the average number of pests perplant N

1584 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

(7)

31

31

T ni

A rapae

P xyfostefla

00010 a8

a6Physiological

Age

constants estimated by maximumlikelihood as described by Hoy etal (1989)

gt 449535~~ 2lli90ig~ 149845IIOJc6 aooaf 10 08

Fig 3 Predicted feeding rates of P xylo8tella Arapae and T ni on cabbage

Because the shape parameters for the Beta distri-bution a and h change with temperature theshape of the distribution and value of the integralsdescribed in Equation (8) change accordinglyHigher temperatures tend to result in greater prob-ability of movement and higher probability ofmovement towards the lower leaves than towardsthe head lower temperatures tend to result in lowerprobability of movement and higher probabilityof movement towards the head than towards thelower leaves

The elements of the transition probability ma-trices for P xylostella and A rapae are estimatedfrom observations reported in the literature (Har-court 1963 1966 Chua amp Lim 1979 Samson amp

~ 15llli6S~~ 1(57 n

1sectGl 5281IlttlaOJc6af 06

PhysiologicalAge

~~ JI64

~ce 576

sectGl

l2 1288OJc6GlGl

U

previous time steps by

Ej(t) = plusmn plusmn ~ [NkT)FPDkj(T)] ~tTO -I k-I 100

where

Ej(t) area of feeding (cm2) on stratum j accu-mulated at time t

T ~t 2~t 3~t M 002 d

Pj(t)

= f ~ 1__ U1a(I)-11(1 - U)lb(l)-ll duJ~l B[a(t) b(t)] (8)

where

the probability of a T ni (species3) late instar moving from stratumi to stratum j during one dayeel +C2 avtemPi(t)

ed +d2atemp)

The three empirical constants (hh hz and h31inEquation 6) for estimating feeding rates as a func-tion of temperature and larval age were estimatedby multiple linear regression (SAS Institute 1982)of the natural log of feedingday (mm2) on ageage temperature and agemiddottemperature2 (Table 1)The measure of larval age was the proportion oflarval stage completed or days the larva had livedso far divided by total days spent by that larvafrom eclosion to pupation Measurements of areaof cabbage leaf consumed each day of the larvalperiod for each of 20 larvaereplicate and threereplicatestemperature at 167 211 and 267degCfor each species were taken by AMS and P BBaker (unpublished data) Inspection of predictions(Fig 3) compared with data reported in the lit-erature (Harcourt et al 1955 McEwen amp Hervey1960 Rahman 1970 Harper 1973 Boldt et al 1975Chen amp Su 1978 1982 Samson amp Geier 1983Theunissen et al 1985) indicates that the feedingrate model fit well Data on feeding by A rapaereported by Tatchell (1981) indicate much higherrates than those we estimated but Tatchells datadisagree with the other literature cited above aswell As in the case of development rates we usedthe AMS and P B Baker data because the foodsource was cabbage leaf so these data should bemost appropriate

Movement Rates Larval movement is simulatedwith discrete time transition probability matricesbecause observed larval movements were discretein time Movement of late instar T ni is correlatedwith microclimate (Hoy et al 1989) and must bemodeled accordingly The transition probabilitiesfor late instar T ni are modeled as definite integralsof the Beta probability density function (pdf) withshape parameters a(t) and b(t) which depend ontemperature and the stratum larvae are movingfrom

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS

File Edit

1585

021

339

1131

3241

2568

Fig 4 Computer screen displaying output from a simulation model of feeding damage by Lepidoptera oncabbage

Geier 1983 Salinas 1984) and our own observa-tions Our observations for these species were thefrequency of movements by larvae marked withfluorescent powder and visually censused at ~1-hintervals in research cabbage plots near GenevaNY The number of these observations was notsufficient to estimate individual transition proba-bilities so the data were used roughly to estimatefrequency of movement and probability of movingup or down on the plant For P xylostella thefrequency of movement was low and approxi-mately equal numbers of upwards and downwardsmovements were observed For A rapae virtuallyall late instars were observed to move upwards tothe head or wrapper leaves as noted by Harcourt(1963 1966) and Hoy amp Shelton (1987) Transitionprobabilities that reflect these observations werechosen for these two species and are given in Ta-ble 1

The change in state variables due to movementis thus calculated by

s

Nkj(t + ~t) = ~ Nkj(t)pj(t)I(t + ~t) (9)

where

k =k =

I(t + ~t)

~t

13 14 20 for s = 110 11 20 for s = 2 or 3

1 if (t + ~t) = 1 2 3 o otherwise002d

Movement is simulated only once each day andbecause the time step for the model is lfso of a daythe indicator I(t) is used to determine when themovements occur The values of k given above arechosen so that movement is simulated only for olderlarvae which are represented by higher values ofk (k ~ 13 for P xylostella and k ~ 10 for A rapaeor T ni)Model Output The output generated using the

equations described above is a summary of thevalues of state variables and the value of the aux-iliary variable each day for the next 7 d This ispresented on the computer screen depicted in Fig4 The number of large and small larvae of eachspecies on each stratum also can be obtained for aprintout by summing over the appropriate sub-classes in the distributed delay The picture of acabbage plant on the screen gives the user an ap-proximate idea of what the predicted damage onthe cabbage crop would look like

Validation

Methods Validation analysis was performed todemonstrate how well the model predicts data thatwere not used in model design or parameterizationData collected by a commercial field monitoringand pest control advising service were used to com-pare model predictions with observed populationdensities and feeding damage 7 d after the original

1586 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

A rapae

P xylostella

18161412108642o 00 06 12 18 24

557371

1114

92

743

1300

A rapae

10

P xylostella

20

oO0 16 32 48 64

30

10

20

1 ffi

0O0 1 2 2 4 3 6 4 8

000-05 00 05 10 15

1300

11 14

929 T ni T ni

743

55710

3 71

186

0 00- O32 -O16 O00 016 032 O0 O8 16 2 4 3 2

Standardized Residuals Standardized Residualsfor the Head for the Wrapper Leaves

-ogtucQ)=J0Q)-LL

Fig 5 Histograms of standardized cell residuals for comparing predicted numbers with observed averagenumbers of larvae on the cabbage head and wrapper leaves in commercial cabbage fields near Geneva NY

sample Scouts sampled cabbage fields on a weeklybasis using a variable-intensity sampling scheme(Hoy et al 1983) Separate counts of P xylostellalarvae (all instars combined) and A rapae and Tni eggs small (first and second instars) and large(third fourth and fifth instars) larvae were taken

on the head (stratum 1) wrapper (stratum 2) andframe leaves (strata 3-5 combined) and were usedto initialize the model Predictions of numbers ofP xylostella large A rapae and T ni and ac-cumulated feeding on the head and wrapper leaveswere compared with the scouts observations taken

October 1990 HoY ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1587

o [] a [] C D

QOO n~ Q~ n~ 100 1~ t~ 1~ 200Average Damage Rating

Average Damage Rating

Fig 6 Comparison of predicted feeding damagewith average observed damage rating on the heads andwrapper leaves of commercial cabbage crops near Ge-neva NY

the following week Initial spatial distribution with-in the frame and initial age distribution with Arapae and T ni small and large larval populationswere assumed to be uniform for lack of more pre-cise information The scouts observations includedratings of feeding damage on a scale of 0 to 4indicating approximately no damage less than onefeeding hole per leaf one to three feeding holesper leaf 10 defoliation and 40 defoliationrespectively These ratings were compared withpredictions of accumulated area of feeding withscatter plots and correlation analysis

Weather data for model inputs (maximum andminimum temperatures and daily total solar ra-diation) were recorded at the New York State Ag-ricultural Experiment Station in Geneva NY thec1vsest weather station to the commercial fieldsbeing monitored (within 20 km) Data from 34pairs of field samples-each pair taken one weekapart during July August and September in 1983and 1984 under widely varying weather condi-tions-were used for this analysis

Model predictions for number of larvae on thehead and wrapper leaves were compared with ob-servations using standardized cell residuals givenby

observed no larvae - predicted no larvaeVpredicted no larvae

Evaluation of Existing Treatment Guidelines

Because the model predicts numbers of larvaeand feeding damage on different parts of the plantwell model predictions cap be used to evaluatetreatment guidelines currently in use for cabbagepest management In particular the model can beused to explore the relative effects of each pest onthe crop and how useful a static threshold for pestpopulation density will be in predicting a given

as described by Bishop et al (1975) These ap-proximate a standard normal distribution so thecriterion for evaluation is whether or not most ofthe residuals are within 2 SD of the mean (- 2and ~2) because lt=95of the standard normaldistribution falls within this range Observations ofthe feeding damage rating also were plotted againstpredicted accumulated area of feeding and asso-ciated correlation coefficients were calculated

Results and Discussion Most standardized cellresiduals for predicted versus observed counts oflarvae on the head and wrapper leaves were wellwithin the range -2 to +2 (Fig 5) The few largedeviations that were calculated were positive in-dicating that occasionally greater average num-bers of larvae than predicted were observed Theinterplant spatial distribution of each species is ag-gregated (Harcourt 1966) and sample sizes wereoften small (as few as 11 plants) so these occasionallarge positive deviations are not surprising Theseresults indicate that the model predicts number andlocation of larvae well particularly when the lowresolution in the data for initial age and spatialdistribution within the frame and potential sam-pling error in both samples are considered Con-clusions from this analysis must be tempered some-what however by the low population densitiesobserved in these fields Bishop et al (1975) warnthat the approximation of the standardized cellresiduals to the standard normal is poorest whenpredictions in the cells are small Most of the initialpopulation densities and associated predictions weresmall because pest population densities are keptlow by farmers Evaluation of the model underthese conditions is most appropriate however be-cause these are the conditions under which themodel would be used

Predicted area of feeding was correlated withobserved damage rating (Fig 6) Damage ratingincluded assessment of recent feeding as well asolder damage done before the first sample Thiscould explain circumstances in which little feedingdamage was predicted but high damage ratingswere observed Cases where large amounts of feed-ing damage were predicted but observed damagerating was low did not occur Feeding damage isthe most important variable to managers becauseit determines the market value of the crop Thedata indicate that the model can be used to predictthe effects on the cabbage crop of a given pestpopulation under specific conditions

3

(10)

D

o

D

D

o

CC

lJ 8DaD co lJ 0

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1588 ENVIRONMEITAL ENTOMOLOGY Vol 19 no 5

Head Wrapper Leaves

T ni 565134

377089

189045

2020

- Temporatura Avorago plon1CJ DCEC)---0)c A rapaea 1t82Q) a18Q)U 546 7890Q) 273 396sect0 30 30eD

Temperature Avorago pIontDC Temperalure Avomg bullbull p1ont

DC

P xylostella074 178050 11902i 061

20

rompera1ur Avorago plantDC Tempera1ure Averag bullbull p1on1

DC

Fig 7 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves after 7 d atdifferent temperatures and population densities of lepidopteran pests

amount of damage on the marketable parts of thecrop

Methods Response surfaces of predicted area offeeding on the head and wrapper leaves to tem-perature and population density of each pest weregenerated with the model A standard initial in-traplant spatial distribution typical of distributionsobserved in cabbage fields was chosen for eachspecies as follows P xylostella 005 01 03 03and 025 A rapae 0 015 04 03 and 015 Tni 0 01 02 04 and 03 of the average numberper plant on the head wrapper leaves upper framemidframe and lower frame respectively For Pxylostella the larval ages were uniformly distrib-uted among the 20 subclasses in the distributeddelay For A rapae and T ni the larvae wereinitialized into the first 10 subclasses simulatingfirst second and third instars For each of 10 pop-ulation densities ranging from well below to well

above the action threshold currently used in NewYork (Shelton et al 1982) feeding was predictedat six constant temperatures

Additional response surfaces were generated offeeding area on the head and wrapper leaves pre-dicted at different temperatures and initial age dis-tributions for a given population density of eachspecies Given the initial spatial distribution de-scribed above and an average temperature be-tween 20 and 25degC the first set of response surfaceswas used to select a population density predictedto cause damage most farmers would consider un-acceptable This density twice the currently rec-ommended action threshold was 1 larvaplant forT ni 15 larvaeplant for A rapae and 10 larvaeplant for P xylostella Different age distributionswere generated by dividing the population densi-ties chosen above evenly among larval maturitysubclasses 1 through 6 then 2 through 7 etc up

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1589

Head Wrapper Leaves

1n

519

260

T1i

TemperatureDC

10

Youngest Age ProSQnt

10

10

YOungG81 AGe PrQsan

A rapal2333

557

78

10

Youngest Ago PreSGnt

TemperatureDC

142 P xylostllia

098

053

0009

Youngesl Ago PresentTemperature

DCTemperalUIlliDc

Fig 8 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves in 7 d due todifferent temperatures and age distributions at a given population density of three lepidopteran pests of cabbagePopulation densities were lplant for T ni loSplant for A rapae 10plant for P xylostella

to 10 through 15 Model predictions were gener-ated at each of these age distributions for each ofthe 6 constant temperatures used above

Results and Discussion Response surfaces gen-erated with the model predict that A rapae con-tributes most to feeding damage on the head andwrapper leaves (Fig 7) Although total consump-tion by A rapae larvae is less than that of T ni(Harcourt et al 1955) the amount consumed onthese economically important strata is greater be-cause of the difference in intra plant spatial dynam-ics of the two species In Fig 7 the model predictsthat for a given constant temperature and giveninitial age and spatial distributions feeding on thehead and wrapper leaves increases linearly withpopulation density for each species Systems thatweight the counts of each species according to ex-pected feeding damage and base the action thresh-old on the weighted counts have been proposed

(Harcourt et al 1955 Shelton et al 1982) but thesedid not consider the spatial dynamics of the pestsThus one potential use of our model is to designa new rating scale to weight the population densityof each species according to expected feeding dam-age considering the spatial dynamics of eachspecies This rating scale however would also haveto account for temperature effects which cangreatly affect predicted feeding

At temperatures lt15DC very little feeding ispredicted on the head and wrapper leaves by eachspecies at any population density (Fig 7) Increas-ing temperatures have a nonlinear effect on pre-dicted feeding by each species For P xylostellaand A rapae the increase in predicted feedingrate may be primarily due to increased develop-ment and feeding rates For T ni however in-creased development and feeding rates at highertemperatures may be offset to some extent by higher

1590 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

probabilities of moving away from the head andwrapper leaves towards the lower leaves (Hoy etal 1989)

For a given population density predicted feed-ing on the marketable parts of the plant variedwidely with age distribution again interacting withtemperature (Fig 8) The results indicate that thedamage caused by a given population density afixed economic threshold for example will varyconsiderably with temperature age structure of thepopulation and species composition Againweighting systems have been described that con-sider larval age (Andaloro et al 1983a) but notwith the resolution that Fig 8 implies is necessaryand they do not include the interaction with tem-perature

Considering the profound effects of tempera-ture age distribution and species-specific spatialdynamics on the predicted area of feeding on eco-nomically important parts of the plant a staticeconomic threshold does not seem to be appropri-ate Rather feeding should be predicted for specificpopulation densities age distributions and spatialdistributions of the three species as well as weatherforecasts and management strategies should be de-signed accordingly The model described here couldbe used to make those predictions either by cal-culating a new species weighting system each dayof the growing season to be used with a fixed actionthreshold or simply by making the required pre-dictions on a case-by-case basis

Sensitivity Analysis

Two goals were addressed in the sensitivity anal-ysis First individual model parameters were evalmiddotuated as potential causes of inaccurate predictionsBy examining the change in model output after achange in the individual parameters parametersthat affect the output most can be identified Sec-ond by examining the effects of changes in dif-ferent parameters in combination insight can begained into the effects of the different processesbeing simulated and their interactions on the out-put variables of interest

Methods Model predictions were evaluated af-ter changing each parameter and input suppliedby the user by +10 and -10 of its valueChanges were made one parameter at a time witha standard set of initial conditions Standard initialpest population densities were a mean of 1 larvalplant of each species on each stratum in the secondinstar for A rapae and T ni and uniformly dis-tributed among the 20 age subclasses for P xylo-stella The analysis was performed at each of threetemperature regimes typical summer weather forwestern New York (maximum temperature 267degCminimum temperature 155degC 8 h sunshine eachday) hot and sunny weather (maximum temper-ature 322degC minimum temperature 211oC 12h sunshine each day) and cool and cloudy weather

(maximum temperature 183degC minimum tem-perature 10degC 2 h sunshine)

Constants were changed by adding or subtract-ing 10 of their value Input weather variableswere changed by adding or subtracting 10 of thevalue of each pays forecasted maximum and min-imum temperature and hours of sunshine Age atwhich larvae begin to move was shifted plus orminus two subclasses to effect a 10 change Initialage distribution for A rapae and T ni was alsoshifted 10 by shifting the subclasses initialized byplus or minus two Initial age distribution for Pxylostella is assumed to be uniform so this was notchanged For each species the initial intraplantdistribution was altered by shifting 10 of eachage group on each stratum except the lower frameleaves down one stratum or shifting 10 of eachage group on each stratum except the head upone stratum (eg a downward shift of an averageof one larva on each stratum would result in anaverage of 09 1 1 1 and 11 larvae on the headwrapper upper frame midframe and lower frameleaves respectively) Transition probabilities for Arapae and P xylostella were changed by a similarmethod shifting 10 of the probability of movingto each stratum except the lower frame leaves tothe next lower stratum or shifting 10 of the prob-ability of moving to each stratum except the headto the next stratum up (eg a downward shift ina transition probability vector of 09 01000 resultsin a vector of 081 018 001 0 0) Sensitivity tochanges in transition probabilities for T ni wereexamined by changing the Beta pdf shape param-eters that govern transition probabilities for thisspecies by + 10 and -10 of their value Theeffects of each of these changes were examined bycalculating the percentage of change in number oflarvae of each species and the percentage of changein accumulated area of feeding on the head andwrapper leaves

To examine interactions between different pro-cesses and their effects on model output we per-formed two analyses in which variables suspectedof interacting were varied in all combinations theequivalent of a factorial design with three levelsof each factor given by +5 -5 and 0 Be-cause development and feeding rates are temper-ature-dependent and govern the amount of feedingaccumulated interactions between temperaturefeeding rates and development rates might affectaccumulated area of feeding Three levels of tem-perature were generated starting with the typicalsummer weather regime described above and add-ing 5 -5 or 0 of the daily maximum andminimum At each temperature level develop-ment rate for each species was varied by +5-5 and 0 from its value and at each of thesedevelopment rates for each species feeding ratewas changed by +5 -5 and 0 of its valueThe effects of these parameter changes on the pre-dicted area of feeding on the head and wrapperleaves were calculated

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1591

Table 2 Output from a model to predict lepidopteranfeeding damage on cabbage at three temperature regimeswith a standard set of inputs and no change in the param-eters Changes in output during the sensitivity analysis (Fig9-12) are compared with these standards

StratumPopulation density (avg noplant) Feeding

P xylostella A rapae Tni cm2

High temperaturesHead 0252 2118 0095 12764Wrapper 0390 2594 0662 21716

Moderate temperaturesHead 0423 1957 0299 6805Wrapper 0578 2524 1001 9667

Low temperaturesHead 0635 1296 0829 1945Wrapper 0834 1651 0886 2348

A similar analysis of interacting processes wasperformed for spatial effects Initial distributionand transition probabilities could be expected tointeract in their effects on spatial distribution oflarvae and feeding damage For each species theinitial distribution was treated by (a) shifting 10of each age group on each stratum (except thelower frame leaves) down one stratum (b) shifting10of each age group on each stratum (except thehead) up one stratum and (c) leaving the initialdistribution unchanged At each of these shifts ininitial distribution for each species the transitionprobabilities for that species were changed as de-

scribed above Shifting 10 of the probability ofmoving to each stratum except the lower frameleaves to the next lower stratum resulted in higherprobabilities of downward movement shifting 10of the probability of moving to each stratum exceptthe head to the next stratum up resulted in higherprobability of upward movement

Results and Discussion Standard results for highmoderate and low temperature regimes withoutchanging any of the parameters or input variablesare given in Table 2 and the effects of changingeach parameter and input variable on selected out-put variables are displayed in Fig 9-12 for themoderate temperature regime We begin the anal-ysisby examining sensitivity of the model to changesin the parameters at moderate temperatures andfollow with the differences in model sensitivity seenunder high and low temperature regimes

At moderate temperatures numbers of larvae ofeach species on the head and wrapper leaves wereleast sensitive to initial spatial distribution of larvaedispersion in development time and hours of sun-shine (Fig 9) Change in the initial intraplant dis-tribution of larvae may be compensated for bymovement of larvae within a short time after thebeginning of the simulation Dispersion in devel-opment time for these species was low in the lab-oratory development studies resulting in a small

Svalue of -D for each species A 10 change in

EL~these small values does not change the dispersion

o Effect 01 +10 changebull Effect 01 -10 change on larvae on the head alief 7 days

Inldal dlsbibudonInitial ages

Age 01 first movementTransition probabilities

Dispersion In developmenlgl

DEL g2C

Hours 01 sunshineTemperalure

-20 -10 0 10

P xylostella20 30 -20 -10 0 10 20

A rapae

oT nl

100

on larvae on the wrapper leaves alter 7 days

10-10

Initial distributionInitial ages

Age 01 firsl movementTransition probabilities

Dispersion in developmentgl

DEL g2C

Hours of sunshineTemperature

-20 o 10 -20 -10 0 -10 0P xylostella A rapas T nI

Fig 9 Percentage of change in predicted number of P xylostella A rapae and T nt larvae on the head andwrapper leavesafter changing model parameters + and -10

1592 ENVIRONME~TAL ENTOMOLOGY Vol 19 no 5

Fig 10 Percentage of change in number of T nilarvae predicted on the head and wrapper leaves aftera + or - 1 0 change in parameters governing their tran-sition probabilities on the cabbage plant

greatly Hours of sunshine influence temperaturein each stratum but apparently not enough to causelarge changes in rate functions

Changes in temperature initial age distributionage at which larvae begin to move between strataand transition probabilities had the greatest effectson predicted number of larvae on the head or wrap-per leaves (Fig 9) These are all linked to spatialdynamics since both temperature and initial agedistribution affect the time at which larvae beginto move between strata Changes in parametersgoverning T ni transition probabilities were anexception causing only moderate or small changesin output (Fig 10) Changes in development rateparameters had large effects only for P xylostellaon the head and wrapper leaves and for T ni onthe head

Predictions of accumulated feeding on the headand wrapper leaves were generally less sensitive tochanges in parameters than were predictions ofnumbers of larvae on these strata (Fig 11 and 12)Because the predictions of accumulated area offeeding are most important to the farmer the ro-bustness of the model in predicting feeding sug-gests that it could be a useful management toolThe greatest changes in accumulated area of feed-ing were caused by changing parameters governingA rapae development or feeding particularly ini-tial age distribution Fortunately development ratesfor all three species considered here have been wellstudied and studies done at widely different timesand locations with different food sources suggestthat average development rate at a given temper-ature is fairly constant (Hardy 1938 Richards 1940Given 1944 Miner 1947 Harcourt et al 1955Shorey et al 1962 Jackson et al 1969 Toba et al

1973 Boldt et al 1975 Butler et al 1975 Smithamp Smilowitz 1976 Chen amp Su 1978 1982 Tatchell1981 Yamada amp Kawasaki 1983 Theunissen et al1985) Changes in forecast temperatures cause thenext largest change in accumulated feeding prob-ably because of their effects on development andfeeding rates Parameters governing spatial effectshad smaller effects on accumulated feeding par-ticularly when compared with their effects on pre-dicted number of larvae on different parts of theplant

Under the low-temperature regime predictionsof numbers of larvae on the head and wrapperleaves were more sensitive to parameters affectingdevelopment than to parameters affecting spatialdynamics At low temperatures larvae take longerto reach the age when movement starts and prob-ability of movement by T ni to the head andwrapper leaves is lower Furthermore fewer smalllarvae become large larvae at low temperatures sototal numbers of large larvae on all strata are re-duced At moderate and high temperatures pre-dictions of numbers of larvae on the head andwrapper leaves were more sensitive to changes inparameters affecting spatial dynamics

Effects of changing forecast temperatures onpredictions of accumulated feeding were muchgreater when the forecast temperatures were lowand less when the forecast temperatures were highthan at moderate temperatures Changing devel-opment rate parameters had a greater effect onaccumulated feeding at low temperatures butchanging feeding rate parameters had a greatereffect at high temperatures than at moderate tem-peratures Accumulated feeding was less sensitiveto changes in transition probabilities at low tem-peratures and more sensitive to changes in tran-sition probabilities at high temperatures than atmoderate temperatures

In general interactions between temperaturedevelopment and feeding rates as well as param-eters governing spatial effects were not evidentTypically the effect of changes in each of theseparameters was similar regardless of the value ofthe other parameters One interaction did occurWhen temperature was increased a negativechange in T ni development rate resulted in lesspredicted feeding on the head than when no changein T ni development rate was made In all othercases negative change in development rates re-sulted in higher predicted feeding on the head thanwhen development rates were not changed Re-gardless 5 changes in development rates for Tni resulted in lt3 differences in feeding on thehead so the effects of this interaction are not ofgreat importance Thus this analysis reinforced thesingle parameter analysis Feeding rates themselveswere changed in this analysis rather than the pa-rameters that govern them and accumulated feed-ing on the head and wrapper leaves was still moresensitive to changes in development rate and tem-perature

5o

middot5 0

Feeding on Heed

-5Feeding on Wrapper Leaves

o 10

Larvae on Head

middot10

b5b4b3b2bl858483a281

middot20l( Change in

-20 middot10 0 10 Change in Larvae on Wrapper leaves

II2l

~toa0gtatoten

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

SDElA rapae g2

g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

October 1990 HoY ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1579

weekly application provided gt95 marketableheads (rated according to Greene et al 1969) attwo other locations A threshold of one new feedinghole per plant based on the results of Chalfant etal (1979) yielded results as poor as 396 mar-ketable heads in a subsequent test (Workman et al1980) Other examples in which results of usingeither calendar schedules or proposed thresholdsvary in different locations or at different times havebeen reported as well (Sears et al 1983 Shelton etal 1983 Morisak et al 1984 Kirby amp Slosser 1984Cartwright et al 1987) These varying results implythat growers require a more reliable means of pre-dicting damage to their crop

We have proceeded by first validating our mod-el comparing predictions with observed data todetermine whether the predictions are accurateenough to be useful for our analysis Second wehave examined our more complex models predic-tions of damage resulting from a static thresholdpopulation density when factors affecting intra-plant spatial dynamics are varied Results suggestthat a useful model that predicts damage to themarketable parts of cabbage plants must incorpo-rate intra plant spatial dynamics of the lepidopteranpest complex Finally to gain insight into the po-tential for use of our model as a management toolwe analyzed the sensitivity of model predictions tochanges in the values of parameters and variablesinput by the user Before discussing these analyseswe describe the model and how parameters wereestimated

Model Description

Simulation modeling involves forecasting changesin the value of state variables which represent thestate of a system over time The system describedby this model includes populations of P xylostellaA rapae and T ni a cabbage crop and the in-fluence of weather conditions The cabbage cropis assumed to consist of mature or nearly mature(growth stage 8 or 9 Andaloro et al 1983b) plantsof uniform size State variables in the model are

Nkj(t) the average number N per plant of larvaeof species s and age subclass k on stratum jat time t (in days)

where

s = 1 2 3 representing P xylostella A rapaeand T ni respectively

k 1 2 20 representing subclasses in thedevelopment model and approximate agegroups

j 1 2 5 representing the head four sur-rounding wrapper leaves upper frame leavesmid frame leaves and lower frame leaves re-spectively

Thus the entire crop is represented by five verticalstrata and the entire population of each species is

represented by an average number and age struc-ture per plant on each of the five strata Althoughdistribution of larvae and their damage betweenplants is quite important it goes beyond the scopeof this study An auxiliary variable

Ej = average accumulated area offeeding (cm2) on stratum j

is calculated to estimate damage to the cropBelow we describe how the state variables change

as larval development and movement are simulat-ed and how the auxiliary variable is calculated asthe state variables change We have observed thatmortality due to naturally occurring agents over a7-d period in commercial cabbage fields is eithernegligible or too rare to be a useful addition to themodel Diurnal temperature fluctuations in eachof the different plant strata are incorporated asexternal variables A list of variables with defini-tions and parameter estimates is given in Table 1Inputs each of the submodels and output are de-scribed below for the model when run on a Macin-tosh computer (Apple Computer Cupertino Cal-if)Model Inputs Initial values for the state vari-

ables and the microclimate sub model must be inputby the user These include a weather forecast highand low temperatures and hours of sunshine forthe next 7 d and the average number per plant ofeach species on each stratum obtained by samplinga cabbage field Initial age distribution is estab-lished for A rapae and T ni by providing separateaverages for eggs small (first and second instars)and large (third fourth and fifth instars) larvaeThe initial age distribution is further defined byidentifying the proportion of larvae over the entireplant estimated to be in each of the five instarsThese initial values of state variables are input in-teractively in the screen depicted in Fig I (theweather forecast is input similarly)Microclimate A cabbage plant offers insects a

variety of microhabitats from exposed and sunnyleaves to leaves in almost perpetual shade there-fore temperature is modeled separately for eachof the plant strata Temperature (0C) in each stra-tum j at a given time t (days) tempj(t) is modeledwith sine functions to simulate diurnal fluctuationin temperature according to

tempt) = avtempt) + ampj(t)sine(t271) (1)

where

avtempj(t) the days average ambient air tem-perature in stratum j[=(maximum temperature + mini-mum temperature)2]

ampj(t) half of the days temperature rangein stratum j[=(maximum temperature - mini-mum temperature)2]

t is updated in increments of 002 d

1580 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

Table 1 List of variables used in a model to predict feeding damage by Lepidoptera on cabbage For parametervalues eSlimaled from our dala estimates (and standard errors in parentheses) are given

Variable Definition Type (or used Estimated valueto calculate)

Nkit) Average number N per plant of larvae of species s in State f(time rates)age subclass k on stratum j at time t (in days)

Eit) Average accumulated area of feeding (cm2) on stratum Auxiliary f(time rates)j at time t

temPI(t) Temperature in stratum j at time t (C) Exogenous f(time forecast)avtemPI(t) Days average temperature in stratum j at time t eC) Exogenous From weather forecastamPit) - days range in temperature in stratum j (C) Exogenous From weather forecastmlj m2j Constants to calculate ampj(t) as a function of amps(t) Exogenous j = 1 06658 (0089) 0

and forecasted hours of sunshine j = 2 (interpolated)j = 3 07634 (0487)00968 (0057)j = 4 (interpolated)j= 5 00

DELit) Development time (days) for the larval period of Rate f(temPI(t))species s in stratum j

C Maximum developmental rate for species s Rate P xylostella 01429middot[1 + eXP(gls + g20T)] A rapae 00909

T nt 01120Topt Temperature for maximum development rate (C) Rate 33C for all speciesgls820 Empirically estimated constants for development rate Rate A rapae 30707 (0201) -01624 (0012)

equations P xylostella 32317 (0118)-01458 (0007)

T nt 42059 (0130) -01884 (0008)DEL Relative dispersion in development time for species s Rate P xylostella 40

T A rapae 30T nt 50

Fs Proportional shift in substages of the distributed delay Rate P xylostella 05model of development A rapae 025

T nt 06U(t) Indicator variable in distributed delay Rate f(F DEL)FPDkj(t) Area of leaf (mm2) consumed per larva of species s in Rate f(temperature age)

age subclass k per day on stratum j at time this hz hJs Empirically estimated constants to calculate leaf area Rate P xylostella -23055 (108)

consumed per day as a function of temperature and 05273 (0108) -00117 (0003)larval age A rapite 36466 (125) 03183 (0124)

-00068 (0003)T nt 25730 (0968) 04072 (0097)

-00071 (0002) bullP4t) Transition probabilities for species s at time t from Rate For P xylostella

stratum t to stratum j [75~ 00 0]125 75 125 0 0o 125 75 125 0o 0 125 75 125o 0 0 2 8

For A rapae

[ 20 00]28 0 0 02 5 3 0 01 5 3 1 01 4 3 1 1

For T nt f(avgj(t))CI C2d] Constants (c] dl) and coefficients of temperature (C2 Rate See Hoy et al (1989)

d2 d2) for estimating shape parameters of Beta proba-bility density functions according to temperature

ajk bjk Shape parameters for the Beta pdfs described above Rate fCc] C2d] d2 avgj(t))(used to calculate transition probabilities for T nt)

Thus to simulate different microclimates in thedifferent strata we require a separate temperatureaverage and range for each of the strata Theseaverages and ranges were simulated by a simplemodel based on energy balance relationships in acrop canopy

Average temperature in each stratum is modeledas the forecast average ambient air temperaturemultiplied by a constant The constant for the lowerframe leaves was estimated as 10 (ie the tem-perature in the shaded lower frame is close to the

temperature that would be measured in a standardweather recording shelter) The constants for thehead and upper frame were modeled as the av-erage ratio of temperature measurements (de-scribed below) in those strata to measurements tak-en in the lower frame (103 104 105 1025 forthe head wrapper upper frame and midframeleaves respectively) For the wrapper leaves andmidframe leaves (j = 2 and 4) where temperaturemeasurements were not available average tem-perature is estimated by linear interpolation be-

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1581

r- bullbullbull File

iOEdit

Inputs

Fill in the bOXl8with the nquirld numblu

I~~li~~Cli~~II~~Itjinlr~degr~li~cr~8Ii~~81APIo~ J J) ) j j jj~

DB leW eL

Hledm~ 811 I[JCJ 8~11 I[]wrepPlrl 0 II 0 I 0 II 0 II 0 I 0 II 0 I

Uppn I 0 II 0 I =0=11 0 II 0 I 0 II 0 Il1id I 0 II 0 I =0 11 0 II 025 I 0 II 120 I

Lo~rl 0 II 0 1_0 ---II 0 II 100 I 002 II 030 I( RUN ) ( STRRT OUER

tt ------

Fig 1 Computer screen displaying the interactive input table for initializing a model to predict feeding damageby Lepidoptera on cabbage

tween averages for the other strata (j = 1 3 and35 respectively)

Like average temperature the temperature rangeis assumed to be the same in the lower frame leavesas in the forecast for ambient conditions Aroundthe cabbage head the observed temperature rangewas consistently narrower than it was under thelower frame leaves The head has considerable massand moderates the temperature around it There-fore the temperature range in stratum 1 the headis modeled as a proportion of the range in the lowerframe The temperature range in the upper frameis modeled as the range in the lower frame plus aneffect of sunshine

amp3(t) = amp5(t) + m3 + m2) (forecasted hours of

sunshine on day t) (2)

where ml and m2 are empirically estimated con-stants The upper frame leaves absorb radiant heatenergy from sunlight resulting in higher daytimetemperatures than on the lower leaves they radiateheat more easily at night than the lower leavesbecause they are exposed to the sky resulting inlower night temperatures in this part of the canopy

Measurements were not available for the tem-perature range in the wrapper and midframe leavesTemperature ranges in these strata were modeledsimilarly to the upper frame leaves but the effect

of sunshine was reduced to two-thirds that of theupper frame for the wrapper leaves and one-thirdthat of the upper frame for the midframe leavesbecause these strata receive less sunlight

To estimate the differences in average temper-ature and amplitude between strata temperaturewas monitored on the undersides of the leaves inthree of the strata (the head upper frame leavesand lower frame leaves) from 13 August to 23October 1986 in research plots in Geneva N Y asdescribed in Hoy et al (1989) Hourly temperatureaverages from 2-min samples were recorded Dailytotal solar radiation and ambient air temperatureswere measured at the New York State AgriculturalExperiment Station weather station Geneva NYDaily total solar radiation (caljcm) was dividedby an estimate of average solar radiation per hourfor Geneva N Y during the time the measure-ments were taken to approximate hours of sun-shine Estimated coefficients for the regression de-scribed above and for each of the constants aregiven in Table 1 (SAS Institute 1982) Quadraticand higher order polynomial coefficients for solarradiation were not significantly different from zero(P = 01228 n = 43) indicating that the relation-ship could be described as linear T-statistics onslope coefficients in these regression analyses alsoindicated that the linear effects of solar radiationon amplitude in the upper frame leaves were sig-

1582 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

(3)

Fig 2 Calculated development times for P xylo-stella A rapae and T ni larvae on cabbage (solidlines)compared with development times previously reportedin the literature at specific temperatures

30

A rapaebull Chenamp Su1982bull Smithamp Smilowitz1976o Tatchell1981o Theunissenet al198511 Given1944bull Richards1940bull Harcourt1955

P xylosteJao Hardy1938bull Chenamp Su1978o Miner194711 Yamadaamp Kawasaki1983

20

Tni+ Shoreyet al1962(males)bull Shoreyet al1962(females)o Jackson1969[] Tobaat al197311 Boldtat al1975bull Butleretal1975bull Chenamp Su1982

o

Temperature (Oe)

o

o10

20

40

80

60

10

20

30

40

10

20

30

Ulgtctl0-Q)

Ei=EQ)

EaoQ)gtQ)Cl

algorithm shifts a proportion of the contents of eachsubclass to the next subclass at certain time stepsThe number of time steps before each shift occursand the proportion of the contents of each subclassshifted are determined by the average develop-ment time or delay and the estimated dispersionin development times The controlled dispersionmodel was used because fewer subclasses were re-quired to represent the observed distribution ofdevelopment times adequately (with 20 subclasses

whereDELj(t) average development time (days) for

the larval period in species s on stra-tum j at time t

C (maximum development rate)(l +eBb + R2s Top

Top temperature at which maximum de-velopment rate occurs

Tj(t) temperature on stratum j at time tif tempj(t) 5 Top2 Top - tempj(t) if tempj(t) gt Top

gt g2gt empirically estimated constants forspecies s

This model was used because it fits developmentrate data for T ni well (Butler et a1 1976) and itcould easily be fit to data for the other species usingstandard nonlinear regression packages Becausethe relationship between temperature and devel-opment time of P xylostella and A rapae is qual-itatively similar to that of T ni the function abovewas expected to provide a good fit to the data forthese species as well The gls and g2gt from equation3 were estimated by nonlinear regression (SASInstitute 1982) with the Marquardt computationmethod from data collected by AMS and P BBaker (unpublished data) (Table 1) Minimum de-velopment times (days) for each species were es-timated from data in the literature to be 8 d forP xylostella 12 d for A rapae and 9 d for T niall at 33degC The inverse of these minimum devel-opment times was used to approximate each of theC (equation 3) in the estimations

Development times calculated using the algo-rithm with parameters calculated from AMS andP B Bakers data were very similar to those re-ported in the literature for A rapae and T niwhereas development times for P xylostella wereslightly longer than those previously reported (Fig2) The parameter estimates obtained from AMSand P B Bakers unpublished data were used be-cause the food source in their study excised cab-bage leaves was most similar to the food source ofthe population being modeled Because food sourcecan affect larval development rate (Shorey et a11962 Jones amp Ives 1979 Wolfson 1982) use ofthese data rather than data from the literatureshould provide more accurate results

Dispersion in development times was simulatedby a time-varying distributed delay (Manetsch 1976)with controlled dispersion (Goudriaan 1973) This

nificant (P lt 005 n = 43) In addition the effectof solar radiation on temperatures in the head wasnot significant (P = 02733 n = 43)

Development Rates Average larval develop-ment rates are calculated as a function of temper-ature for each species according to the algorithmproposed by Stinner et al (1974)

1 CDELt) (1 + egh+8r(I))

October 1990 Hoy ET ALINTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1583

where

Nkt + At) = Nkt(t) + U(t)Fmiddot[Nlk_Jlt) - Nkt)] (4)

feeding area (mm2) per day perlarva of species s in subclass k onstratum j at time tdays average temperature instratum j at time taverage proportion of larval de-velopment completed by sub-class k

(2~- 0)empirical constants for species s

avtempt)

where

1If each subclass is assumed to represent 20 of a

larvas development time average feeding rate foreach subclass in the distributed delay is calculated

(k 1) at the midpoint of the class agek = 20 - 40 ill

Equation (6) Thus accumulated feeding in cm2 issummed over all age classes of all species and all

instars) and large (third fourth and fifth instars)larvae on a given stratum We typically observeconsiderable overlap in P xylostella life stages inthe field Therefore the initial number of P xy-lostella on each stratum is evenly divided amongthe 20 delay subclasses that represent this speciesand only forecast total numbers of P xylostellalarvae are reported

Feeding Rates Accumulated feeding by eachspecies on each stratum is calculated as a functionof temperature and larval age The larvae of eachspecies tend to eat very little until the final instarswhen feeding rates increase dramatically (Chen ampSu 1978 1982) An exponential model is used toensure that the predicted feeding rate is positiveand to provide a qualitatively good fit Plots of In(feeding aread) against proportion of develop-ment time completed at three temperatures ap-peared linear with intercept close to zero and slopedependent on temperature Tatchell (1981) studiedconsumption by A rapae at lower temperaturesand found that total consumption (leaf area in cm2)

increased between 13 and 19degC then decreasedbetween 19 and 24degCj Boldt et a1(1975) found thatT ni consumption increased from 20 to 25degC andthen decreased between 25 and 30degC These studiesand the plots described above indicate that theeffects of temperature on feeding rates are not lin-ear rather they are greater at intermediate tem-peratures and less at low and high temperaturesWe describe this effect of temperature on feedingrate by defining the slope in a regression of In(feeding aread) predicted by larval age as a qua-dratic function of temperature Feeding rate perlarva per day as a function of temperature and ageof the larva can then be expressed as an exponentialfunction

(5)

F

U(t)

M(t)

5(t) 1 - 20DEV(t) the proportion of each

Sj

subclass shiftedthe standard deviation of developmenttimes for species s1 for M(t) = 123 o otherwise At

~ F DELi(r) 20

At 002 dr = At 2At 3M

52-- - was found to be fairly constant for eachDEVspeci~s over three temperatures (AMS and P BBaker unpublished data) so F was assumed to bea constant (Table 1) When programmed U(t) actsas an indicator for the shift of contents from eachsubclass to the next subclass and F gives the pro-portion of each subclass shifted

The subclasses are used to approximate larvalage groups which are required to calculate age-specific feeding rates and to assign an age to thelarvae that move between strata Larvae on dif-ferent strata develop at different rates because ofdifferent temperaturesj therefore larvae that movebetween strata must be placed in the appropriateage group at the new location (technically thesubclasses refer to relative maturity rather thanchronological age)

The average number of a given instar per plantis divided evenly among delay subclasses desig-nated to represent that instar as follows k = 1-34-6 7-10 11-15 16-20 for A rapae instars onethrough five and k = 1-3 4-6 7-9 10-14 15-20for T ni instars one through five The number ofsubclasses used to represent each instar for a givenspecies was based on estimates of the proportionof total larval development time spent in each in-star (AMS and P B Baker unpublished data)For example if approximately one-fourth of thelarval period is spent in the last instar the last instarwould be represented by one-fourth of the sub-classes the last five Summing over the appropriatesubclasses gives the number of individuals in a giv-en instar at a given time In practice instar des-ignations are used only for initialization and re-porting forecast numbers of small (first and second

for each species the output was similar to a delaywithout controlled dispersion using approximatelytwice the number of subclasses and twice theamount of computing time)

Programming the distributed delay with con-trolled dispersion yields the following differenceequation for the average number of pests perplant N

1584 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

(7)

31

31

T ni

A rapae

P xyfostefla

00010 a8

a6Physiological

Age

constants estimated by maximumlikelihood as described by Hoy etal (1989)

gt 449535~~ 2lli90ig~ 149845IIOJc6 aooaf 10 08

Fig 3 Predicted feeding rates of P xylo8tella Arapae and T ni on cabbage

Because the shape parameters for the Beta distri-bution a and h change with temperature theshape of the distribution and value of the integralsdescribed in Equation (8) change accordinglyHigher temperatures tend to result in greater prob-ability of movement and higher probability ofmovement towards the lower leaves than towardsthe head lower temperatures tend to result in lowerprobability of movement and higher probabilityof movement towards the head than towards thelower leaves

The elements of the transition probability ma-trices for P xylostella and A rapae are estimatedfrom observations reported in the literature (Har-court 1963 1966 Chua amp Lim 1979 Samson amp

~ 15llli6S~~ 1(57 n

1sectGl 5281IlttlaOJc6af 06

PhysiologicalAge

~~ JI64

~ce 576

sectGl

l2 1288OJc6GlGl

U

previous time steps by

Ej(t) = plusmn plusmn ~ [NkT)FPDkj(T)] ~tTO -I k-I 100

where

Ej(t) area of feeding (cm2) on stratum j accu-mulated at time t

T ~t 2~t 3~t M 002 d

Pj(t)

= f ~ 1__ U1a(I)-11(1 - U)lb(l)-ll duJ~l B[a(t) b(t)] (8)

where

the probability of a T ni (species3) late instar moving from stratumi to stratum j during one dayeel +C2 avtemPi(t)

ed +d2atemp)

The three empirical constants (hh hz and h31inEquation 6) for estimating feeding rates as a func-tion of temperature and larval age were estimatedby multiple linear regression (SAS Institute 1982)of the natural log of feedingday (mm2) on ageage temperature and agemiddottemperature2 (Table 1)The measure of larval age was the proportion oflarval stage completed or days the larva had livedso far divided by total days spent by that larvafrom eclosion to pupation Measurements of areaof cabbage leaf consumed each day of the larvalperiod for each of 20 larvaereplicate and threereplicatestemperature at 167 211 and 267degCfor each species were taken by AMS and P BBaker (unpublished data) Inspection of predictions(Fig 3) compared with data reported in the lit-erature (Harcourt et al 1955 McEwen amp Hervey1960 Rahman 1970 Harper 1973 Boldt et al 1975Chen amp Su 1978 1982 Samson amp Geier 1983Theunissen et al 1985) indicates that the feedingrate model fit well Data on feeding by A rapaereported by Tatchell (1981) indicate much higherrates than those we estimated but Tatchells datadisagree with the other literature cited above aswell As in the case of development rates we usedthe AMS and P B Baker data because the foodsource was cabbage leaf so these data should bemost appropriate

Movement Rates Larval movement is simulatedwith discrete time transition probability matricesbecause observed larval movements were discretein time Movement of late instar T ni is correlatedwith microclimate (Hoy et al 1989) and must bemodeled accordingly The transition probabilitiesfor late instar T ni are modeled as definite integralsof the Beta probability density function (pdf) withshape parameters a(t) and b(t) which depend ontemperature and the stratum larvae are movingfrom

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS

File Edit

1585

021

339

1131

3241

2568

Fig 4 Computer screen displaying output from a simulation model of feeding damage by Lepidoptera oncabbage

Geier 1983 Salinas 1984) and our own observa-tions Our observations for these species were thefrequency of movements by larvae marked withfluorescent powder and visually censused at ~1-hintervals in research cabbage plots near GenevaNY The number of these observations was notsufficient to estimate individual transition proba-bilities so the data were used roughly to estimatefrequency of movement and probability of movingup or down on the plant For P xylostella thefrequency of movement was low and approxi-mately equal numbers of upwards and downwardsmovements were observed For A rapae virtuallyall late instars were observed to move upwards tothe head or wrapper leaves as noted by Harcourt(1963 1966) and Hoy amp Shelton (1987) Transitionprobabilities that reflect these observations werechosen for these two species and are given in Ta-ble 1

The change in state variables due to movementis thus calculated by

s

Nkj(t + ~t) = ~ Nkj(t)pj(t)I(t + ~t) (9)

where

k =k =

I(t + ~t)

~t

13 14 20 for s = 110 11 20 for s = 2 or 3

1 if (t + ~t) = 1 2 3 o otherwise002d

Movement is simulated only once each day andbecause the time step for the model is lfso of a daythe indicator I(t) is used to determine when themovements occur The values of k given above arechosen so that movement is simulated only for olderlarvae which are represented by higher values ofk (k ~ 13 for P xylostella and k ~ 10 for A rapaeor T ni)Model Output The output generated using the

equations described above is a summary of thevalues of state variables and the value of the aux-iliary variable each day for the next 7 d This ispresented on the computer screen depicted in Fig4 The number of large and small larvae of eachspecies on each stratum also can be obtained for aprintout by summing over the appropriate sub-classes in the distributed delay The picture of acabbage plant on the screen gives the user an ap-proximate idea of what the predicted damage onthe cabbage crop would look like

Validation

Methods Validation analysis was performed todemonstrate how well the model predicts data thatwere not used in model design or parameterizationData collected by a commercial field monitoringand pest control advising service were used to com-pare model predictions with observed populationdensities and feeding damage 7 d after the original

1586 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

A rapae

P xylostella

18161412108642o 00 06 12 18 24

557371

1114

92

743

1300

A rapae

10

P xylostella

20

oO0 16 32 48 64

30

10

20

1 ffi

0O0 1 2 2 4 3 6 4 8

000-05 00 05 10 15

1300

11 14

929 T ni T ni

743

55710

3 71

186

0 00- O32 -O16 O00 016 032 O0 O8 16 2 4 3 2

Standardized Residuals Standardized Residualsfor the Head for the Wrapper Leaves

-ogtucQ)=J0Q)-LL

Fig 5 Histograms of standardized cell residuals for comparing predicted numbers with observed averagenumbers of larvae on the cabbage head and wrapper leaves in commercial cabbage fields near Geneva NY

sample Scouts sampled cabbage fields on a weeklybasis using a variable-intensity sampling scheme(Hoy et al 1983) Separate counts of P xylostellalarvae (all instars combined) and A rapae and Tni eggs small (first and second instars) and large(third fourth and fifth instars) larvae were taken

on the head (stratum 1) wrapper (stratum 2) andframe leaves (strata 3-5 combined) and were usedto initialize the model Predictions of numbers ofP xylostella large A rapae and T ni and ac-cumulated feeding on the head and wrapper leaveswere compared with the scouts observations taken

October 1990 HoY ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1587

o [] a [] C D

QOO n~ Q~ n~ 100 1~ t~ 1~ 200Average Damage Rating

Average Damage Rating

Fig 6 Comparison of predicted feeding damagewith average observed damage rating on the heads andwrapper leaves of commercial cabbage crops near Ge-neva NY

the following week Initial spatial distribution with-in the frame and initial age distribution with Arapae and T ni small and large larval populationswere assumed to be uniform for lack of more pre-cise information The scouts observations includedratings of feeding damage on a scale of 0 to 4indicating approximately no damage less than onefeeding hole per leaf one to three feeding holesper leaf 10 defoliation and 40 defoliationrespectively These ratings were compared withpredictions of accumulated area of feeding withscatter plots and correlation analysis

Weather data for model inputs (maximum andminimum temperatures and daily total solar ra-diation) were recorded at the New York State Ag-ricultural Experiment Station in Geneva NY thec1vsest weather station to the commercial fieldsbeing monitored (within 20 km) Data from 34pairs of field samples-each pair taken one weekapart during July August and September in 1983and 1984 under widely varying weather condi-tions-were used for this analysis

Model predictions for number of larvae on thehead and wrapper leaves were compared with ob-servations using standardized cell residuals givenby

observed no larvae - predicted no larvaeVpredicted no larvae

Evaluation of Existing Treatment Guidelines

Because the model predicts numbers of larvaeand feeding damage on different parts of the plantwell model predictions cap be used to evaluatetreatment guidelines currently in use for cabbagepest management In particular the model can beused to explore the relative effects of each pest onthe crop and how useful a static threshold for pestpopulation density will be in predicting a given

as described by Bishop et al (1975) These ap-proximate a standard normal distribution so thecriterion for evaluation is whether or not most ofthe residuals are within 2 SD of the mean (- 2and ~2) because lt=95of the standard normaldistribution falls within this range Observations ofthe feeding damage rating also were plotted againstpredicted accumulated area of feeding and asso-ciated correlation coefficients were calculated

Results and Discussion Most standardized cellresiduals for predicted versus observed counts oflarvae on the head and wrapper leaves were wellwithin the range -2 to +2 (Fig 5) The few largedeviations that were calculated were positive in-dicating that occasionally greater average num-bers of larvae than predicted were observed Theinterplant spatial distribution of each species is ag-gregated (Harcourt 1966) and sample sizes wereoften small (as few as 11 plants) so these occasionallarge positive deviations are not surprising Theseresults indicate that the model predicts number andlocation of larvae well particularly when the lowresolution in the data for initial age and spatialdistribution within the frame and potential sam-pling error in both samples are considered Con-clusions from this analysis must be tempered some-what however by the low population densitiesobserved in these fields Bishop et al (1975) warnthat the approximation of the standardized cellresiduals to the standard normal is poorest whenpredictions in the cells are small Most of the initialpopulation densities and associated predictions weresmall because pest population densities are keptlow by farmers Evaluation of the model underthese conditions is most appropriate however be-cause these are the conditions under which themodel would be used

Predicted area of feeding was correlated withobserved damage rating (Fig 6) Damage ratingincluded assessment of recent feeding as well asolder damage done before the first sample Thiscould explain circumstances in which little feedingdamage was predicted but high damage ratingswere observed Cases where large amounts of feed-ing damage were predicted but observed damagerating was low did not occur Feeding damage isthe most important variable to managers becauseit determines the market value of the crop Thedata indicate that the model can be used to predictthe effects on the cabbage crop of a given pestpopulation under specific conditions

3

(10)

D

o

D

D

o

CC

lJ 8DaD co lJ 0

D D0

2

D

1

D D

C C

D

Wrapper Leaves

r-069

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~ 10fa

E8

40

oo

E8 30Dlc6Q)t 20tJQ)

Ug 1a

1588 ENVIRONMEITAL ENTOMOLOGY Vol 19 no 5

Head Wrapper Leaves

T ni 565134

377089

189045

2020

- Temporatura Avorago plon1CJ DCEC)---0)c A rapaea 1t82Q) a18Q)U 546 7890Q) 273 396sect0 30 30eD

Temperature Avorago pIontDC Temperalure Avomg bullbull p1ont

DC

P xylostella074 178050 11902i 061

20

rompera1ur Avorago plantDC Tempera1ure Averag bullbull p1on1

DC

Fig 7 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves after 7 d atdifferent temperatures and population densities of lepidopteran pests

amount of damage on the marketable parts of thecrop

Methods Response surfaces of predicted area offeeding on the head and wrapper leaves to tem-perature and population density of each pest weregenerated with the model A standard initial in-traplant spatial distribution typical of distributionsobserved in cabbage fields was chosen for eachspecies as follows P xylostella 005 01 03 03and 025 A rapae 0 015 04 03 and 015 Tni 0 01 02 04 and 03 of the average numberper plant on the head wrapper leaves upper framemidframe and lower frame respectively For Pxylostella the larval ages were uniformly distrib-uted among the 20 subclasses in the distributeddelay For A rapae and T ni the larvae wereinitialized into the first 10 subclasses simulatingfirst second and third instars For each of 10 pop-ulation densities ranging from well below to well

above the action threshold currently used in NewYork (Shelton et al 1982) feeding was predictedat six constant temperatures

Additional response surfaces were generated offeeding area on the head and wrapper leaves pre-dicted at different temperatures and initial age dis-tributions for a given population density of eachspecies Given the initial spatial distribution de-scribed above and an average temperature be-tween 20 and 25degC the first set of response surfaceswas used to select a population density predictedto cause damage most farmers would consider un-acceptable This density twice the currently rec-ommended action threshold was 1 larvaplant forT ni 15 larvaeplant for A rapae and 10 larvaeplant for P xylostella Different age distributionswere generated by dividing the population densi-ties chosen above evenly among larval maturitysubclasses 1 through 6 then 2 through 7 etc up

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1589

Head Wrapper Leaves

1n

519

260

T1i

TemperatureDC

10

Youngest Age ProSQnt

10

10

YOungG81 AGe PrQsan

A rapal2333

557

78

10

Youngest Ago PreSGnt

TemperatureDC

142 P xylostllia

098

053

0009

Youngesl Ago PresentTemperature

DCTemperalUIlliDc

Fig 8 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves in 7 d due todifferent temperatures and age distributions at a given population density of three lepidopteran pests of cabbagePopulation densities were lplant for T ni loSplant for A rapae 10plant for P xylostella

to 10 through 15 Model predictions were gener-ated at each of these age distributions for each ofthe 6 constant temperatures used above

Results and Discussion Response surfaces gen-erated with the model predict that A rapae con-tributes most to feeding damage on the head andwrapper leaves (Fig 7) Although total consump-tion by A rapae larvae is less than that of T ni(Harcourt et al 1955) the amount consumed onthese economically important strata is greater be-cause of the difference in intra plant spatial dynam-ics of the two species In Fig 7 the model predictsthat for a given constant temperature and giveninitial age and spatial distributions feeding on thehead and wrapper leaves increases linearly withpopulation density for each species Systems thatweight the counts of each species according to ex-pected feeding damage and base the action thresh-old on the weighted counts have been proposed

(Harcourt et al 1955 Shelton et al 1982) but thesedid not consider the spatial dynamics of the pestsThus one potential use of our model is to designa new rating scale to weight the population densityof each species according to expected feeding dam-age considering the spatial dynamics of eachspecies This rating scale however would also haveto account for temperature effects which cangreatly affect predicted feeding

At temperatures lt15DC very little feeding ispredicted on the head and wrapper leaves by eachspecies at any population density (Fig 7) Increas-ing temperatures have a nonlinear effect on pre-dicted feeding by each species For P xylostellaand A rapae the increase in predicted feedingrate may be primarily due to increased develop-ment and feeding rates For T ni however in-creased development and feeding rates at highertemperatures may be offset to some extent by higher

1590 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

probabilities of moving away from the head andwrapper leaves towards the lower leaves (Hoy etal 1989)

For a given population density predicted feed-ing on the marketable parts of the plant variedwidely with age distribution again interacting withtemperature (Fig 8) The results indicate that thedamage caused by a given population density afixed economic threshold for example will varyconsiderably with temperature age structure of thepopulation and species composition Againweighting systems have been described that con-sider larval age (Andaloro et al 1983a) but notwith the resolution that Fig 8 implies is necessaryand they do not include the interaction with tem-perature

Considering the profound effects of tempera-ture age distribution and species-specific spatialdynamics on the predicted area of feeding on eco-nomically important parts of the plant a staticeconomic threshold does not seem to be appropri-ate Rather feeding should be predicted for specificpopulation densities age distributions and spatialdistributions of the three species as well as weatherforecasts and management strategies should be de-signed accordingly The model described here couldbe used to make those predictions either by cal-culating a new species weighting system each dayof the growing season to be used with a fixed actionthreshold or simply by making the required pre-dictions on a case-by-case basis

Sensitivity Analysis

Two goals were addressed in the sensitivity anal-ysis First individual model parameters were evalmiddotuated as potential causes of inaccurate predictionsBy examining the change in model output after achange in the individual parameters parametersthat affect the output most can be identified Sec-ond by examining the effects of changes in dif-ferent parameters in combination insight can begained into the effects of the different processesbeing simulated and their interactions on the out-put variables of interest

Methods Model predictions were evaluated af-ter changing each parameter and input suppliedby the user by +10 and -10 of its valueChanges were made one parameter at a time witha standard set of initial conditions Standard initialpest population densities were a mean of 1 larvalplant of each species on each stratum in the secondinstar for A rapae and T ni and uniformly dis-tributed among the 20 age subclasses for P xylo-stella The analysis was performed at each of threetemperature regimes typical summer weather forwestern New York (maximum temperature 267degCminimum temperature 155degC 8 h sunshine eachday) hot and sunny weather (maximum temper-ature 322degC minimum temperature 211oC 12h sunshine each day) and cool and cloudy weather

(maximum temperature 183degC minimum tem-perature 10degC 2 h sunshine)

Constants were changed by adding or subtract-ing 10 of their value Input weather variableswere changed by adding or subtracting 10 of thevalue of each pays forecasted maximum and min-imum temperature and hours of sunshine Age atwhich larvae begin to move was shifted plus orminus two subclasses to effect a 10 change Initialage distribution for A rapae and T ni was alsoshifted 10 by shifting the subclasses initialized byplus or minus two Initial age distribution for Pxylostella is assumed to be uniform so this was notchanged For each species the initial intraplantdistribution was altered by shifting 10 of eachage group on each stratum except the lower frameleaves down one stratum or shifting 10 of eachage group on each stratum except the head upone stratum (eg a downward shift of an averageof one larva on each stratum would result in anaverage of 09 1 1 1 and 11 larvae on the headwrapper upper frame midframe and lower frameleaves respectively) Transition probabilities for Arapae and P xylostella were changed by a similarmethod shifting 10 of the probability of movingto each stratum except the lower frame leaves tothe next lower stratum or shifting 10 of the prob-ability of moving to each stratum except the headto the next stratum up (eg a downward shift ina transition probability vector of 09 01000 resultsin a vector of 081 018 001 0 0) Sensitivity tochanges in transition probabilities for T ni wereexamined by changing the Beta pdf shape param-eters that govern transition probabilities for thisspecies by + 10 and -10 of their value Theeffects of each of these changes were examined bycalculating the percentage of change in number oflarvae of each species and the percentage of changein accumulated area of feeding on the head andwrapper leaves

To examine interactions between different pro-cesses and their effects on model output we per-formed two analyses in which variables suspectedof interacting were varied in all combinations theequivalent of a factorial design with three levelsof each factor given by +5 -5 and 0 Be-cause development and feeding rates are temper-ature-dependent and govern the amount of feedingaccumulated interactions between temperaturefeeding rates and development rates might affectaccumulated area of feeding Three levels of tem-perature were generated starting with the typicalsummer weather regime described above and add-ing 5 -5 or 0 of the daily maximum andminimum At each temperature level develop-ment rate for each species was varied by +5-5 and 0 from its value and at each of thesedevelopment rates for each species feeding ratewas changed by +5 -5 and 0 of its valueThe effects of these parameter changes on the pre-dicted area of feeding on the head and wrapperleaves were calculated

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1591

Table 2 Output from a model to predict lepidopteranfeeding damage on cabbage at three temperature regimeswith a standard set of inputs and no change in the param-eters Changes in output during the sensitivity analysis (Fig9-12) are compared with these standards

StratumPopulation density (avg noplant) Feeding

P xylostella A rapae Tni cm2

High temperaturesHead 0252 2118 0095 12764Wrapper 0390 2594 0662 21716

Moderate temperaturesHead 0423 1957 0299 6805Wrapper 0578 2524 1001 9667

Low temperaturesHead 0635 1296 0829 1945Wrapper 0834 1651 0886 2348

A similar analysis of interacting processes wasperformed for spatial effects Initial distributionand transition probabilities could be expected tointeract in their effects on spatial distribution oflarvae and feeding damage For each species theinitial distribution was treated by (a) shifting 10of each age group on each stratum (except thelower frame leaves) down one stratum (b) shifting10of each age group on each stratum (except thehead) up one stratum and (c) leaving the initialdistribution unchanged At each of these shifts ininitial distribution for each species the transitionprobabilities for that species were changed as de-

scribed above Shifting 10 of the probability ofmoving to each stratum except the lower frameleaves to the next lower stratum resulted in higherprobabilities of downward movement shifting 10of the probability of moving to each stratum exceptthe head to the next stratum up resulted in higherprobability of upward movement

Results and Discussion Standard results for highmoderate and low temperature regimes withoutchanging any of the parameters or input variablesare given in Table 2 and the effects of changingeach parameter and input variable on selected out-put variables are displayed in Fig 9-12 for themoderate temperature regime We begin the anal-ysisby examining sensitivity of the model to changesin the parameters at moderate temperatures andfollow with the differences in model sensitivity seenunder high and low temperature regimes

At moderate temperatures numbers of larvae ofeach species on the head and wrapper leaves wereleast sensitive to initial spatial distribution of larvaedispersion in development time and hours of sun-shine (Fig 9) Change in the initial intraplant dis-tribution of larvae may be compensated for bymovement of larvae within a short time after thebeginning of the simulation Dispersion in devel-opment time for these species was low in the lab-oratory development studies resulting in a small

Svalue of -D for each species A 10 change in

EL~these small values does not change the dispersion

o Effect 01 +10 changebull Effect 01 -10 change on larvae on the head alief 7 days

Inldal dlsbibudonInitial ages

Age 01 first movementTransition probabilities

Dispersion In developmenlgl

DEL g2C

Hours 01 sunshineTemperalure

-20 -10 0 10

P xylostella20 30 -20 -10 0 10 20

A rapae

oT nl

100

on larvae on the wrapper leaves alter 7 days

10-10

Initial distributionInitial ages

Age 01 firsl movementTransition probabilities

Dispersion in developmentgl

DEL g2C

Hours of sunshineTemperature

-20 o 10 -20 -10 0 -10 0P xylostella A rapas T nI

Fig 9 Percentage of change in predicted number of P xylostella A rapae and T nt larvae on the head andwrapper leavesafter changing model parameters + and -10

1592 ENVIRONME~TAL ENTOMOLOGY Vol 19 no 5

Fig 10 Percentage of change in number of T nilarvae predicted on the head and wrapper leaves aftera + or - 1 0 change in parameters governing their tran-sition probabilities on the cabbage plant

greatly Hours of sunshine influence temperaturein each stratum but apparently not enough to causelarge changes in rate functions

Changes in temperature initial age distributionage at which larvae begin to move between strataand transition probabilities had the greatest effectson predicted number of larvae on the head or wrap-per leaves (Fig 9) These are all linked to spatialdynamics since both temperature and initial agedistribution affect the time at which larvae beginto move between strata Changes in parametersgoverning T ni transition probabilities were anexception causing only moderate or small changesin output (Fig 10) Changes in development rateparameters had large effects only for P xylostellaon the head and wrapper leaves and for T ni onthe head

Predictions of accumulated feeding on the headand wrapper leaves were generally less sensitive tochanges in parameters than were predictions ofnumbers of larvae on these strata (Fig 11 and 12)Because the predictions of accumulated area offeeding are most important to the farmer the ro-bustness of the model in predicting feeding sug-gests that it could be a useful management toolThe greatest changes in accumulated area of feed-ing were caused by changing parameters governingA rapae development or feeding particularly ini-tial age distribution Fortunately development ratesfor all three species considered here have been wellstudied and studies done at widely different timesand locations with different food sources suggestthat average development rate at a given temper-ature is fairly constant (Hardy 1938 Richards 1940Given 1944 Miner 1947 Harcourt et al 1955Shorey et al 1962 Jackson et al 1969 Toba et al

1973 Boldt et al 1975 Butler et al 1975 Smithamp Smilowitz 1976 Chen amp Su 1978 1982 Tatchell1981 Yamada amp Kawasaki 1983 Theunissen et al1985) Changes in forecast temperatures cause thenext largest change in accumulated feeding prob-ably because of their effects on development andfeeding rates Parameters governing spatial effectshad smaller effects on accumulated feeding par-ticularly when compared with their effects on pre-dicted number of larvae on different parts of theplant

Under the low-temperature regime predictionsof numbers of larvae on the head and wrapperleaves were more sensitive to parameters affectingdevelopment than to parameters affecting spatialdynamics At low temperatures larvae take longerto reach the age when movement starts and prob-ability of movement by T ni to the head andwrapper leaves is lower Furthermore fewer smalllarvae become large larvae at low temperatures sototal numbers of large larvae on all strata are re-duced At moderate and high temperatures pre-dictions of numbers of larvae on the head andwrapper leaves were more sensitive to changes inparameters affecting spatial dynamics

Effects of changing forecast temperatures onpredictions of accumulated feeding were muchgreater when the forecast temperatures were lowand less when the forecast temperatures were highthan at moderate temperatures Changing devel-opment rate parameters had a greater effect onaccumulated feeding at low temperatures butchanging feeding rate parameters had a greatereffect at high temperatures than at moderate tem-peratures Accumulated feeding was less sensitiveto changes in transition probabilities at low tem-peratures and more sensitive to changes in tran-sition probabilities at high temperatures than atmoderate temperatures

In general interactions between temperaturedevelopment and feeding rates as well as param-eters governing spatial effects were not evidentTypically the effect of changes in each of theseparameters was similar regardless of the value ofthe other parameters One interaction did occurWhen temperature was increased a negativechange in T ni development rate resulted in lesspredicted feeding on the head than when no changein T ni development rate was made In all othercases negative change in development rates re-sulted in higher predicted feeding on the head thanwhen development rates were not changed Re-gardless 5 changes in development rates for Tni resulted in lt3 differences in feeding on thehead so the effects of this interaction are not ofgreat importance Thus this analysis reinforced thesingle parameter analysis Feeding rates themselveswere changed in this analysis rather than the pa-rameters that govern them and accumulated feed-ing on the head and wrapper leaves was still moresensitive to changes in development rate and tem-perature

5o

middot5 0

Feeding on Heed

-5Feeding on Wrapper Leaves

o 10

Larvae on Head

middot10

b5b4b3b2bl858483a281

middot20l( Change in

-20 middot10 0 10 Change in Larvae on Wrapper leaves

II2l

~toa0gtatoten

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

SDElA rapae g2

g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

1580 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

Table 1 List of variables used in a model to predict feeding damage by Lepidoptera on cabbage For parametervalues eSlimaled from our dala estimates (and standard errors in parentheses) are given

Variable Definition Type (or used Estimated valueto calculate)

Nkit) Average number N per plant of larvae of species s in State f(time rates)age subclass k on stratum j at time t (in days)

Eit) Average accumulated area of feeding (cm2) on stratum Auxiliary f(time rates)j at time t

temPI(t) Temperature in stratum j at time t (C) Exogenous f(time forecast)avtemPI(t) Days average temperature in stratum j at time t eC) Exogenous From weather forecastamPit) - days range in temperature in stratum j (C) Exogenous From weather forecastmlj m2j Constants to calculate ampj(t) as a function of amps(t) Exogenous j = 1 06658 (0089) 0

and forecasted hours of sunshine j = 2 (interpolated)j = 3 07634 (0487)00968 (0057)j = 4 (interpolated)j= 5 00

DELit) Development time (days) for the larval period of Rate f(temPI(t))species s in stratum j

C Maximum developmental rate for species s Rate P xylostella 01429middot[1 + eXP(gls + g20T)] A rapae 00909

T nt 01120Topt Temperature for maximum development rate (C) Rate 33C for all speciesgls820 Empirically estimated constants for development rate Rate A rapae 30707 (0201) -01624 (0012)

equations P xylostella 32317 (0118)-01458 (0007)

T nt 42059 (0130) -01884 (0008)DEL Relative dispersion in development time for species s Rate P xylostella 40

T A rapae 30T nt 50

Fs Proportional shift in substages of the distributed delay Rate P xylostella 05model of development A rapae 025

T nt 06U(t) Indicator variable in distributed delay Rate f(F DEL)FPDkj(t) Area of leaf (mm2) consumed per larva of species s in Rate f(temperature age)

age subclass k per day on stratum j at time this hz hJs Empirically estimated constants to calculate leaf area Rate P xylostella -23055 (108)

consumed per day as a function of temperature and 05273 (0108) -00117 (0003)larval age A rapite 36466 (125) 03183 (0124)

-00068 (0003)T nt 25730 (0968) 04072 (0097)

-00071 (0002) bullP4t) Transition probabilities for species s at time t from Rate For P xylostella

stratum t to stratum j [75~ 00 0]125 75 125 0 0o 125 75 125 0o 0 125 75 125o 0 0 2 8

For A rapae

[ 20 00]28 0 0 02 5 3 0 01 5 3 1 01 4 3 1 1

For T nt f(avgj(t))CI C2d] Constants (c] dl) and coefficients of temperature (C2 Rate See Hoy et al (1989)

d2 d2) for estimating shape parameters of Beta proba-bility density functions according to temperature

ajk bjk Shape parameters for the Beta pdfs described above Rate fCc] C2d] d2 avgj(t))(used to calculate transition probabilities for T nt)

Thus to simulate different microclimates in thedifferent strata we require a separate temperatureaverage and range for each of the strata Theseaverages and ranges were simulated by a simplemodel based on energy balance relationships in acrop canopy

Average temperature in each stratum is modeledas the forecast average ambient air temperaturemultiplied by a constant The constant for the lowerframe leaves was estimated as 10 (ie the tem-perature in the shaded lower frame is close to the

temperature that would be measured in a standardweather recording shelter) The constants for thehead and upper frame were modeled as the av-erage ratio of temperature measurements (de-scribed below) in those strata to measurements tak-en in the lower frame (103 104 105 1025 forthe head wrapper upper frame and midframeleaves respectively) For the wrapper leaves andmidframe leaves (j = 2 and 4) where temperaturemeasurements were not available average tem-perature is estimated by linear interpolation be-

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1581

r- bullbullbull File

iOEdit

Inputs

Fill in the bOXl8with the nquirld numblu

I~~li~~Cli~~II~~Itjinlr~degr~li~cr~8Ii~~81APIo~ J J) ) j j jj~

DB leW eL

Hledm~ 811 I[JCJ 8~11 I[]wrepPlrl 0 II 0 I 0 II 0 II 0 I 0 II 0 I

Uppn I 0 II 0 I =0=11 0 II 0 I 0 II 0 Il1id I 0 II 0 I =0 11 0 II 025 I 0 II 120 I

Lo~rl 0 II 0 1_0 ---II 0 II 100 I 002 II 030 I( RUN ) ( STRRT OUER

tt ------

Fig 1 Computer screen displaying the interactive input table for initializing a model to predict feeding damageby Lepidoptera on cabbage

tween averages for the other strata (j = 1 3 and35 respectively)

Like average temperature the temperature rangeis assumed to be the same in the lower frame leavesas in the forecast for ambient conditions Aroundthe cabbage head the observed temperature rangewas consistently narrower than it was under thelower frame leaves The head has considerable massand moderates the temperature around it There-fore the temperature range in stratum 1 the headis modeled as a proportion of the range in the lowerframe The temperature range in the upper frameis modeled as the range in the lower frame plus aneffect of sunshine

amp3(t) = amp5(t) + m3 + m2) (forecasted hours of

sunshine on day t) (2)

where ml and m2 are empirically estimated con-stants The upper frame leaves absorb radiant heatenergy from sunlight resulting in higher daytimetemperatures than on the lower leaves they radiateheat more easily at night than the lower leavesbecause they are exposed to the sky resulting inlower night temperatures in this part of the canopy

Measurements were not available for the tem-perature range in the wrapper and midframe leavesTemperature ranges in these strata were modeledsimilarly to the upper frame leaves but the effect

of sunshine was reduced to two-thirds that of theupper frame for the wrapper leaves and one-thirdthat of the upper frame for the midframe leavesbecause these strata receive less sunlight

To estimate the differences in average temper-ature and amplitude between strata temperaturewas monitored on the undersides of the leaves inthree of the strata (the head upper frame leavesand lower frame leaves) from 13 August to 23October 1986 in research plots in Geneva N Y asdescribed in Hoy et al (1989) Hourly temperatureaverages from 2-min samples were recorded Dailytotal solar radiation and ambient air temperatureswere measured at the New York State AgriculturalExperiment Station weather station Geneva NYDaily total solar radiation (caljcm) was dividedby an estimate of average solar radiation per hourfor Geneva N Y during the time the measure-ments were taken to approximate hours of sun-shine Estimated coefficients for the regression de-scribed above and for each of the constants aregiven in Table 1 (SAS Institute 1982) Quadraticand higher order polynomial coefficients for solarradiation were not significantly different from zero(P = 01228 n = 43) indicating that the relation-ship could be described as linear T-statistics onslope coefficients in these regression analyses alsoindicated that the linear effects of solar radiationon amplitude in the upper frame leaves were sig-

1582 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

(3)

Fig 2 Calculated development times for P xylo-stella A rapae and T ni larvae on cabbage (solidlines)compared with development times previously reportedin the literature at specific temperatures

30

A rapaebull Chenamp Su1982bull Smithamp Smilowitz1976o Tatchell1981o Theunissenet al198511 Given1944bull Richards1940bull Harcourt1955

P xylosteJao Hardy1938bull Chenamp Su1978o Miner194711 Yamadaamp Kawasaki1983

20

Tni+ Shoreyet al1962(males)bull Shoreyet al1962(females)o Jackson1969[] Tobaat al197311 Boldtat al1975bull Butleretal1975bull Chenamp Su1982

o

Temperature (Oe)

o

o10

20

40

80

60

10

20

30

40

10

20

30

Ulgtctl0-Q)

Ei=EQ)

EaoQ)gtQ)Cl

algorithm shifts a proportion of the contents of eachsubclass to the next subclass at certain time stepsThe number of time steps before each shift occursand the proportion of the contents of each subclassshifted are determined by the average develop-ment time or delay and the estimated dispersionin development times The controlled dispersionmodel was used because fewer subclasses were re-quired to represent the observed distribution ofdevelopment times adequately (with 20 subclasses

whereDELj(t) average development time (days) for

the larval period in species s on stra-tum j at time t

C (maximum development rate)(l +eBb + R2s Top

Top temperature at which maximum de-velopment rate occurs

Tj(t) temperature on stratum j at time tif tempj(t) 5 Top2 Top - tempj(t) if tempj(t) gt Top

gt g2gt empirically estimated constants forspecies s

This model was used because it fits developmentrate data for T ni well (Butler et a1 1976) and itcould easily be fit to data for the other species usingstandard nonlinear regression packages Becausethe relationship between temperature and devel-opment time of P xylostella and A rapae is qual-itatively similar to that of T ni the function abovewas expected to provide a good fit to the data forthese species as well The gls and g2gt from equation3 were estimated by nonlinear regression (SASInstitute 1982) with the Marquardt computationmethod from data collected by AMS and P BBaker (unpublished data) (Table 1) Minimum de-velopment times (days) for each species were es-timated from data in the literature to be 8 d forP xylostella 12 d for A rapae and 9 d for T niall at 33degC The inverse of these minimum devel-opment times was used to approximate each of theC (equation 3) in the estimations

Development times calculated using the algo-rithm with parameters calculated from AMS andP B Bakers data were very similar to those re-ported in the literature for A rapae and T niwhereas development times for P xylostella wereslightly longer than those previously reported (Fig2) The parameter estimates obtained from AMSand P B Bakers unpublished data were used be-cause the food source in their study excised cab-bage leaves was most similar to the food source ofthe population being modeled Because food sourcecan affect larval development rate (Shorey et a11962 Jones amp Ives 1979 Wolfson 1982) use ofthese data rather than data from the literatureshould provide more accurate results

Dispersion in development times was simulatedby a time-varying distributed delay (Manetsch 1976)with controlled dispersion (Goudriaan 1973) This

nificant (P lt 005 n = 43) In addition the effectof solar radiation on temperatures in the head wasnot significant (P = 02733 n = 43)

Development Rates Average larval develop-ment rates are calculated as a function of temper-ature for each species according to the algorithmproposed by Stinner et al (1974)

1 CDELt) (1 + egh+8r(I))

October 1990 Hoy ET ALINTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1583

where

Nkt + At) = Nkt(t) + U(t)Fmiddot[Nlk_Jlt) - Nkt)] (4)

feeding area (mm2) per day perlarva of species s in subclass k onstratum j at time tdays average temperature instratum j at time taverage proportion of larval de-velopment completed by sub-class k

(2~- 0)empirical constants for species s

avtempt)

where

1If each subclass is assumed to represent 20 of a

larvas development time average feeding rate foreach subclass in the distributed delay is calculated

(k 1) at the midpoint of the class agek = 20 - 40 ill

Equation (6) Thus accumulated feeding in cm2 issummed over all age classes of all species and all

instars) and large (third fourth and fifth instars)larvae on a given stratum We typically observeconsiderable overlap in P xylostella life stages inthe field Therefore the initial number of P xy-lostella on each stratum is evenly divided amongthe 20 delay subclasses that represent this speciesand only forecast total numbers of P xylostellalarvae are reported

Feeding Rates Accumulated feeding by eachspecies on each stratum is calculated as a functionof temperature and larval age The larvae of eachspecies tend to eat very little until the final instarswhen feeding rates increase dramatically (Chen ampSu 1978 1982) An exponential model is used toensure that the predicted feeding rate is positiveand to provide a qualitatively good fit Plots of In(feeding aread) against proportion of develop-ment time completed at three temperatures ap-peared linear with intercept close to zero and slopedependent on temperature Tatchell (1981) studiedconsumption by A rapae at lower temperaturesand found that total consumption (leaf area in cm2)

increased between 13 and 19degC then decreasedbetween 19 and 24degCj Boldt et a1(1975) found thatT ni consumption increased from 20 to 25degC andthen decreased between 25 and 30degC These studiesand the plots described above indicate that theeffects of temperature on feeding rates are not lin-ear rather they are greater at intermediate tem-peratures and less at low and high temperaturesWe describe this effect of temperature on feedingrate by defining the slope in a regression of In(feeding aread) predicted by larval age as a qua-dratic function of temperature Feeding rate perlarva per day as a function of temperature and ageof the larva can then be expressed as an exponentialfunction

(5)

F

U(t)

M(t)

5(t) 1 - 20DEV(t) the proportion of each

Sj

subclass shiftedthe standard deviation of developmenttimes for species s1 for M(t) = 123 o otherwise At

~ F DELi(r) 20

At 002 dr = At 2At 3M

52-- - was found to be fairly constant for eachDEVspeci~s over three temperatures (AMS and P BBaker unpublished data) so F was assumed to bea constant (Table 1) When programmed U(t) actsas an indicator for the shift of contents from eachsubclass to the next subclass and F gives the pro-portion of each subclass shifted

The subclasses are used to approximate larvalage groups which are required to calculate age-specific feeding rates and to assign an age to thelarvae that move between strata Larvae on dif-ferent strata develop at different rates because ofdifferent temperaturesj therefore larvae that movebetween strata must be placed in the appropriateage group at the new location (technically thesubclasses refer to relative maturity rather thanchronological age)

The average number of a given instar per plantis divided evenly among delay subclasses desig-nated to represent that instar as follows k = 1-34-6 7-10 11-15 16-20 for A rapae instars onethrough five and k = 1-3 4-6 7-9 10-14 15-20for T ni instars one through five The number ofsubclasses used to represent each instar for a givenspecies was based on estimates of the proportionof total larval development time spent in each in-star (AMS and P B Baker unpublished data)For example if approximately one-fourth of thelarval period is spent in the last instar the last instarwould be represented by one-fourth of the sub-classes the last five Summing over the appropriatesubclasses gives the number of individuals in a giv-en instar at a given time In practice instar des-ignations are used only for initialization and re-porting forecast numbers of small (first and second

for each species the output was similar to a delaywithout controlled dispersion using approximatelytwice the number of subclasses and twice theamount of computing time)

Programming the distributed delay with con-trolled dispersion yields the following differenceequation for the average number of pests perplant N

1584 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

(7)

31

31

T ni

A rapae

P xyfostefla

00010 a8

a6Physiological

Age

constants estimated by maximumlikelihood as described by Hoy etal (1989)

gt 449535~~ 2lli90ig~ 149845IIOJc6 aooaf 10 08

Fig 3 Predicted feeding rates of P xylo8tella Arapae and T ni on cabbage

Because the shape parameters for the Beta distri-bution a and h change with temperature theshape of the distribution and value of the integralsdescribed in Equation (8) change accordinglyHigher temperatures tend to result in greater prob-ability of movement and higher probability ofmovement towards the lower leaves than towardsthe head lower temperatures tend to result in lowerprobability of movement and higher probabilityof movement towards the head than towards thelower leaves

The elements of the transition probability ma-trices for P xylostella and A rapae are estimatedfrom observations reported in the literature (Har-court 1963 1966 Chua amp Lim 1979 Samson amp

~ 15llli6S~~ 1(57 n

1sectGl 5281IlttlaOJc6af 06

PhysiologicalAge

~~ JI64

~ce 576

sectGl

l2 1288OJc6GlGl

U

previous time steps by

Ej(t) = plusmn plusmn ~ [NkT)FPDkj(T)] ~tTO -I k-I 100

where

Ej(t) area of feeding (cm2) on stratum j accu-mulated at time t

T ~t 2~t 3~t M 002 d

Pj(t)

= f ~ 1__ U1a(I)-11(1 - U)lb(l)-ll duJ~l B[a(t) b(t)] (8)

where

the probability of a T ni (species3) late instar moving from stratumi to stratum j during one dayeel +C2 avtemPi(t)

ed +d2atemp)

The three empirical constants (hh hz and h31inEquation 6) for estimating feeding rates as a func-tion of temperature and larval age were estimatedby multiple linear regression (SAS Institute 1982)of the natural log of feedingday (mm2) on ageage temperature and agemiddottemperature2 (Table 1)The measure of larval age was the proportion oflarval stage completed or days the larva had livedso far divided by total days spent by that larvafrom eclosion to pupation Measurements of areaof cabbage leaf consumed each day of the larvalperiod for each of 20 larvaereplicate and threereplicatestemperature at 167 211 and 267degCfor each species were taken by AMS and P BBaker (unpublished data) Inspection of predictions(Fig 3) compared with data reported in the lit-erature (Harcourt et al 1955 McEwen amp Hervey1960 Rahman 1970 Harper 1973 Boldt et al 1975Chen amp Su 1978 1982 Samson amp Geier 1983Theunissen et al 1985) indicates that the feedingrate model fit well Data on feeding by A rapaereported by Tatchell (1981) indicate much higherrates than those we estimated but Tatchells datadisagree with the other literature cited above aswell As in the case of development rates we usedthe AMS and P B Baker data because the foodsource was cabbage leaf so these data should bemost appropriate

Movement Rates Larval movement is simulatedwith discrete time transition probability matricesbecause observed larval movements were discretein time Movement of late instar T ni is correlatedwith microclimate (Hoy et al 1989) and must bemodeled accordingly The transition probabilitiesfor late instar T ni are modeled as definite integralsof the Beta probability density function (pdf) withshape parameters a(t) and b(t) which depend ontemperature and the stratum larvae are movingfrom

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS

File Edit

1585

021

339

1131

3241

2568

Fig 4 Computer screen displaying output from a simulation model of feeding damage by Lepidoptera oncabbage

Geier 1983 Salinas 1984) and our own observa-tions Our observations for these species were thefrequency of movements by larvae marked withfluorescent powder and visually censused at ~1-hintervals in research cabbage plots near GenevaNY The number of these observations was notsufficient to estimate individual transition proba-bilities so the data were used roughly to estimatefrequency of movement and probability of movingup or down on the plant For P xylostella thefrequency of movement was low and approxi-mately equal numbers of upwards and downwardsmovements were observed For A rapae virtuallyall late instars were observed to move upwards tothe head or wrapper leaves as noted by Harcourt(1963 1966) and Hoy amp Shelton (1987) Transitionprobabilities that reflect these observations werechosen for these two species and are given in Ta-ble 1

The change in state variables due to movementis thus calculated by

s

Nkj(t + ~t) = ~ Nkj(t)pj(t)I(t + ~t) (9)

where

k =k =

I(t + ~t)

~t

13 14 20 for s = 110 11 20 for s = 2 or 3

1 if (t + ~t) = 1 2 3 o otherwise002d

Movement is simulated only once each day andbecause the time step for the model is lfso of a daythe indicator I(t) is used to determine when themovements occur The values of k given above arechosen so that movement is simulated only for olderlarvae which are represented by higher values ofk (k ~ 13 for P xylostella and k ~ 10 for A rapaeor T ni)Model Output The output generated using the

equations described above is a summary of thevalues of state variables and the value of the aux-iliary variable each day for the next 7 d This ispresented on the computer screen depicted in Fig4 The number of large and small larvae of eachspecies on each stratum also can be obtained for aprintout by summing over the appropriate sub-classes in the distributed delay The picture of acabbage plant on the screen gives the user an ap-proximate idea of what the predicted damage onthe cabbage crop would look like

Validation

Methods Validation analysis was performed todemonstrate how well the model predicts data thatwere not used in model design or parameterizationData collected by a commercial field monitoringand pest control advising service were used to com-pare model predictions with observed populationdensities and feeding damage 7 d after the original

1586 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

A rapae

P xylostella

18161412108642o 00 06 12 18 24

557371

1114

92

743

1300

A rapae

10

P xylostella

20

oO0 16 32 48 64

30

10

20

1 ffi

0O0 1 2 2 4 3 6 4 8

000-05 00 05 10 15

1300

11 14

929 T ni T ni

743

55710

3 71

186

0 00- O32 -O16 O00 016 032 O0 O8 16 2 4 3 2

Standardized Residuals Standardized Residualsfor the Head for the Wrapper Leaves

-ogtucQ)=J0Q)-LL

Fig 5 Histograms of standardized cell residuals for comparing predicted numbers with observed averagenumbers of larvae on the cabbage head and wrapper leaves in commercial cabbage fields near Geneva NY

sample Scouts sampled cabbage fields on a weeklybasis using a variable-intensity sampling scheme(Hoy et al 1983) Separate counts of P xylostellalarvae (all instars combined) and A rapae and Tni eggs small (first and second instars) and large(third fourth and fifth instars) larvae were taken

on the head (stratum 1) wrapper (stratum 2) andframe leaves (strata 3-5 combined) and were usedto initialize the model Predictions of numbers ofP xylostella large A rapae and T ni and ac-cumulated feeding on the head and wrapper leaveswere compared with the scouts observations taken

October 1990 HoY ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1587

o [] a [] C D

QOO n~ Q~ n~ 100 1~ t~ 1~ 200Average Damage Rating

Average Damage Rating

Fig 6 Comparison of predicted feeding damagewith average observed damage rating on the heads andwrapper leaves of commercial cabbage crops near Ge-neva NY

the following week Initial spatial distribution with-in the frame and initial age distribution with Arapae and T ni small and large larval populationswere assumed to be uniform for lack of more pre-cise information The scouts observations includedratings of feeding damage on a scale of 0 to 4indicating approximately no damage less than onefeeding hole per leaf one to three feeding holesper leaf 10 defoliation and 40 defoliationrespectively These ratings were compared withpredictions of accumulated area of feeding withscatter plots and correlation analysis

Weather data for model inputs (maximum andminimum temperatures and daily total solar ra-diation) were recorded at the New York State Ag-ricultural Experiment Station in Geneva NY thec1vsest weather station to the commercial fieldsbeing monitored (within 20 km) Data from 34pairs of field samples-each pair taken one weekapart during July August and September in 1983and 1984 under widely varying weather condi-tions-were used for this analysis

Model predictions for number of larvae on thehead and wrapper leaves were compared with ob-servations using standardized cell residuals givenby

observed no larvae - predicted no larvaeVpredicted no larvae

Evaluation of Existing Treatment Guidelines

Because the model predicts numbers of larvaeand feeding damage on different parts of the plantwell model predictions cap be used to evaluatetreatment guidelines currently in use for cabbagepest management In particular the model can beused to explore the relative effects of each pest onthe crop and how useful a static threshold for pestpopulation density will be in predicting a given

as described by Bishop et al (1975) These ap-proximate a standard normal distribution so thecriterion for evaluation is whether or not most ofthe residuals are within 2 SD of the mean (- 2and ~2) because lt=95of the standard normaldistribution falls within this range Observations ofthe feeding damage rating also were plotted againstpredicted accumulated area of feeding and asso-ciated correlation coefficients were calculated

Results and Discussion Most standardized cellresiduals for predicted versus observed counts oflarvae on the head and wrapper leaves were wellwithin the range -2 to +2 (Fig 5) The few largedeviations that were calculated were positive in-dicating that occasionally greater average num-bers of larvae than predicted were observed Theinterplant spatial distribution of each species is ag-gregated (Harcourt 1966) and sample sizes wereoften small (as few as 11 plants) so these occasionallarge positive deviations are not surprising Theseresults indicate that the model predicts number andlocation of larvae well particularly when the lowresolution in the data for initial age and spatialdistribution within the frame and potential sam-pling error in both samples are considered Con-clusions from this analysis must be tempered some-what however by the low population densitiesobserved in these fields Bishop et al (1975) warnthat the approximation of the standardized cellresiduals to the standard normal is poorest whenpredictions in the cells are small Most of the initialpopulation densities and associated predictions weresmall because pest population densities are keptlow by farmers Evaluation of the model underthese conditions is most appropriate however be-cause these are the conditions under which themodel would be used

Predicted area of feeding was correlated withobserved damage rating (Fig 6) Damage ratingincluded assessment of recent feeding as well asolder damage done before the first sample Thiscould explain circumstances in which little feedingdamage was predicted but high damage ratingswere observed Cases where large amounts of feed-ing damage were predicted but observed damagerating was low did not occur Feeding damage isthe most important variable to managers becauseit determines the market value of the crop Thedata indicate that the model can be used to predictthe effects on the cabbage crop of a given pestpopulation under specific conditions

3

(10)

D

o

D

D

o

CC

lJ 8DaD co lJ 0

D D0

2

D

1

D D

C C

D

Wrapper Leaves

r-069

Head

r-053

oo 0

q CD

ggt 206Q)

~0Q)

~ 10fa

E8

40

oo

E8 30Dlc6Q)t 20tJQ)

Ug 1a

1588 ENVIRONMEITAL ENTOMOLOGY Vol 19 no 5

Head Wrapper Leaves

T ni 565134

377089

189045

2020

- Temporatura Avorago plon1CJ DCEC)---0)c A rapaea 1t82Q) a18Q)U 546 7890Q) 273 396sect0 30 30eD

Temperature Avorago pIontDC Temperalure Avomg bullbull p1ont

DC

P xylostella074 178050 11902i 061

20

rompera1ur Avorago plantDC Tempera1ure Averag bullbull p1on1

DC

Fig 7 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves after 7 d atdifferent temperatures and population densities of lepidopteran pests

amount of damage on the marketable parts of thecrop

Methods Response surfaces of predicted area offeeding on the head and wrapper leaves to tem-perature and population density of each pest weregenerated with the model A standard initial in-traplant spatial distribution typical of distributionsobserved in cabbage fields was chosen for eachspecies as follows P xylostella 005 01 03 03and 025 A rapae 0 015 04 03 and 015 Tni 0 01 02 04 and 03 of the average numberper plant on the head wrapper leaves upper framemidframe and lower frame respectively For Pxylostella the larval ages were uniformly distrib-uted among the 20 subclasses in the distributeddelay For A rapae and T ni the larvae wereinitialized into the first 10 subclasses simulatingfirst second and third instars For each of 10 pop-ulation densities ranging from well below to well

above the action threshold currently used in NewYork (Shelton et al 1982) feeding was predictedat six constant temperatures

Additional response surfaces were generated offeeding area on the head and wrapper leaves pre-dicted at different temperatures and initial age dis-tributions for a given population density of eachspecies Given the initial spatial distribution de-scribed above and an average temperature be-tween 20 and 25degC the first set of response surfaceswas used to select a population density predictedto cause damage most farmers would consider un-acceptable This density twice the currently rec-ommended action threshold was 1 larvaplant forT ni 15 larvaeplant for A rapae and 10 larvaeplant for P xylostella Different age distributionswere generated by dividing the population densi-ties chosen above evenly among larval maturitysubclasses 1 through 6 then 2 through 7 etc up

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1589

Head Wrapper Leaves

1n

519

260

T1i

TemperatureDC

10

Youngest Age ProSQnt

10

10

YOungG81 AGe PrQsan

A rapal2333

557

78

10

Youngest Ago PreSGnt

TemperatureDC

142 P xylostllia

098

053

0009

Youngesl Ago PresentTemperature

DCTemperalUIlliDc

Fig 8 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves in 7 d due todifferent temperatures and age distributions at a given population density of three lepidopteran pests of cabbagePopulation densities were lplant for T ni loSplant for A rapae 10plant for P xylostella

to 10 through 15 Model predictions were gener-ated at each of these age distributions for each ofthe 6 constant temperatures used above

Results and Discussion Response surfaces gen-erated with the model predict that A rapae con-tributes most to feeding damage on the head andwrapper leaves (Fig 7) Although total consump-tion by A rapae larvae is less than that of T ni(Harcourt et al 1955) the amount consumed onthese economically important strata is greater be-cause of the difference in intra plant spatial dynam-ics of the two species In Fig 7 the model predictsthat for a given constant temperature and giveninitial age and spatial distributions feeding on thehead and wrapper leaves increases linearly withpopulation density for each species Systems thatweight the counts of each species according to ex-pected feeding damage and base the action thresh-old on the weighted counts have been proposed

(Harcourt et al 1955 Shelton et al 1982) but thesedid not consider the spatial dynamics of the pestsThus one potential use of our model is to designa new rating scale to weight the population densityof each species according to expected feeding dam-age considering the spatial dynamics of eachspecies This rating scale however would also haveto account for temperature effects which cangreatly affect predicted feeding

At temperatures lt15DC very little feeding ispredicted on the head and wrapper leaves by eachspecies at any population density (Fig 7) Increas-ing temperatures have a nonlinear effect on pre-dicted feeding by each species For P xylostellaand A rapae the increase in predicted feedingrate may be primarily due to increased develop-ment and feeding rates For T ni however in-creased development and feeding rates at highertemperatures may be offset to some extent by higher

1590 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

probabilities of moving away from the head andwrapper leaves towards the lower leaves (Hoy etal 1989)

For a given population density predicted feed-ing on the marketable parts of the plant variedwidely with age distribution again interacting withtemperature (Fig 8) The results indicate that thedamage caused by a given population density afixed economic threshold for example will varyconsiderably with temperature age structure of thepopulation and species composition Againweighting systems have been described that con-sider larval age (Andaloro et al 1983a) but notwith the resolution that Fig 8 implies is necessaryand they do not include the interaction with tem-perature

Considering the profound effects of tempera-ture age distribution and species-specific spatialdynamics on the predicted area of feeding on eco-nomically important parts of the plant a staticeconomic threshold does not seem to be appropri-ate Rather feeding should be predicted for specificpopulation densities age distributions and spatialdistributions of the three species as well as weatherforecasts and management strategies should be de-signed accordingly The model described here couldbe used to make those predictions either by cal-culating a new species weighting system each dayof the growing season to be used with a fixed actionthreshold or simply by making the required pre-dictions on a case-by-case basis

Sensitivity Analysis

Two goals were addressed in the sensitivity anal-ysis First individual model parameters were evalmiddotuated as potential causes of inaccurate predictionsBy examining the change in model output after achange in the individual parameters parametersthat affect the output most can be identified Sec-ond by examining the effects of changes in dif-ferent parameters in combination insight can begained into the effects of the different processesbeing simulated and their interactions on the out-put variables of interest

Methods Model predictions were evaluated af-ter changing each parameter and input suppliedby the user by +10 and -10 of its valueChanges were made one parameter at a time witha standard set of initial conditions Standard initialpest population densities were a mean of 1 larvalplant of each species on each stratum in the secondinstar for A rapae and T ni and uniformly dis-tributed among the 20 age subclasses for P xylo-stella The analysis was performed at each of threetemperature regimes typical summer weather forwestern New York (maximum temperature 267degCminimum temperature 155degC 8 h sunshine eachday) hot and sunny weather (maximum temper-ature 322degC minimum temperature 211oC 12h sunshine each day) and cool and cloudy weather

(maximum temperature 183degC minimum tem-perature 10degC 2 h sunshine)

Constants were changed by adding or subtract-ing 10 of their value Input weather variableswere changed by adding or subtracting 10 of thevalue of each pays forecasted maximum and min-imum temperature and hours of sunshine Age atwhich larvae begin to move was shifted plus orminus two subclasses to effect a 10 change Initialage distribution for A rapae and T ni was alsoshifted 10 by shifting the subclasses initialized byplus or minus two Initial age distribution for Pxylostella is assumed to be uniform so this was notchanged For each species the initial intraplantdistribution was altered by shifting 10 of eachage group on each stratum except the lower frameleaves down one stratum or shifting 10 of eachage group on each stratum except the head upone stratum (eg a downward shift of an averageof one larva on each stratum would result in anaverage of 09 1 1 1 and 11 larvae on the headwrapper upper frame midframe and lower frameleaves respectively) Transition probabilities for Arapae and P xylostella were changed by a similarmethod shifting 10 of the probability of movingto each stratum except the lower frame leaves tothe next lower stratum or shifting 10 of the prob-ability of moving to each stratum except the headto the next stratum up (eg a downward shift ina transition probability vector of 09 01000 resultsin a vector of 081 018 001 0 0) Sensitivity tochanges in transition probabilities for T ni wereexamined by changing the Beta pdf shape param-eters that govern transition probabilities for thisspecies by + 10 and -10 of their value Theeffects of each of these changes were examined bycalculating the percentage of change in number oflarvae of each species and the percentage of changein accumulated area of feeding on the head andwrapper leaves

To examine interactions between different pro-cesses and their effects on model output we per-formed two analyses in which variables suspectedof interacting were varied in all combinations theequivalent of a factorial design with three levelsof each factor given by +5 -5 and 0 Be-cause development and feeding rates are temper-ature-dependent and govern the amount of feedingaccumulated interactions between temperaturefeeding rates and development rates might affectaccumulated area of feeding Three levels of tem-perature were generated starting with the typicalsummer weather regime described above and add-ing 5 -5 or 0 of the daily maximum andminimum At each temperature level develop-ment rate for each species was varied by +5-5 and 0 from its value and at each of thesedevelopment rates for each species feeding ratewas changed by +5 -5 and 0 of its valueThe effects of these parameter changes on the pre-dicted area of feeding on the head and wrapperleaves were calculated

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1591

Table 2 Output from a model to predict lepidopteranfeeding damage on cabbage at three temperature regimeswith a standard set of inputs and no change in the param-eters Changes in output during the sensitivity analysis (Fig9-12) are compared with these standards

StratumPopulation density (avg noplant) Feeding

P xylostella A rapae Tni cm2

High temperaturesHead 0252 2118 0095 12764Wrapper 0390 2594 0662 21716

Moderate temperaturesHead 0423 1957 0299 6805Wrapper 0578 2524 1001 9667

Low temperaturesHead 0635 1296 0829 1945Wrapper 0834 1651 0886 2348

A similar analysis of interacting processes wasperformed for spatial effects Initial distributionand transition probabilities could be expected tointeract in their effects on spatial distribution oflarvae and feeding damage For each species theinitial distribution was treated by (a) shifting 10of each age group on each stratum (except thelower frame leaves) down one stratum (b) shifting10of each age group on each stratum (except thehead) up one stratum and (c) leaving the initialdistribution unchanged At each of these shifts ininitial distribution for each species the transitionprobabilities for that species were changed as de-

scribed above Shifting 10 of the probability ofmoving to each stratum except the lower frameleaves to the next lower stratum resulted in higherprobabilities of downward movement shifting 10of the probability of moving to each stratum exceptthe head to the next stratum up resulted in higherprobability of upward movement

Results and Discussion Standard results for highmoderate and low temperature regimes withoutchanging any of the parameters or input variablesare given in Table 2 and the effects of changingeach parameter and input variable on selected out-put variables are displayed in Fig 9-12 for themoderate temperature regime We begin the anal-ysisby examining sensitivity of the model to changesin the parameters at moderate temperatures andfollow with the differences in model sensitivity seenunder high and low temperature regimes

At moderate temperatures numbers of larvae ofeach species on the head and wrapper leaves wereleast sensitive to initial spatial distribution of larvaedispersion in development time and hours of sun-shine (Fig 9) Change in the initial intraplant dis-tribution of larvae may be compensated for bymovement of larvae within a short time after thebeginning of the simulation Dispersion in devel-opment time for these species was low in the lab-oratory development studies resulting in a small

Svalue of -D for each species A 10 change in

EL~these small values does not change the dispersion

o Effect 01 +10 changebull Effect 01 -10 change on larvae on the head alief 7 days

Inldal dlsbibudonInitial ages

Age 01 first movementTransition probabilities

Dispersion In developmenlgl

DEL g2C

Hours 01 sunshineTemperalure

-20 -10 0 10

P xylostella20 30 -20 -10 0 10 20

A rapae

oT nl

100

on larvae on the wrapper leaves alter 7 days

10-10

Initial distributionInitial ages

Age 01 firsl movementTransition probabilities

Dispersion in developmentgl

DEL g2C

Hours of sunshineTemperature

-20 o 10 -20 -10 0 -10 0P xylostella A rapas T nI

Fig 9 Percentage of change in predicted number of P xylostella A rapae and T nt larvae on the head andwrapper leavesafter changing model parameters + and -10

1592 ENVIRONME~TAL ENTOMOLOGY Vol 19 no 5

Fig 10 Percentage of change in number of T nilarvae predicted on the head and wrapper leaves aftera + or - 1 0 change in parameters governing their tran-sition probabilities on the cabbage plant

greatly Hours of sunshine influence temperaturein each stratum but apparently not enough to causelarge changes in rate functions

Changes in temperature initial age distributionage at which larvae begin to move between strataand transition probabilities had the greatest effectson predicted number of larvae on the head or wrap-per leaves (Fig 9) These are all linked to spatialdynamics since both temperature and initial agedistribution affect the time at which larvae beginto move between strata Changes in parametersgoverning T ni transition probabilities were anexception causing only moderate or small changesin output (Fig 10) Changes in development rateparameters had large effects only for P xylostellaon the head and wrapper leaves and for T ni onthe head

Predictions of accumulated feeding on the headand wrapper leaves were generally less sensitive tochanges in parameters than were predictions ofnumbers of larvae on these strata (Fig 11 and 12)Because the predictions of accumulated area offeeding are most important to the farmer the ro-bustness of the model in predicting feeding sug-gests that it could be a useful management toolThe greatest changes in accumulated area of feed-ing were caused by changing parameters governingA rapae development or feeding particularly ini-tial age distribution Fortunately development ratesfor all three species considered here have been wellstudied and studies done at widely different timesand locations with different food sources suggestthat average development rate at a given temper-ature is fairly constant (Hardy 1938 Richards 1940Given 1944 Miner 1947 Harcourt et al 1955Shorey et al 1962 Jackson et al 1969 Toba et al

1973 Boldt et al 1975 Butler et al 1975 Smithamp Smilowitz 1976 Chen amp Su 1978 1982 Tatchell1981 Yamada amp Kawasaki 1983 Theunissen et al1985) Changes in forecast temperatures cause thenext largest change in accumulated feeding prob-ably because of their effects on development andfeeding rates Parameters governing spatial effectshad smaller effects on accumulated feeding par-ticularly when compared with their effects on pre-dicted number of larvae on different parts of theplant

Under the low-temperature regime predictionsof numbers of larvae on the head and wrapperleaves were more sensitive to parameters affectingdevelopment than to parameters affecting spatialdynamics At low temperatures larvae take longerto reach the age when movement starts and prob-ability of movement by T ni to the head andwrapper leaves is lower Furthermore fewer smalllarvae become large larvae at low temperatures sototal numbers of large larvae on all strata are re-duced At moderate and high temperatures pre-dictions of numbers of larvae on the head andwrapper leaves were more sensitive to changes inparameters affecting spatial dynamics

Effects of changing forecast temperatures onpredictions of accumulated feeding were muchgreater when the forecast temperatures were lowand less when the forecast temperatures were highthan at moderate temperatures Changing devel-opment rate parameters had a greater effect onaccumulated feeding at low temperatures butchanging feeding rate parameters had a greatereffect at high temperatures than at moderate tem-peratures Accumulated feeding was less sensitiveto changes in transition probabilities at low tem-peratures and more sensitive to changes in tran-sition probabilities at high temperatures than atmoderate temperatures

In general interactions between temperaturedevelopment and feeding rates as well as param-eters governing spatial effects were not evidentTypically the effect of changes in each of theseparameters was similar regardless of the value ofthe other parameters One interaction did occurWhen temperature was increased a negativechange in T ni development rate resulted in lesspredicted feeding on the head than when no changein T ni development rate was made In all othercases negative change in development rates re-sulted in higher predicted feeding on the head thanwhen development rates were not changed Re-gardless 5 changes in development rates for Tni resulted in lt3 differences in feeding on thehead so the effects of this interaction are not ofgreat importance Thus this analysis reinforced thesingle parameter analysis Feeding rates themselveswere changed in this analysis rather than the pa-rameters that govern them and accumulated feed-ing on the head and wrapper leaves was still moresensitive to changes in development rate and tem-perature

5o

middot5 0

Feeding on Heed

-5Feeding on Wrapper Leaves

o 10

Larvae on Head

middot10

b5b4b3b2bl858483a281

middot20l( Change in

-20 middot10 0 10 Change in Larvae on Wrapper leaves

II2l

~toa0gtatoten

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

SDElA rapae g2

g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1581

r- bullbullbull File

iOEdit

Inputs

Fill in the bOXl8with the nquirld numblu

I~~li~~Cli~~II~~Itjinlr~degr~li~cr~8Ii~~81APIo~ J J) ) j j jj~

DB leW eL

Hledm~ 811 I[JCJ 8~11 I[]wrepPlrl 0 II 0 I 0 II 0 II 0 I 0 II 0 I

Uppn I 0 II 0 I =0=11 0 II 0 I 0 II 0 Il1id I 0 II 0 I =0 11 0 II 025 I 0 II 120 I

Lo~rl 0 II 0 1_0 ---II 0 II 100 I 002 II 030 I( RUN ) ( STRRT OUER

tt ------

Fig 1 Computer screen displaying the interactive input table for initializing a model to predict feeding damageby Lepidoptera on cabbage

tween averages for the other strata (j = 1 3 and35 respectively)

Like average temperature the temperature rangeis assumed to be the same in the lower frame leavesas in the forecast for ambient conditions Aroundthe cabbage head the observed temperature rangewas consistently narrower than it was under thelower frame leaves The head has considerable massand moderates the temperature around it There-fore the temperature range in stratum 1 the headis modeled as a proportion of the range in the lowerframe The temperature range in the upper frameis modeled as the range in the lower frame plus aneffect of sunshine

amp3(t) = amp5(t) + m3 + m2) (forecasted hours of

sunshine on day t) (2)

where ml and m2 are empirically estimated con-stants The upper frame leaves absorb radiant heatenergy from sunlight resulting in higher daytimetemperatures than on the lower leaves they radiateheat more easily at night than the lower leavesbecause they are exposed to the sky resulting inlower night temperatures in this part of the canopy

Measurements were not available for the tem-perature range in the wrapper and midframe leavesTemperature ranges in these strata were modeledsimilarly to the upper frame leaves but the effect

of sunshine was reduced to two-thirds that of theupper frame for the wrapper leaves and one-thirdthat of the upper frame for the midframe leavesbecause these strata receive less sunlight

To estimate the differences in average temper-ature and amplitude between strata temperaturewas monitored on the undersides of the leaves inthree of the strata (the head upper frame leavesand lower frame leaves) from 13 August to 23October 1986 in research plots in Geneva N Y asdescribed in Hoy et al (1989) Hourly temperatureaverages from 2-min samples were recorded Dailytotal solar radiation and ambient air temperatureswere measured at the New York State AgriculturalExperiment Station weather station Geneva NYDaily total solar radiation (caljcm) was dividedby an estimate of average solar radiation per hourfor Geneva N Y during the time the measure-ments were taken to approximate hours of sun-shine Estimated coefficients for the regression de-scribed above and for each of the constants aregiven in Table 1 (SAS Institute 1982) Quadraticand higher order polynomial coefficients for solarradiation were not significantly different from zero(P = 01228 n = 43) indicating that the relation-ship could be described as linear T-statistics onslope coefficients in these regression analyses alsoindicated that the linear effects of solar radiationon amplitude in the upper frame leaves were sig-

1582 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

(3)

Fig 2 Calculated development times for P xylo-stella A rapae and T ni larvae on cabbage (solidlines)compared with development times previously reportedin the literature at specific temperatures

30

A rapaebull Chenamp Su1982bull Smithamp Smilowitz1976o Tatchell1981o Theunissenet al198511 Given1944bull Richards1940bull Harcourt1955

P xylosteJao Hardy1938bull Chenamp Su1978o Miner194711 Yamadaamp Kawasaki1983

20

Tni+ Shoreyet al1962(males)bull Shoreyet al1962(females)o Jackson1969[] Tobaat al197311 Boldtat al1975bull Butleretal1975bull Chenamp Su1982

o

Temperature (Oe)

o

o10

20

40

80

60

10

20

30

40

10

20

30

Ulgtctl0-Q)

Ei=EQ)

EaoQ)gtQ)Cl

algorithm shifts a proportion of the contents of eachsubclass to the next subclass at certain time stepsThe number of time steps before each shift occursand the proportion of the contents of each subclassshifted are determined by the average develop-ment time or delay and the estimated dispersionin development times The controlled dispersionmodel was used because fewer subclasses were re-quired to represent the observed distribution ofdevelopment times adequately (with 20 subclasses

whereDELj(t) average development time (days) for

the larval period in species s on stra-tum j at time t

C (maximum development rate)(l +eBb + R2s Top

Top temperature at which maximum de-velopment rate occurs

Tj(t) temperature on stratum j at time tif tempj(t) 5 Top2 Top - tempj(t) if tempj(t) gt Top

gt g2gt empirically estimated constants forspecies s

This model was used because it fits developmentrate data for T ni well (Butler et a1 1976) and itcould easily be fit to data for the other species usingstandard nonlinear regression packages Becausethe relationship between temperature and devel-opment time of P xylostella and A rapae is qual-itatively similar to that of T ni the function abovewas expected to provide a good fit to the data forthese species as well The gls and g2gt from equation3 were estimated by nonlinear regression (SASInstitute 1982) with the Marquardt computationmethod from data collected by AMS and P BBaker (unpublished data) (Table 1) Minimum de-velopment times (days) for each species were es-timated from data in the literature to be 8 d forP xylostella 12 d for A rapae and 9 d for T niall at 33degC The inverse of these minimum devel-opment times was used to approximate each of theC (equation 3) in the estimations

Development times calculated using the algo-rithm with parameters calculated from AMS andP B Bakers data were very similar to those re-ported in the literature for A rapae and T niwhereas development times for P xylostella wereslightly longer than those previously reported (Fig2) The parameter estimates obtained from AMSand P B Bakers unpublished data were used be-cause the food source in their study excised cab-bage leaves was most similar to the food source ofthe population being modeled Because food sourcecan affect larval development rate (Shorey et a11962 Jones amp Ives 1979 Wolfson 1982) use ofthese data rather than data from the literatureshould provide more accurate results

Dispersion in development times was simulatedby a time-varying distributed delay (Manetsch 1976)with controlled dispersion (Goudriaan 1973) This

nificant (P lt 005 n = 43) In addition the effectof solar radiation on temperatures in the head wasnot significant (P = 02733 n = 43)

Development Rates Average larval develop-ment rates are calculated as a function of temper-ature for each species according to the algorithmproposed by Stinner et al (1974)

1 CDELt) (1 + egh+8r(I))

October 1990 Hoy ET ALINTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1583

where

Nkt + At) = Nkt(t) + U(t)Fmiddot[Nlk_Jlt) - Nkt)] (4)

feeding area (mm2) per day perlarva of species s in subclass k onstratum j at time tdays average temperature instratum j at time taverage proportion of larval de-velopment completed by sub-class k

(2~- 0)empirical constants for species s

avtempt)

where

1If each subclass is assumed to represent 20 of a

larvas development time average feeding rate foreach subclass in the distributed delay is calculated

(k 1) at the midpoint of the class agek = 20 - 40 ill

Equation (6) Thus accumulated feeding in cm2 issummed over all age classes of all species and all

instars) and large (third fourth and fifth instars)larvae on a given stratum We typically observeconsiderable overlap in P xylostella life stages inthe field Therefore the initial number of P xy-lostella on each stratum is evenly divided amongthe 20 delay subclasses that represent this speciesand only forecast total numbers of P xylostellalarvae are reported

Feeding Rates Accumulated feeding by eachspecies on each stratum is calculated as a functionof temperature and larval age The larvae of eachspecies tend to eat very little until the final instarswhen feeding rates increase dramatically (Chen ampSu 1978 1982) An exponential model is used toensure that the predicted feeding rate is positiveand to provide a qualitatively good fit Plots of In(feeding aread) against proportion of develop-ment time completed at three temperatures ap-peared linear with intercept close to zero and slopedependent on temperature Tatchell (1981) studiedconsumption by A rapae at lower temperaturesand found that total consumption (leaf area in cm2)

increased between 13 and 19degC then decreasedbetween 19 and 24degCj Boldt et a1(1975) found thatT ni consumption increased from 20 to 25degC andthen decreased between 25 and 30degC These studiesand the plots described above indicate that theeffects of temperature on feeding rates are not lin-ear rather they are greater at intermediate tem-peratures and less at low and high temperaturesWe describe this effect of temperature on feedingrate by defining the slope in a regression of In(feeding aread) predicted by larval age as a qua-dratic function of temperature Feeding rate perlarva per day as a function of temperature and ageof the larva can then be expressed as an exponentialfunction

(5)

F

U(t)

M(t)

5(t) 1 - 20DEV(t) the proportion of each

Sj

subclass shiftedthe standard deviation of developmenttimes for species s1 for M(t) = 123 o otherwise At

~ F DELi(r) 20

At 002 dr = At 2At 3M

52-- - was found to be fairly constant for eachDEVspeci~s over three temperatures (AMS and P BBaker unpublished data) so F was assumed to bea constant (Table 1) When programmed U(t) actsas an indicator for the shift of contents from eachsubclass to the next subclass and F gives the pro-portion of each subclass shifted

The subclasses are used to approximate larvalage groups which are required to calculate age-specific feeding rates and to assign an age to thelarvae that move between strata Larvae on dif-ferent strata develop at different rates because ofdifferent temperaturesj therefore larvae that movebetween strata must be placed in the appropriateage group at the new location (technically thesubclasses refer to relative maturity rather thanchronological age)

The average number of a given instar per plantis divided evenly among delay subclasses desig-nated to represent that instar as follows k = 1-34-6 7-10 11-15 16-20 for A rapae instars onethrough five and k = 1-3 4-6 7-9 10-14 15-20for T ni instars one through five The number ofsubclasses used to represent each instar for a givenspecies was based on estimates of the proportionof total larval development time spent in each in-star (AMS and P B Baker unpublished data)For example if approximately one-fourth of thelarval period is spent in the last instar the last instarwould be represented by one-fourth of the sub-classes the last five Summing over the appropriatesubclasses gives the number of individuals in a giv-en instar at a given time In practice instar des-ignations are used only for initialization and re-porting forecast numbers of small (first and second

for each species the output was similar to a delaywithout controlled dispersion using approximatelytwice the number of subclasses and twice theamount of computing time)

Programming the distributed delay with con-trolled dispersion yields the following differenceequation for the average number of pests perplant N

1584 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

(7)

31

31

T ni

A rapae

P xyfostefla

00010 a8

a6Physiological

Age

constants estimated by maximumlikelihood as described by Hoy etal (1989)

gt 449535~~ 2lli90ig~ 149845IIOJc6 aooaf 10 08

Fig 3 Predicted feeding rates of P xylo8tella Arapae and T ni on cabbage

Because the shape parameters for the Beta distri-bution a and h change with temperature theshape of the distribution and value of the integralsdescribed in Equation (8) change accordinglyHigher temperatures tend to result in greater prob-ability of movement and higher probability ofmovement towards the lower leaves than towardsthe head lower temperatures tend to result in lowerprobability of movement and higher probabilityof movement towards the head than towards thelower leaves

The elements of the transition probability ma-trices for P xylostella and A rapae are estimatedfrom observations reported in the literature (Har-court 1963 1966 Chua amp Lim 1979 Samson amp

~ 15llli6S~~ 1(57 n

1sectGl 5281IlttlaOJc6af 06

PhysiologicalAge

~~ JI64

~ce 576

sectGl

l2 1288OJc6GlGl

U

previous time steps by

Ej(t) = plusmn plusmn ~ [NkT)FPDkj(T)] ~tTO -I k-I 100

where

Ej(t) area of feeding (cm2) on stratum j accu-mulated at time t

T ~t 2~t 3~t M 002 d

Pj(t)

= f ~ 1__ U1a(I)-11(1 - U)lb(l)-ll duJ~l B[a(t) b(t)] (8)

where

the probability of a T ni (species3) late instar moving from stratumi to stratum j during one dayeel +C2 avtemPi(t)

ed +d2atemp)

The three empirical constants (hh hz and h31inEquation 6) for estimating feeding rates as a func-tion of temperature and larval age were estimatedby multiple linear regression (SAS Institute 1982)of the natural log of feedingday (mm2) on ageage temperature and agemiddottemperature2 (Table 1)The measure of larval age was the proportion oflarval stage completed or days the larva had livedso far divided by total days spent by that larvafrom eclosion to pupation Measurements of areaof cabbage leaf consumed each day of the larvalperiod for each of 20 larvaereplicate and threereplicatestemperature at 167 211 and 267degCfor each species were taken by AMS and P BBaker (unpublished data) Inspection of predictions(Fig 3) compared with data reported in the lit-erature (Harcourt et al 1955 McEwen amp Hervey1960 Rahman 1970 Harper 1973 Boldt et al 1975Chen amp Su 1978 1982 Samson amp Geier 1983Theunissen et al 1985) indicates that the feedingrate model fit well Data on feeding by A rapaereported by Tatchell (1981) indicate much higherrates than those we estimated but Tatchells datadisagree with the other literature cited above aswell As in the case of development rates we usedthe AMS and P B Baker data because the foodsource was cabbage leaf so these data should bemost appropriate

Movement Rates Larval movement is simulatedwith discrete time transition probability matricesbecause observed larval movements were discretein time Movement of late instar T ni is correlatedwith microclimate (Hoy et al 1989) and must bemodeled accordingly The transition probabilitiesfor late instar T ni are modeled as definite integralsof the Beta probability density function (pdf) withshape parameters a(t) and b(t) which depend ontemperature and the stratum larvae are movingfrom

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS

File Edit

1585

021

339

1131

3241

2568

Fig 4 Computer screen displaying output from a simulation model of feeding damage by Lepidoptera oncabbage

Geier 1983 Salinas 1984) and our own observa-tions Our observations for these species were thefrequency of movements by larvae marked withfluorescent powder and visually censused at ~1-hintervals in research cabbage plots near GenevaNY The number of these observations was notsufficient to estimate individual transition proba-bilities so the data were used roughly to estimatefrequency of movement and probability of movingup or down on the plant For P xylostella thefrequency of movement was low and approxi-mately equal numbers of upwards and downwardsmovements were observed For A rapae virtuallyall late instars were observed to move upwards tothe head or wrapper leaves as noted by Harcourt(1963 1966) and Hoy amp Shelton (1987) Transitionprobabilities that reflect these observations werechosen for these two species and are given in Ta-ble 1

The change in state variables due to movementis thus calculated by

s

Nkj(t + ~t) = ~ Nkj(t)pj(t)I(t + ~t) (9)

where

k =k =

I(t + ~t)

~t

13 14 20 for s = 110 11 20 for s = 2 or 3

1 if (t + ~t) = 1 2 3 o otherwise002d

Movement is simulated only once each day andbecause the time step for the model is lfso of a daythe indicator I(t) is used to determine when themovements occur The values of k given above arechosen so that movement is simulated only for olderlarvae which are represented by higher values ofk (k ~ 13 for P xylostella and k ~ 10 for A rapaeor T ni)Model Output The output generated using the

equations described above is a summary of thevalues of state variables and the value of the aux-iliary variable each day for the next 7 d This ispresented on the computer screen depicted in Fig4 The number of large and small larvae of eachspecies on each stratum also can be obtained for aprintout by summing over the appropriate sub-classes in the distributed delay The picture of acabbage plant on the screen gives the user an ap-proximate idea of what the predicted damage onthe cabbage crop would look like

Validation

Methods Validation analysis was performed todemonstrate how well the model predicts data thatwere not used in model design or parameterizationData collected by a commercial field monitoringand pest control advising service were used to com-pare model predictions with observed populationdensities and feeding damage 7 d after the original

1586 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

A rapae

P xylostella

18161412108642o 00 06 12 18 24

557371

1114

92

743

1300

A rapae

10

P xylostella

20

oO0 16 32 48 64

30

10

20

1 ffi

0O0 1 2 2 4 3 6 4 8

000-05 00 05 10 15

1300

11 14

929 T ni T ni

743

55710

3 71

186

0 00- O32 -O16 O00 016 032 O0 O8 16 2 4 3 2

Standardized Residuals Standardized Residualsfor the Head for the Wrapper Leaves

-ogtucQ)=J0Q)-LL

Fig 5 Histograms of standardized cell residuals for comparing predicted numbers with observed averagenumbers of larvae on the cabbage head and wrapper leaves in commercial cabbage fields near Geneva NY

sample Scouts sampled cabbage fields on a weeklybasis using a variable-intensity sampling scheme(Hoy et al 1983) Separate counts of P xylostellalarvae (all instars combined) and A rapae and Tni eggs small (first and second instars) and large(third fourth and fifth instars) larvae were taken

on the head (stratum 1) wrapper (stratum 2) andframe leaves (strata 3-5 combined) and were usedto initialize the model Predictions of numbers ofP xylostella large A rapae and T ni and ac-cumulated feeding on the head and wrapper leaveswere compared with the scouts observations taken

October 1990 HoY ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1587

o [] a [] C D

QOO n~ Q~ n~ 100 1~ t~ 1~ 200Average Damage Rating

Average Damage Rating

Fig 6 Comparison of predicted feeding damagewith average observed damage rating on the heads andwrapper leaves of commercial cabbage crops near Ge-neva NY

the following week Initial spatial distribution with-in the frame and initial age distribution with Arapae and T ni small and large larval populationswere assumed to be uniform for lack of more pre-cise information The scouts observations includedratings of feeding damage on a scale of 0 to 4indicating approximately no damage less than onefeeding hole per leaf one to three feeding holesper leaf 10 defoliation and 40 defoliationrespectively These ratings were compared withpredictions of accumulated area of feeding withscatter plots and correlation analysis

Weather data for model inputs (maximum andminimum temperatures and daily total solar ra-diation) were recorded at the New York State Ag-ricultural Experiment Station in Geneva NY thec1vsest weather station to the commercial fieldsbeing monitored (within 20 km) Data from 34pairs of field samples-each pair taken one weekapart during July August and September in 1983and 1984 under widely varying weather condi-tions-were used for this analysis

Model predictions for number of larvae on thehead and wrapper leaves were compared with ob-servations using standardized cell residuals givenby

observed no larvae - predicted no larvaeVpredicted no larvae

Evaluation of Existing Treatment Guidelines

Because the model predicts numbers of larvaeand feeding damage on different parts of the plantwell model predictions cap be used to evaluatetreatment guidelines currently in use for cabbagepest management In particular the model can beused to explore the relative effects of each pest onthe crop and how useful a static threshold for pestpopulation density will be in predicting a given

as described by Bishop et al (1975) These ap-proximate a standard normal distribution so thecriterion for evaluation is whether or not most ofthe residuals are within 2 SD of the mean (- 2and ~2) because lt=95of the standard normaldistribution falls within this range Observations ofthe feeding damage rating also were plotted againstpredicted accumulated area of feeding and asso-ciated correlation coefficients were calculated

Results and Discussion Most standardized cellresiduals for predicted versus observed counts oflarvae on the head and wrapper leaves were wellwithin the range -2 to +2 (Fig 5) The few largedeviations that were calculated were positive in-dicating that occasionally greater average num-bers of larvae than predicted were observed Theinterplant spatial distribution of each species is ag-gregated (Harcourt 1966) and sample sizes wereoften small (as few as 11 plants) so these occasionallarge positive deviations are not surprising Theseresults indicate that the model predicts number andlocation of larvae well particularly when the lowresolution in the data for initial age and spatialdistribution within the frame and potential sam-pling error in both samples are considered Con-clusions from this analysis must be tempered some-what however by the low population densitiesobserved in these fields Bishop et al (1975) warnthat the approximation of the standardized cellresiduals to the standard normal is poorest whenpredictions in the cells are small Most of the initialpopulation densities and associated predictions weresmall because pest population densities are keptlow by farmers Evaluation of the model underthese conditions is most appropriate however be-cause these are the conditions under which themodel would be used

Predicted area of feeding was correlated withobserved damage rating (Fig 6) Damage ratingincluded assessment of recent feeding as well asolder damage done before the first sample Thiscould explain circumstances in which little feedingdamage was predicted but high damage ratingswere observed Cases where large amounts of feed-ing damage were predicted but observed damagerating was low did not occur Feeding damage isthe most important variable to managers becauseit determines the market value of the crop Thedata indicate that the model can be used to predictthe effects on the cabbage crop of a given pestpopulation under specific conditions

3

(10)

D

o

D

D

o

CC

lJ 8DaD co lJ 0

D D0

2

D

1

D D

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D

Wrapper Leaves

r-069

Head

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oo 0

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ggt 206Q)

~0Q)

~ 10fa

E8

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Ug 1a

1588 ENVIRONMEITAL ENTOMOLOGY Vol 19 no 5

Head Wrapper Leaves

T ni 565134

377089

189045

2020

- Temporatura Avorago plon1CJ DCEC)---0)c A rapaea 1t82Q) a18Q)U 546 7890Q) 273 396sect0 30 30eD

Temperature Avorago pIontDC Temperalure Avomg bullbull p1ont

DC

P xylostella074 178050 11902i 061

20

rompera1ur Avorago plantDC Tempera1ure Averag bullbull p1on1

DC

Fig 7 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves after 7 d atdifferent temperatures and population densities of lepidopteran pests

amount of damage on the marketable parts of thecrop

Methods Response surfaces of predicted area offeeding on the head and wrapper leaves to tem-perature and population density of each pest weregenerated with the model A standard initial in-traplant spatial distribution typical of distributionsobserved in cabbage fields was chosen for eachspecies as follows P xylostella 005 01 03 03and 025 A rapae 0 015 04 03 and 015 Tni 0 01 02 04 and 03 of the average numberper plant on the head wrapper leaves upper framemidframe and lower frame respectively For Pxylostella the larval ages were uniformly distrib-uted among the 20 subclasses in the distributeddelay For A rapae and T ni the larvae wereinitialized into the first 10 subclasses simulatingfirst second and third instars For each of 10 pop-ulation densities ranging from well below to well

above the action threshold currently used in NewYork (Shelton et al 1982) feeding was predictedat six constant temperatures

Additional response surfaces were generated offeeding area on the head and wrapper leaves pre-dicted at different temperatures and initial age dis-tributions for a given population density of eachspecies Given the initial spatial distribution de-scribed above and an average temperature be-tween 20 and 25degC the first set of response surfaceswas used to select a population density predictedto cause damage most farmers would consider un-acceptable This density twice the currently rec-ommended action threshold was 1 larvaplant forT ni 15 larvaeplant for A rapae and 10 larvaeplant for P xylostella Different age distributionswere generated by dividing the population densi-ties chosen above evenly among larval maturitysubclasses 1 through 6 then 2 through 7 etc up

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1589

Head Wrapper Leaves

1n

519

260

T1i

TemperatureDC

10

Youngest Age ProSQnt

10

10

YOungG81 AGe PrQsan

A rapal2333

557

78

10

Youngest Ago PreSGnt

TemperatureDC

142 P xylostllia

098

053

0009

Youngesl Ago PresentTemperature

DCTemperalUIlliDc

Fig 8 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves in 7 d due todifferent temperatures and age distributions at a given population density of three lepidopteran pests of cabbagePopulation densities were lplant for T ni loSplant for A rapae 10plant for P xylostella

to 10 through 15 Model predictions were gener-ated at each of these age distributions for each ofthe 6 constant temperatures used above

Results and Discussion Response surfaces gen-erated with the model predict that A rapae con-tributes most to feeding damage on the head andwrapper leaves (Fig 7) Although total consump-tion by A rapae larvae is less than that of T ni(Harcourt et al 1955) the amount consumed onthese economically important strata is greater be-cause of the difference in intra plant spatial dynam-ics of the two species In Fig 7 the model predictsthat for a given constant temperature and giveninitial age and spatial distributions feeding on thehead and wrapper leaves increases linearly withpopulation density for each species Systems thatweight the counts of each species according to ex-pected feeding damage and base the action thresh-old on the weighted counts have been proposed

(Harcourt et al 1955 Shelton et al 1982) but thesedid not consider the spatial dynamics of the pestsThus one potential use of our model is to designa new rating scale to weight the population densityof each species according to expected feeding dam-age considering the spatial dynamics of eachspecies This rating scale however would also haveto account for temperature effects which cangreatly affect predicted feeding

At temperatures lt15DC very little feeding ispredicted on the head and wrapper leaves by eachspecies at any population density (Fig 7) Increas-ing temperatures have a nonlinear effect on pre-dicted feeding by each species For P xylostellaand A rapae the increase in predicted feedingrate may be primarily due to increased develop-ment and feeding rates For T ni however in-creased development and feeding rates at highertemperatures may be offset to some extent by higher

1590 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

probabilities of moving away from the head andwrapper leaves towards the lower leaves (Hoy etal 1989)

For a given population density predicted feed-ing on the marketable parts of the plant variedwidely with age distribution again interacting withtemperature (Fig 8) The results indicate that thedamage caused by a given population density afixed economic threshold for example will varyconsiderably with temperature age structure of thepopulation and species composition Againweighting systems have been described that con-sider larval age (Andaloro et al 1983a) but notwith the resolution that Fig 8 implies is necessaryand they do not include the interaction with tem-perature

Considering the profound effects of tempera-ture age distribution and species-specific spatialdynamics on the predicted area of feeding on eco-nomically important parts of the plant a staticeconomic threshold does not seem to be appropri-ate Rather feeding should be predicted for specificpopulation densities age distributions and spatialdistributions of the three species as well as weatherforecasts and management strategies should be de-signed accordingly The model described here couldbe used to make those predictions either by cal-culating a new species weighting system each dayof the growing season to be used with a fixed actionthreshold or simply by making the required pre-dictions on a case-by-case basis

Sensitivity Analysis

Two goals were addressed in the sensitivity anal-ysis First individual model parameters were evalmiddotuated as potential causes of inaccurate predictionsBy examining the change in model output after achange in the individual parameters parametersthat affect the output most can be identified Sec-ond by examining the effects of changes in dif-ferent parameters in combination insight can begained into the effects of the different processesbeing simulated and their interactions on the out-put variables of interest

Methods Model predictions were evaluated af-ter changing each parameter and input suppliedby the user by +10 and -10 of its valueChanges were made one parameter at a time witha standard set of initial conditions Standard initialpest population densities were a mean of 1 larvalplant of each species on each stratum in the secondinstar for A rapae and T ni and uniformly dis-tributed among the 20 age subclasses for P xylo-stella The analysis was performed at each of threetemperature regimes typical summer weather forwestern New York (maximum temperature 267degCminimum temperature 155degC 8 h sunshine eachday) hot and sunny weather (maximum temper-ature 322degC minimum temperature 211oC 12h sunshine each day) and cool and cloudy weather

(maximum temperature 183degC minimum tem-perature 10degC 2 h sunshine)

Constants were changed by adding or subtract-ing 10 of their value Input weather variableswere changed by adding or subtracting 10 of thevalue of each pays forecasted maximum and min-imum temperature and hours of sunshine Age atwhich larvae begin to move was shifted plus orminus two subclasses to effect a 10 change Initialage distribution for A rapae and T ni was alsoshifted 10 by shifting the subclasses initialized byplus or minus two Initial age distribution for Pxylostella is assumed to be uniform so this was notchanged For each species the initial intraplantdistribution was altered by shifting 10 of eachage group on each stratum except the lower frameleaves down one stratum or shifting 10 of eachage group on each stratum except the head upone stratum (eg a downward shift of an averageof one larva on each stratum would result in anaverage of 09 1 1 1 and 11 larvae on the headwrapper upper frame midframe and lower frameleaves respectively) Transition probabilities for Arapae and P xylostella were changed by a similarmethod shifting 10 of the probability of movingto each stratum except the lower frame leaves tothe next lower stratum or shifting 10 of the prob-ability of moving to each stratum except the headto the next stratum up (eg a downward shift ina transition probability vector of 09 01000 resultsin a vector of 081 018 001 0 0) Sensitivity tochanges in transition probabilities for T ni wereexamined by changing the Beta pdf shape param-eters that govern transition probabilities for thisspecies by + 10 and -10 of their value Theeffects of each of these changes were examined bycalculating the percentage of change in number oflarvae of each species and the percentage of changein accumulated area of feeding on the head andwrapper leaves

To examine interactions between different pro-cesses and their effects on model output we per-formed two analyses in which variables suspectedof interacting were varied in all combinations theequivalent of a factorial design with three levelsof each factor given by +5 -5 and 0 Be-cause development and feeding rates are temper-ature-dependent and govern the amount of feedingaccumulated interactions between temperaturefeeding rates and development rates might affectaccumulated area of feeding Three levels of tem-perature were generated starting with the typicalsummer weather regime described above and add-ing 5 -5 or 0 of the daily maximum andminimum At each temperature level develop-ment rate for each species was varied by +5-5 and 0 from its value and at each of thesedevelopment rates for each species feeding ratewas changed by +5 -5 and 0 of its valueThe effects of these parameter changes on the pre-dicted area of feeding on the head and wrapperleaves were calculated

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1591

Table 2 Output from a model to predict lepidopteranfeeding damage on cabbage at three temperature regimeswith a standard set of inputs and no change in the param-eters Changes in output during the sensitivity analysis (Fig9-12) are compared with these standards

StratumPopulation density (avg noplant) Feeding

P xylostella A rapae Tni cm2

High temperaturesHead 0252 2118 0095 12764Wrapper 0390 2594 0662 21716

Moderate temperaturesHead 0423 1957 0299 6805Wrapper 0578 2524 1001 9667

Low temperaturesHead 0635 1296 0829 1945Wrapper 0834 1651 0886 2348

A similar analysis of interacting processes wasperformed for spatial effects Initial distributionand transition probabilities could be expected tointeract in their effects on spatial distribution oflarvae and feeding damage For each species theinitial distribution was treated by (a) shifting 10of each age group on each stratum (except thelower frame leaves) down one stratum (b) shifting10of each age group on each stratum (except thehead) up one stratum and (c) leaving the initialdistribution unchanged At each of these shifts ininitial distribution for each species the transitionprobabilities for that species were changed as de-

scribed above Shifting 10 of the probability ofmoving to each stratum except the lower frameleaves to the next lower stratum resulted in higherprobabilities of downward movement shifting 10of the probability of moving to each stratum exceptthe head to the next stratum up resulted in higherprobability of upward movement

Results and Discussion Standard results for highmoderate and low temperature regimes withoutchanging any of the parameters or input variablesare given in Table 2 and the effects of changingeach parameter and input variable on selected out-put variables are displayed in Fig 9-12 for themoderate temperature regime We begin the anal-ysisby examining sensitivity of the model to changesin the parameters at moderate temperatures andfollow with the differences in model sensitivity seenunder high and low temperature regimes

At moderate temperatures numbers of larvae ofeach species on the head and wrapper leaves wereleast sensitive to initial spatial distribution of larvaedispersion in development time and hours of sun-shine (Fig 9) Change in the initial intraplant dis-tribution of larvae may be compensated for bymovement of larvae within a short time after thebeginning of the simulation Dispersion in devel-opment time for these species was low in the lab-oratory development studies resulting in a small

Svalue of -D for each species A 10 change in

EL~these small values does not change the dispersion

o Effect 01 +10 changebull Effect 01 -10 change on larvae on the head alief 7 days

Inldal dlsbibudonInitial ages

Age 01 first movementTransition probabilities

Dispersion In developmenlgl

DEL g2C

Hours 01 sunshineTemperalure

-20 -10 0 10

P xylostella20 30 -20 -10 0 10 20

A rapae

oT nl

100

on larvae on the wrapper leaves alter 7 days

10-10

Initial distributionInitial ages

Age 01 firsl movementTransition probabilities

Dispersion in developmentgl

DEL g2C

Hours of sunshineTemperature

-20 o 10 -20 -10 0 -10 0P xylostella A rapas T nI

Fig 9 Percentage of change in predicted number of P xylostella A rapae and T nt larvae on the head andwrapper leavesafter changing model parameters + and -10

1592 ENVIRONME~TAL ENTOMOLOGY Vol 19 no 5

Fig 10 Percentage of change in number of T nilarvae predicted on the head and wrapper leaves aftera + or - 1 0 change in parameters governing their tran-sition probabilities on the cabbage plant

greatly Hours of sunshine influence temperaturein each stratum but apparently not enough to causelarge changes in rate functions

Changes in temperature initial age distributionage at which larvae begin to move between strataand transition probabilities had the greatest effectson predicted number of larvae on the head or wrap-per leaves (Fig 9) These are all linked to spatialdynamics since both temperature and initial agedistribution affect the time at which larvae beginto move between strata Changes in parametersgoverning T ni transition probabilities were anexception causing only moderate or small changesin output (Fig 10) Changes in development rateparameters had large effects only for P xylostellaon the head and wrapper leaves and for T ni onthe head

Predictions of accumulated feeding on the headand wrapper leaves were generally less sensitive tochanges in parameters than were predictions ofnumbers of larvae on these strata (Fig 11 and 12)Because the predictions of accumulated area offeeding are most important to the farmer the ro-bustness of the model in predicting feeding sug-gests that it could be a useful management toolThe greatest changes in accumulated area of feed-ing were caused by changing parameters governingA rapae development or feeding particularly ini-tial age distribution Fortunately development ratesfor all three species considered here have been wellstudied and studies done at widely different timesand locations with different food sources suggestthat average development rate at a given temper-ature is fairly constant (Hardy 1938 Richards 1940Given 1944 Miner 1947 Harcourt et al 1955Shorey et al 1962 Jackson et al 1969 Toba et al

1973 Boldt et al 1975 Butler et al 1975 Smithamp Smilowitz 1976 Chen amp Su 1978 1982 Tatchell1981 Yamada amp Kawasaki 1983 Theunissen et al1985) Changes in forecast temperatures cause thenext largest change in accumulated feeding prob-ably because of their effects on development andfeeding rates Parameters governing spatial effectshad smaller effects on accumulated feeding par-ticularly when compared with their effects on pre-dicted number of larvae on different parts of theplant

Under the low-temperature regime predictionsof numbers of larvae on the head and wrapperleaves were more sensitive to parameters affectingdevelopment than to parameters affecting spatialdynamics At low temperatures larvae take longerto reach the age when movement starts and prob-ability of movement by T ni to the head andwrapper leaves is lower Furthermore fewer smalllarvae become large larvae at low temperatures sototal numbers of large larvae on all strata are re-duced At moderate and high temperatures pre-dictions of numbers of larvae on the head andwrapper leaves were more sensitive to changes inparameters affecting spatial dynamics

Effects of changing forecast temperatures onpredictions of accumulated feeding were muchgreater when the forecast temperatures were lowand less when the forecast temperatures were highthan at moderate temperatures Changing devel-opment rate parameters had a greater effect onaccumulated feeding at low temperatures butchanging feeding rate parameters had a greatereffect at high temperatures than at moderate tem-peratures Accumulated feeding was less sensitiveto changes in transition probabilities at low tem-peratures and more sensitive to changes in tran-sition probabilities at high temperatures than atmoderate temperatures

In general interactions between temperaturedevelopment and feeding rates as well as param-eters governing spatial effects were not evidentTypically the effect of changes in each of theseparameters was similar regardless of the value ofthe other parameters One interaction did occurWhen temperature was increased a negativechange in T ni development rate resulted in lesspredicted feeding on the head than when no changein T ni development rate was made In all othercases negative change in development rates re-sulted in higher predicted feeding on the head thanwhen development rates were not changed Re-gardless 5 changes in development rates for Tni resulted in lt3 differences in feeding on thehead so the effects of this interaction are not ofgreat importance Thus this analysis reinforced thesingle parameter analysis Feeding rates themselveswere changed in this analysis rather than the pa-rameters that govern them and accumulated feed-ing on the head and wrapper leaves was still moresensitive to changes in development rate and tem-perature

5o

middot5 0

Feeding on Heed

-5Feeding on Wrapper Leaves

o 10

Larvae on Head

middot10

b5b4b3b2bl858483a281

middot20l( Change in

-20 middot10 0 10 Change in Larvae on Wrapper leaves

II2l

~toa0gtatoten

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

SDElA rapae g2

g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

1582 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

(3)

Fig 2 Calculated development times for P xylo-stella A rapae and T ni larvae on cabbage (solidlines)compared with development times previously reportedin the literature at specific temperatures

30

A rapaebull Chenamp Su1982bull Smithamp Smilowitz1976o Tatchell1981o Theunissenet al198511 Given1944bull Richards1940bull Harcourt1955

P xylosteJao Hardy1938bull Chenamp Su1978o Miner194711 Yamadaamp Kawasaki1983

20

Tni+ Shoreyet al1962(males)bull Shoreyet al1962(females)o Jackson1969[] Tobaat al197311 Boldtat al1975bull Butleretal1975bull Chenamp Su1982

o

Temperature (Oe)

o

o10

20

40

80

60

10

20

30

40

10

20

30

Ulgtctl0-Q)

Ei=EQ)

EaoQ)gtQ)Cl

algorithm shifts a proportion of the contents of eachsubclass to the next subclass at certain time stepsThe number of time steps before each shift occursand the proportion of the contents of each subclassshifted are determined by the average develop-ment time or delay and the estimated dispersionin development times The controlled dispersionmodel was used because fewer subclasses were re-quired to represent the observed distribution ofdevelopment times adequately (with 20 subclasses

whereDELj(t) average development time (days) for

the larval period in species s on stra-tum j at time t

C (maximum development rate)(l +eBb + R2s Top

Top temperature at which maximum de-velopment rate occurs

Tj(t) temperature on stratum j at time tif tempj(t) 5 Top2 Top - tempj(t) if tempj(t) gt Top

gt g2gt empirically estimated constants forspecies s

This model was used because it fits developmentrate data for T ni well (Butler et a1 1976) and itcould easily be fit to data for the other species usingstandard nonlinear regression packages Becausethe relationship between temperature and devel-opment time of P xylostella and A rapae is qual-itatively similar to that of T ni the function abovewas expected to provide a good fit to the data forthese species as well The gls and g2gt from equation3 were estimated by nonlinear regression (SASInstitute 1982) with the Marquardt computationmethod from data collected by AMS and P BBaker (unpublished data) (Table 1) Minimum de-velopment times (days) for each species were es-timated from data in the literature to be 8 d forP xylostella 12 d for A rapae and 9 d for T niall at 33degC The inverse of these minimum devel-opment times was used to approximate each of theC (equation 3) in the estimations

Development times calculated using the algo-rithm with parameters calculated from AMS andP B Bakers data were very similar to those re-ported in the literature for A rapae and T niwhereas development times for P xylostella wereslightly longer than those previously reported (Fig2) The parameter estimates obtained from AMSand P B Bakers unpublished data were used be-cause the food source in their study excised cab-bage leaves was most similar to the food source ofthe population being modeled Because food sourcecan affect larval development rate (Shorey et a11962 Jones amp Ives 1979 Wolfson 1982) use ofthese data rather than data from the literatureshould provide more accurate results

Dispersion in development times was simulatedby a time-varying distributed delay (Manetsch 1976)with controlled dispersion (Goudriaan 1973) This

nificant (P lt 005 n = 43) In addition the effectof solar radiation on temperatures in the head wasnot significant (P = 02733 n = 43)

Development Rates Average larval develop-ment rates are calculated as a function of temper-ature for each species according to the algorithmproposed by Stinner et al (1974)

1 CDELt) (1 + egh+8r(I))

October 1990 Hoy ET ALINTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1583

where

Nkt + At) = Nkt(t) + U(t)Fmiddot[Nlk_Jlt) - Nkt)] (4)

feeding area (mm2) per day perlarva of species s in subclass k onstratum j at time tdays average temperature instratum j at time taverage proportion of larval de-velopment completed by sub-class k

(2~- 0)empirical constants for species s

avtempt)

where

1If each subclass is assumed to represent 20 of a

larvas development time average feeding rate foreach subclass in the distributed delay is calculated

(k 1) at the midpoint of the class agek = 20 - 40 ill

Equation (6) Thus accumulated feeding in cm2 issummed over all age classes of all species and all

instars) and large (third fourth and fifth instars)larvae on a given stratum We typically observeconsiderable overlap in P xylostella life stages inthe field Therefore the initial number of P xy-lostella on each stratum is evenly divided amongthe 20 delay subclasses that represent this speciesand only forecast total numbers of P xylostellalarvae are reported

Feeding Rates Accumulated feeding by eachspecies on each stratum is calculated as a functionof temperature and larval age The larvae of eachspecies tend to eat very little until the final instarswhen feeding rates increase dramatically (Chen ampSu 1978 1982) An exponential model is used toensure that the predicted feeding rate is positiveand to provide a qualitatively good fit Plots of In(feeding aread) against proportion of develop-ment time completed at three temperatures ap-peared linear with intercept close to zero and slopedependent on temperature Tatchell (1981) studiedconsumption by A rapae at lower temperaturesand found that total consumption (leaf area in cm2)

increased between 13 and 19degC then decreasedbetween 19 and 24degCj Boldt et a1(1975) found thatT ni consumption increased from 20 to 25degC andthen decreased between 25 and 30degC These studiesand the plots described above indicate that theeffects of temperature on feeding rates are not lin-ear rather they are greater at intermediate tem-peratures and less at low and high temperaturesWe describe this effect of temperature on feedingrate by defining the slope in a regression of In(feeding aread) predicted by larval age as a qua-dratic function of temperature Feeding rate perlarva per day as a function of temperature and ageof the larva can then be expressed as an exponentialfunction

(5)

F

U(t)

M(t)

5(t) 1 - 20DEV(t) the proportion of each

Sj

subclass shiftedthe standard deviation of developmenttimes for species s1 for M(t) = 123 o otherwise At

~ F DELi(r) 20

At 002 dr = At 2At 3M

52-- - was found to be fairly constant for eachDEVspeci~s over three temperatures (AMS and P BBaker unpublished data) so F was assumed to bea constant (Table 1) When programmed U(t) actsas an indicator for the shift of contents from eachsubclass to the next subclass and F gives the pro-portion of each subclass shifted

The subclasses are used to approximate larvalage groups which are required to calculate age-specific feeding rates and to assign an age to thelarvae that move between strata Larvae on dif-ferent strata develop at different rates because ofdifferent temperaturesj therefore larvae that movebetween strata must be placed in the appropriateage group at the new location (technically thesubclasses refer to relative maturity rather thanchronological age)

The average number of a given instar per plantis divided evenly among delay subclasses desig-nated to represent that instar as follows k = 1-34-6 7-10 11-15 16-20 for A rapae instars onethrough five and k = 1-3 4-6 7-9 10-14 15-20for T ni instars one through five The number ofsubclasses used to represent each instar for a givenspecies was based on estimates of the proportionof total larval development time spent in each in-star (AMS and P B Baker unpublished data)For example if approximately one-fourth of thelarval period is spent in the last instar the last instarwould be represented by one-fourth of the sub-classes the last five Summing over the appropriatesubclasses gives the number of individuals in a giv-en instar at a given time In practice instar des-ignations are used only for initialization and re-porting forecast numbers of small (first and second

for each species the output was similar to a delaywithout controlled dispersion using approximatelytwice the number of subclasses and twice theamount of computing time)

Programming the distributed delay with con-trolled dispersion yields the following differenceequation for the average number of pests perplant N

1584 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

(7)

31

31

T ni

A rapae

P xyfostefla

00010 a8

a6Physiological

Age

constants estimated by maximumlikelihood as described by Hoy etal (1989)

gt 449535~~ 2lli90ig~ 149845IIOJc6 aooaf 10 08

Fig 3 Predicted feeding rates of P xylo8tella Arapae and T ni on cabbage

Because the shape parameters for the Beta distri-bution a and h change with temperature theshape of the distribution and value of the integralsdescribed in Equation (8) change accordinglyHigher temperatures tend to result in greater prob-ability of movement and higher probability ofmovement towards the lower leaves than towardsthe head lower temperatures tend to result in lowerprobability of movement and higher probabilityof movement towards the head than towards thelower leaves

The elements of the transition probability ma-trices for P xylostella and A rapae are estimatedfrom observations reported in the literature (Har-court 1963 1966 Chua amp Lim 1979 Samson amp

~ 15llli6S~~ 1(57 n

1sectGl 5281IlttlaOJc6af 06

PhysiologicalAge

~~ JI64

~ce 576

sectGl

l2 1288OJc6GlGl

U

previous time steps by

Ej(t) = plusmn plusmn ~ [NkT)FPDkj(T)] ~tTO -I k-I 100

where

Ej(t) area of feeding (cm2) on stratum j accu-mulated at time t

T ~t 2~t 3~t M 002 d

Pj(t)

= f ~ 1__ U1a(I)-11(1 - U)lb(l)-ll duJ~l B[a(t) b(t)] (8)

where

the probability of a T ni (species3) late instar moving from stratumi to stratum j during one dayeel +C2 avtemPi(t)

ed +d2atemp)

The three empirical constants (hh hz and h31inEquation 6) for estimating feeding rates as a func-tion of temperature and larval age were estimatedby multiple linear regression (SAS Institute 1982)of the natural log of feedingday (mm2) on ageage temperature and agemiddottemperature2 (Table 1)The measure of larval age was the proportion oflarval stage completed or days the larva had livedso far divided by total days spent by that larvafrom eclosion to pupation Measurements of areaof cabbage leaf consumed each day of the larvalperiod for each of 20 larvaereplicate and threereplicatestemperature at 167 211 and 267degCfor each species were taken by AMS and P BBaker (unpublished data) Inspection of predictions(Fig 3) compared with data reported in the lit-erature (Harcourt et al 1955 McEwen amp Hervey1960 Rahman 1970 Harper 1973 Boldt et al 1975Chen amp Su 1978 1982 Samson amp Geier 1983Theunissen et al 1985) indicates that the feedingrate model fit well Data on feeding by A rapaereported by Tatchell (1981) indicate much higherrates than those we estimated but Tatchells datadisagree with the other literature cited above aswell As in the case of development rates we usedthe AMS and P B Baker data because the foodsource was cabbage leaf so these data should bemost appropriate

Movement Rates Larval movement is simulatedwith discrete time transition probability matricesbecause observed larval movements were discretein time Movement of late instar T ni is correlatedwith microclimate (Hoy et al 1989) and must bemodeled accordingly The transition probabilitiesfor late instar T ni are modeled as definite integralsof the Beta probability density function (pdf) withshape parameters a(t) and b(t) which depend ontemperature and the stratum larvae are movingfrom

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS

File Edit

1585

021

339

1131

3241

2568

Fig 4 Computer screen displaying output from a simulation model of feeding damage by Lepidoptera oncabbage

Geier 1983 Salinas 1984) and our own observa-tions Our observations for these species were thefrequency of movements by larvae marked withfluorescent powder and visually censused at ~1-hintervals in research cabbage plots near GenevaNY The number of these observations was notsufficient to estimate individual transition proba-bilities so the data were used roughly to estimatefrequency of movement and probability of movingup or down on the plant For P xylostella thefrequency of movement was low and approxi-mately equal numbers of upwards and downwardsmovements were observed For A rapae virtuallyall late instars were observed to move upwards tothe head or wrapper leaves as noted by Harcourt(1963 1966) and Hoy amp Shelton (1987) Transitionprobabilities that reflect these observations werechosen for these two species and are given in Ta-ble 1

The change in state variables due to movementis thus calculated by

s

Nkj(t + ~t) = ~ Nkj(t)pj(t)I(t + ~t) (9)

where

k =k =

I(t + ~t)

~t

13 14 20 for s = 110 11 20 for s = 2 or 3

1 if (t + ~t) = 1 2 3 o otherwise002d

Movement is simulated only once each day andbecause the time step for the model is lfso of a daythe indicator I(t) is used to determine when themovements occur The values of k given above arechosen so that movement is simulated only for olderlarvae which are represented by higher values ofk (k ~ 13 for P xylostella and k ~ 10 for A rapaeor T ni)Model Output The output generated using the

equations described above is a summary of thevalues of state variables and the value of the aux-iliary variable each day for the next 7 d This ispresented on the computer screen depicted in Fig4 The number of large and small larvae of eachspecies on each stratum also can be obtained for aprintout by summing over the appropriate sub-classes in the distributed delay The picture of acabbage plant on the screen gives the user an ap-proximate idea of what the predicted damage onthe cabbage crop would look like

Validation

Methods Validation analysis was performed todemonstrate how well the model predicts data thatwere not used in model design or parameterizationData collected by a commercial field monitoringand pest control advising service were used to com-pare model predictions with observed populationdensities and feeding damage 7 d after the original

1586 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

A rapae

P xylostella

18161412108642o 00 06 12 18 24

557371

1114

92

743

1300

A rapae

10

P xylostella

20

oO0 16 32 48 64

30

10

20

1 ffi

0O0 1 2 2 4 3 6 4 8

000-05 00 05 10 15

1300

11 14

929 T ni T ni

743

55710

3 71

186

0 00- O32 -O16 O00 016 032 O0 O8 16 2 4 3 2

Standardized Residuals Standardized Residualsfor the Head for the Wrapper Leaves

-ogtucQ)=J0Q)-LL

Fig 5 Histograms of standardized cell residuals for comparing predicted numbers with observed averagenumbers of larvae on the cabbage head and wrapper leaves in commercial cabbage fields near Geneva NY

sample Scouts sampled cabbage fields on a weeklybasis using a variable-intensity sampling scheme(Hoy et al 1983) Separate counts of P xylostellalarvae (all instars combined) and A rapae and Tni eggs small (first and second instars) and large(third fourth and fifth instars) larvae were taken

on the head (stratum 1) wrapper (stratum 2) andframe leaves (strata 3-5 combined) and were usedto initialize the model Predictions of numbers ofP xylostella large A rapae and T ni and ac-cumulated feeding on the head and wrapper leaveswere compared with the scouts observations taken

October 1990 HoY ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1587

o [] a [] C D

QOO n~ Q~ n~ 100 1~ t~ 1~ 200Average Damage Rating

Average Damage Rating

Fig 6 Comparison of predicted feeding damagewith average observed damage rating on the heads andwrapper leaves of commercial cabbage crops near Ge-neva NY

the following week Initial spatial distribution with-in the frame and initial age distribution with Arapae and T ni small and large larval populationswere assumed to be uniform for lack of more pre-cise information The scouts observations includedratings of feeding damage on a scale of 0 to 4indicating approximately no damage less than onefeeding hole per leaf one to three feeding holesper leaf 10 defoliation and 40 defoliationrespectively These ratings were compared withpredictions of accumulated area of feeding withscatter plots and correlation analysis

Weather data for model inputs (maximum andminimum temperatures and daily total solar ra-diation) were recorded at the New York State Ag-ricultural Experiment Station in Geneva NY thec1vsest weather station to the commercial fieldsbeing monitored (within 20 km) Data from 34pairs of field samples-each pair taken one weekapart during July August and September in 1983and 1984 under widely varying weather condi-tions-were used for this analysis

Model predictions for number of larvae on thehead and wrapper leaves were compared with ob-servations using standardized cell residuals givenby

observed no larvae - predicted no larvaeVpredicted no larvae

Evaluation of Existing Treatment Guidelines

Because the model predicts numbers of larvaeand feeding damage on different parts of the plantwell model predictions cap be used to evaluatetreatment guidelines currently in use for cabbagepest management In particular the model can beused to explore the relative effects of each pest onthe crop and how useful a static threshold for pestpopulation density will be in predicting a given

as described by Bishop et al (1975) These ap-proximate a standard normal distribution so thecriterion for evaluation is whether or not most ofthe residuals are within 2 SD of the mean (- 2and ~2) because lt=95of the standard normaldistribution falls within this range Observations ofthe feeding damage rating also were plotted againstpredicted accumulated area of feeding and asso-ciated correlation coefficients were calculated

Results and Discussion Most standardized cellresiduals for predicted versus observed counts oflarvae on the head and wrapper leaves were wellwithin the range -2 to +2 (Fig 5) The few largedeviations that were calculated were positive in-dicating that occasionally greater average num-bers of larvae than predicted were observed Theinterplant spatial distribution of each species is ag-gregated (Harcourt 1966) and sample sizes wereoften small (as few as 11 plants) so these occasionallarge positive deviations are not surprising Theseresults indicate that the model predicts number andlocation of larvae well particularly when the lowresolution in the data for initial age and spatialdistribution within the frame and potential sam-pling error in both samples are considered Con-clusions from this analysis must be tempered some-what however by the low population densitiesobserved in these fields Bishop et al (1975) warnthat the approximation of the standardized cellresiduals to the standard normal is poorest whenpredictions in the cells are small Most of the initialpopulation densities and associated predictions weresmall because pest population densities are keptlow by farmers Evaluation of the model underthese conditions is most appropriate however be-cause these are the conditions under which themodel would be used

Predicted area of feeding was correlated withobserved damage rating (Fig 6) Damage ratingincluded assessment of recent feeding as well asolder damage done before the first sample Thiscould explain circumstances in which little feedingdamage was predicted but high damage ratingswere observed Cases where large amounts of feed-ing damage were predicted but observed damagerating was low did not occur Feeding damage isthe most important variable to managers becauseit determines the market value of the crop Thedata indicate that the model can be used to predictthe effects on the cabbage crop of a given pestpopulation under specific conditions

3

(10)

D

o

D

D

o

CC

lJ 8DaD co lJ 0

D D0

2

D

1

D D

C C

D

Wrapper Leaves

r-069

Head

r-053

oo 0

q CD

ggt 206Q)

~0Q)

~ 10fa

E8

40

oo

E8 30Dlc6Q)t 20tJQ)

Ug 1a

1588 ENVIRONMEITAL ENTOMOLOGY Vol 19 no 5

Head Wrapper Leaves

T ni 565134

377089

189045

2020

- Temporatura Avorago plon1CJ DCEC)---0)c A rapaea 1t82Q) a18Q)U 546 7890Q) 273 396sect0 30 30eD

Temperature Avorago pIontDC Temperalure Avomg bullbull p1ont

DC

P xylostella074 178050 11902i 061

20

rompera1ur Avorago plantDC Tempera1ure Averag bullbull p1on1

DC

Fig 7 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves after 7 d atdifferent temperatures and population densities of lepidopteran pests

amount of damage on the marketable parts of thecrop

Methods Response surfaces of predicted area offeeding on the head and wrapper leaves to tem-perature and population density of each pest weregenerated with the model A standard initial in-traplant spatial distribution typical of distributionsobserved in cabbage fields was chosen for eachspecies as follows P xylostella 005 01 03 03and 025 A rapae 0 015 04 03 and 015 Tni 0 01 02 04 and 03 of the average numberper plant on the head wrapper leaves upper framemidframe and lower frame respectively For Pxylostella the larval ages were uniformly distrib-uted among the 20 subclasses in the distributeddelay For A rapae and T ni the larvae wereinitialized into the first 10 subclasses simulatingfirst second and third instars For each of 10 pop-ulation densities ranging from well below to well

above the action threshold currently used in NewYork (Shelton et al 1982) feeding was predictedat six constant temperatures

Additional response surfaces were generated offeeding area on the head and wrapper leaves pre-dicted at different temperatures and initial age dis-tributions for a given population density of eachspecies Given the initial spatial distribution de-scribed above and an average temperature be-tween 20 and 25degC the first set of response surfaceswas used to select a population density predictedto cause damage most farmers would consider un-acceptable This density twice the currently rec-ommended action threshold was 1 larvaplant forT ni 15 larvaeplant for A rapae and 10 larvaeplant for P xylostella Different age distributionswere generated by dividing the population densi-ties chosen above evenly among larval maturitysubclasses 1 through 6 then 2 through 7 etc up

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1589

Head Wrapper Leaves

1n

519

260

T1i

TemperatureDC

10

Youngest Age ProSQnt

10

10

YOungG81 AGe PrQsan

A rapal2333

557

78

10

Youngest Ago PreSGnt

TemperatureDC

142 P xylostllia

098

053

0009

Youngesl Ago PresentTemperature

DCTemperalUIlliDc

Fig 8 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves in 7 d due todifferent temperatures and age distributions at a given population density of three lepidopteran pests of cabbagePopulation densities were lplant for T ni loSplant for A rapae 10plant for P xylostella

to 10 through 15 Model predictions were gener-ated at each of these age distributions for each ofthe 6 constant temperatures used above

Results and Discussion Response surfaces gen-erated with the model predict that A rapae con-tributes most to feeding damage on the head andwrapper leaves (Fig 7) Although total consump-tion by A rapae larvae is less than that of T ni(Harcourt et al 1955) the amount consumed onthese economically important strata is greater be-cause of the difference in intra plant spatial dynam-ics of the two species In Fig 7 the model predictsthat for a given constant temperature and giveninitial age and spatial distributions feeding on thehead and wrapper leaves increases linearly withpopulation density for each species Systems thatweight the counts of each species according to ex-pected feeding damage and base the action thresh-old on the weighted counts have been proposed

(Harcourt et al 1955 Shelton et al 1982) but thesedid not consider the spatial dynamics of the pestsThus one potential use of our model is to designa new rating scale to weight the population densityof each species according to expected feeding dam-age considering the spatial dynamics of eachspecies This rating scale however would also haveto account for temperature effects which cangreatly affect predicted feeding

At temperatures lt15DC very little feeding ispredicted on the head and wrapper leaves by eachspecies at any population density (Fig 7) Increas-ing temperatures have a nonlinear effect on pre-dicted feeding by each species For P xylostellaand A rapae the increase in predicted feedingrate may be primarily due to increased develop-ment and feeding rates For T ni however in-creased development and feeding rates at highertemperatures may be offset to some extent by higher

1590 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

probabilities of moving away from the head andwrapper leaves towards the lower leaves (Hoy etal 1989)

For a given population density predicted feed-ing on the marketable parts of the plant variedwidely with age distribution again interacting withtemperature (Fig 8) The results indicate that thedamage caused by a given population density afixed economic threshold for example will varyconsiderably with temperature age structure of thepopulation and species composition Againweighting systems have been described that con-sider larval age (Andaloro et al 1983a) but notwith the resolution that Fig 8 implies is necessaryand they do not include the interaction with tem-perature

Considering the profound effects of tempera-ture age distribution and species-specific spatialdynamics on the predicted area of feeding on eco-nomically important parts of the plant a staticeconomic threshold does not seem to be appropri-ate Rather feeding should be predicted for specificpopulation densities age distributions and spatialdistributions of the three species as well as weatherforecasts and management strategies should be de-signed accordingly The model described here couldbe used to make those predictions either by cal-culating a new species weighting system each dayof the growing season to be used with a fixed actionthreshold or simply by making the required pre-dictions on a case-by-case basis

Sensitivity Analysis

Two goals were addressed in the sensitivity anal-ysis First individual model parameters were evalmiddotuated as potential causes of inaccurate predictionsBy examining the change in model output after achange in the individual parameters parametersthat affect the output most can be identified Sec-ond by examining the effects of changes in dif-ferent parameters in combination insight can begained into the effects of the different processesbeing simulated and their interactions on the out-put variables of interest

Methods Model predictions were evaluated af-ter changing each parameter and input suppliedby the user by +10 and -10 of its valueChanges were made one parameter at a time witha standard set of initial conditions Standard initialpest population densities were a mean of 1 larvalplant of each species on each stratum in the secondinstar for A rapae and T ni and uniformly dis-tributed among the 20 age subclasses for P xylo-stella The analysis was performed at each of threetemperature regimes typical summer weather forwestern New York (maximum temperature 267degCminimum temperature 155degC 8 h sunshine eachday) hot and sunny weather (maximum temper-ature 322degC minimum temperature 211oC 12h sunshine each day) and cool and cloudy weather

(maximum temperature 183degC minimum tem-perature 10degC 2 h sunshine)

Constants were changed by adding or subtract-ing 10 of their value Input weather variableswere changed by adding or subtracting 10 of thevalue of each pays forecasted maximum and min-imum temperature and hours of sunshine Age atwhich larvae begin to move was shifted plus orminus two subclasses to effect a 10 change Initialage distribution for A rapae and T ni was alsoshifted 10 by shifting the subclasses initialized byplus or minus two Initial age distribution for Pxylostella is assumed to be uniform so this was notchanged For each species the initial intraplantdistribution was altered by shifting 10 of eachage group on each stratum except the lower frameleaves down one stratum or shifting 10 of eachage group on each stratum except the head upone stratum (eg a downward shift of an averageof one larva on each stratum would result in anaverage of 09 1 1 1 and 11 larvae on the headwrapper upper frame midframe and lower frameleaves respectively) Transition probabilities for Arapae and P xylostella were changed by a similarmethod shifting 10 of the probability of movingto each stratum except the lower frame leaves tothe next lower stratum or shifting 10 of the prob-ability of moving to each stratum except the headto the next stratum up (eg a downward shift ina transition probability vector of 09 01000 resultsin a vector of 081 018 001 0 0) Sensitivity tochanges in transition probabilities for T ni wereexamined by changing the Beta pdf shape param-eters that govern transition probabilities for thisspecies by + 10 and -10 of their value Theeffects of each of these changes were examined bycalculating the percentage of change in number oflarvae of each species and the percentage of changein accumulated area of feeding on the head andwrapper leaves

To examine interactions between different pro-cesses and their effects on model output we per-formed two analyses in which variables suspectedof interacting were varied in all combinations theequivalent of a factorial design with three levelsof each factor given by +5 -5 and 0 Be-cause development and feeding rates are temper-ature-dependent and govern the amount of feedingaccumulated interactions between temperaturefeeding rates and development rates might affectaccumulated area of feeding Three levels of tem-perature were generated starting with the typicalsummer weather regime described above and add-ing 5 -5 or 0 of the daily maximum andminimum At each temperature level develop-ment rate for each species was varied by +5-5 and 0 from its value and at each of thesedevelopment rates for each species feeding ratewas changed by +5 -5 and 0 of its valueThe effects of these parameter changes on the pre-dicted area of feeding on the head and wrapperleaves were calculated

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1591

Table 2 Output from a model to predict lepidopteranfeeding damage on cabbage at three temperature regimeswith a standard set of inputs and no change in the param-eters Changes in output during the sensitivity analysis (Fig9-12) are compared with these standards

StratumPopulation density (avg noplant) Feeding

P xylostella A rapae Tni cm2

High temperaturesHead 0252 2118 0095 12764Wrapper 0390 2594 0662 21716

Moderate temperaturesHead 0423 1957 0299 6805Wrapper 0578 2524 1001 9667

Low temperaturesHead 0635 1296 0829 1945Wrapper 0834 1651 0886 2348

A similar analysis of interacting processes wasperformed for spatial effects Initial distributionand transition probabilities could be expected tointeract in their effects on spatial distribution oflarvae and feeding damage For each species theinitial distribution was treated by (a) shifting 10of each age group on each stratum (except thelower frame leaves) down one stratum (b) shifting10of each age group on each stratum (except thehead) up one stratum and (c) leaving the initialdistribution unchanged At each of these shifts ininitial distribution for each species the transitionprobabilities for that species were changed as de-

scribed above Shifting 10 of the probability ofmoving to each stratum except the lower frameleaves to the next lower stratum resulted in higherprobabilities of downward movement shifting 10of the probability of moving to each stratum exceptthe head to the next stratum up resulted in higherprobability of upward movement

Results and Discussion Standard results for highmoderate and low temperature regimes withoutchanging any of the parameters or input variablesare given in Table 2 and the effects of changingeach parameter and input variable on selected out-put variables are displayed in Fig 9-12 for themoderate temperature regime We begin the anal-ysisby examining sensitivity of the model to changesin the parameters at moderate temperatures andfollow with the differences in model sensitivity seenunder high and low temperature regimes

At moderate temperatures numbers of larvae ofeach species on the head and wrapper leaves wereleast sensitive to initial spatial distribution of larvaedispersion in development time and hours of sun-shine (Fig 9) Change in the initial intraplant dis-tribution of larvae may be compensated for bymovement of larvae within a short time after thebeginning of the simulation Dispersion in devel-opment time for these species was low in the lab-oratory development studies resulting in a small

Svalue of -D for each species A 10 change in

EL~these small values does not change the dispersion

o Effect 01 +10 changebull Effect 01 -10 change on larvae on the head alief 7 days

Inldal dlsbibudonInitial ages

Age 01 first movementTransition probabilities

Dispersion In developmenlgl

DEL g2C

Hours 01 sunshineTemperalure

-20 -10 0 10

P xylostella20 30 -20 -10 0 10 20

A rapae

oT nl

100

on larvae on the wrapper leaves alter 7 days

10-10

Initial distributionInitial ages

Age 01 firsl movementTransition probabilities

Dispersion in developmentgl

DEL g2C

Hours of sunshineTemperature

-20 o 10 -20 -10 0 -10 0P xylostella A rapas T nI

Fig 9 Percentage of change in predicted number of P xylostella A rapae and T nt larvae on the head andwrapper leavesafter changing model parameters + and -10

1592 ENVIRONME~TAL ENTOMOLOGY Vol 19 no 5

Fig 10 Percentage of change in number of T nilarvae predicted on the head and wrapper leaves aftera + or - 1 0 change in parameters governing their tran-sition probabilities on the cabbage plant

greatly Hours of sunshine influence temperaturein each stratum but apparently not enough to causelarge changes in rate functions

Changes in temperature initial age distributionage at which larvae begin to move between strataand transition probabilities had the greatest effectson predicted number of larvae on the head or wrap-per leaves (Fig 9) These are all linked to spatialdynamics since both temperature and initial agedistribution affect the time at which larvae beginto move between strata Changes in parametersgoverning T ni transition probabilities were anexception causing only moderate or small changesin output (Fig 10) Changes in development rateparameters had large effects only for P xylostellaon the head and wrapper leaves and for T ni onthe head

Predictions of accumulated feeding on the headand wrapper leaves were generally less sensitive tochanges in parameters than were predictions ofnumbers of larvae on these strata (Fig 11 and 12)Because the predictions of accumulated area offeeding are most important to the farmer the ro-bustness of the model in predicting feeding sug-gests that it could be a useful management toolThe greatest changes in accumulated area of feed-ing were caused by changing parameters governingA rapae development or feeding particularly ini-tial age distribution Fortunately development ratesfor all three species considered here have been wellstudied and studies done at widely different timesand locations with different food sources suggestthat average development rate at a given temper-ature is fairly constant (Hardy 1938 Richards 1940Given 1944 Miner 1947 Harcourt et al 1955Shorey et al 1962 Jackson et al 1969 Toba et al

1973 Boldt et al 1975 Butler et al 1975 Smithamp Smilowitz 1976 Chen amp Su 1978 1982 Tatchell1981 Yamada amp Kawasaki 1983 Theunissen et al1985) Changes in forecast temperatures cause thenext largest change in accumulated feeding prob-ably because of their effects on development andfeeding rates Parameters governing spatial effectshad smaller effects on accumulated feeding par-ticularly when compared with their effects on pre-dicted number of larvae on different parts of theplant

Under the low-temperature regime predictionsof numbers of larvae on the head and wrapperleaves were more sensitive to parameters affectingdevelopment than to parameters affecting spatialdynamics At low temperatures larvae take longerto reach the age when movement starts and prob-ability of movement by T ni to the head andwrapper leaves is lower Furthermore fewer smalllarvae become large larvae at low temperatures sototal numbers of large larvae on all strata are re-duced At moderate and high temperatures pre-dictions of numbers of larvae on the head andwrapper leaves were more sensitive to changes inparameters affecting spatial dynamics

Effects of changing forecast temperatures onpredictions of accumulated feeding were muchgreater when the forecast temperatures were lowand less when the forecast temperatures were highthan at moderate temperatures Changing devel-opment rate parameters had a greater effect onaccumulated feeding at low temperatures butchanging feeding rate parameters had a greatereffect at high temperatures than at moderate tem-peratures Accumulated feeding was less sensitiveto changes in transition probabilities at low tem-peratures and more sensitive to changes in tran-sition probabilities at high temperatures than atmoderate temperatures

In general interactions between temperaturedevelopment and feeding rates as well as param-eters governing spatial effects were not evidentTypically the effect of changes in each of theseparameters was similar regardless of the value ofthe other parameters One interaction did occurWhen temperature was increased a negativechange in T ni development rate resulted in lesspredicted feeding on the head than when no changein T ni development rate was made In all othercases negative change in development rates re-sulted in higher predicted feeding on the head thanwhen development rates were not changed Re-gardless 5 changes in development rates for Tni resulted in lt3 differences in feeding on thehead so the effects of this interaction are not ofgreat importance Thus this analysis reinforced thesingle parameter analysis Feeding rates themselveswere changed in this analysis rather than the pa-rameters that govern them and accumulated feed-ing on the head and wrapper leaves was still moresensitive to changes in development rate and tem-perature

5o

middot5 0

Feeding on Heed

-5Feeding on Wrapper Leaves

o 10

Larvae on Head

middot10

b5b4b3b2bl858483a281

middot20l( Change in

-20 middot10 0 10 Change in Larvae on Wrapper leaves

II2l

~toa0gtatoten

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

SDElA rapae g2

g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

October 1990 Hoy ET ALINTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1583

where

Nkt + At) = Nkt(t) + U(t)Fmiddot[Nlk_Jlt) - Nkt)] (4)

feeding area (mm2) per day perlarva of species s in subclass k onstratum j at time tdays average temperature instratum j at time taverage proportion of larval de-velopment completed by sub-class k

(2~- 0)empirical constants for species s

avtempt)

where

1If each subclass is assumed to represent 20 of a

larvas development time average feeding rate foreach subclass in the distributed delay is calculated

(k 1) at the midpoint of the class agek = 20 - 40 ill

Equation (6) Thus accumulated feeding in cm2 issummed over all age classes of all species and all

instars) and large (third fourth and fifth instars)larvae on a given stratum We typically observeconsiderable overlap in P xylostella life stages inthe field Therefore the initial number of P xy-lostella on each stratum is evenly divided amongthe 20 delay subclasses that represent this speciesand only forecast total numbers of P xylostellalarvae are reported

Feeding Rates Accumulated feeding by eachspecies on each stratum is calculated as a functionof temperature and larval age The larvae of eachspecies tend to eat very little until the final instarswhen feeding rates increase dramatically (Chen ampSu 1978 1982) An exponential model is used toensure that the predicted feeding rate is positiveand to provide a qualitatively good fit Plots of In(feeding aread) against proportion of develop-ment time completed at three temperatures ap-peared linear with intercept close to zero and slopedependent on temperature Tatchell (1981) studiedconsumption by A rapae at lower temperaturesand found that total consumption (leaf area in cm2)

increased between 13 and 19degC then decreasedbetween 19 and 24degCj Boldt et a1(1975) found thatT ni consumption increased from 20 to 25degC andthen decreased between 25 and 30degC These studiesand the plots described above indicate that theeffects of temperature on feeding rates are not lin-ear rather they are greater at intermediate tem-peratures and less at low and high temperaturesWe describe this effect of temperature on feedingrate by defining the slope in a regression of In(feeding aread) predicted by larval age as a qua-dratic function of temperature Feeding rate perlarva per day as a function of temperature and ageof the larva can then be expressed as an exponentialfunction

(5)

F

U(t)

M(t)

5(t) 1 - 20DEV(t) the proportion of each

Sj

subclass shiftedthe standard deviation of developmenttimes for species s1 for M(t) = 123 o otherwise At

~ F DELi(r) 20

At 002 dr = At 2At 3M

52-- - was found to be fairly constant for eachDEVspeci~s over three temperatures (AMS and P BBaker unpublished data) so F was assumed to bea constant (Table 1) When programmed U(t) actsas an indicator for the shift of contents from eachsubclass to the next subclass and F gives the pro-portion of each subclass shifted

The subclasses are used to approximate larvalage groups which are required to calculate age-specific feeding rates and to assign an age to thelarvae that move between strata Larvae on dif-ferent strata develop at different rates because ofdifferent temperaturesj therefore larvae that movebetween strata must be placed in the appropriateage group at the new location (technically thesubclasses refer to relative maturity rather thanchronological age)

The average number of a given instar per plantis divided evenly among delay subclasses desig-nated to represent that instar as follows k = 1-34-6 7-10 11-15 16-20 for A rapae instars onethrough five and k = 1-3 4-6 7-9 10-14 15-20for T ni instars one through five The number ofsubclasses used to represent each instar for a givenspecies was based on estimates of the proportionof total larval development time spent in each in-star (AMS and P B Baker unpublished data)For example if approximately one-fourth of thelarval period is spent in the last instar the last instarwould be represented by one-fourth of the sub-classes the last five Summing over the appropriatesubclasses gives the number of individuals in a giv-en instar at a given time In practice instar des-ignations are used only for initialization and re-porting forecast numbers of small (first and second

for each species the output was similar to a delaywithout controlled dispersion using approximatelytwice the number of subclasses and twice theamount of computing time)

Programming the distributed delay with con-trolled dispersion yields the following differenceequation for the average number of pests perplant N

1584 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

(7)

31

31

T ni

A rapae

P xyfostefla

00010 a8

a6Physiological

Age

constants estimated by maximumlikelihood as described by Hoy etal (1989)

gt 449535~~ 2lli90ig~ 149845IIOJc6 aooaf 10 08

Fig 3 Predicted feeding rates of P xylo8tella Arapae and T ni on cabbage

Because the shape parameters for the Beta distri-bution a and h change with temperature theshape of the distribution and value of the integralsdescribed in Equation (8) change accordinglyHigher temperatures tend to result in greater prob-ability of movement and higher probability ofmovement towards the lower leaves than towardsthe head lower temperatures tend to result in lowerprobability of movement and higher probabilityof movement towards the head than towards thelower leaves

The elements of the transition probability ma-trices for P xylostella and A rapae are estimatedfrom observations reported in the literature (Har-court 1963 1966 Chua amp Lim 1979 Samson amp

~ 15llli6S~~ 1(57 n

1sectGl 5281IlttlaOJc6af 06

PhysiologicalAge

~~ JI64

~ce 576

sectGl

l2 1288OJc6GlGl

U

previous time steps by

Ej(t) = plusmn plusmn ~ [NkT)FPDkj(T)] ~tTO -I k-I 100

where

Ej(t) area of feeding (cm2) on stratum j accu-mulated at time t

T ~t 2~t 3~t M 002 d

Pj(t)

= f ~ 1__ U1a(I)-11(1 - U)lb(l)-ll duJ~l B[a(t) b(t)] (8)

where

the probability of a T ni (species3) late instar moving from stratumi to stratum j during one dayeel +C2 avtemPi(t)

ed +d2atemp)

The three empirical constants (hh hz and h31inEquation 6) for estimating feeding rates as a func-tion of temperature and larval age were estimatedby multiple linear regression (SAS Institute 1982)of the natural log of feedingday (mm2) on ageage temperature and agemiddottemperature2 (Table 1)The measure of larval age was the proportion oflarval stage completed or days the larva had livedso far divided by total days spent by that larvafrom eclosion to pupation Measurements of areaof cabbage leaf consumed each day of the larvalperiod for each of 20 larvaereplicate and threereplicatestemperature at 167 211 and 267degCfor each species were taken by AMS and P BBaker (unpublished data) Inspection of predictions(Fig 3) compared with data reported in the lit-erature (Harcourt et al 1955 McEwen amp Hervey1960 Rahman 1970 Harper 1973 Boldt et al 1975Chen amp Su 1978 1982 Samson amp Geier 1983Theunissen et al 1985) indicates that the feedingrate model fit well Data on feeding by A rapaereported by Tatchell (1981) indicate much higherrates than those we estimated but Tatchells datadisagree with the other literature cited above aswell As in the case of development rates we usedthe AMS and P B Baker data because the foodsource was cabbage leaf so these data should bemost appropriate

Movement Rates Larval movement is simulatedwith discrete time transition probability matricesbecause observed larval movements were discretein time Movement of late instar T ni is correlatedwith microclimate (Hoy et al 1989) and must bemodeled accordingly The transition probabilitiesfor late instar T ni are modeled as definite integralsof the Beta probability density function (pdf) withshape parameters a(t) and b(t) which depend ontemperature and the stratum larvae are movingfrom

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS

File Edit

1585

021

339

1131

3241

2568

Fig 4 Computer screen displaying output from a simulation model of feeding damage by Lepidoptera oncabbage

Geier 1983 Salinas 1984) and our own observa-tions Our observations for these species were thefrequency of movements by larvae marked withfluorescent powder and visually censused at ~1-hintervals in research cabbage plots near GenevaNY The number of these observations was notsufficient to estimate individual transition proba-bilities so the data were used roughly to estimatefrequency of movement and probability of movingup or down on the plant For P xylostella thefrequency of movement was low and approxi-mately equal numbers of upwards and downwardsmovements were observed For A rapae virtuallyall late instars were observed to move upwards tothe head or wrapper leaves as noted by Harcourt(1963 1966) and Hoy amp Shelton (1987) Transitionprobabilities that reflect these observations werechosen for these two species and are given in Ta-ble 1

The change in state variables due to movementis thus calculated by

s

Nkj(t + ~t) = ~ Nkj(t)pj(t)I(t + ~t) (9)

where

k =k =

I(t + ~t)

~t

13 14 20 for s = 110 11 20 for s = 2 or 3

1 if (t + ~t) = 1 2 3 o otherwise002d

Movement is simulated only once each day andbecause the time step for the model is lfso of a daythe indicator I(t) is used to determine when themovements occur The values of k given above arechosen so that movement is simulated only for olderlarvae which are represented by higher values ofk (k ~ 13 for P xylostella and k ~ 10 for A rapaeor T ni)Model Output The output generated using the

equations described above is a summary of thevalues of state variables and the value of the aux-iliary variable each day for the next 7 d This ispresented on the computer screen depicted in Fig4 The number of large and small larvae of eachspecies on each stratum also can be obtained for aprintout by summing over the appropriate sub-classes in the distributed delay The picture of acabbage plant on the screen gives the user an ap-proximate idea of what the predicted damage onthe cabbage crop would look like

Validation

Methods Validation analysis was performed todemonstrate how well the model predicts data thatwere not used in model design or parameterizationData collected by a commercial field monitoringand pest control advising service were used to com-pare model predictions with observed populationdensities and feeding damage 7 d after the original

1586 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

A rapae

P xylostella

18161412108642o 00 06 12 18 24

557371

1114

92

743

1300

A rapae

10

P xylostella

20

oO0 16 32 48 64

30

10

20

1 ffi

0O0 1 2 2 4 3 6 4 8

000-05 00 05 10 15

1300

11 14

929 T ni T ni

743

55710

3 71

186

0 00- O32 -O16 O00 016 032 O0 O8 16 2 4 3 2

Standardized Residuals Standardized Residualsfor the Head for the Wrapper Leaves

-ogtucQ)=J0Q)-LL

Fig 5 Histograms of standardized cell residuals for comparing predicted numbers with observed averagenumbers of larvae on the cabbage head and wrapper leaves in commercial cabbage fields near Geneva NY

sample Scouts sampled cabbage fields on a weeklybasis using a variable-intensity sampling scheme(Hoy et al 1983) Separate counts of P xylostellalarvae (all instars combined) and A rapae and Tni eggs small (first and second instars) and large(third fourth and fifth instars) larvae were taken

on the head (stratum 1) wrapper (stratum 2) andframe leaves (strata 3-5 combined) and were usedto initialize the model Predictions of numbers ofP xylostella large A rapae and T ni and ac-cumulated feeding on the head and wrapper leaveswere compared with the scouts observations taken

October 1990 HoY ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1587

o [] a [] C D

QOO n~ Q~ n~ 100 1~ t~ 1~ 200Average Damage Rating

Average Damage Rating

Fig 6 Comparison of predicted feeding damagewith average observed damage rating on the heads andwrapper leaves of commercial cabbage crops near Ge-neva NY

the following week Initial spatial distribution with-in the frame and initial age distribution with Arapae and T ni small and large larval populationswere assumed to be uniform for lack of more pre-cise information The scouts observations includedratings of feeding damage on a scale of 0 to 4indicating approximately no damage less than onefeeding hole per leaf one to three feeding holesper leaf 10 defoliation and 40 defoliationrespectively These ratings were compared withpredictions of accumulated area of feeding withscatter plots and correlation analysis

Weather data for model inputs (maximum andminimum temperatures and daily total solar ra-diation) were recorded at the New York State Ag-ricultural Experiment Station in Geneva NY thec1vsest weather station to the commercial fieldsbeing monitored (within 20 km) Data from 34pairs of field samples-each pair taken one weekapart during July August and September in 1983and 1984 under widely varying weather condi-tions-were used for this analysis

Model predictions for number of larvae on thehead and wrapper leaves were compared with ob-servations using standardized cell residuals givenby

observed no larvae - predicted no larvaeVpredicted no larvae

Evaluation of Existing Treatment Guidelines

Because the model predicts numbers of larvaeand feeding damage on different parts of the plantwell model predictions cap be used to evaluatetreatment guidelines currently in use for cabbagepest management In particular the model can beused to explore the relative effects of each pest onthe crop and how useful a static threshold for pestpopulation density will be in predicting a given

as described by Bishop et al (1975) These ap-proximate a standard normal distribution so thecriterion for evaluation is whether or not most ofthe residuals are within 2 SD of the mean (- 2and ~2) because lt=95of the standard normaldistribution falls within this range Observations ofthe feeding damage rating also were plotted againstpredicted accumulated area of feeding and asso-ciated correlation coefficients were calculated

Results and Discussion Most standardized cellresiduals for predicted versus observed counts oflarvae on the head and wrapper leaves were wellwithin the range -2 to +2 (Fig 5) The few largedeviations that were calculated were positive in-dicating that occasionally greater average num-bers of larvae than predicted were observed Theinterplant spatial distribution of each species is ag-gregated (Harcourt 1966) and sample sizes wereoften small (as few as 11 plants) so these occasionallarge positive deviations are not surprising Theseresults indicate that the model predicts number andlocation of larvae well particularly when the lowresolution in the data for initial age and spatialdistribution within the frame and potential sam-pling error in both samples are considered Con-clusions from this analysis must be tempered some-what however by the low population densitiesobserved in these fields Bishop et al (1975) warnthat the approximation of the standardized cellresiduals to the standard normal is poorest whenpredictions in the cells are small Most of the initialpopulation densities and associated predictions weresmall because pest population densities are keptlow by farmers Evaluation of the model underthese conditions is most appropriate however be-cause these are the conditions under which themodel would be used

Predicted area of feeding was correlated withobserved damage rating (Fig 6) Damage ratingincluded assessment of recent feeding as well asolder damage done before the first sample Thiscould explain circumstances in which little feedingdamage was predicted but high damage ratingswere observed Cases where large amounts of feed-ing damage were predicted but observed damagerating was low did not occur Feeding damage isthe most important variable to managers becauseit determines the market value of the crop Thedata indicate that the model can be used to predictthe effects on the cabbage crop of a given pestpopulation under specific conditions

3

(10)

D

o

D

D

o

CC

lJ 8DaD co lJ 0

D D0

2

D

1

D D

C C

D

Wrapper Leaves

r-069

Head

r-053

oo 0

q CD

ggt 206Q)

~0Q)

~ 10fa

E8

40

oo

E8 30Dlc6Q)t 20tJQ)

Ug 1a

1588 ENVIRONMEITAL ENTOMOLOGY Vol 19 no 5

Head Wrapper Leaves

T ni 565134

377089

189045

2020

- Temporatura Avorago plon1CJ DCEC)---0)c A rapaea 1t82Q) a18Q)U 546 7890Q) 273 396sect0 30 30eD

Temperature Avorago pIontDC Temperalure Avomg bullbull p1ont

DC

P xylostella074 178050 11902i 061

20

rompera1ur Avorago plantDC Tempera1ure Averag bullbull p1on1

DC

Fig 7 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves after 7 d atdifferent temperatures and population densities of lepidopteran pests

amount of damage on the marketable parts of thecrop

Methods Response surfaces of predicted area offeeding on the head and wrapper leaves to tem-perature and population density of each pest weregenerated with the model A standard initial in-traplant spatial distribution typical of distributionsobserved in cabbage fields was chosen for eachspecies as follows P xylostella 005 01 03 03and 025 A rapae 0 015 04 03 and 015 Tni 0 01 02 04 and 03 of the average numberper plant on the head wrapper leaves upper framemidframe and lower frame respectively For Pxylostella the larval ages were uniformly distrib-uted among the 20 subclasses in the distributeddelay For A rapae and T ni the larvae wereinitialized into the first 10 subclasses simulatingfirst second and third instars For each of 10 pop-ulation densities ranging from well below to well

above the action threshold currently used in NewYork (Shelton et al 1982) feeding was predictedat six constant temperatures

Additional response surfaces were generated offeeding area on the head and wrapper leaves pre-dicted at different temperatures and initial age dis-tributions for a given population density of eachspecies Given the initial spatial distribution de-scribed above and an average temperature be-tween 20 and 25degC the first set of response surfaceswas used to select a population density predictedto cause damage most farmers would consider un-acceptable This density twice the currently rec-ommended action threshold was 1 larvaplant forT ni 15 larvaeplant for A rapae and 10 larvaeplant for P xylostella Different age distributionswere generated by dividing the population densi-ties chosen above evenly among larval maturitysubclasses 1 through 6 then 2 through 7 etc up

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1589

Head Wrapper Leaves

1n

519

260

T1i

TemperatureDC

10

Youngest Age ProSQnt

10

10

YOungG81 AGe PrQsan

A rapal2333

557

78

10

Youngest Ago PreSGnt

TemperatureDC

142 P xylostllia

098

053

0009

Youngesl Ago PresentTemperature

DCTemperalUIlliDc

Fig 8 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves in 7 d due todifferent temperatures and age distributions at a given population density of three lepidopteran pests of cabbagePopulation densities were lplant for T ni loSplant for A rapae 10plant for P xylostella

to 10 through 15 Model predictions were gener-ated at each of these age distributions for each ofthe 6 constant temperatures used above

Results and Discussion Response surfaces gen-erated with the model predict that A rapae con-tributes most to feeding damage on the head andwrapper leaves (Fig 7) Although total consump-tion by A rapae larvae is less than that of T ni(Harcourt et al 1955) the amount consumed onthese economically important strata is greater be-cause of the difference in intra plant spatial dynam-ics of the two species In Fig 7 the model predictsthat for a given constant temperature and giveninitial age and spatial distributions feeding on thehead and wrapper leaves increases linearly withpopulation density for each species Systems thatweight the counts of each species according to ex-pected feeding damage and base the action thresh-old on the weighted counts have been proposed

(Harcourt et al 1955 Shelton et al 1982) but thesedid not consider the spatial dynamics of the pestsThus one potential use of our model is to designa new rating scale to weight the population densityof each species according to expected feeding dam-age considering the spatial dynamics of eachspecies This rating scale however would also haveto account for temperature effects which cangreatly affect predicted feeding

At temperatures lt15DC very little feeding ispredicted on the head and wrapper leaves by eachspecies at any population density (Fig 7) Increas-ing temperatures have a nonlinear effect on pre-dicted feeding by each species For P xylostellaand A rapae the increase in predicted feedingrate may be primarily due to increased develop-ment and feeding rates For T ni however in-creased development and feeding rates at highertemperatures may be offset to some extent by higher

1590 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

probabilities of moving away from the head andwrapper leaves towards the lower leaves (Hoy etal 1989)

For a given population density predicted feed-ing on the marketable parts of the plant variedwidely with age distribution again interacting withtemperature (Fig 8) The results indicate that thedamage caused by a given population density afixed economic threshold for example will varyconsiderably with temperature age structure of thepopulation and species composition Againweighting systems have been described that con-sider larval age (Andaloro et al 1983a) but notwith the resolution that Fig 8 implies is necessaryand they do not include the interaction with tem-perature

Considering the profound effects of tempera-ture age distribution and species-specific spatialdynamics on the predicted area of feeding on eco-nomically important parts of the plant a staticeconomic threshold does not seem to be appropri-ate Rather feeding should be predicted for specificpopulation densities age distributions and spatialdistributions of the three species as well as weatherforecasts and management strategies should be de-signed accordingly The model described here couldbe used to make those predictions either by cal-culating a new species weighting system each dayof the growing season to be used with a fixed actionthreshold or simply by making the required pre-dictions on a case-by-case basis

Sensitivity Analysis

Two goals were addressed in the sensitivity anal-ysis First individual model parameters were evalmiddotuated as potential causes of inaccurate predictionsBy examining the change in model output after achange in the individual parameters parametersthat affect the output most can be identified Sec-ond by examining the effects of changes in dif-ferent parameters in combination insight can begained into the effects of the different processesbeing simulated and their interactions on the out-put variables of interest

Methods Model predictions were evaluated af-ter changing each parameter and input suppliedby the user by +10 and -10 of its valueChanges were made one parameter at a time witha standard set of initial conditions Standard initialpest population densities were a mean of 1 larvalplant of each species on each stratum in the secondinstar for A rapae and T ni and uniformly dis-tributed among the 20 age subclasses for P xylo-stella The analysis was performed at each of threetemperature regimes typical summer weather forwestern New York (maximum temperature 267degCminimum temperature 155degC 8 h sunshine eachday) hot and sunny weather (maximum temper-ature 322degC minimum temperature 211oC 12h sunshine each day) and cool and cloudy weather

(maximum temperature 183degC minimum tem-perature 10degC 2 h sunshine)

Constants were changed by adding or subtract-ing 10 of their value Input weather variableswere changed by adding or subtracting 10 of thevalue of each pays forecasted maximum and min-imum temperature and hours of sunshine Age atwhich larvae begin to move was shifted plus orminus two subclasses to effect a 10 change Initialage distribution for A rapae and T ni was alsoshifted 10 by shifting the subclasses initialized byplus or minus two Initial age distribution for Pxylostella is assumed to be uniform so this was notchanged For each species the initial intraplantdistribution was altered by shifting 10 of eachage group on each stratum except the lower frameleaves down one stratum or shifting 10 of eachage group on each stratum except the head upone stratum (eg a downward shift of an averageof one larva on each stratum would result in anaverage of 09 1 1 1 and 11 larvae on the headwrapper upper frame midframe and lower frameleaves respectively) Transition probabilities for Arapae and P xylostella were changed by a similarmethod shifting 10 of the probability of movingto each stratum except the lower frame leaves tothe next lower stratum or shifting 10 of the prob-ability of moving to each stratum except the headto the next stratum up (eg a downward shift ina transition probability vector of 09 01000 resultsin a vector of 081 018 001 0 0) Sensitivity tochanges in transition probabilities for T ni wereexamined by changing the Beta pdf shape param-eters that govern transition probabilities for thisspecies by + 10 and -10 of their value Theeffects of each of these changes were examined bycalculating the percentage of change in number oflarvae of each species and the percentage of changein accumulated area of feeding on the head andwrapper leaves

To examine interactions between different pro-cesses and their effects on model output we per-formed two analyses in which variables suspectedof interacting were varied in all combinations theequivalent of a factorial design with three levelsof each factor given by +5 -5 and 0 Be-cause development and feeding rates are temper-ature-dependent and govern the amount of feedingaccumulated interactions between temperaturefeeding rates and development rates might affectaccumulated area of feeding Three levels of tem-perature were generated starting with the typicalsummer weather regime described above and add-ing 5 -5 or 0 of the daily maximum andminimum At each temperature level develop-ment rate for each species was varied by +5-5 and 0 from its value and at each of thesedevelopment rates for each species feeding ratewas changed by +5 -5 and 0 of its valueThe effects of these parameter changes on the pre-dicted area of feeding on the head and wrapperleaves were calculated

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1591

Table 2 Output from a model to predict lepidopteranfeeding damage on cabbage at three temperature regimeswith a standard set of inputs and no change in the param-eters Changes in output during the sensitivity analysis (Fig9-12) are compared with these standards

StratumPopulation density (avg noplant) Feeding

P xylostella A rapae Tni cm2

High temperaturesHead 0252 2118 0095 12764Wrapper 0390 2594 0662 21716

Moderate temperaturesHead 0423 1957 0299 6805Wrapper 0578 2524 1001 9667

Low temperaturesHead 0635 1296 0829 1945Wrapper 0834 1651 0886 2348

A similar analysis of interacting processes wasperformed for spatial effects Initial distributionand transition probabilities could be expected tointeract in their effects on spatial distribution oflarvae and feeding damage For each species theinitial distribution was treated by (a) shifting 10of each age group on each stratum (except thelower frame leaves) down one stratum (b) shifting10of each age group on each stratum (except thehead) up one stratum and (c) leaving the initialdistribution unchanged At each of these shifts ininitial distribution for each species the transitionprobabilities for that species were changed as de-

scribed above Shifting 10 of the probability ofmoving to each stratum except the lower frameleaves to the next lower stratum resulted in higherprobabilities of downward movement shifting 10of the probability of moving to each stratum exceptthe head to the next stratum up resulted in higherprobability of upward movement

Results and Discussion Standard results for highmoderate and low temperature regimes withoutchanging any of the parameters or input variablesare given in Table 2 and the effects of changingeach parameter and input variable on selected out-put variables are displayed in Fig 9-12 for themoderate temperature regime We begin the anal-ysisby examining sensitivity of the model to changesin the parameters at moderate temperatures andfollow with the differences in model sensitivity seenunder high and low temperature regimes

At moderate temperatures numbers of larvae ofeach species on the head and wrapper leaves wereleast sensitive to initial spatial distribution of larvaedispersion in development time and hours of sun-shine (Fig 9) Change in the initial intraplant dis-tribution of larvae may be compensated for bymovement of larvae within a short time after thebeginning of the simulation Dispersion in devel-opment time for these species was low in the lab-oratory development studies resulting in a small

Svalue of -D for each species A 10 change in

EL~these small values does not change the dispersion

o Effect 01 +10 changebull Effect 01 -10 change on larvae on the head alief 7 days

Inldal dlsbibudonInitial ages

Age 01 first movementTransition probabilities

Dispersion In developmenlgl

DEL g2C

Hours 01 sunshineTemperalure

-20 -10 0 10

P xylostella20 30 -20 -10 0 10 20

A rapae

oT nl

100

on larvae on the wrapper leaves alter 7 days

10-10

Initial distributionInitial ages

Age 01 firsl movementTransition probabilities

Dispersion in developmentgl

DEL g2C

Hours of sunshineTemperature

-20 o 10 -20 -10 0 -10 0P xylostella A rapas T nI

Fig 9 Percentage of change in predicted number of P xylostella A rapae and T nt larvae on the head andwrapper leavesafter changing model parameters + and -10

1592 ENVIRONME~TAL ENTOMOLOGY Vol 19 no 5

Fig 10 Percentage of change in number of T nilarvae predicted on the head and wrapper leaves aftera + or - 1 0 change in parameters governing their tran-sition probabilities on the cabbage plant

greatly Hours of sunshine influence temperaturein each stratum but apparently not enough to causelarge changes in rate functions

Changes in temperature initial age distributionage at which larvae begin to move between strataand transition probabilities had the greatest effectson predicted number of larvae on the head or wrap-per leaves (Fig 9) These are all linked to spatialdynamics since both temperature and initial agedistribution affect the time at which larvae beginto move between strata Changes in parametersgoverning T ni transition probabilities were anexception causing only moderate or small changesin output (Fig 10) Changes in development rateparameters had large effects only for P xylostellaon the head and wrapper leaves and for T ni onthe head

Predictions of accumulated feeding on the headand wrapper leaves were generally less sensitive tochanges in parameters than were predictions ofnumbers of larvae on these strata (Fig 11 and 12)Because the predictions of accumulated area offeeding are most important to the farmer the ro-bustness of the model in predicting feeding sug-gests that it could be a useful management toolThe greatest changes in accumulated area of feed-ing were caused by changing parameters governingA rapae development or feeding particularly ini-tial age distribution Fortunately development ratesfor all three species considered here have been wellstudied and studies done at widely different timesand locations with different food sources suggestthat average development rate at a given temper-ature is fairly constant (Hardy 1938 Richards 1940Given 1944 Miner 1947 Harcourt et al 1955Shorey et al 1962 Jackson et al 1969 Toba et al

1973 Boldt et al 1975 Butler et al 1975 Smithamp Smilowitz 1976 Chen amp Su 1978 1982 Tatchell1981 Yamada amp Kawasaki 1983 Theunissen et al1985) Changes in forecast temperatures cause thenext largest change in accumulated feeding prob-ably because of their effects on development andfeeding rates Parameters governing spatial effectshad smaller effects on accumulated feeding par-ticularly when compared with their effects on pre-dicted number of larvae on different parts of theplant

Under the low-temperature regime predictionsof numbers of larvae on the head and wrapperleaves were more sensitive to parameters affectingdevelopment than to parameters affecting spatialdynamics At low temperatures larvae take longerto reach the age when movement starts and prob-ability of movement by T ni to the head andwrapper leaves is lower Furthermore fewer smalllarvae become large larvae at low temperatures sototal numbers of large larvae on all strata are re-duced At moderate and high temperatures pre-dictions of numbers of larvae on the head andwrapper leaves were more sensitive to changes inparameters affecting spatial dynamics

Effects of changing forecast temperatures onpredictions of accumulated feeding were muchgreater when the forecast temperatures were lowand less when the forecast temperatures were highthan at moderate temperatures Changing devel-opment rate parameters had a greater effect onaccumulated feeding at low temperatures butchanging feeding rate parameters had a greatereffect at high temperatures than at moderate tem-peratures Accumulated feeding was less sensitiveto changes in transition probabilities at low tem-peratures and more sensitive to changes in tran-sition probabilities at high temperatures than atmoderate temperatures

In general interactions between temperaturedevelopment and feeding rates as well as param-eters governing spatial effects were not evidentTypically the effect of changes in each of theseparameters was similar regardless of the value ofthe other parameters One interaction did occurWhen temperature was increased a negativechange in T ni development rate resulted in lesspredicted feeding on the head than when no changein T ni development rate was made In all othercases negative change in development rates re-sulted in higher predicted feeding on the head thanwhen development rates were not changed Re-gardless 5 changes in development rates for Tni resulted in lt3 differences in feeding on thehead so the effects of this interaction are not ofgreat importance Thus this analysis reinforced thesingle parameter analysis Feeding rates themselveswere changed in this analysis rather than the pa-rameters that govern them and accumulated feed-ing on the head and wrapper leaves was still moresensitive to changes in development rate and tem-perature

5o

middot5 0

Feeding on Heed

-5Feeding on Wrapper Leaves

o 10

Larvae on Head

middot10

b5b4b3b2bl858483a281

middot20l( Change in

-20 middot10 0 10 Change in Larvae on Wrapper leaves

II2l

~toa0gtatoten

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

SDElA rapae g2

g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

1584 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

(7)

31

31

T ni

A rapae

P xyfostefla

00010 a8

a6Physiological

Age

constants estimated by maximumlikelihood as described by Hoy etal (1989)

gt 449535~~ 2lli90ig~ 149845IIOJc6 aooaf 10 08

Fig 3 Predicted feeding rates of P xylo8tella Arapae and T ni on cabbage

Because the shape parameters for the Beta distri-bution a and h change with temperature theshape of the distribution and value of the integralsdescribed in Equation (8) change accordinglyHigher temperatures tend to result in greater prob-ability of movement and higher probability ofmovement towards the lower leaves than towardsthe head lower temperatures tend to result in lowerprobability of movement and higher probabilityof movement towards the head than towards thelower leaves

The elements of the transition probability ma-trices for P xylostella and A rapae are estimatedfrom observations reported in the literature (Har-court 1963 1966 Chua amp Lim 1979 Samson amp

~ 15llli6S~~ 1(57 n

1sectGl 5281IlttlaOJc6af 06

PhysiologicalAge

~~ JI64

~ce 576

sectGl

l2 1288OJc6GlGl

U

previous time steps by

Ej(t) = plusmn plusmn ~ [NkT)FPDkj(T)] ~tTO -I k-I 100

where

Ej(t) area of feeding (cm2) on stratum j accu-mulated at time t

T ~t 2~t 3~t M 002 d

Pj(t)

= f ~ 1__ U1a(I)-11(1 - U)lb(l)-ll duJ~l B[a(t) b(t)] (8)

where

the probability of a T ni (species3) late instar moving from stratumi to stratum j during one dayeel +C2 avtemPi(t)

ed +d2atemp)

The three empirical constants (hh hz and h31inEquation 6) for estimating feeding rates as a func-tion of temperature and larval age were estimatedby multiple linear regression (SAS Institute 1982)of the natural log of feedingday (mm2) on ageage temperature and agemiddottemperature2 (Table 1)The measure of larval age was the proportion oflarval stage completed or days the larva had livedso far divided by total days spent by that larvafrom eclosion to pupation Measurements of areaof cabbage leaf consumed each day of the larvalperiod for each of 20 larvaereplicate and threereplicatestemperature at 167 211 and 267degCfor each species were taken by AMS and P BBaker (unpublished data) Inspection of predictions(Fig 3) compared with data reported in the lit-erature (Harcourt et al 1955 McEwen amp Hervey1960 Rahman 1970 Harper 1973 Boldt et al 1975Chen amp Su 1978 1982 Samson amp Geier 1983Theunissen et al 1985) indicates that the feedingrate model fit well Data on feeding by A rapaereported by Tatchell (1981) indicate much higherrates than those we estimated but Tatchells datadisagree with the other literature cited above aswell As in the case of development rates we usedthe AMS and P B Baker data because the foodsource was cabbage leaf so these data should bemost appropriate

Movement Rates Larval movement is simulatedwith discrete time transition probability matricesbecause observed larval movements were discretein time Movement of late instar T ni is correlatedwith microclimate (Hoy et al 1989) and must bemodeled accordingly The transition probabilitiesfor late instar T ni are modeled as definite integralsof the Beta probability density function (pdf) withshape parameters a(t) and b(t) which depend ontemperature and the stratum larvae are movingfrom

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS

File Edit

1585

021

339

1131

3241

2568

Fig 4 Computer screen displaying output from a simulation model of feeding damage by Lepidoptera oncabbage

Geier 1983 Salinas 1984) and our own observa-tions Our observations for these species were thefrequency of movements by larvae marked withfluorescent powder and visually censused at ~1-hintervals in research cabbage plots near GenevaNY The number of these observations was notsufficient to estimate individual transition proba-bilities so the data were used roughly to estimatefrequency of movement and probability of movingup or down on the plant For P xylostella thefrequency of movement was low and approxi-mately equal numbers of upwards and downwardsmovements were observed For A rapae virtuallyall late instars were observed to move upwards tothe head or wrapper leaves as noted by Harcourt(1963 1966) and Hoy amp Shelton (1987) Transitionprobabilities that reflect these observations werechosen for these two species and are given in Ta-ble 1

The change in state variables due to movementis thus calculated by

s

Nkj(t + ~t) = ~ Nkj(t)pj(t)I(t + ~t) (9)

where

k =k =

I(t + ~t)

~t

13 14 20 for s = 110 11 20 for s = 2 or 3

1 if (t + ~t) = 1 2 3 o otherwise002d

Movement is simulated only once each day andbecause the time step for the model is lfso of a daythe indicator I(t) is used to determine when themovements occur The values of k given above arechosen so that movement is simulated only for olderlarvae which are represented by higher values ofk (k ~ 13 for P xylostella and k ~ 10 for A rapaeor T ni)Model Output The output generated using the

equations described above is a summary of thevalues of state variables and the value of the aux-iliary variable each day for the next 7 d This ispresented on the computer screen depicted in Fig4 The number of large and small larvae of eachspecies on each stratum also can be obtained for aprintout by summing over the appropriate sub-classes in the distributed delay The picture of acabbage plant on the screen gives the user an ap-proximate idea of what the predicted damage onthe cabbage crop would look like

Validation

Methods Validation analysis was performed todemonstrate how well the model predicts data thatwere not used in model design or parameterizationData collected by a commercial field monitoringand pest control advising service were used to com-pare model predictions with observed populationdensities and feeding damage 7 d after the original

1586 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

A rapae

P xylostella

18161412108642o 00 06 12 18 24

557371

1114

92

743

1300

A rapae

10

P xylostella

20

oO0 16 32 48 64

30

10

20

1 ffi

0O0 1 2 2 4 3 6 4 8

000-05 00 05 10 15

1300

11 14

929 T ni T ni

743

55710

3 71

186

0 00- O32 -O16 O00 016 032 O0 O8 16 2 4 3 2

Standardized Residuals Standardized Residualsfor the Head for the Wrapper Leaves

-ogtucQ)=J0Q)-LL

Fig 5 Histograms of standardized cell residuals for comparing predicted numbers with observed averagenumbers of larvae on the cabbage head and wrapper leaves in commercial cabbage fields near Geneva NY

sample Scouts sampled cabbage fields on a weeklybasis using a variable-intensity sampling scheme(Hoy et al 1983) Separate counts of P xylostellalarvae (all instars combined) and A rapae and Tni eggs small (first and second instars) and large(third fourth and fifth instars) larvae were taken

on the head (stratum 1) wrapper (stratum 2) andframe leaves (strata 3-5 combined) and were usedto initialize the model Predictions of numbers ofP xylostella large A rapae and T ni and ac-cumulated feeding on the head and wrapper leaveswere compared with the scouts observations taken

October 1990 HoY ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1587

o [] a [] C D

QOO n~ Q~ n~ 100 1~ t~ 1~ 200Average Damage Rating

Average Damage Rating

Fig 6 Comparison of predicted feeding damagewith average observed damage rating on the heads andwrapper leaves of commercial cabbage crops near Ge-neva NY

the following week Initial spatial distribution with-in the frame and initial age distribution with Arapae and T ni small and large larval populationswere assumed to be uniform for lack of more pre-cise information The scouts observations includedratings of feeding damage on a scale of 0 to 4indicating approximately no damage less than onefeeding hole per leaf one to three feeding holesper leaf 10 defoliation and 40 defoliationrespectively These ratings were compared withpredictions of accumulated area of feeding withscatter plots and correlation analysis

Weather data for model inputs (maximum andminimum temperatures and daily total solar ra-diation) were recorded at the New York State Ag-ricultural Experiment Station in Geneva NY thec1vsest weather station to the commercial fieldsbeing monitored (within 20 km) Data from 34pairs of field samples-each pair taken one weekapart during July August and September in 1983and 1984 under widely varying weather condi-tions-were used for this analysis

Model predictions for number of larvae on thehead and wrapper leaves were compared with ob-servations using standardized cell residuals givenby

observed no larvae - predicted no larvaeVpredicted no larvae

Evaluation of Existing Treatment Guidelines

Because the model predicts numbers of larvaeand feeding damage on different parts of the plantwell model predictions cap be used to evaluatetreatment guidelines currently in use for cabbagepest management In particular the model can beused to explore the relative effects of each pest onthe crop and how useful a static threshold for pestpopulation density will be in predicting a given

as described by Bishop et al (1975) These ap-proximate a standard normal distribution so thecriterion for evaluation is whether or not most ofthe residuals are within 2 SD of the mean (- 2and ~2) because lt=95of the standard normaldistribution falls within this range Observations ofthe feeding damage rating also were plotted againstpredicted accumulated area of feeding and asso-ciated correlation coefficients were calculated

Results and Discussion Most standardized cellresiduals for predicted versus observed counts oflarvae on the head and wrapper leaves were wellwithin the range -2 to +2 (Fig 5) The few largedeviations that were calculated were positive in-dicating that occasionally greater average num-bers of larvae than predicted were observed Theinterplant spatial distribution of each species is ag-gregated (Harcourt 1966) and sample sizes wereoften small (as few as 11 plants) so these occasionallarge positive deviations are not surprising Theseresults indicate that the model predicts number andlocation of larvae well particularly when the lowresolution in the data for initial age and spatialdistribution within the frame and potential sam-pling error in both samples are considered Con-clusions from this analysis must be tempered some-what however by the low population densitiesobserved in these fields Bishop et al (1975) warnthat the approximation of the standardized cellresiduals to the standard normal is poorest whenpredictions in the cells are small Most of the initialpopulation densities and associated predictions weresmall because pest population densities are keptlow by farmers Evaluation of the model underthese conditions is most appropriate however be-cause these are the conditions under which themodel would be used

Predicted area of feeding was correlated withobserved damage rating (Fig 6) Damage ratingincluded assessment of recent feeding as well asolder damage done before the first sample Thiscould explain circumstances in which little feedingdamage was predicted but high damage ratingswere observed Cases where large amounts of feed-ing damage were predicted but observed damagerating was low did not occur Feeding damage isthe most important variable to managers becauseit determines the market value of the crop Thedata indicate that the model can be used to predictthe effects on the cabbage crop of a given pestpopulation under specific conditions

3

(10)

D

o

D

D

o

CC

lJ 8DaD co lJ 0

D D0

2

D

1

D D

C C

D

Wrapper Leaves

r-069

Head

r-053

oo 0

q CD

ggt 206Q)

~0Q)

~ 10fa

E8

40

oo

E8 30Dlc6Q)t 20tJQ)

Ug 1a

1588 ENVIRONMEITAL ENTOMOLOGY Vol 19 no 5

Head Wrapper Leaves

T ni 565134

377089

189045

2020

- Temporatura Avorago plon1CJ DCEC)---0)c A rapaea 1t82Q) a18Q)U 546 7890Q) 273 396sect0 30 30eD

Temperature Avorago pIontDC Temperalure Avomg bullbull p1ont

DC

P xylostella074 178050 11902i 061

20

rompera1ur Avorago plantDC Tempera1ure Averag bullbull p1on1

DC

Fig 7 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves after 7 d atdifferent temperatures and population densities of lepidopteran pests

amount of damage on the marketable parts of thecrop

Methods Response surfaces of predicted area offeeding on the head and wrapper leaves to tem-perature and population density of each pest weregenerated with the model A standard initial in-traplant spatial distribution typical of distributionsobserved in cabbage fields was chosen for eachspecies as follows P xylostella 005 01 03 03and 025 A rapae 0 015 04 03 and 015 Tni 0 01 02 04 and 03 of the average numberper plant on the head wrapper leaves upper framemidframe and lower frame respectively For Pxylostella the larval ages were uniformly distrib-uted among the 20 subclasses in the distributeddelay For A rapae and T ni the larvae wereinitialized into the first 10 subclasses simulatingfirst second and third instars For each of 10 pop-ulation densities ranging from well below to well

above the action threshold currently used in NewYork (Shelton et al 1982) feeding was predictedat six constant temperatures

Additional response surfaces were generated offeeding area on the head and wrapper leaves pre-dicted at different temperatures and initial age dis-tributions for a given population density of eachspecies Given the initial spatial distribution de-scribed above and an average temperature be-tween 20 and 25degC the first set of response surfaceswas used to select a population density predictedto cause damage most farmers would consider un-acceptable This density twice the currently rec-ommended action threshold was 1 larvaplant forT ni 15 larvaeplant for A rapae and 10 larvaeplant for P xylostella Different age distributionswere generated by dividing the population densi-ties chosen above evenly among larval maturitysubclasses 1 through 6 then 2 through 7 etc up

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1589

Head Wrapper Leaves

1n

519

260

T1i

TemperatureDC

10

Youngest Age ProSQnt

10

10

YOungG81 AGe PrQsan

A rapal2333

557

78

10

Youngest Ago PreSGnt

TemperatureDC

142 P xylostllia

098

053

0009

Youngesl Ago PresentTemperature

DCTemperalUIlliDc

Fig 8 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves in 7 d due todifferent temperatures and age distributions at a given population density of three lepidopteran pests of cabbagePopulation densities were lplant for T ni loSplant for A rapae 10plant for P xylostella

to 10 through 15 Model predictions were gener-ated at each of these age distributions for each ofthe 6 constant temperatures used above

Results and Discussion Response surfaces gen-erated with the model predict that A rapae con-tributes most to feeding damage on the head andwrapper leaves (Fig 7) Although total consump-tion by A rapae larvae is less than that of T ni(Harcourt et al 1955) the amount consumed onthese economically important strata is greater be-cause of the difference in intra plant spatial dynam-ics of the two species In Fig 7 the model predictsthat for a given constant temperature and giveninitial age and spatial distributions feeding on thehead and wrapper leaves increases linearly withpopulation density for each species Systems thatweight the counts of each species according to ex-pected feeding damage and base the action thresh-old on the weighted counts have been proposed

(Harcourt et al 1955 Shelton et al 1982) but thesedid not consider the spatial dynamics of the pestsThus one potential use of our model is to designa new rating scale to weight the population densityof each species according to expected feeding dam-age considering the spatial dynamics of eachspecies This rating scale however would also haveto account for temperature effects which cangreatly affect predicted feeding

At temperatures lt15DC very little feeding ispredicted on the head and wrapper leaves by eachspecies at any population density (Fig 7) Increas-ing temperatures have a nonlinear effect on pre-dicted feeding by each species For P xylostellaand A rapae the increase in predicted feedingrate may be primarily due to increased develop-ment and feeding rates For T ni however in-creased development and feeding rates at highertemperatures may be offset to some extent by higher

1590 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

probabilities of moving away from the head andwrapper leaves towards the lower leaves (Hoy etal 1989)

For a given population density predicted feed-ing on the marketable parts of the plant variedwidely with age distribution again interacting withtemperature (Fig 8) The results indicate that thedamage caused by a given population density afixed economic threshold for example will varyconsiderably with temperature age structure of thepopulation and species composition Againweighting systems have been described that con-sider larval age (Andaloro et al 1983a) but notwith the resolution that Fig 8 implies is necessaryand they do not include the interaction with tem-perature

Considering the profound effects of tempera-ture age distribution and species-specific spatialdynamics on the predicted area of feeding on eco-nomically important parts of the plant a staticeconomic threshold does not seem to be appropri-ate Rather feeding should be predicted for specificpopulation densities age distributions and spatialdistributions of the three species as well as weatherforecasts and management strategies should be de-signed accordingly The model described here couldbe used to make those predictions either by cal-culating a new species weighting system each dayof the growing season to be used with a fixed actionthreshold or simply by making the required pre-dictions on a case-by-case basis

Sensitivity Analysis

Two goals were addressed in the sensitivity anal-ysis First individual model parameters were evalmiddotuated as potential causes of inaccurate predictionsBy examining the change in model output after achange in the individual parameters parametersthat affect the output most can be identified Sec-ond by examining the effects of changes in dif-ferent parameters in combination insight can begained into the effects of the different processesbeing simulated and their interactions on the out-put variables of interest

Methods Model predictions were evaluated af-ter changing each parameter and input suppliedby the user by +10 and -10 of its valueChanges were made one parameter at a time witha standard set of initial conditions Standard initialpest population densities were a mean of 1 larvalplant of each species on each stratum in the secondinstar for A rapae and T ni and uniformly dis-tributed among the 20 age subclasses for P xylo-stella The analysis was performed at each of threetemperature regimes typical summer weather forwestern New York (maximum temperature 267degCminimum temperature 155degC 8 h sunshine eachday) hot and sunny weather (maximum temper-ature 322degC minimum temperature 211oC 12h sunshine each day) and cool and cloudy weather

(maximum temperature 183degC minimum tem-perature 10degC 2 h sunshine)

Constants were changed by adding or subtract-ing 10 of their value Input weather variableswere changed by adding or subtracting 10 of thevalue of each pays forecasted maximum and min-imum temperature and hours of sunshine Age atwhich larvae begin to move was shifted plus orminus two subclasses to effect a 10 change Initialage distribution for A rapae and T ni was alsoshifted 10 by shifting the subclasses initialized byplus or minus two Initial age distribution for Pxylostella is assumed to be uniform so this was notchanged For each species the initial intraplantdistribution was altered by shifting 10 of eachage group on each stratum except the lower frameleaves down one stratum or shifting 10 of eachage group on each stratum except the head upone stratum (eg a downward shift of an averageof one larva on each stratum would result in anaverage of 09 1 1 1 and 11 larvae on the headwrapper upper frame midframe and lower frameleaves respectively) Transition probabilities for Arapae and P xylostella were changed by a similarmethod shifting 10 of the probability of movingto each stratum except the lower frame leaves tothe next lower stratum or shifting 10 of the prob-ability of moving to each stratum except the headto the next stratum up (eg a downward shift ina transition probability vector of 09 01000 resultsin a vector of 081 018 001 0 0) Sensitivity tochanges in transition probabilities for T ni wereexamined by changing the Beta pdf shape param-eters that govern transition probabilities for thisspecies by + 10 and -10 of their value Theeffects of each of these changes were examined bycalculating the percentage of change in number oflarvae of each species and the percentage of changein accumulated area of feeding on the head andwrapper leaves

To examine interactions between different pro-cesses and their effects on model output we per-formed two analyses in which variables suspectedof interacting were varied in all combinations theequivalent of a factorial design with three levelsof each factor given by +5 -5 and 0 Be-cause development and feeding rates are temper-ature-dependent and govern the amount of feedingaccumulated interactions between temperaturefeeding rates and development rates might affectaccumulated area of feeding Three levels of tem-perature were generated starting with the typicalsummer weather regime described above and add-ing 5 -5 or 0 of the daily maximum andminimum At each temperature level develop-ment rate for each species was varied by +5-5 and 0 from its value and at each of thesedevelopment rates for each species feeding ratewas changed by +5 -5 and 0 of its valueThe effects of these parameter changes on the pre-dicted area of feeding on the head and wrapperleaves were calculated

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1591

Table 2 Output from a model to predict lepidopteranfeeding damage on cabbage at three temperature regimeswith a standard set of inputs and no change in the param-eters Changes in output during the sensitivity analysis (Fig9-12) are compared with these standards

StratumPopulation density (avg noplant) Feeding

P xylostella A rapae Tni cm2

High temperaturesHead 0252 2118 0095 12764Wrapper 0390 2594 0662 21716

Moderate temperaturesHead 0423 1957 0299 6805Wrapper 0578 2524 1001 9667

Low temperaturesHead 0635 1296 0829 1945Wrapper 0834 1651 0886 2348

A similar analysis of interacting processes wasperformed for spatial effects Initial distributionand transition probabilities could be expected tointeract in their effects on spatial distribution oflarvae and feeding damage For each species theinitial distribution was treated by (a) shifting 10of each age group on each stratum (except thelower frame leaves) down one stratum (b) shifting10of each age group on each stratum (except thehead) up one stratum and (c) leaving the initialdistribution unchanged At each of these shifts ininitial distribution for each species the transitionprobabilities for that species were changed as de-

scribed above Shifting 10 of the probability ofmoving to each stratum except the lower frameleaves to the next lower stratum resulted in higherprobabilities of downward movement shifting 10of the probability of moving to each stratum exceptthe head to the next stratum up resulted in higherprobability of upward movement

Results and Discussion Standard results for highmoderate and low temperature regimes withoutchanging any of the parameters or input variablesare given in Table 2 and the effects of changingeach parameter and input variable on selected out-put variables are displayed in Fig 9-12 for themoderate temperature regime We begin the anal-ysisby examining sensitivity of the model to changesin the parameters at moderate temperatures andfollow with the differences in model sensitivity seenunder high and low temperature regimes

At moderate temperatures numbers of larvae ofeach species on the head and wrapper leaves wereleast sensitive to initial spatial distribution of larvaedispersion in development time and hours of sun-shine (Fig 9) Change in the initial intraplant dis-tribution of larvae may be compensated for bymovement of larvae within a short time after thebeginning of the simulation Dispersion in devel-opment time for these species was low in the lab-oratory development studies resulting in a small

Svalue of -D for each species A 10 change in

EL~these small values does not change the dispersion

o Effect 01 +10 changebull Effect 01 -10 change on larvae on the head alief 7 days

Inldal dlsbibudonInitial ages

Age 01 first movementTransition probabilities

Dispersion In developmenlgl

DEL g2C

Hours 01 sunshineTemperalure

-20 -10 0 10

P xylostella20 30 -20 -10 0 10 20

A rapae

oT nl

100

on larvae on the wrapper leaves alter 7 days

10-10

Initial distributionInitial ages

Age 01 firsl movementTransition probabilities

Dispersion in developmentgl

DEL g2C

Hours of sunshineTemperature

-20 o 10 -20 -10 0 -10 0P xylostella A rapas T nI

Fig 9 Percentage of change in predicted number of P xylostella A rapae and T nt larvae on the head andwrapper leavesafter changing model parameters + and -10

1592 ENVIRONME~TAL ENTOMOLOGY Vol 19 no 5

Fig 10 Percentage of change in number of T nilarvae predicted on the head and wrapper leaves aftera + or - 1 0 change in parameters governing their tran-sition probabilities on the cabbage plant

greatly Hours of sunshine influence temperaturein each stratum but apparently not enough to causelarge changes in rate functions

Changes in temperature initial age distributionage at which larvae begin to move between strataand transition probabilities had the greatest effectson predicted number of larvae on the head or wrap-per leaves (Fig 9) These are all linked to spatialdynamics since both temperature and initial agedistribution affect the time at which larvae beginto move between strata Changes in parametersgoverning T ni transition probabilities were anexception causing only moderate or small changesin output (Fig 10) Changes in development rateparameters had large effects only for P xylostellaon the head and wrapper leaves and for T ni onthe head

Predictions of accumulated feeding on the headand wrapper leaves were generally less sensitive tochanges in parameters than were predictions ofnumbers of larvae on these strata (Fig 11 and 12)Because the predictions of accumulated area offeeding are most important to the farmer the ro-bustness of the model in predicting feeding sug-gests that it could be a useful management toolThe greatest changes in accumulated area of feed-ing were caused by changing parameters governingA rapae development or feeding particularly ini-tial age distribution Fortunately development ratesfor all three species considered here have been wellstudied and studies done at widely different timesand locations with different food sources suggestthat average development rate at a given temper-ature is fairly constant (Hardy 1938 Richards 1940Given 1944 Miner 1947 Harcourt et al 1955Shorey et al 1962 Jackson et al 1969 Toba et al

1973 Boldt et al 1975 Butler et al 1975 Smithamp Smilowitz 1976 Chen amp Su 1978 1982 Tatchell1981 Yamada amp Kawasaki 1983 Theunissen et al1985) Changes in forecast temperatures cause thenext largest change in accumulated feeding prob-ably because of their effects on development andfeeding rates Parameters governing spatial effectshad smaller effects on accumulated feeding par-ticularly when compared with their effects on pre-dicted number of larvae on different parts of theplant

Under the low-temperature regime predictionsof numbers of larvae on the head and wrapperleaves were more sensitive to parameters affectingdevelopment than to parameters affecting spatialdynamics At low temperatures larvae take longerto reach the age when movement starts and prob-ability of movement by T ni to the head andwrapper leaves is lower Furthermore fewer smalllarvae become large larvae at low temperatures sototal numbers of large larvae on all strata are re-duced At moderate and high temperatures pre-dictions of numbers of larvae on the head andwrapper leaves were more sensitive to changes inparameters affecting spatial dynamics

Effects of changing forecast temperatures onpredictions of accumulated feeding were muchgreater when the forecast temperatures were lowand less when the forecast temperatures were highthan at moderate temperatures Changing devel-opment rate parameters had a greater effect onaccumulated feeding at low temperatures butchanging feeding rate parameters had a greatereffect at high temperatures than at moderate tem-peratures Accumulated feeding was less sensitiveto changes in transition probabilities at low tem-peratures and more sensitive to changes in tran-sition probabilities at high temperatures than atmoderate temperatures

In general interactions between temperaturedevelopment and feeding rates as well as param-eters governing spatial effects were not evidentTypically the effect of changes in each of theseparameters was similar regardless of the value ofthe other parameters One interaction did occurWhen temperature was increased a negativechange in T ni development rate resulted in lesspredicted feeding on the head than when no changein T ni development rate was made In all othercases negative change in development rates re-sulted in higher predicted feeding on the head thanwhen development rates were not changed Re-gardless 5 changes in development rates for Tni resulted in lt3 differences in feeding on thehead so the effects of this interaction are not ofgreat importance Thus this analysis reinforced thesingle parameter analysis Feeding rates themselveswere changed in this analysis rather than the pa-rameters that govern them and accumulated feed-ing on the head and wrapper leaves was still moresensitive to changes in development rate and tem-perature

5o

middot5 0

Feeding on Heed

-5Feeding on Wrapper Leaves

o 10

Larvae on Head

middot10

b5b4b3b2bl858483a281

middot20l( Change in

-20 middot10 0 10 Change in Larvae on Wrapper leaves

II2l

~toa0gtatoten

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

SDElA rapae g2

g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS

File Edit

1585

021

339

1131

3241

2568

Fig 4 Computer screen displaying output from a simulation model of feeding damage by Lepidoptera oncabbage

Geier 1983 Salinas 1984) and our own observa-tions Our observations for these species were thefrequency of movements by larvae marked withfluorescent powder and visually censused at ~1-hintervals in research cabbage plots near GenevaNY The number of these observations was notsufficient to estimate individual transition proba-bilities so the data were used roughly to estimatefrequency of movement and probability of movingup or down on the plant For P xylostella thefrequency of movement was low and approxi-mately equal numbers of upwards and downwardsmovements were observed For A rapae virtuallyall late instars were observed to move upwards tothe head or wrapper leaves as noted by Harcourt(1963 1966) and Hoy amp Shelton (1987) Transitionprobabilities that reflect these observations werechosen for these two species and are given in Ta-ble 1

The change in state variables due to movementis thus calculated by

s

Nkj(t + ~t) = ~ Nkj(t)pj(t)I(t + ~t) (9)

where

k =k =

I(t + ~t)

~t

13 14 20 for s = 110 11 20 for s = 2 or 3

1 if (t + ~t) = 1 2 3 o otherwise002d

Movement is simulated only once each day andbecause the time step for the model is lfso of a daythe indicator I(t) is used to determine when themovements occur The values of k given above arechosen so that movement is simulated only for olderlarvae which are represented by higher values ofk (k ~ 13 for P xylostella and k ~ 10 for A rapaeor T ni)Model Output The output generated using the

equations described above is a summary of thevalues of state variables and the value of the aux-iliary variable each day for the next 7 d This ispresented on the computer screen depicted in Fig4 The number of large and small larvae of eachspecies on each stratum also can be obtained for aprintout by summing over the appropriate sub-classes in the distributed delay The picture of acabbage plant on the screen gives the user an ap-proximate idea of what the predicted damage onthe cabbage crop would look like

Validation

Methods Validation analysis was performed todemonstrate how well the model predicts data thatwere not used in model design or parameterizationData collected by a commercial field monitoringand pest control advising service were used to com-pare model predictions with observed populationdensities and feeding damage 7 d after the original

1586 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

A rapae

P xylostella

18161412108642o 00 06 12 18 24

557371

1114

92

743

1300

A rapae

10

P xylostella

20

oO0 16 32 48 64

30

10

20

1 ffi

0O0 1 2 2 4 3 6 4 8

000-05 00 05 10 15

1300

11 14

929 T ni T ni

743

55710

3 71

186

0 00- O32 -O16 O00 016 032 O0 O8 16 2 4 3 2

Standardized Residuals Standardized Residualsfor the Head for the Wrapper Leaves

-ogtucQ)=J0Q)-LL

Fig 5 Histograms of standardized cell residuals for comparing predicted numbers with observed averagenumbers of larvae on the cabbage head and wrapper leaves in commercial cabbage fields near Geneva NY

sample Scouts sampled cabbage fields on a weeklybasis using a variable-intensity sampling scheme(Hoy et al 1983) Separate counts of P xylostellalarvae (all instars combined) and A rapae and Tni eggs small (first and second instars) and large(third fourth and fifth instars) larvae were taken

on the head (stratum 1) wrapper (stratum 2) andframe leaves (strata 3-5 combined) and were usedto initialize the model Predictions of numbers ofP xylostella large A rapae and T ni and ac-cumulated feeding on the head and wrapper leaveswere compared with the scouts observations taken

October 1990 HoY ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1587

o [] a [] C D

QOO n~ Q~ n~ 100 1~ t~ 1~ 200Average Damage Rating

Average Damage Rating

Fig 6 Comparison of predicted feeding damagewith average observed damage rating on the heads andwrapper leaves of commercial cabbage crops near Ge-neva NY

the following week Initial spatial distribution with-in the frame and initial age distribution with Arapae and T ni small and large larval populationswere assumed to be uniform for lack of more pre-cise information The scouts observations includedratings of feeding damage on a scale of 0 to 4indicating approximately no damage less than onefeeding hole per leaf one to three feeding holesper leaf 10 defoliation and 40 defoliationrespectively These ratings were compared withpredictions of accumulated area of feeding withscatter plots and correlation analysis

Weather data for model inputs (maximum andminimum temperatures and daily total solar ra-diation) were recorded at the New York State Ag-ricultural Experiment Station in Geneva NY thec1vsest weather station to the commercial fieldsbeing monitored (within 20 km) Data from 34pairs of field samples-each pair taken one weekapart during July August and September in 1983and 1984 under widely varying weather condi-tions-were used for this analysis

Model predictions for number of larvae on thehead and wrapper leaves were compared with ob-servations using standardized cell residuals givenby

observed no larvae - predicted no larvaeVpredicted no larvae

Evaluation of Existing Treatment Guidelines

Because the model predicts numbers of larvaeand feeding damage on different parts of the plantwell model predictions cap be used to evaluatetreatment guidelines currently in use for cabbagepest management In particular the model can beused to explore the relative effects of each pest onthe crop and how useful a static threshold for pestpopulation density will be in predicting a given

as described by Bishop et al (1975) These ap-proximate a standard normal distribution so thecriterion for evaluation is whether or not most ofthe residuals are within 2 SD of the mean (- 2and ~2) because lt=95of the standard normaldistribution falls within this range Observations ofthe feeding damage rating also were plotted againstpredicted accumulated area of feeding and asso-ciated correlation coefficients were calculated

Results and Discussion Most standardized cellresiduals for predicted versus observed counts oflarvae on the head and wrapper leaves were wellwithin the range -2 to +2 (Fig 5) The few largedeviations that were calculated were positive in-dicating that occasionally greater average num-bers of larvae than predicted were observed Theinterplant spatial distribution of each species is ag-gregated (Harcourt 1966) and sample sizes wereoften small (as few as 11 plants) so these occasionallarge positive deviations are not surprising Theseresults indicate that the model predicts number andlocation of larvae well particularly when the lowresolution in the data for initial age and spatialdistribution within the frame and potential sam-pling error in both samples are considered Con-clusions from this analysis must be tempered some-what however by the low population densitiesobserved in these fields Bishop et al (1975) warnthat the approximation of the standardized cellresiduals to the standard normal is poorest whenpredictions in the cells are small Most of the initialpopulation densities and associated predictions weresmall because pest population densities are keptlow by farmers Evaluation of the model underthese conditions is most appropriate however be-cause these are the conditions under which themodel would be used

Predicted area of feeding was correlated withobserved damage rating (Fig 6) Damage ratingincluded assessment of recent feeding as well asolder damage done before the first sample Thiscould explain circumstances in which little feedingdamage was predicted but high damage ratingswere observed Cases where large amounts of feed-ing damage were predicted but observed damagerating was low did not occur Feeding damage isthe most important variable to managers becauseit determines the market value of the crop Thedata indicate that the model can be used to predictthe effects on the cabbage crop of a given pestpopulation under specific conditions

3

(10)

D

o

D

D

o

CC

lJ 8DaD co lJ 0

D D0

2

D

1

D D

C C

D

Wrapper Leaves

r-069

Head

r-053

oo 0

q CD

ggt 206Q)

~0Q)

~ 10fa

E8

40

oo

E8 30Dlc6Q)t 20tJQ)

Ug 1a

1588 ENVIRONMEITAL ENTOMOLOGY Vol 19 no 5

Head Wrapper Leaves

T ni 565134

377089

189045

2020

- Temporatura Avorago plon1CJ DCEC)---0)c A rapaea 1t82Q) a18Q)U 546 7890Q) 273 396sect0 30 30eD

Temperature Avorago pIontDC Temperalure Avomg bullbull p1ont

DC

P xylostella074 178050 11902i 061

20

rompera1ur Avorago plantDC Tempera1ure Averag bullbull p1on1

DC

Fig 7 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves after 7 d atdifferent temperatures and population densities of lepidopteran pests

amount of damage on the marketable parts of thecrop

Methods Response surfaces of predicted area offeeding on the head and wrapper leaves to tem-perature and population density of each pest weregenerated with the model A standard initial in-traplant spatial distribution typical of distributionsobserved in cabbage fields was chosen for eachspecies as follows P xylostella 005 01 03 03and 025 A rapae 0 015 04 03 and 015 Tni 0 01 02 04 and 03 of the average numberper plant on the head wrapper leaves upper framemidframe and lower frame respectively For Pxylostella the larval ages were uniformly distrib-uted among the 20 subclasses in the distributeddelay For A rapae and T ni the larvae wereinitialized into the first 10 subclasses simulatingfirst second and third instars For each of 10 pop-ulation densities ranging from well below to well

above the action threshold currently used in NewYork (Shelton et al 1982) feeding was predictedat six constant temperatures

Additional response surfaces were generated offeeding area on the head and wrapper leaves pre-dicted at different temperatures and initial age dis-tributions for a given population density of eachspecies Given the initial spatial distribution de-scribed above and an average temperature be-tween 20 and 25degC the first set of response surfaceswas used to select a population density predictedto cause damage most farmers would consider un-acceptable This density twice the currently rec-ommended action threshold was 1 larvaplant forT ni 15 larvaeplant for A rapae and 10 larvaeplant for P xylostella Different age distributionswere generated by dividing the population densi-ties chosen above evenly among larval maturitysubclasses 1 through 6 then 2 through 7 etc up

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1589

Head Wrapper Leaves

1n

519

260

T1i

TemperatureDC

10

Youngest Age ProSQnt

10

10

YOungG81 AGe PrQsan

A rapal2333

557

78

10

Youngest Ago PreSGnt

TemperatureDC

142 P xylostllia

098

053

0009

Youngesl Ago PresentTemperature

DCTemperalUIlliDc

Fig 8 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves in 7 d due todifferent temperatures and age distributions at a given population density of three lepidopteran pests of cabbagePopulation densities were lplant for T ni loSplant for A rapae 10plant for P xylostella

to 10 through 15 Model predictions were gener-ated at each of these age distributions for each ofthe 6 constant temperatures used above

Results and Discussion Response surfaces gen-erated with the model predict that A rapae con-tributes most to feeding damage on the head andwrapper leaves (Fig 7) Although total consump-tion by A rapae larvae is less than that of T ni(Harcourt et al 1955) the amount consumed onthese economically important strata is greater be-cause of the difference in intra plant spatial dynam-ics of the two species In Fig 7 the model predictsthat for a given constant temperature and giveninitial age and spatial distributions feeding on thehead and wrapper leaves increases linearly withpopulation density for each species Systems thatweight the counts of each species according to ex-pected feeding damage and base the action thresh-old on the weighted counts have been proposed

(Harcourt et al 1955 Shelton et al 1982) but thesedid not consider the spatial dynamics of the pestsThus one potential use of our model is to designa new rating scale to weight the population densityof each species according to expected feeding dam-age considering the spatial dynamics of eachspecies This rating scale however would also haveto account for temperature effects which cangreatly affect predicted feeding

At temperatures lt15DC very little feeding ispredicted on the head and wrapper leaves by eachspecies at any population density (Fig 7) Increas-ing temperatures have a nonlinear effect on pre-dicted feeding by each species For P xylostellaand A rapae the increase in predicted feedingrate may be primarily due to increased develop-ment and feeding rates For T ni however in-creased development and feeding rates at highertemperatures may be offset to some extent by higher

1590 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

probabilities of moving away from the head andwrapper leaves towards the lower leaves (Hoy etal 1989)

For a given population density predicted feed-ing on the marketable parts of the plant variedwidely with age distribution again interacting withtemperature (Fig 8) The results indicate that thedamage caused by a given population density afixed economic threshold for example will varyconsiderably with temperature age structure of thepopulation and species composition Againweighting systems have been described that con-sider larval age (Andaloro et al 1983a) but notwith the resolution that Fig 8 implies is necessaryand they do not include the interaction with tem-perature

Considering the profound effects of tempera-ture age distribution and species-specific spatialdynamics on the predicted area of feeding on eco-nomically important parts of the plant a staticeconomic threshold does not seem to be appropri-ate Rather feeding should be predicted for specificpopulation densities age distributions and spatialdistributions of the three species as well as weatherforecasts and management strategies should be de-signed accordingly The model described here couldbe used to make those predictions either by cal-culating a new species weighting system each dayof the growing season to be used with a fixed actionthreshold or simply by making the required pre-dictions on a case-by-case basis

Sensitivity Analysis

Two goals were addressed in the sensitivity anal-ysis First individual model parameters were evalmiddotuated as potential causes of inaccurate predictionsBy examining the change in model output after achange in the individual parameters parametersthat affect the output most can be identified Sec-ond by examining the effects of changes in dif-ferent parameters in combination insight can begained into the effects of the different processesbeing simulated and their interactions on the out-put variables of interest

Methods Model predictions were evaluated af-ter changing each parameter and input suppliedby the user by +10 and -10 of its valueChanges were made one parameter at a time witha standard set of initial conditions Standard initialpest population densities were a mean of 1 larvalplant of each species on each stratum in the secondinstar for A rapae and T ni and uniformly dis-tributed among the 20 age subclasses for P xylo-stella The analysis was performed at each of threetemperature regimes typical summer weather forwestern New York (maximum temperature 267degCminimum temperature 155degC 8 h sunshine eachday) hot and sunny weather (maximum temper-ature 322degC minimum temperature 211oC 12h sunshine each day) and cool and cloudy weather

(maximum temperature 183degC minimum tem-perature 10degC 2 h sunshine)

Constants were changed by adding or subtract-ing 10 of their value Input weather variableswere changed by adding or subtracting 10 of thevalue of each pays forecasted maximum and min-imum temperature and hours of sunshine Age atwhich larvae begin to move was shifted plus orminus two subclasses to effect a 10 change Initialage distribution for A rapae and T ni was alsoshifted 10 by shifting the subclasses initialized byplus or minus two Initial age distribution for Pxylostella is assumed to be uniform so this was notchanged For each species the initial intraplantdistribution was altered by shifting 10 of eachage group on each stratum except the lower frameleaves down one stratum or shifting 10 of eachage group on each stratum except the head upone stratum (eg a downward shift of an averageof one larva on each stratum would result in anaverage of 09 1 1 1 and 11 larvae on the headwrapper upper frame midframe and lower frameleaves respectively) Transition probabilities for Arapae and P xylostella were changed by a similarmethod shifting 10 of the probability of movingto each stratum except the lower frame leaves tothe next lower stratum or shifting 10 of the prob-ability of moving to each stratum except the headto the next stratum up (eg a downward shift ina transition probability vector of 09 01000 resultsin a vector of 081 018 001 0 0) Sensitivity tochanges in transition probabilities for T ni wereexamined by changing the Beta pdf shape param-eters that govern transition probabilities for thisspecies by + 10 and -10 of their value Theeffects of each of these changes were examined bycalculating the percentage of change in number oflarvae of each species and the percentage of changein accumulated area of feeding on the head andwrapper leaves

To examine interactions between different pro-cesses and their effects on model output we per-formed two analyses in which variables suspectedof interacting were varied in all combinations theequivalent of a factorial design with three levelsof each factor given by +5 -5 and 0 Be-cause development and feeding rates are temper-ature-dependent and govern the amount of feedingaccumulated interactions between temperaturefeeding rates and development rates might affectaccumulated area of feeding Three levels of tem-perature were generated starting with the typicalsummer weather regime described above and add-ing 5 -5 or 0 of the daily maximum andminimum At each temperature level develop-ment rate for each species was varied by +5-5 and 0 from its value and at each of thesedevelopment rates for each species feeding ratewas changed by +5 -5 and 0 of its valueThe effects of these parameter changes on the pre-dicted area of feeding on the head and wrapperleaves were calculated

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1591

Table 2 Output from a model to predict lepidopteranfeeding damage on cabbage at three temperature regimeswith a standard set of inputs and no change in the param-eters Changes in output during the sensitivity analysis (Fig9-12) are compared with these standards

StratumPopulation density (avg noplant) Feeding

P xylostella A rapae Tni cm2

High temperaturesHead 0252 2118 0095 12764Wrapper 0390 2594 0662 21716

Moderate temperaturesHead 0423 1957 0299 6805Wrapper 0578 2524 1001 9667

Low temperaturesHead 0635 1296 0829 1945Wrapper 0834 1651 0886 2348

A similar analysis of interacting processes wasperformed for spatial effects Initial distributionand transition probabilities could be expected tointeract in their effects on spatial distribution oflarvae and feeding damage For each species theinitial distribution was treated by (a) shifting 10of each age group on each stratum (except thelower frame leaves) down one stratum (b) shifting10of each age group on each stratum (except thehead) up one stratum and (c) leaving the initialdistribution unchanged At each of these shifts ininitial distribution for each species the transitionprobabilities for that species were changed as de-

scribed above Shifting 10 of the probability ofmoving to each stratum except the lower frameleaves to the next lower stratum resulted in higherprobabilities of downward movement shifting 10of the probability of moving to each stratum exceptthe head to the next stratum up resulted in higherprobability of upward movement

Results and Discussion Standard results for highmoderate and low temperature regimes withoutchanging any of the parameters or input variablesare given in Table 2 and the effects of changingeach parameter and input variable on selected out-put variables are displayed in Fig 9-12 for themoderate temperature regime We begin the anal-ysisby examining sensitivity of the model to changesin the parameters at moderate temperatures andfollow with the differences in model sensitivity seenunder high and low temperature regimes

At moderate temperatures numbers of larvae ofeach species on the head and wrapper leaves wereleast sensitive to initial spatial distribution of larvaedispersion in development time and hours of sun-shine (Fig 9) Change in the initial intraplant dis-tribution of larvae may be compensated for bymovement of larvae within a short time after thebeginning of the simulation Dispersion in devel-opment time for these species was low in the lab-oratory development studies resulting in a small

Svalue of -D for each species A 10 change in

EL~these small values does not change the dispersion

o Effect 01 +10 changebull Effect 01 -10 change on larvae on the head alief 7 days

Inldal dlsbibudonInitial ages

Age 01 first movementTransition probabilities

Dispersion In developmenlgl

DEL g2C

Hours 01 sunshineTemperalure

-20 -10 0 10

P xylostella20 30 -20 -10 0 10 20

A rapae

oT nl

100

on larvae on the wrapper leaves alter 7 days

10-10

Initial distributionInitial ages

Age 01 firsl movementTransition probabilities

Dispersion in developmentgl

DEL g2C

Hours of sunshineTemperature

-20 o 10 -20 -10 0 -10 0P xylostella A rapas T nI

Fig 9 Percentage of change in predicted number of P xylostella A rapae and T nt larvae on the head andwrapper leavesafter changing model parameters + and -10

1592 ENVIRONME~TAL ENTOMOLOGY Vol 19 no 5

Fig 10 Percentage of change in number of T nilarvae predicted on the head and wrapper leaves aftera + or - 1 0 change in parameters governing their tran-sition probabilities on the cabbage plant

greatly Hours of sunshine influence temperaturein each stratum but apparently not enough to causelarge changes in rate functions

Changes in temperature initial age distributionage at which larvae begin to move between strataand transition probabilities had the greatest effectson predicted number of larvae on the head or wrap-per leaves (Fig 9) These are all linked to spatialdynamics since both temperature and initial agedistribution affect the time at which larvae beginto move between strata Changes in parametersgoverning T ni transition probabilities were anexception causing only moderate or small changesin output (Fig 10) Changes in development rateparameters had large effects only for P xylostellaon the head and wrapper leaves and for T ni onthe head

Predictions of accumulated feeding on the headand wrapper leaves were generally less sensitive tochanges in parameters than were predictions ofnumbers of larvae on these strata (Fig 11 and 12)Because the predictions of accumulated area offeeding are most important to the farmer the ro-bustness of the model in predicting feeding sug-gests that it could be a useful management toolThe greatest changes in accumulated area of feed-ing were caused by changing parameters governingA rapae development or feeding particularly ini-tial age distribution Fortunately development ratesfor all three species considered here have been wellstudied and studies done at widely different timesand locations with different food sources suggestthat average development rate at a given temper-ature is fairly constant (Hardy 1938 Richards 1940Given 1944 Miner 1947 Harcourt et al 1955Shorey et al 1962 Jackson et al 1969 Toba et al

1973 Boldt et al 1975 Butler et al 1975 Smithamp Smilowitz 1976 Chen amp Su 1978 1982 Tatchell1981 Yamada amp Kawasaki 1983 Theunissen et al1985) Changes in forecast temperatures cause thenext largest change in accumulated feeding prob-ably because of their effects on development andfeeding rates Parameters governing spatial effectshad smaller effects on accumulated feeding par-ticularly when compared with their effects on pre-dicted number of larvae on different parts of theplant

Under the low-temperature regime predictionsof numbers of larvae on the head and wrapperleaves were more sensitive to parameters affectingdevelopment than to parameters affecting spatialdynamics At low temperatures larvae take longerto reach the age when movement starts and prob-ability of movement by T ni to the head andwrapper leaves is lower Furthermore fewer smalllarvae become large larvae at low temperatures sototal numbers of large larvae on all strata are re-duced At moderate and high temperatures pre-dictions of numbers of larvae on the head andwrapper leaves were more sensitive to changes inparameters affecting spatial dynamics

Effects of changing forecast temperatures onpredictions of accumulated feeding were muchgreater when the forecast temperatures were lowand less when the forecast temperatures were highthan at moderate temperatures Changing devel-opment rate parameters had a greater effect onaccumulated feeding at low temperatures butchanging feeding rate parameters had a greatereffect at high temperatures than at moderate tem-peratures Accumulated feeding was less sensitiveto changes in transition probabilities at low tem-peratures and more sensitive to changes in tran-sition probabilities at high temperatures than atmoderate temperatures

In general interactions between temperaturedevelopment and feeding rates as well as param-eters governing spatial effects were not evidentTypically the effect of changes in each of theseparameters was similar regardless of the value ofthe other parameters One interaction did occurWhen temperature was increased a negativechange in T ni development rate resulted in lesspredicted feeding on the head than when no changein T ni development rate was made In all othercases negative change in development rates re-sulted in higher predicted feeding on the head thanwhen development rates were not changed Re-gardless 5 changes in development rates for Tni resulted in lt3 differences in feeding on thehead so the effects of this interaction are not ofgreat importance Thus this analysis reinforced thesingle parameter analysis Feeding rates themselveswere changed in this analysis rather than the pa-rameters that govern them and accumulated feed-ing on the head and wrapper leaves was still moresensitive to changes in development rate and tem-perature

5o

middot5 0

Feeding on Heed

-5Feeding on Wrapper Leaves

o 10

Larvae on Head

middot10

b5b4b3b2bl858483a281

middot20l( Change in

-20 middot10 0 10 Change in Larvae on Wrapper leaves

II2l

~toa0gtatoten

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

SDElA rapae g2

g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

1586 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

A rapae

P xylostella

18161412108642o 00 06 12 18 24

557371

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Standardized Residuals Standardized Residualsfor the Head for the Wrapper Leaves

-ogtucQ)=J0Q)-LL

Fig 5 Histograms of standardized cell residuals for comparing predicted numbers with observed averagenumbers of larvae on the cabbage head and wrapper leaves in commercial cabbage fields near Geneva NY

sample Scouts sampled cabbage fields on a weeklybasis using a variable-intensity sampling scheme(Hoy et al 1983) Separate counts of P xylostellalarvae (all instars combined) and A rapae and Tni eggs small (first and second instars) and large(third fourth and fifth instars) larvae were taken

on the head (stratum 1) wrapper (stratum 2) andframe leaves (strata 3-5 combined) and were usedto initialize the model Predictions of numbers ofP xylostella large A rapae and T ni and ac-cumulated feeding on the head and wrapper leaveswere compared with the scouts observations taken

October 1990 HoY ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1587

o [] a [] C D

QOO n~ Q~ n~ 100 1~ t~ 1~ 200Average Damage Rating

Average Damage Rating

Fig 6 Comparison of predicted feeding damagewith average observed damage rating on the heads andwrapper leaves of commercial cabbage crops near Ge-neva NY

the following week Initial spatial distribution with-in the frame and initial age distribution with Arapae and T ni small and large larval populationswere assumed to be uniform for lack of more pre-cise information The scouts observations includedratings of feeding damage on a scale of 0 to 4indicating approximately no damage less than onefeeding hole per leaf one to three feeding holesper leaf 10 defoliation and 40 defoliationrespectively These ratings were compared withpredictions of accumulated area of feeding withscatter plots and correlation analysis

Weather data for model inputs (maximum andminimum temperatures and daily total solar ra-diation) were recorded at the New York State Ag-ricultural Experiment Station in Geneva NY thec1vsest weather station to the commercial fieldsbeing monitored (within 20 km) Data from 34pairs of field samples-each pair taken one weekapart during July August and September in 1983and 1984 under widely varying weather condi-tions-were used for this analysis

Model predictions for number of larvae on thehead and wrapper leaves were compared with ob-servations using standardized cell residuals givenby

observed no larvae - predicted no larvaeVpredicted no larvae

Evaluation of Existing Treatment Guidelines

Because the model predicts numbers of larvaeand feeding damage on different parts of the plantwell model predictions cap be used to evaluatetreatment guidelines currently in use for cabbagepest management In particular the model can beused to explore the relative effects of each pest onthe crop and how useful a static threshold for pestpopulation density will be in predicting a given

as described by Bishop et al (1975) These ap-proximate a standard normal distribution so thecriterion for evaluation is whether or not most ofthe residuals are within 2 SD of the mean (- 2and ~2) because lt=95of the standard normaldistribution falls within this range Observations ofthe feeding damage rating also were plotted againstpredicted accumulated area of feeding and asso-ciated correlation coefficients were calculated

Results and Discussion Most standardized cellresiduals for predicted versus observed counts oflarvae on the head and wrapper leaves were wellwithin the range -2 to +2 (Fig 5) The few largedeviations that were calculated were positive in-dicating that occasionally greater average num-bers of larvae than predicted were observed Theinterplant spatial distribution of each species is ag-gregated (Harcourt 1966) and sample sizes wereoften small (as few as 11 plants) so these occasionallarge positive deviations are not surprising Theseresults indicate that the model predicts number andlocation of larvae well particularly when the lowresolution in the data for initial age and spatialdistribution within the frame and potential sam-pling error in both samples are considered Con-clusions from this analysis must be tempered some-what however by the low population densitiesobserved in these fields Bishop et al (1975) warnthat the approximation of the standardized cellresiduals to the standard normal is poorest whenpredictions in the cells are small Most of the initialpopulation densities and associated predictions weresmall because pest population densities are keptlow by farmers Evaluation of the model underthese conditions is most appropriate however be-cause these are the conditions under which themodel would be used

Predicted area of feeding was correlated withobserved damage rating (Fig 6) Damage ratingincluded assessment of recent feeding as well asolder damage done before the first sample Thiscould explain circumstances in which little feedingdamage was predicted but high damage ratingswere observed Cases where large amounts of feed-ing damage were predicted but observed damagerating was low did not occur Feeding damage isthe most important variable to managers becauseit determines the market value of the crop Thedata indicate that the model can be used to predictthe effects on the cabbage crop of a given pestpopulation under specific conditions

3

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1588 ENVIRONMEITAL ENTOMOLOGY Vol 19 no 5

Head Wrapper Leaves

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- Temporatura Avorago plon1CJ DCEC)---0)c A rapaea 1t82Q) a18Q)U 546 7890Q) 273 396sect0 30 30eD

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DC

P xylostella074 178050 11902i 061

20

rompera1ur Avorago plantDC Tempera1ure Averag bullbull p1on1

DC

Fig 7 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves after 7 d atdifferent temperatures and population densities of lepidopteran pests

amount of damage on the marketable parts of thecrop

Methods Response surfaces of predicted area offeeding on the head and wrapper leaves to tem-perature and population density of each pest weregenerated with the model A standard initial in-traplant spatial distribution typical of distributionsobserved in cabbage fields was chosen for eachspecies as follows P xylostella 005 01 03 03and 025 A rapae 0 015 04 03 and 015 Tni 0 01 02 04 and 03 of the average numberper plant on the head wrapper leaves upper framemidframe and lower frame respectively For Pxylostella the larval ages were uniformly distrib-uted among the 20 subclasses in the distributeddelay For A rapae and T ni the larvae wereinitialized into the first 10 subclasses simulatingfirst second and third instars For each of 10 pop-ulation densities ranging from well below to well

above the action threshold currently used in NewYork (Shelton et al 1982) feeding was predictedat six constant temperatures

Additional response surfaces were generated offeeding area on the head and wrapper leaves pre-dicted at different temperatures and initial age dis-tributions for a given population density of eachspecies Given the initial spatial distribution de-scribed above and an average temperature be-tween 20 and 25degC the first set of response surfaceswas used to select a population density predictedto cause damage most farmers would consider un-acceptable This density twice the currently rec-ommended action threshold was 1 larvaplant forT ni 15 larvaeplant for A rapae and 10 larvaeplant for P xylostella Different age distributionswere generated by dividing the population densi-ties chosen above evenly among larval maturitysubclasses 1 through 6 then 2 through 7 etc up

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1589

Head Wrapper Leaves

1n

519

260

T1i

TemperatureDC

10

Youngest Age ProSQnt

10

10

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557

78

10

Youngest Ago PreSGnt

TemperatureDC

142 P xylostllia

098

053

0009

Youngesl Ago PresentTemperature

DCTemperalUIlliDc

Fig 8 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves in 7 d due todifferent temperatures and age distributions at a given population density of three lepidopteran pests of cabbagePopulation densities were lplant for T ni loSplant for A rapae 10plant for P xylostella

to 10 through 15 Model predictions were gener-ated at each of these age distributions for each ofthe 6 constant temperatures used above

Results and Discussion Response surfaces gen-erated with the model predict that A rapae con-tributes most to feeding damage on the head andwrapper leaves (Fig 7) Although total consump-tion by A rapae larvae is less than that of T ni(Harcourt et al 1955) the amount consumed onthese economically important strata is greater be-cause of the difference in intra plant spatial dynam-ics of the two species In Fig 7 the model predictsthat for a given constant temperature and giveninitial age and spatial distributions feeding on thehead and wrapper leaves increases linearly withpopulation density for each species Systems thatweight the counts of each species according to ex-pected feeding damage and base the action thresh-old on the weighted counts have been proposed

(Harcourt et al 1955 Shelton et al 1982) but thesedid not consider the spatial dynamics of the pestsThus one potential use of our model is to designa new rating scale to weight the population densityof each species according to expected feeding dam-age considering the spatial dynamics of eachspecies This rating scale however would also haveto account for temperature effects which cangreatly affect predicted feeding

At temperatures lt15DC very little feeding ispredicted on the head and wrapper leaves by eachspecies at any population density (Fig 7) Increas-ing temperatures have a nonlinear effect on pre-dicted feeding by each species For P xylostellaand A rapae the increase in predicted feedingrate may be primarily due to increased develop-ment and feeding rates For T ni however in-creased development and feeding rates at highertemperatures may be offset to some extent by higher

1590 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

probabilities of moving away from the head andwrapper leaves towards the lower leaves (Hoy etal 1989)

For a given population density predicted feed-ing on the marketable parts of the plant variedwidely with age distribution again interacting withtemperature (Fig 8) The results indicate that thedamage caused by a given population density afixed economic threshold for example will varyconsiderably with temperature age structure of thepopulation and species composition Againweighting systems have been described that con-sider larval age (Andaloro et al 1983a) but notwith the resolution that Fig 8 implies is necessaryand they do not include the interaction with tem-perature

Considering the profound effects of tempera-ture age distribution and species-specific spatialdynamics on the predicted area of feeding on eco-nomically important parts of the plant a staticeconomic threshold does not seem to be appropri-ate Rather feeding should be predicted for specificpopulation densities age distributions and spatialdistributions of the three species as well as weatherforecasts and management strategies should be de-signed accordingly The model described here couldbe used to make those predictions either by cal-culating a new species weighting system each dayof the growing season to be used with a fixed actionthreshold or simply by making the required pre-dictions on a case-by-case basis

Sensitivity Analysis

Two goals were addressed in the sensitivity anal-ysis First individual model parameters were evalmiddotuated as potential causes of inaccurate predictionsBy examining the change in model output after achange in the individual parameters parametersthat affect the output most can be identified Sec-ond by examining the effects of changes in dif-ferent parameters in combination insight can begained into the effects of the different processesbeing simulated and their interactions on the out-put variables of interest

Methods Model predictions were evaluated af-ter changing each parameter and input suppliedby the user by +10 and -10 of its valueChanges were made one parameter at a time witha standard set of initial conditions Standard initialpest population densities were a mean of 1 larvalplant of each species on each stratum in the secondinstar for A rapae and T ni and uniformly dis-tributed among the 20 age subclasses for P xylo-stella The analysis was performed at each of threetemperature regimes typical summer weather forwestern New York (maximum temperature 267degCminimum temperature 155degC 8 h sunshine eachday) hot and sunny weather (maximum temper-ature 322degC minimum temperature 211oC 12h sunshine each day) and cool and cloudy weather

(maximum temperature 183degC minimum tem-perature 10degC 2 h sunshine)

Constants were changed by adding or subtract-ing 10 of their value Input weather variableswere changed by adding or subtracting 10 of thevalue of each pays forecasted maximum and min-imum temperature and hours of sunshine Age atwhich larvae begin to move was shifted plus orminus two subclasses to effect a 10 change Initialage distribution for A rapae and T ni was alsoshifted 10 by shifting the subclasses initialized byplus or minus two Initial age distribution for Pxylostella is assumed to be uniform so this was notchanged For each species the initial intraplantdistribution was altered by shifting 10 of eachage group on each stratum except the lower frameleaves down one stratum or shifting 10 of eachage group on each stratum except the head upone stratum (eg a downward shift of an averageof one larva on each stratum would result in anaverage of 09 1 1 1 and 11 larvae on the headwrapper upper frame midframe and lower frameleaves respectively) Transition probabilities for Arapae and P xylostella were changed by a similarmethod shifting 10 of the probability of movingto each stratum except the lower frame leaves tothe next lower stratum or shifting 10 of the prob-ability of moving to each stratum except the headto the next stratum up (eg a downward shift ina transition probability vector of 09 01000 resultsin a vector of 081 018 001 0 0) Sensitivity tochanges in transition probabilities for T ni wereexamined by changing the Beta pdf shape param-eters that govern transition probabilities for thisspecies by + 10 and -10 of their value Theeffects of each of these changes were examined bycalculating the percentage of change in number oflarvae of each species and the percentage of changein accumulated area of feeding on the head andwrapper leaves

To examine interactions between different pro-cesses and their effects on model output we per-formed two analyses in which variables suspectedof interacting were varied in all combinations theequivalent of a factorial design with three levelsof each factor given by +5 -5 and 0 Be-cause development and feeding rates are temper-ature-dependent and govern the amount of feedingaccumulated interactions between temperaturefeeding rates and development rates might affectaccumulated area of feeding Three levels of tem-perature were generated starting with the typicalsummer weather regime described above and add-ing 5 -5 or 0 of the daily maximum andminimum At each temperature level develop-ment rate for each species was varied by +5-5 and 0 from its value and at each of thesedevelopment rates for each species feeding ratewas changed by +5 -5 and 0 of its valueThe effects of these parameter changes on the pre-dicted area of feeding on the head and wrapperleaves were calculated

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1591

Table 2 Output from a model to predict lepidopteranfeeding damage on cabbage at three temperature regimeswith a standard set of inputs and no change in the param-eters Changes in output during the sensitivity analysis (Fig9-12) are compared with these standards

StratumPopulation density (avg noplant) Feeding

P xylostella A rapae Tni cm2

High temperaturesHead 0252 2118 0095 12764Wrapper 0390 2594 0662 21716

Moderate temperaturesHead 0423 1957 0299 6805Wrapper 0578 2524 1001 9667

Low temperaturesHead 0635 1296 0829 1945Wrapper 0834 1651 0886 2348

A similar analysis of interacting processes wasperformed for spatial effects Initial distributionand transition probabilities could be expected tointeract in their effects on spatial distribution oflarvae and feeding damage For each species theinitial distribution was treated by (a) shifting 10of each age group on each stratum (except thelower frame leaves) down one stratum (b) shifting10of each age group on each stratum (except thehead) up one stratum and (c) leaving the initialdistribution unchanged At each of these shifts ininitial distribution for each species the transitionprobabilities for that species were changed as de-

scribed above Shifting 10 of the probability ofmoving to each stratum except the lower frameleaves to the next lower stratum resulted in higherprobabilities of downward movement shifting 10of the probability of moving to each stratum exceptthe head to the next stratum up resulted in higherprobability of upward movement

Results and Discussion Standard results for highmoderate and low temperature regimes withoutchanging any of the parameters or input variablesare given in Table 2 and the effects of changingeach parameter and input variable on selected out-put variables are displayed in Fig 9-12 for themoderate temperature regime We begin the anal-ysisby examining sensitivity of the model to changesin the parameters at moderate temperatures andfollow with the differences in model sensitivity seenunder high and low temperature regimes

At moderate temperatures numbers of larvae ofeach species on the head and wrapper leaves wereleast sensitive to initial spatial distribution of larvaedispersion in development time and hours of sun-shine (Fig 9) Change in the initial intraplant dis-tribution of larvae may be compensated for bymovement of larvae within a short time after thebeginning of the simulation Dispersion in devel-opment time for these species was low in the lab-oratory development studies resulting in a small

Svalue of -D for each species A 10 change in

EL~these small values does not change the dispersion

o Effect 01 +10 changebull Effect 01 -10 change on larvae on the head alief 7 days

Inldal dlsbibudonInitial ages

Age 01 first movementTransition probabilities

Dispersion In developmenlgl

DEL g2C

Hours 01 sunshineTemperalure

-20 -10 0 10

P xylostella20 30 -20 -10 0 10 20

A rapae

oT nl

100

on larvae on the wrapper leaves alter 7 days

10-10

Initial distributionInitial ages

Age 01 firsl movementTransition probabilities

Dispersion in developmentgl

DEL g2C

Hours of sunshineTemperature

-20 o 10 -20 -10 0 -10 0P xylostella A rapas T nI

Fig 9 Percentage of change in predicted number of P xylostella A rapae and T nt larvae on the head andwrapper leavesafter changing model parameters + and -10

1592 ENVIRONME~TAL ENTOMOLOGY Vol 19 no 5

Fig 10 Percentage of change in number of T nilarvae predicted on the head and wrapper leaves aftera + or - 1 0 change in parameters governing their tran-sition probabilities on the cabbage plant

greatly Hours of sunshine influence temperaturein each stratum but apparently not enough to causelarge changes in rate functions

Changes in temperature initial age distributionage at which larvae begin to move between strataand transition probabilities had the greatest effectson predicted number of larvae on the head or wrap-per leaves (Fig 9) These are all linked to spatialdynamics since both temperature and initial agedistribution affect the time at which larvae beginto move between strata Changes in parametersgoverning T ni transition probabilities were anexception causing only moderate or small changesin output (Fig 10) Changes in development rateparameters had large effects only for P xylostellaon the head and wrapper leaves and for T ni onthe head

Predictions of accumulated feeding on the headand wrapper leaves were generally less sensitive tochanges in parameters than were predictions ofnumbers of larvae on these strata (Fig 11 and 12)Because the predictions of accumulated area offeeding are most important to the farmer the ro-bustness of the model in predicting feeding sug-gests that it could be a useful management toolThe greatest changes in accumulated area of feed-ing were caused by changing parameters governingA rapae development or feeding particularly ini-tial age distribution Fortunately development ratesfor all three species considered here have been wellstudied and studies done at widely different timesand locations with different food sources suggestthat average development rate at a given temper-ature is fairly constant (Hardy 1938 Richards 1940Given 1944 Miner 1947 Harcourt et al 1955Shorey et al 1962 Jackson et al 1969 Toba et al

1973 Boldt et al 1975 Butler et al 1975 Smithamp Smilowitz 1976 Chen amp Su 1978 1982 Tatchell1981 Yamada amp Kawasaki 1983 Theunissen et al1985) Changes in forecast temperatures cause thenext largest change in accumulated feeding prob-ably because of their effects on development andfeeding rates Parameters governing spatial effectshad smaller effects on accumulated feeding par-ticularly when compared with their effects on pre-dicted number of larvae on different parts of theplant

Under the low-temperature regime predictionsof numbers of larvae on the head and wrapperleaves were more sensitive to parameters affectingdevelopment than to parameters affecting spatialdynamics At low temperatures larvae take longerto reach the age when movement starts and prob-ability of movement by T ni to the head andwrapper leaves is lower Furthermore fewer smalllarvae become large larvae at low temperatures sototal numbers of large larvae on all strata are re-duced At moderate and high temperatures pre-dictions of numbers of larvae on the head andwrapper leaves were more sensitive to changes inparameters affecting spatial dynamics

Effects of changing forecast temperatures onpredictions of accumulated feeding were muchgreater when the forecast temperatures were lowand less when the forecast temperatures were highthan at moderate temperatures Changing devel-opment rate parameters had a greater effect onaccumulated feeding at low temperatures butchanging feeding rate parameters had a greatereffect at high temperatures than at moderate tem-peratures Accumulated feeding was less sensitiveto changes in transition probabilities at low tem-peratures and more sensitive to changes in tran-sition probabilities at high temperatures than atmoderate temperatures

In general interactions between temperaturedevelopment and feeding rates as well as param-eters governing spatial effects were not evidentTypically the effect of changes in each of theseparameters was similar regardless of the value ofthe other parameters One interaction did occurWhen temperature was increased a negativechange in T ni development rate resulted in lesspredicted feeding on the head than when no changein T ni development rate was made In all othercases negative change in development rates re-sulted in higher predicted feeding on the head thanwhen development rates were not changed Re-gardless 5 changes in development rates for Tni resulted in lt3 differences in feeding on thehead so the effects of this interaction are not ofgreat importance Thus this analysis reinforced thesingle parameter analysis Feeding rates themselveswere changed in this analysis rather than the pa-rameters that govern them and accumulated feed-ing on the head and wrapper leaves was still moresensitive to changes in development rate and tem-perature

5o

middot5 0

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-5Feeding on Wrapper Leaves

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October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

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g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

October 1990 HoY ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1587

o [] a [] C D

QOO n~ Q~ n~ 100 1~ t~ 1~ 200Average Damage Rating

Average Damage Rating

Fig 6 Comparison of predicted feeding damagewith average observed damage rating on the heads andwrapper leaves of commercial cabbage crops near Ge-neva NY

the following week Initial spatial distribution with-in the frame and initial age distribution with Arapae and T ni small and large larval populationswere assumed to be uniform for lack of more pre-cise information The scouts observations includedratings of feeding damage on a scale of 0 to 4indicating approximately no damage less than onefeeding hole per leaf one to three feeding holesper leaf 10 defoliation and 40 defoliationrespectively These ratings were compared withpredictions of accumulated area of feeding withscatter plots and correlation analysis

Weather data for model inputs (maximum andminimum temperatures and daily total solar ra-diation) were recorded at the New York State Ag-ricultural Experiment Station in Geneva NY thec1vsest weather station to the commercial fieldsbeing monitored (within 20 km) Data from 34pairs of field samples-each pair taken one weekapart during July August and September in 1983and 1984 under widely varying weather condi-tions-were used for this analysis

Model predictions for number of larvae on thehead and wrapper leaves were compared with ob-servations using standardized cell residuals givenby

observed no larvae - predicted no larvaeVpredicted no larvae

Evaluation of Existing Treatment Guidelines

Because the model predicts numbers of larvaeand feeding damage on different parts of the plantwell model predictions cap be used to evaluatetreatment guidelines currently in use for cabbagepest management In particular the model can beused to explore the relative effects of each pest onthe crop and how useful a static threshold for pestpopulation density will be in predicting a given

as described by Bishop et al (1975) These ap-proximate a standard normal distribution so thecriterion for evaluation is whether or not most ofthe residuals are within 2 SD of the mean (- 2and ~2) because lt=95of the standard normaldistribution falls within this range Observations ofthe feeding damage rating also were plotted againstpredicted accumulated area of feeding and asso-ciated correlation coefficients were calculated

Results and Discussion Most standardized cellresiduals for predicted versus observed counts oflarvae on the head and wrapper leaves were wellwithin the range -2 to +2 (Fig 5) The few largedeviations that were calculated were positive in-dicating that occasionally greater average num-bers of larvae than predicted were observed Theinterplant spatial distribution of each species is ag-gregated (Harcourt 1966) and sample sizes wereoften small (as few as 11 plants) so these occasionallarge positive deviations are not surprising Theseresults indicate that the model predicts number andlocation of larvae well particularly when the lowresolution in the data for initial age and spatialdistribution within the frame and potential sam-pling error in both samples are considered Con-clusions from this analysis must be tempered some-what however by the low population densitiesobserved in these fields Bishop et al (1975) warnthat the approximation of the standardized cellresiduals to the standard normal is poorest whenpredictions in the cells are small Most of the initialpopulation densities and associated predictions weresmall because pest population densities are keptlow by farmers Evaluation of the model underthese conditions is most appropriate however be-cause these are the conditions under which themodel would be used

Predicted area of feeding was correlated withobserved damage rating (Fig 6) Damage ratingincluded assessment of recent feeding as well asolder damage done before the first sample Thiscould explain circumstances in which little feedingdamage was predicted but high damage ratingswere observed Cases where large amounts of feed-ing damage were predicted but observed damagerating was low did not occur Feeding damage isthe most important variable to managers becauseit determines the market value of the crop Thedata indicate that the model can be used to predictthe effects on the cabbage crop of a given pestpopulation under specific conditions

3

(10)

D

o

D

D

o

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1588 ENVIRONMEITAL ENTOMOLOGY Vol 19 no 5

Head Wrapper Leaves

T ni 565134

377089

189045

2020

- Temporatura Avorago plon1CJ DCEC)---0)c A rapaea 1t82Q) a18Q)U 546 7890Q) 273 396sect0 30 30eD

Temperature Avorago pIontDC Temperalure Avomg bullbull p1ont

DC

P xylostella074 178050 11902i 061

20

rompera1ur Avorago plantDC Tempera1ure Averag bullbull p1on1

DC

Fig 7 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves after 7 d atdifferent temperatures and population densities of lepidopteran pests

amount of damage on the marketable parts of thecrop

Methods Response surfaces of predicted area offeeding on the head and wrapper leaves to tem-perature and population density of each pest weregenerated with the model A standard initial in-traplant spatial distribution typical of distributionsobserved in cabbage fields was chosen for eachspecies as follows P xylostella 005 01 03 03and 025 A rapae 0 015 04 03 and 015 Tni 0 01 02 04 and 03 of the average numberper plant on the head wrapper leaves upper framemidframe and lower frame respectively For Pxylostella the larval ages were uniformly distrib-uted among the 20 subclasses in the distributeddelay For A rapae and T ni the larvae wereinitialized into the first 10 subclasses simulatingfirst second and third instars For each of 10 pop-ulation densities ranging from well below to well

above the action threshold currently used in NewYork (Shelton et al 1982) feeding was predictedat six constant temperatures

Additional response surfaces were generated offeeding area on the head and wrapper leaves pre-dicted at different temperatures and initial age dis-tributions for a given population density of eachspecies Given the initial spatial distribution de-scribed above and an average temperature be-tween 20 and 25degC the first set of response surfaceswas used to select a population density predictedto cause damage most farmers would consider un-acceptable This density twice the currently rec-ommended action threshold was 1 larvaplant forT ni 15 larvaeplant for A rapae and 10 larvaeplant for P xylostella Different age distributionswere generated by dividing the population densi-ties chosen above evenly among larval maturitysubclasses 1 through 6 then 2 through 7 etc up

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1589

Head Wrapper Leaves

1n

519

260

T1i

TemperatureDC

10

Youngest Age ProSQnt

10

10

YOungG81 AGe PrQsan

A rapal2333

557

78

10

Youngest Ago PreSGnt

TemperatureDC

142 P xylostllia

098

053

0009

Youngesl Ago PresentTemperature

DCTemperalUIlliDc

Fig 8 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves in 7 d due todifferent temperatures and age distributions at a given population density of three lepidopteran pests of cabbagePopulation densities were lplant for T ni loSplant for A rapae 10plant for P xylostella

to 10 through 15 Model predictions were gener-ated at each of these age distributions for each ofthe 6 constant temperatures used above

Results and Discussion Response surfaces gen-erated with the model predict that A rapae con-tributes most to feeding damage on the head andwrapper leaves (Fig 7) Although total consump-tion by A rapae larvae is less than that of T ni(Harcourt et al 1955) the amount consumed onthese economically important strata is greater be-cause of the difference in intra plant spatial dynam-ics of the two species In Fig 7 the model predictsthat for a given constant temperature and giveninitial age and spatial distributions feeding on thehead and wrapper leaves increases linearly withpopulation density for each species Systems thatweight the counts of each species according to ex-pected feeding damage and base the action thresh-old on the weighted counts have been proposed

(Harcourt et al 1955 Shelton et al 1982) but thesedid not consider the spatial dynamics of the pestsThus one potential use of our model is to designa new rating scale to weight the population densityof each species according to expected feeding dam-age considering the spatial dynamics of eachspecies This rating scale however would also haveto account for temperature effects which cangreatly affect predicted feeding

At temperatures lt15DC very little feeding ispredicted on the head and wrapper leaves by eachspecies at any population density (Fig 7) Increas-ing temperatures have a nonlinear effect on pre-dicted feeding by each species For P xylostellaand A rapae the increase in predicted feedingrate may be primarily due to increased develop-ment and feeding rates For T ni however in-creased development and feeding rates at highertemperatures may be offset to some extent by higher

1590 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

probabilities of moving away from the head andwrapper leaves towards the lower leaves (Hoy etal 1989)

For a given population density predicted feed-ing on the marketable parts of the plant variedwidely with age distribution again interacting withtemperature (Fig 8) The results indicate that thedamage caused by a given population density afixed economic threshold for example will varyconsiderably with temperature age structure of thepopulation and species composition Againweighting systems have been described that con-sider larval age (Andaloro et al 1983a) but notwith the resolution that Fig 8 implies is necessaryand they do not include the interaction with tem-perature

Considering the profound effects of tempera-ture age distribution and species-specific spatialdynamics on the predicted area of feeding on eco-nomically important parts of the plant a staticeconomic threshold does not seem to be appropri-ate Rather feeding should be predicted for specificpopulation densities age distributions and spatialdistributions of the three species as well as weatherforecasts and management strategies should be de-signed accordingly The model described here couldbe used to make those predictions either by cal-culating a new species weighting system each dayof the growing season to be used with a fixed actionthreshold or simply by making the required pre-dictions on a case-by-case basis

Sensitivity Analysis

Two goals were addressed in the sensitivity anal-ysis First individual model parameters were evalmiddotuated as potential causes of inaccurate predictionsBy examining the change in model output after achange in the individual parameters parametersthat affect the output most can be identified Sec-ond by examining the effects of changes in dif-ferent parameters in combination insight can begained into the effects of the different processesbeing simulated and their interactions on the out-put variables of interest

Methods Model predictions were evaluated af-ter changing each parameter and input suppliedby the user by +10 and -10 of its valueChanges were made one parameter at a time witha standard set of initial conditions Standard initialpest population densities were a mean of 1 larvalplant of each species on each stratum in the secondinstar for A rapae and T ni and uniformly dis-tributed among the 20 age subclasses for P xylo-stella The analysis was performed at each of threetemperature regimes typical summer weather forwestern New York (maximum temperature 267degCminimum temperature 155degC 8 h sunshine eachday) hot and sunny weather (maximum temper-ature 322degC minimum temperature 211oC 12h sunshine each day) and cool and cloudy weather

(maximum temperature 183degC minimum tem-perature 10degC 2 h sunshine)

Constants were changed by adding or subtract-ing 10 of their value Input weather variableswere changed by adding or subtracting 10 of thevalue of each pays forecasted maximum and min-imum temperature and hours of sunshine Age atwhich larvae begin to move was shifted plus orminus two subclasses to effect a 10 change Initialage distribution for A rapae and T ni was alsoshifted 10 by shifting the subclasses initialized byplus or minus two Initial age distribution for Pxylostella is assumed to be uniform so this was notchanged For each species the initial intraplantdistribution was altered by shifting 10 of eachage group on each stratum except the lower frameleaves down one stratum or shifting 10 of eachage group on each stratum except the head upone stratum (eg a downward shift of an averageof one larva on each stratum would result in anaverage of 09 1 1 1 and 11 larvae on the headwrapper upper frame midframe and lower frameleaves respectively) Transition probabilities for Arapae and P xylostella were changed by a similarmethod shifting 10 of the probability of movingto each stratum except the lower frame leaves tothe next lower stratum or shifting 10 of the prob-ability of moving to each stratum except the headto the next stratum up (eg a downward shift ina transition probability vector of 09 01000 resultsin a vector of 081 018 001 0 0) Sensitivity tochanges in transition probabilities for T ni wereexamined by changing the Beta pdf shape param-eters that govern transition probabilities for thisspecies by + 10 and -10 of their value Theeffects of each of these changes were examined bycalculating the percentage of change in number oflarvae of each species and the percentage of changein accumulated area of feeding on the head andwrapper leaves

To examine interactions between different pro-cesses and their effects on model output we per-formed two analyses in which variables suspectedof interacting were varied in all combinations theequivalent of a factorial design with three levelsof each factor given by +5 -5 and 0 Be-cause development and feeding rates are temper-ature-dependent and govern the amount of feedingaccumulated interactions between temperaturefeeding rates and development rates might affectaccumulated area of feeding Three levels of tem-perature were generated starting with the typicalsummer weather regime described above and add-ing 5 -5 or 0 of the daily maximum andminimum At each temperature level develop-ment rate for each species was varied by +5-5 and 0 from its value and at each of thesedevelopment rates for each species feeding ratewas changed by +5 -5 and 0 of its valueThe effects of these parameter changes on the pre-dicted area of feeding on the head and wrapperleaves were calculated

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1591

Table 2 Output from a model to predict lepidopteranfeeding damage on cabbage at three temperature regimeswith a standard set of inputs and no change in the param-eters Changes in output during the sensitivity analysis (Fig9-12) are compared with these standards

StratumPopulation density (avg noplant) Feeding

P xylostella A rapae Tni cm2

High temperaturesHead 0252 2118 0095 12764Wrapper 0390 2594 0662 21716

Moderate temperaturesHead 0423 1957 0299 6805Wrapper 0578 2524 1001 9667

Low temperaturesHead 0635 1296 0829 1945Wrapper 0834 1651 0886 2348

A similar analysis of interacting processes wasperformed for spatial effects Initial distributionand transition probabilities could be expected tointeract in their effects on spatial distribution oflarvae and feeding damage For each species theinitial distribution was treated by (a) shifting 10of each age group on each stratum (except thelower frame leaves) down one stratum (b) shifting10of each age group on each stratum (except thehead) up one stratum and (c) leaving the initialdistribution unchanged At each of these shifts ininitial distribution for each species the transitionprobabilities for that species were changed as de-

scribed above Shifting 10 of the probability ofmoving to each stratum except the lower frameleaves to the next lower stratum resulted in higherprobabilities of downward movement shifting 10of the probability of moving to each stratum exceptthe head to the next stratum up resulted in higherprobability of upward movement

Results and Discussion Standard results for highmoderate and low temperature regimes withoutchanging any of the parameters or input variablesare given in Table 2 and the effects of changingeach parameter and input variable on selected out-put variables are displayed in Fig 9-12 for themoderate temperature regime We begin the anal-ysisby examining sensitivity of the model to changesin the parameters at moderate temperatures andfollow with the differences in model sensitivity seenunder high and low temperature regimes

At moderate temperatures numbers of larvae ofeach species on the head and wrapper leaves wereleast sensitive to initial spatial distribution of larvaedispersion in development time and hours of sun-shine (Fig 9) Change in the initial intraplant dis-tribution of larvae may be compensated for bymovement of larvae within a short time after thebeginning of the simulation Dispersion in devel-opment time for these species was low in the lab-oratory development studies resulting in a small

Svalue of -D for each species A 10 change in

EL~these small values does not change the dispersion

o Effect 01 +10 changebull Effect 01 -10 change on larvae on the head alief 7 days

Inldal dlsbibudonInitial ages

Age 01 first movementTransition probabilities

Dispersion In developmenlgl

DEL g2C

Hours 01 sunshineTemperalure

-20 -10 0 10

P xylostella20 30 -20 -10 0 10 20

A rapae

oT nl

100

on larvae on the wrapper leaves alter 7 days

10-10

Initial distributionInitial ages

Age 01 firsl movementTransition probabilities

Dispersion in developmentgl

DEL g2C

Hours of sunshineTemperature

-20 o 10 -20 -10 0 -10 0P xylostella A rapas T nI

Fig 9 Percentage of change in predicted number of P xylostella A rapae and T nt larvae on the head andwrapper leavesafter changing model parameters + and -10

1592 ENVIRONME~TAL ENTOMOLOGY Vol 19 no 5

Fig 10 Percentage of change in number of T nilarvae predicted on the head and wrapper leaves aftera + or - 1 0 change in parameters governing their tran-sition probabilities on the cabbage plant

greatly Hours of sunshine influence temperaturein each stratum but apparently not enough to causelarge changes in rate functions

Changes in temperature initial age distributionage at which larvae begin to move between strataand transition probabilities had the greatest effectson predicted number of larvae on the head or wrap-per leaves (Fig 9) These are all linked to spatialdynamics since both temperature and initial agedistribution affect the time at which larvae beginto move between strata Changes in parametersgoverning T ni transition probabilities were anexception causing only moderate or small changesin output (Fig 10) Changes in development rateparameters had large effects only for P xylostellaon the head and wrapper leaves and for T ni onthe head

Predictions of accumulated feeding on the headand wrapper leaves were generally less sensitive tochanges in parameters than were predictions ofnumbers of larvae on these strata (Fig 11 and 12)Because the predictions of accumulated area offeeding are most important to the farmer the ro-bustness of the model in predicting feeding sug-gests that it could be a useful management toolThe greatest changes in accumulated area of feed-ing were caused by changing parameters governingA rapae development or feeding particularly ini-tial age distribution Fortunately development ratesfor all three species considered here have been wellstudied and studies done at widely different timesand locations with different food sources suggestthat average development rate at a given temper-ature is fairly constant (Hardy 1938 Richards 1940Given 1944 Miner 1947 Harcourt et al 1955Shorey et al 1962 Jackson et al 1969 Toba et al

1973 Boldt et al 1975 Butler et al 1975 Smithamp Smilowitz 1976 Chen amp Su 1978 1982 Tatchell1981 Yamada amp Kawasaki 1983 Theunissen et al1985) Changes in forecast temperatures cause thenext largest change in accumulated feeding prob-ably because of their effects on development andfeeding rates Parameters governing spatial effectshad smaller effects on accumulated feeding par-ticularly when compared with their effects on pre-dicted number of larvae on different parts of theplant

Under the low-temperature regime predictionsof numbers of larvae on the head and wrapperleaves were more sensitive to parameters affectingdevelopment than to parameters affecting spatialdynamics At low temperatures larvae take longerto reach the age when movement starts and prob-ability of movement by T ni to the head andwrapper leaves is lower Furthermore fewer smalllarvae become large larvae at low temperatures sototal numbers of large larvae on all strata are re-duced At moderate and high temperatures pre-dictions of numbers of larvae on the head andwrapper leaves were more sensitive to changes inparameters affecting spatial dynamics

Effects of changing forecast temperatures onpredictions of accumulated feeding were muchgreater when the forecast temperatures were lowand less when the forecast temperatures were highthan at moderate temperatures Changing devel-opment rate parameters had a greater effect onaccumulated feeding at low temperatures butchanging feeding rate parameters had a greatereffect at high temperatures than at moderate tem-peratures Accumulated feeding was less sensitiveto changes in transition probabilities at low tem-peratures and more sensitive to changes in tran-sition probabilities at high temperatures than atmoderate temperatures

In general interactions between temperaturedevelopment and feeding rates as well as param-eters governing spatial effects were not evidentTypically the effect of changes in each of theseparameters was similar regardless of the value ofthe other parameters One interaction did occurWhen temperature was increased a negativechange in T ni development rate resulted in lesspredicted feeding on the head than when no changein T ni development rate was made In all othercases negative change in development rates re-sulted in higher predicted feeding on the head thanwhen development rates were not changed Re-gardless 5 changes in development rates for Tni resulted in lt3 differences in feeding on thehead so the effects of this interaction are not ofgreat importance Thus this analysis reinforced thesingle parameter analysis Feeding rates themselveswere changed in this analysis rather than the pa-rameters that govern them and accumulated feed-ing on the head and wrapper leaves was still moresensitive to changes in development rate and tem-perature

5o

middot5 0

Feeding on Heed

-5Feeding on Wrapper Leaves

o 10

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middot10

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October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

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g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

1588 ENVIRONMEITAL ENTOMOLOGY Vol 19 no 5

Head Wrapper Leaves

T ni 565134

377089

189045

2020

- Temporatura Avorago plon1CJ DCEC)---0)c A rapaea 1t82Q) a18Q)U 546 7890Q) 273 396sect0 30 30eD

Temperature Avorago pIontDC Temperalure Avomg bullbull p1ont

DC

P xylostella074 178050 11902i 061

20

rompera1ur Avorago plantDC Tempera1ure Averag bullbull p1on1

DC

Fig 7 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves after 7 d atdifferent temperatures and population densities of lepidopteran pests

amount of damage on the marketable parts of thecrop

Methods Response surfaces of predicted area offeeding on the head and wrapper leaves to tem-perature and population density of each pest weregenerated with the model A standard initial in-traplant spatial distribution typical of distributionsobserved in cabbage fields was chosen for eachspecies as follows P xylostella 005 01 03 03and 025 A rapae 0 015 04 03 and 015 Tni 0 01 02 04 and 03 of the average numberper plant on the head wrapper leaves upper framemidframe and lower frame respectively For Pxylostella the larval ages were uniformly distrib-uted among the 20 subclasses in the distributeddelay For A rapae and T ni the larvae wereinitialized into the first 10 subclasses simulatingfirst second and third instars For each of 10 pop-ulation densities ranging from well below to well

above the action threshold currently used in NewYork (Shelton et al 1982) feeding was predictedat six constant temperatures

Additional response surfaces were generated offeeding area on the head and wrapper leaves pre-dicted at different temperatures and initial age dis-tributions for a given population density of eachspecies Given the initial spatial distribution de-scribed above and an average temperature be-tween 20 and 25degC the first set of response surfaceswas used to select a population density predictedto cause damage most farmers would consider un-acceptable This density twice the currently rec-ommended action threshold was 1 larvaplant forT ni 15 larvaeplant for A rapae and 10 larvaeplant for P xylostella Different age distributionswere generated by dividing the population densi-ties chosen above evenly among larval maturitysubclasses 1 through 6 then 2 through 7 etc up

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1589

Head Wrapper Leaves

1n

519

260

T1i

TemperatureDC

10

Youngest Age ProSQnt

10

10

YOungG81 AGe PrQsan

A rapal2333

557

78

10

Youngest Ago PreSGnt

TemperatureDC

142 P xylostllia

098

053

0009

Youngesl Ago PresentTemperature

DCTemperalUIlliDc

Fig 8 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves in 7 d due todifferent temperatures and age distributions at a given population density of three lepidopteran pests of cabbagePopulation densities were lplant for T ni loSplant for A rapae 10plant for P xylostella

to 10 through 15 Model predictions were gener-ated at each of these age distributions for each ofthe 6 constant temperatures used above

Results and Discussion Response surfaces gen-erated with the model predict that A rapae con-tributes most to feeding damage on the head andwrapper leaves (Fig 7) Although total consump-tion by A rapae larvae is less than that of T ni(Harcourt et al 1955) the amount consumed onthese economically important strata is greater be-cause of the difference in intra plant spatial dynam-ics of the two species In Fig 7 the model predictsthat for a given constant temperature and giveninitial age and spatial distributions feeding on thehead and wrapper leaves increases linearly withpopulation density for each species Systems thatweight the counts of each species according to ex-pected feeding damage and base the action thresh-old on the weighted counts have been proposed

(Harcourt et al 1955 Shelton et al 1982) but thesedid not consider the spatial dynamics of the pestsThus one potential use of our model is to designa new rating scale to weight the population densityof each species according to expected feeding dam-age considering the spatial dynamics of eachspecies This rating scale however would also haveto account for temperature effects which cangreatly affect predicted feeding

At temperatures lt15DC very little feeding ispredicted on the head and wrapper leaves by eachspecies at any population density (Fig 7) Increas-ing temperatures have a nonlinear effect on pre-dicted feeding by each species For P xylostellaand A rapae the increase in predicted feedingrate may be primarily due to increased develop-ment and feeding rates For T ni however in-creased development and feeding rates at highertemperatures may be offset to some extent by higher

1590 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

probabilities of moving away from the head andwrapper leaves towards the lower leaves (Hoy etal 1989)

For a given population density predicted feed-ing on the marketable parts of the plant variedwidely with age distribution again interacting withtemperature (Fig 8) The results indicate that thedamage caused by a given population density afixed economic threshold for example will varyconsiderably with temperature age structure of thepopulation and species composition Againweighting systems have been described that con-sider larval age (Andaloro et al 1983a) but notwith the resolution that Fig 8 implies is necessaryand they do not include the interaction with tem-perature

Considering the profound effects of tempera-ture age distribution and species-specific spatialdynamics on the predicted area of feeding on eco-nomically important parts of the plant a staticeconomic threshold does not seem to be appropri-ate Rather feeding should be predicted for specificpopulation densities age distributions and spatialdistributions of the three species as well as weatherforecasts and management strategies should be de-signed accordingly The model described here couldbe used to make those predictions either by cal-culating a new species weighting system each dayof the growing season to be used with a fixed actionthreshold or simply by making the required pre-dictions on a case-by-case basis

Sensitivity Analysis

Two goals were addressed in the sensitivity anal-ysis First individual model parameters were evalmiddotuated as potential causes of inaccurate predictionsBy examining the change in model output after achange in the individual parameters parametersthat affect the output most can be identified Sec-ond by examining the effects of changes in dif-ferent parameters in combination insight can begained into the effects of the different processesbeing simulated and their interactions on the out-put variables of interest

Methods Model predictions were evaluated af-ter changing each parameter and input suppliedby the user by +10 and -10 of its valueChanges were made one parameter at a time witha standard set of initial conditions Standard initialpest population densities were a mean of 1 larvalplant of each species on each stratum in the secondinstar for A rapae and T ni and uniformly dis-tributed among the 20 age subclasses for P xylo-stella The analysis was performed at each of threetemperature regimes typical summer weather forwestern New York (maximum temperature 267degCminimum temperature 155degC 8 h sunshine eachday) hot and sunny weather (maximum temper-ature 322degC minimum temperature 211oC 12h sunshine each day) and cool and cloudy weather

(maximum temperature 183degC minimum tem-perature 10degC 2 h sunshine)

Constants were changed by adding or subtract-ing 10 of their value Input weather variableswere changed by adding or subtracting 10 of thevalue of each pays forecasted maximum and min-imum temperature and hours of sunshine Age atwhich larvae begin to move was shifted plus orminus two subclasses to effect a 10 change Initialage distribution for A rapae and T ni was alsoshifted 10 by shifting the subclasses initialized byplus or minus two Initial age distribution for Pxylostella is assumed to be uniform so this was notchanged For each species the initial intraplantdistribution was altered by shifting 10 of eachage group on each stratum except the lower frameleaves down one stratum or shifting 10 of eachage group on each stratum except the head upone stratum (eg a downward shift of an averageof one larva on each stratum would result in anaverage of 09 1 1 1 and 11 larvae on the headwrapper upper frame midframe and lower frameleaves respectively) Transition probabilities for Arapae and P xylostella were changed by a similarmethod shifting 10 of the probability of movingto each stratum except the lower frame leaves tothe next lower stratum or shifting 10 of the prob-ability of moving to each stratum except the headto the next stratum up (eg a downward shift ina transition probability vector of 09 01000 resultsin a vector of 081 018 001 0 0) Sensitivity tochanges in transition probabilities for T ni wereexamined by changing the Beta pdf shape param-eters that govern transition probabilities for thisspecies by + 10 and -10 of their value Theeffects of each of these changes were examined bycalculating the percentage of change in number oflarvae of each species and the percentage of changein accumulated area of feeding on the head andwrapper leaves

To examine interactions between different pro-cesses and their effects on model output we per-formed two analyses in which variables suspectedof interacting were varied in all combinations theequivalent of a factorial design with three levelsof each factor given by +5 -5 and 0 Be-cause development and feeding rates are temper-ature-dependent and govern the amount of feedingaccumulated interactions between temperaturefeeding rates and development rates might affectaccumulated area of feeding Three levels of tem-perature were generated starting with the typicalsummer weather regime described above and add-ing 5 -5 or 0 of the daily maximum andminimum At each temperature level develop-ment rate for each species was varied by +5-5 and 0 from its value and at each of thesedevelopment rates for each species feeding ratewas changed by +5 -5 and 0 of its valueThe effects of these parameter changes on the pre-dicted area of feeding on the head and wrapperleaves were calculated

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1591

Table 2 Output from a model to predict lepidopteranfeeding damage on cabbage at three temperature regimeswith a standard set of inputs and no change in the param-eters Changes in output during the sensitivity analysis (Fig9-12) are compared with these standards

StratumPopulation density (avg noplant) Feeding

P xylostella A rapae Tni cm2

High temperaturesHead 0252 2118 0095 12764Wrapper 0390 2594 0662 21716

Moderate temperaturesHead 0423 1957 0299 6805Wrapper 0578 2524 1001 9667

Low temperaturesHead 0635 1296 0829 1945Wrapper 0834 1651 0886 2348

A similar analysis of interacting processes wasperformed for spatial effects Initial distributionand transition probabilities could be expected tointeract in their effects on spatial distribution oflarvae and feeding damage For each species theinitial distribution was treated by (a) shifting 10of each age group on each stratum (except thelower frame leaves) down one stratum (b) shifting10of each age group on each stratum (except thehead) up one stratum and (c) leaving the initialdistribution unchanged At each of these shifts ininitial distribution for each species the transitionprobabilities for that species were changed as de-

scribed above Shifting 10 of the probability ofmoving to each stratum except the lower frameleaves to the next lower stratum resulted in higherprobabilities of downward movement shifting 10of the probability of moving to each stratum exceptthe head to the next stratum up resulted in higherprobability of upward movement

Results and Discussion Standard results for highmoderate and low temperature regimes withoutchanging any of the parameters or input variablesare given in Table 2 and the effects of changingeach parameter and input variable on selected out-put variables are displayed in Fig 9-12 for themoderate temperature regime We begin the anal-ysisby examining sensitivity of the model to changesin the parameters at moderate temperatures andfollow with the differences in model sensitivity seenunder high and low temperature regimes

At moderate temperatures numbers of larvae ofeach species on the head and wrapper leaves wereleast sensitive to initial spatial distribution of larvaedispersion in development time and hours of sun-shine (Fig 9) Change in the initial intraplant dis-tribution of larvae may be compensated for bymovement of larvae within a short time after thebeginning of the simulation Dispersion in devel-opment time for these species was low in the lab-oratory development studies resulting in a small

Svalue of -D for each species A 10 change in

EL~these small values does not change the dispersion

o Effect 01 +10 changebull Effect 01 -10 change on larvae on the head alief 7 days

Inldal dlsbibudonInitial ages

Age 01 first movementTransition probabilities

Dispersion In developmenlgl

DEL g2C

Hours 01 sunshineTemperalure

-20 -10 0 10

P xylostella20 30 -20 -10 0 10 20

A rapae

oT nl

100

on larvae on the wrapper leaves alter 7 days

10-10

Initial distributionInitial ages

Age 01 firsl movementTransition probabilities

Dispersion in developmentgl

DEL g2C

Hours of sunshineTemperature

-20 o 10 -20 -10 0 -10 0P xylostella A rapas T nI

Fig 9 Percentage of change in predicted number of P xylostella A rapae and T nt larvae on the head andwrapper leavesafter changing model parameters + and -10

1592 ENVIRONME~TAL ENTOMOLOGY Vol 19 no 5

Fig 10 Percentage of change in number of T nilarvae predicted on the head and wrapper leaves aftera + or - 1 0 change in parameters governing their tran-sition probabilities on the cabbage plant

greatly Hours of sunshine influence temperaturein each stratum but apparently not enough to causelarge changes in rate functions

Changes in temperature initial age distributionage at which larvae begin to move between strataand transition probabilities had the greatest effectson predicted number of larvae on the head or wrap-per leaves (Fig 9) These are all linked to spatialdynamics since both temperature and initial agedistribution affect the time at which larvae beginto move between strata Changes in parametersgoverning T ni transition probabilities were anexception causing only moderate or small changesin output (Fig 10) Changes in development rateparameters had large effects only for P xylostellaon the head and wrapper leaves and for T ni onthe head

Predictions of accumulated feeding on the headand wrapper leaves were generally less sensitive tochanges in parameters than were predictions ofnumbers of larvae on these strata (Fig 11 and 12)Because the predictions of accumulated area offeeding are most important to the farmer the ro-bustness of the model in predicting feeding sug-gests that it could be a useful management toolThe greatest changes in accumulated area of feed-ing were caused by changing parameters governingA rapae development or feeding particularly ini-tial age distribution Fortunately development ratesfor all three species considered here have been wellstudied and studies done at widely different timesand locations with different food sources suggestthat average development rate at a given temper-ature is fairly constant (Hardy 1938 Richards 1940Given 1944 Miner 1947 Harcourt et al 1955Shorey et al 1962 Jackson et al 1969 Toba et al

1973 Boldt et al 1975 Butler et al 1975 Smithamp Smilowitz 1976 Chen amp Su 1978 1982 Tatchell1981 Yamada amp Kawasaki 1983 Theunissen et al1985) Changes in forecast temperatures cause thenext largest change in accumulated feeding prob-ably because of their effects on development andfeeding rates Parameters governing spatial effectshad smaller effects on accumulated feeding par-ticularly when compared with their effects on pre-dicted number of larvae on different parts of theplant

Under the low-temperature regime predictionsof numbers of larvae on the head and wrapperleaves were more sensitive to parameters affectingdevelopment than to parameters affecting spatialdynamics At low temperatures larvae take longerto reach the age when movement starts and prob-ability of movement by T ni to the head andwrapper leaves is lower Furthermore fewer smalllarvae become large larvae at low temperatures sototal numbers of large larvae on all strata are re-duced At moderate and high temperatures pre-dictions of numbers of larvae on the head andwrapper leaves were more sensitive to changes inparameters affecting spatial dynamics

Effects of changing forecast temperatures onpredictions of accumulated feeding were muchgreater when the forecast temperatures were lowand less when the forecast temperatures were highthan at moderate temperatures Changing devel-opment rate parameters had a greater effect onaccumulated feeding at low temperatures butchanging feeding rate parameters had a greatereffect at high temperatures than at moderate tem-peratures Accumulated feeding was less sensitiveto changes in transition probabilities at low tem-peratures and more sensitive to changes in tran-sition probabilities at high temperatures than atmoderate temperatures

In general interactions between temperaturedevelopment and feeding rates as well as param-eters governing spatial effects were not evidentTypically the effect of changes in each of theseparameters was similar regardless of the value ofthe other parameters One interaction did occurWhen temperature was increased a negativechange in T ni development rate resulted in lesspredicted feeding on the head than when no changein T ni development rate was made In all othercases negative change in development rates re-sulted in higher predicted feeding on the head thanwhen development rates were not changed Re-gardless 5 changes in development rates for Tni resulted in lt3 differences in feeding on thehead so the effects of this interaction are not ofgreat importance Thus this analysis reinforced thesingle parameter analysis Feeding rates themselveswere changed in this analysis rather than the pa-rameters that govern them and accumulated feed-ing on the head and wrapper leaves was still moresensitive to changes in development rate and tem-perature

5o

middot5 0

Feeding on Heed

-5Feeding on Wrapper Leaves

o 10

Larvae on Head

middot10

b5b4b3b2bl858483a281

middot20l( Change in

-20 middot10 0 10 Change in Larvae on Wrapper leaves

II2l

~toa0gtatoten

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

SDElA rapae g2

g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1589

Head Wrapper Leaves

1n

519

260

T1i

TemperatureDC

10

Youngest Age ProSQnt

10

10

YOungG81 AGe PrQsan

A rapal2333

557

78

10

Youngest Ago PreSGnt

TemperatureDC

142 P xylostllia

098

053

0009

Youngesl Ago PresentTemperature

DCTemperalUIlliDc

Fig 8 Predicted average accumulated area of feeding on the cabbage head and wrapper leaves in 7 d due todifferent temperatures and age distributions at a given population density of three lepidopteran pests of cabbagePopulation densities were lplant for T ni loSplant for A rapae 10plant for P xylostella

to 10 through 15 Model predictions were gener-ated at each of these age distributions for each ofthe 6 constant temperatures used above

Results and Discussion Response surfaces gen-erated with the model predict that A rapae con-tributes most to feeding damage on the head andwrapper leaves (Fig 7) Although total consump-tion by A rapae larvae is less than that of T ni(Harcourt et al 1955) the amount consumed onthese economically important strata is greater be-cause of the difference in intra plant spatial dynam-ics of the two species In Fig 7 the model predictsthat for a given constant temperature and giveninitial age and spatial distributions feeding on thehead and wrapper leaves increases linearly withpopulation density for each species Systems thatweight the counts of each species according to ex-pected feeding damage and base the action thresh-old on the weighted counts have been proposed

(Harcourt et al 1955 Shelton et al 1982) but thesedid not consider the spatial dynamics of the pestsThus one potential use of our model is to designa new rating scale to weight the population densityof each species according to expected feeding dam-age considering the spatial dynamics of eachspecies This rating scale however would also haveto account for temperature effects which cangreatly affect predicted feeding

At temperatures lt15DC very little feeding ispredicted on the head and wrapper leaves by eachspecies at any population density (Fig 7) Increas-ing temperatures have a nonlinear effect on pre-dicted feeding by each species For P xylostellaand A rapae the increase in predicted feedingrate may be primarily due to increased develop-ment and feeding rates For T ni however in-creased development and feeding rates at highertemperatures may be offset to some extent by higher

1590 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

probabilities of moving away from the head andwrapper leaves towards the lower leaves (Hoy etal 1989)

For a given population density predicted feed-ing on the marketable parts of the plant variedwidely with age distribution again interacting withtemperature (Fig 8) The results indicate that thedamage caused by a given population density afixed economic threshold for example will varyconsiderably with temperature age structure of thepopulation and species composition Againweighting systems have been described that con-sider larval age (Andaloro et al 1983a) but notwith the resolution that Fig 8 implies is necessaryand they do not include the interaction with tem-perature

Considering the profound effects of tempera-ture age distribution and species-specific spatialdynamics on the predicted area of feeding on eco-nomically important parts of the plant a staticeconomic threshold does not seem to be appropri-ate Rather feeding should be predicted for specificpopulation densities age distributions and spatialdistributions of the three species as well as weatherforecasts and management strategies should be de-signed accordingly The model described here couldbe used to make those predictions either by cal-culating a new species weighting system each dayof the growing season to be used with a fixed actionthreshold or simply by making the required pre-dictions on a case-by-case basis

Sensitivity Analysis

Two goals were addressed in the sensitivity anal-ysis First individual model parameters were evalmiddotuated as potential causes of inaccurate predictionsBy examining the change in model output after achange in the individual parameters parametersthat affect the output most can be identified Sec-ond by examining the effects of changes in dif-ferent parameters in combination insight can begained into the effects of the different processesbeing simulated and their interactions on the out-put variables of interest

Methods Model predictions were evaluated af-ter changing each parameter and input suppliedby the user by +10 and -10 of its valueChanges were made one parameter at a time witha standard set of initial conditions Standard initialpest population densities were a mean of 1 larvalplant of each species on each stratum in the secondinstar for A rapae and T ni and uniformly dis-tributed among the 20 age subclasses for P xylo-stella The analysis was performed at each of threetemperature regimes typical summer weather forwestern New York (maximum temperature 267degCminimum temperature 155degC 8 h sunshine eachday) hot and sunny weather (maximum temper-ature 322degC minimum temperature 211oC 12h sunshine each day) and cool and cloudy weather

(maximum temperature 183degC minimum tem-perature 10degC 2 h sunshine)

Constants were changed by adding or subtract-ing 10 of their value Input weather variableswere changed by adding or subtracting 10 of thevalue of each pays forecasted maximum and min-imum temperature and hours of sunshine Age atwhich larvae begin to move was shifted plus orminus two subclasses to effect a 10 change Initialage distribution for A rapae and T ni was alsoshifted 10 by shifting the subclasses initialized byplus or minus two Initial age distribution for Pxylostella is assumed to be uniform so this was notchanged For each species the initial intraplantdistribution was altered by shifting 10 of eachage group on each stratum except the lower frameleaves down one stratum or shifting 10 of eachage group on each stratum except the head upone stratum (eg a downward shift of an averageof one larva on each stratum would result in anaverage of 09 1 1 1 and 11 larvae on the headwrapper upper frame midframe and lower frameleaves respectively) Transition probabilities for Arapae and P xylostella were changed by a similarmethod shifting 10 of the probability of movingto each stratum except the lower frame leaves tothe next lower stratum or shifting 10 of the prob-ability of moving to each stratum except the headto the next stratum up (eg a downward shift ina transition probability vector of 09 01000 resultsin a vector of 081 018 001 0 0) Sensitivity tochanges in transition probabilities for T ni wereexamined by changing the Beta pdf shape param-eters that govern transition probabilities for thisspecies by + 10 and -10 of their value Theeffects of each of these changes were examined bycalculating the percentage of change in number oflarvae of each species and the percentage of changein accumulated area of feeding on the head andwrapper leaves

To examine interactions between different pro-cesses and their effects on model output we per-formed two analyses in which variables suspectedof interacting were varied in all combinations theequivalent of a factorial design with three levelsof each factor given by +5 -5 and 0 Be-cause development and feeding rates are temper-ature-dependent and govern the amount of feedingaccumulated interactions between temperaturefeeding rates and development rates might affectaccumulated area of feeding Three levels of tem-perature were generated starting with the typicalsummer weather regime described above and add-ing 5 -5 or 0 of the daily maximum andminimum At each temperature level develop-ment rate for each species was varied by +5-5 and 0 from its value and at each of thesedevelopment rates for each species feeding ratewas changed by +5 -5 and 0 of its valueThe effects of these parameter changes on the pre-dicted area of feeding on the head and wrapperleaves were calculated

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1591

Table 2 Output from a model to predict lepidopteranfeeding damage on cabbage at three temperature regimeswith a standard set of inputs and no change in the param-eters Changes in output during the sensitivity analysis (Fig9-12) are compared with these standards

StratumPopulation density (avg noplant) Feeding

P xylostella A rapae Tni cm2

High temperaturesHead 0252 2118 0095 12764Wrapper 0390 2594 0662 21716

Moderate temperaturesHead 0423 1957 0299 6805Wrapper 0578 2524 1001 9667

Low temperaturesHead 0635 1296 0829 1945Wrapper 0834 1651 0886 2348

A similar analysis of interacting processes wasperformed for spatial effects Initial distributionand transition probabilities could be expected tointeract in their effects on spatial distribution oflarvae and feeding damage For each species theinitial distribution was treated by (a) shifting 10of each age group on each stratum (except thelower frame leaves) down one stratum (b) shifting10of each age group on each stratum (except thehead) up one stratum and (c) leaving the initialdistribution unchanged At each of these shifts ininitial distribution for each species the transitionprobabilities for that species were changed as de-

scribed above Shifting 10 of the probability ofmoving to each stratum except the lower frameleaves to the next lower stratum resulted in higherprobabilities of downward movement shifting 10of the probability of moving to each stratum exceptthe head to the next stratum up resulted in higherprobability of upward movement

Results and Discussion Standard results for highmoderate and low temperature regimes withoutchanging any of the parameters or input variablesare given in Table 2 and the effects of changingeach parameter and input variable on selected out-put variables are displayed in Fig 9-12 for themoderate temperature regime We begin the anal-ysisby examining sensitivity of the model to changesin the parameters at moderate temperatures andfollow with the differences in model sensitivity seenunder high and low temperature regimes

At moderate temperatures numbers of larvae ofeach species on the head and wrapper leaves wereleast sensitive to initial spatial distribution of larvaedispersion in development time and hours of sun-shine (Fig 9) Change in the initial intraplant dis-tribution of larvae may be compensated for bymovement of larvae within a short time after thebeginning of the simulation Dispersion in devel-opment time for these species was low in the lab-oratory development studies resulting in a small

Svalue of -D for each species A 10 change in

EL~these small values does not change the dispersion

o Effect 01 +10 changebull Effect 01 -10 change on larvae on the head alief 7 days

Inldal dlsbibudonInitial ages

Age 01 first movementTransition probabilities

Dispersion In developmenlgl

DEL g2C

Hours 01 sunshineTemperalure

-20 -10 0 10

P xylostella20 30 -20 -10 0 10 20

A rapae

oT nl

100

on larvae on the wrapper leaves alter 7 days

10-10

Initial distributionInitial ages

Age 01 firsl movementTransition probabilities

Dispersion in developmentgl

DEL g2C

Hours of sunshineTemperature

-20 o 10 -20 -10 0 -10 0P xylostella A rapas T nI

Fig 9 Percentage of change in predicted number of P xylostella A rapae and T nt larvae on the head andwrapper leavesafter changing model parameters + and -10

1592 ENVIRONME~TAL ENTOMOLOGY Vol 19 no 5

Fig 10 Percentage of change in number of T nilarvae predicted on the head and wrapper leaves aftera + or - 1 0 change in parameters governing their tran-sition probabilities on the cabbage plant

greatly Hours of sunshine influence temperaturein each stratum but apparently not enough to causelarge changes in rate functions

Changes in temperature initial age distributionage at which larvae begin to move between strataand transition probabilities had the greatest effectson predicted number of larvae on the head or wrap-per leaves (Fig 9) These are all linked to spatialdynamics since both temperature and initial agedistribution affect the time at which larvae beginto move between strata Changes in parametersgoverning T ni transition probabilities were anexception causing only moderate or small changesin output (Fig 10) Changes in development rateparameters had large effects only for P xylostellaon the head and wrapper leaves and for T ni onthe head

Predictions of accumulated feeding on the headand wrapper leaves were generally less sensitive tochanges in parameters than were predictions ofnumbers of larvae on these strata (Fig 11 and 12)Because the predictions of accumulated area offeeding are most important to the farmer the ro-bustness of the model in predicting feeding sug-gests that it could be a useful management toolThe greatest changes in accumulated area of feed-ing were caused by changing parameters governingA rapae development or feeding particularly ini-tial age distribution Fortunately development ratesfor all three species considered here have been wellstudied and studies done at widely different timesand locations with different food sources suggestthat average development rate at a given temper-ature is fairly constant (Hardy 1938 Richards 1940Given 1944 Miner 1947 Harcourt et al 1955Shorey et al 1962 Jackson et al 1969 Toba et al

1973 Boldt et al 1975 Butler et al 1975 Smithamp Smilowitz 1976 Chen amp Su 1978 1982 Tatchell1981 Yamada amp Kawasaki 1983 Theunissen et al1985) Changes in forecast temperatures cause thenext largest change in accumulated feeding prob-ably because of their effects on development andfeeding rates Parameters governing spatial effectshad smaller effects on accumulated feeding par-ticularly when compared with their effects on pre-dicted number of larvae on different parts of theplant

Under the low-temperature regime predictionsof numbers of larvae on the head and wrapperleaves were more sensitive to parameters affectingdevelopment than to parameters affecting spatialdynamics At low temperatures larvae take longerto reach the age when movement starts and prob-ability of movement by T ni to the head andwrapper leaves is lower Furthermore fewer smalllarvae become large larvae at low temperatures sototal numbers of large larvae on all strata are re-duced At moderate and high temperatures pre-dictions of numbers of larvae on the head andwrapper leaves were more sensitive to changes inparameters affecting spatial dynamics

Effects of changing forecast temperatures onpredictions of accumulated feeding were muchgreater when the forecast temperatures were lowand less when the forecast temperatures were highthan at moderate temperatures Changing devel-opment rate parameters had a greater effect onaccumulated feeding at low temperatures butchanging feeding rate parameters had a greatereffect at high temperatures than at moderate tem-peratures Accumulated feeding was less sensitiveto changes in transition probabilities at low tem-peratures and more sensitive to changes in tran-sition probabilities at high temperatures than atmoderate temperatures

In general interactions between temperaturedevelopment and feeding rates as well as param-eters governing spatial effects were not evidentTypically the effect of changes in each of theseparameters was similar regardless of the value ofthe other parameters One interaction did occurWhen temperature was increased a negativechange in T ni development rate resulted in lesspredicted feeding on the head than when no changein T ni development rate was made In all othercases negative change in development rates re-sulted in higher predicted feeding on the head thanwhen development rates were not changed Re-gardless 5 changes in development rates for Tni resulted in lt3 differences in feeding on thehead so the effects of this interaction are not ofgreat importance Thus this analysis reinforced thesingle parameter analysis Feeding rates themselveswere changed in this analysis rather than the pa-rameters that govern them and accumulated feed-ing on the head and wrapper leaves was still moresensitive to changes in development rate and tem-perature

5o

middot5 0

Feeding on Heed

-5Feeding on Wrapper Leaves

o 10

Larvae on Head

middot10

b5b4b3b2bl858483a281

middot20l( Change in

-20 middot10 0 10 Change in Larvae on Wrapper leaves

II2l

~toa0gtatoten

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

SDElA rapae g2

g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

1590 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

probabilities of moving away from the head andwrapper leaves towards the lower leaves (Hoy etal 1989)

For a given population density predicted feed-ing on the marketable parts of the plant variedwidely with age distribution again interacting withtemperature (Fig 8) The results indicate that thedamage caused by a given population density afixed economic threshold for example will varyconsiderably with temperature age structure of thepopulation and species composition Againweighting systems have been described that con-sider larval age (Andaloro et al 1983a) but notwith the resolution that Fig 8 implies is necessaryand they do not include the interaction with tem-perature

Considering the profound effects of tempera-ture age distribution and species-specific spatialdynamics on the predicted area of feeding on eco-nomically important parts of the plant a staticeconomic threshold does not seem to be appropri-ate Rather feeding should be predicted for specificpopulation densities age distributions and spatialdistributions of the three species as well as weatherforecasts and management strategies should be de-signed accordingly The model described here couldbe used to make those predictions either by cal-culating a new species weighting system each dayof the growing season to be used with a fixed actionthreshold or simply by making the required pre-dictions on a case-by-case basis

Sensitivity Analysis

Two goals were addressed in the sensitivity anal-ysis First individual model parameters were evalmiddotuated as potential causes of inaccurate predictionsBy examining the change in model output after achange in the individual parameters parametersthat affect the output most can be identified Sec-ond by examining the effects of changes in dif-ferent parameters in combination insight can begained into the effects of the different processesbeing simulated and their interactions on the out-put variables of interest

Methods Model predictions were evaluated af-ter changing each parameter and input suppliedby the user by +10 and -10 of its valueChanges were made one parameter at a time witha standard set of initial conditions Standard initialpest population densities were a mean of 1 larvalplant of each species on each stratum in the secondinstar for A rapae and T ni and uniformly dis-tributed among the 20 age subclasses for P xylo-stella The analysis was performed at each of threetemperature regimes typical summer weather forwestern New York (maximum temperature 267degCminimum temperature 155degC 8 h sunshine eachday) hot and sunny weather (maximum temper-ature 322degC minimum temperature 211oC 12h sunshine each day) and cool and cloudy weather

(maximum temperature 183degC minimum tem-perature 10degC 2 h sunshine)

Constants were changed by adding or subtract-ing 10 of their value Input weather variableswere changed by adding or subtracting 10 of thevalue of each pays forecasted maximum and min-imum temperature and hours of sunshine Age atwhich larvae begin to move was shifted plus orminus two subclasses to effect a 10 change Initialage distribution for A rapae and T ni was alsoshifted 10 by shifting the subclasses initialized byplus or minus two Initial age distribution for Pxylostella is assumed to be uniform so this was notchanged For each species the initial intraplantdistribution was altered by shifting 10 of eachage group on each stratum except the lower frameleaves down one stratum or shifting 10 of eachage group on each stratum except the head upone stratum (eg a downward shift of an averageof one larva on each stratum would result in anaverage of 09 1 1 1 and 11 larvae on the headwrapper upper frame midframe and lower frameleaves respectively) Transition probabilities for Arapae and P xylostella were changed by a similarmethod shifting 10 of the probability of movingto each stratum except the lower frame leaves tothe next lower stratum or shifting 10 of the prob-ability of moving to each stratum except the headto the next stratum up (eg a downward shift ina transition probability vector of 09 01000 resultsin a vector of 081 018 001 0 0) Sensitivity tochanges in transition probabilities for T ni wereexamined by changing the Beta pdf shape param-eters that govern transition probabilities for thisspecies by + 10 and -10 of their value Theeffects of each of these changes were examined bycalculating the percentage of change in number oflarvae of each species and the percentage of changein accumulated area of feeding on the head andwrapper leaves

To examine interactions between different pro-cesses and their effects on model output we per-formed two analyses in which variables suspectedof interacting were varied in all combinations theequivalent of a factorial design with three levelsof each factor given by +5 -5 and 0 Be-cause development and feeding rates are temper-ature-dependent and govern the amount of feedingaccumulated interactions between temperaturefeeding rates and development rates might affectaccumulated area of feeding Three levels of tem-perature were generated starting with the typicalsummer weather regime described above and add-ing 5 -5 or 0 of the daily maximum andminimum At each temperature level develop-ment rate for each species was varied by +5-5 and 0 from its value and at each of thesedevelopment rates for each species feeding ratewas changed by +5 -5 and 0 of its valueThe effects of these parameter changes on the pre-dicted area of feeding on the head and wrapperleaves were calculated

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1591

Table 2 Output from a model to predict lepidopteranfeeding damage on cabbage at three temperature regimeswith a standard set of inputs and no change in the param-eters Changes in output during the sensitivity analysis (Fig9-12) are compared with these standards

StratumPopulation density (avg noplant) Feeding

P xylostella A rapae Tni cm2

High temperaturesHead 0252 2118 0095 12764Wrapper 0390 2594 0662 21716

Moderate temperaturesHead 0423 1957 0299 6805Wrapper 0578 2524 1001 9667

Low temperaturesHead 0635 1296 0829 1945Wrapper 0834 1651 0886 2348

A similar analysis of interacting processes wasperformed for spatial effects Initial distributionand transition probabilities could be expected tointeract in their effects on spatial distribution oflarvae and feeding damage For each species theinitial distribution was treated by (a) shifting 10of each age group on each stratum (except thelower frame leaves) down one stratum (b) shifting10of each age group on each stratum (except thehead) up one stratum and (c) leaving the initialdistribution unchanged At each of these shifts ininitial distribution for each species the transitionprobabilities for that species were changed as de-

scribed above Shifting 10 of the probability ofmoving to each stratum except the lower frameleaves to the next lower stratum resulted in higherprobabilities of downward movement shifting 10of the probability of moving to each stratum exceptthe head to the next stratum up resulted in higherprobability of upward movement

Results and Discussion Standard results for highmoderate and low temperature regimes withoutchanging any of the parameters or input variablesare given in Table 2 and the effects of changingeach parameter and input variable on selected out-put variables are displayed in Fig 9-12 for themoderate temperature regime We begin the anal-ysisby examining sensitivity of the model to changesin the parameters at moderate temperatures andfollow with the differences in model sensitivity seenunder high and low temperature regimes

At moderate temperatures numbers of larvae ofeach species on the head and wrapper leaves wereleast sensitive to initial spatial distribution of larvaedispersion in development time and hours of sun-shine (Fig 9) Change in the initial intraplant dis-tribution of larvae may be compensated for bymovement of larvae within a short time after thebeginning of the simulation Dispersion in devel-opment time for these species was low in the lab-oratory development studies resulting in a small

Svalue of -D for each species A 10 change in

EL~these small values does not change the dispersion

o Effect 01 +10 changebull Effect 01 -10 change on larvae on the head alief 7 days

Inldal dlsbibudonInitial ages

Age 01 first movementTransition probabilities

Dispersion In developmenlgl

DEL g2C

Hours 01 sunshineTemperalure

-20 -10 0 10

P xylostella20 30 -20 -10 0 10 20

A rapae

oT nl

100

on larvae on the wrapper leaves alter 7 days

10-10

Initial distributionInitial ages

Age 01 firsl movementTransition probabilities

Dispersion in developmentgl

DEL g2C

Hours of sunshineTemperature

-20 o 10 -20 -10 0 -10 0P xylostella A rapas T nI

Fig 9 Percentage of change in predicted number of P xylostella A rapae and T nt larvae on the head andwrapper leavesafter changing model parameters + and -10

1592 ENVIRONME~TAL ENTOMOLOGY Vol 19 no 5

Fig 10 Percentage of change in number of T nilarvae predicted on the head and wrapper leaves aftera + or - 1 0 change in parameters governing their tran-sition probabilities on the cabbage plant

greatly Hours of sunshine influence temperaturein each stratum but apparently not enough to causelarge changes in rate functions

Changes in temperature initial age distributionage at which larvae begin to move between strataand transition probabilities had the greatest effectson predicted number of larvae on the head or wrap-per leaves (Fig 9) These are all linked to spatialdynamics since both temperature and initial agedistribution affect the time at which larvae beginto move between strata Changes in parametersgoverning T ni transition probabilities were anexception causing only moderate or small changesin output (Fig 10) Changes in development rateparameters had large effects only for P xylostellaon the head and wrapper leaves and for T ni onthe head

Predictions of accumulated feeding on the headand wrapper leaves were generally less sensitive tochanges in parameters than were predictions ofnumbers of larvae on these strata (Fig 11 and 12)Because the predictions of accumulated area offeeding are most important to the farmer the ro-bustness of the model in predicting feeding sug-gests that it could be a useful management toolThe greatest changes in accumulated area of feed-ing were caused by changing parameters governingA rapae development or feeding particularly ini-tial age distribution Fortunately development ratesfor all three species considered here have been wellstudied and studies done at widely different timesand locations with different food sources suggestthat average development rate at a given temper-ature is fairly constant (Hardy 1938 Richards 1940Given 1944 Miner 1947 Harcourt et al 1955Shorey et al 1962 Jackson et al 1969 Toba et al

1973 Boldt et al 1975 Butler et al 1975 Smithamp Smilowitz 1976 Chen amp Su 1978 1982 Tatchell1981 Yamada amp Kawasaki 1983 Theunissen et al1985) Changes in forecast temperatures cause thenext largest change in accumulated feeding prob-ably because of their effects on development andfeeding rates Parameters governing spatial effectshad smaller effects on accumulated feeding par-ticularly when compared with their effects on pre-dicted number of larvae on different parts of theplant

Under the low-temperature regime predictionsof numbers of larvae on the head and wrapperleaves were more sensitive to parameters affectingdevelopment than to parameters affecting spatialdynamics At low temperatures larvae take longerto reach the age when movement starts and prob-ability of movement by T ni to the head andwrapper leaves is lower Furthermore fewer smalllarvae become large larvae at low temperatures sototal numbers of large larvae on all strata are re-duced At moderate and high temperatures pre-dictions of numbers of larvae on the head andwrapper leaves were more sensitive to changes inparameters affecting spatial dynamics

Effects of changing forecast temperatures onpredictions of accumulated feeding were muchgreater when the forecast temperatures were lowand less when the forecast temperatures were highthan at moderate temperatures Changing devel-opment rate parameters had a greater effect onaccumulated feeding at low temperatures butchanging feeding rate parameters had a greatereffect at high temperatures than at moderate tem-peratures Accumulated feeding was less sensitiveto changes in transition probabilities at low tem-peratures and more sensitive to changes in tran-sition probabilities at high temperatures than atmoderate temperatures

In general interactions between temperaturedevelopment and feeding rates as well as param-eters governing spatial effects were not evidentTypically the effect of changes in each of theseparameters was similar regardless of the value ofthe other parameters One interaction did occurWhen temperature was increased a negativechange in T ni development rate resulted in lesspredicted feeding on the head than when no changein T ni development rate was made In all othercases negative change in development rates re-sulted in higher predicted feeding on the head thanwhen development rates were not changed Re-gardless 5 changes in development rates for Tni resulted in lt3 differences in feeding on thehead so the effects of this interaction are not ofgreat importance Thus this analysis reinforced thesingle parameter analysis Feeding rates themselveswere changed in this analysis rather than the pa-rameters that govern them and accumulated feed-ing on the head and wrapper leaves was still moresensitive to changes in development rate and tem-perature

5o

middot5 0

Feeding on Heed

-5Feeding on Wrapper Leaves

o 10

Larvae on Head

middot10

b5b4b3b2bl858483a281

middot20l( Change in

-20 middot10 0 10 Change in Larvae on Wrapper leaves

II2l

~toa0gtatoten

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

SDElA rapae g2

g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1591

Table 2 Output from a model to predict lepidopteranfeeding damage on cabbage at three temperature regimeswith a standard set of inputs and no change in the param-eters Changes in output during the sensitivity analysis (Fig9-12) are compared with these standards

StratumPopulation density (avg noplant) Feeding

P xylostella A rapae Tni cm2

High temperaturesHead 0252 2118 0095 12764Wrapper 0390 2594 0662 21716

Moderate temperaturesHead 0423 1957 0299 6805Wrapper 0578 2524 1001 9667

Low temperaturesHead 0635 1296 0829 1945Wrapper 0834 1651 0886 2348

A similar analysis of interacting processes wasperformed for spatial effects Initial distributionand transition probabilities could be expected tointeract in their effects on spatial distribution oflarvae and feeding damage For each species theinitial distribution was treated by (a) shifting 10of each age group on each stratum (except thelower frame leaves) down one stratum (b) shifting10of each age group on each stratum (except thehead) up one stratum and (c) leaving the initialdistribution unchanged At each of these shifts ininitial distribution for each species the transitionprobabilities for that species were changed as de-

scribed above Shifting 10 of the probability ofmoving to each stratum except the lower frameleaves to the next lower stratum resulted in higherprobabilities of downward movement shifting 10of the probability of moving to each stratum exceptthe head to the next stratum up resulted in higherprobability of upward movement

Results and Discussion Standard results for highmoderate and low temperature regimes withoutchanging any of the parameters or input variablesare given in Table 2 and the effects of changingeach parameter and input variable on selected out-put variables are displayed in Fig 9-12 for themoderate temperature regime We begin the anal-ysisby examining sensitivity of the model to changesin the parameters at moderate temperatures andfollow with the differences in model sensitivity seenunder high and low temperature regimes

At moderate temperatures numbers of larvae ofeach species on the head and wrapper leaves wereleast sensitive to initial spatial distribution of larvaedispersion in development time and hours of sun-shine (Fig 9) Change in the initial intraplant dis-tribution of larvae may be compensated for bymovement of larvae within a short time after thebeginning of the simulation Dispersion in devel-opment time for these species was low in the lab-oratory development studies resulting in a small

Svalue of -D for each species A 10 change in

EL~these small values does not change the dispersion

o Effect 01 +10 changebull Effect 01 -10 change on larvae on the head alief 7 days

Inldal dlsbibudonInitial ages

Age 01 first movementTransition probabilities

Dispersion In developmenlgl

DEL g2C

Hours 01 sunshineTemperalure

-20 -10 0 10

P xylostella20 30 -20 -10 0 10 20

A rapae

oT nl

100

on larvae on the wrapper leaves alter 7 days

10-10

Initial distributionInitial ages

Age 01 firsl movementTransition probabilities

Dispersion in developmentgl

DEL g2C

Hours of sunshineTemperature

-20 o 10 -20 -10 0 -10 0P xylostella A rapas T nI

Fig 9 Percentage of change in predicted number of P xylostella A rapae and T nt larvae on the head andwrapper leavesafter changing model parameters + and -10

1592 ENVIRONME~TAL ENTOMOLOGY Vol 19 no 5

Fig 10 Percentage of change in number of T nilarvae predicted on the head and wrapper leaves aftera + or - 1 0 change in parameters governing their tran-sition probabilities on the cabbage plant

greatly Hours of sunshine influence temperaturein each stratum but apparently not enough to causelarge changes in rate functions

Changes in temperature initial age distributionage at which larvae begin to move between strataand transition probabilities had the greatest effectson predicted number of larvae on the head or wrap-per leaves (Fig 9) These are all linked to spatialdynamics since both temperature and initial agedistribution affect the time at which larvae beginto move between strata Changes in parametersgoverning T ni transition probabilities were anexception causing only moderate or small changesin output (Fig 10) Changes in development rateparameters had large effects only for P xylostellaon the head and wrapper leaves and for T ni onthe head

Predictions of accumulated feeding on the headand wrapper leaves were generally less sensitive tochanges in parameters than were predictions ofnumbers of larvae on these strata (Fig 11 and 12)Because the predictions of accumulated area offeeding are most important to the farmer the ro-bustness of the model in predicting feeding sug-gests that it could be a useful management toolThe greatest changes in accumulated area of feed-ing were caused by changing parameters governingA rapae development or feeding particularly ini-tial age distribution Fortunately development ratesfor all three species considered here have been wellstudied and studies done at widely different timesand locations with different food sources suggestthat average development rate at a given temper-ature is fairly constant (Hardy 1938 Richards 1940Given 1944 Miner 1947 Harcourt et al 1955Shorey et al 1962 Jackson et al 1969 Toba et al

1973 Boldt et al 1975 Butler et al 1975 Smithamp Smilowitz 1976 Chen amp Su 1978 1982 Tatchell1981 Yamada amp Kawasaki 1983 Theunissen et al1985) Changes in forecast temperatures cause thenext largest change in accumulated feeding prob-ably because of their effects on development andfeeding rates Parameters governing spatial effectshad smaller effects on accumulated feeding par-ticularly when compared with their effects on pre-dicted number of larvae on different parts of theplant

Under the low-temperature regime predictionsof numbers of larvae on the head and wrapperleaves were more sensitive to parameters affectingdevelopment than to parameters affecting spatialdynamics At low temperatures larvae take longerto reach the age when movement starts and prob-ability of movement by T ni to the head andwrapper leaves is lower Furthermore fewer smalllarvae become large larvae at low temperatures sototal numbers of large larvae on all strata are re-duced At moderate and high temperatures pre-dictions of numbers of larvae on the head andwrapper leaves were more sensitive to changes inparameters affecting spatial dynamics

Effects of changing forecast temperatures onpredictions of accumulated feeding were muchgreater when the forecast temperatures were lowand less when the forecast temperatures were highthan at moderate temperatures Changing devel-opment rate parameters had a greater effect onaccumulated feeding at low temperatures butchanging feeding rate parameters had a greatereffect at high temperatures than at moderate tem-peratures Accumulated feeding was less sensitiveto changes in transition probabilities at low tem-peratures and more sensitive to changes in tran-sition probabilities at high temperatures than atmoderate temperatures

In general interactions between temperaturedevelopment and feeding rates as well as param-eters governing spatial effects were not evidentTypically the effect of changes in each of theseparameters was similar regardless of the value ofthe other parameters One interaction did occurWhen temperature was increased a negativechange in T ni development rate resulted in lesspredicted feeding on the head than when no changein T ni development rate was made In all othercases negative change in development rates re-sulted in higher predicted feeding on the head thanwhen development rates were not changed Re-gardless 5 changes in development rates for Tni resulted in lt3 differences in feeding on thehead so the effects of this interaction are not ofgreat importance Thus this analysis reinforced thesingle parameter analysis Feeding rates themselveswere changed in this analysis rather than the pa-rameters that govern them and accumulated feed-ing on the head and wrapper leaves was still moresensitive to changes in development rate and tem-perature

5o

middot5 0

Feeding on Heed

-5Feeding on Wrapper Leaves

o 10

Larvae on Head

middot10

b5b4b3b2bl858483a281

middot20l( Change in

-20 middot10 0 10 Change in Larvae on Wrapper leaves

II2l

~toa0gtatoten

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

SDElA rapae g2

g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

1592 ENVIRONME~TAL ENTOMOLOGY Vol 19 no 5

Fig 10 Percentage of change in number of T nilarvae predicted on the head and wrapper leaves aftera + or - 1 0 change in parameters governing their tran-sition probabilities on the cabbage plant

greatly Hours of sunshine influence temperaturein each stratum but apparently not enough to causelarge changes in rate functions

Changes in temperature initial age distributionage at which larvae begin to move between strataand transition probabilities had the greatest effectson predicted number of larvae on the head or wrap-per leaves (Fig 9) These are all linked to spatialdynamics since both temperature and initial agedistribution affect the time at which larvae beginto move between strata Changes in parametersgoverning T ni transition probabilities were anexception causing only moderate or small changesin output (Fig 10) Changes in development rateparameters had large effects only for P xylostellaon the head and wrapper leaves and for T ni onthe head

Predictions of accumulated feeding on the headand wrapper leaves were generally less sensitive tochanges in parameters than were predictions ofnumbers of larvae on these strata (Fig 11 and 12)Because the predictions of accumulated area offeeding are most important to the farmer the ro-bustness of the model in predicting feeding sug-gests that it could be a useful management toolThe greatest changes in accumulated area of feed-ing were caused by changing parameters governingA rapae development or feeding particularly ini-tial age distribution Fortunately development ratesfor all three species considered here have been wellstudied and studies done at widely different timesand locations with different food sources suggestthat average development rate at a given temper-ature is fairly constant (Hardy 1938 Richards 1940Given 1944 Miner 1947 Harcourt et al 1955Shorey et al 1962 Jackson et al 1969 Toba et al

1973 Boldt et al 1975 Butler et al 1975 Smithamp Smilowitz 1976 Chen amp Su 1978 1982 Tatchell1981 Yamada amp Kawasaki 1983 Theunissen et al1985) Changes in forecast temperatures cause thenext largest change in accumulated feeding prob-ably because of their effects on development andfeeding rates Parameters governing spatial effectshad smaller effects on accumulated feeding par-ticularly when compared with their effects on pre-dicted number of larvae on different parts of theplant

Under the low-temperature regime predictionsof numbers of larvae on the head and wrapperleaves were more sensitive to parameters affectingdevelopment than to parameters affecting spatialdynamics At low temperatures larvae take longerto reach the age when movement starts and prob-ability of movement by T ni to the head andwrapper leaves is lower Furthermore fewer smalllarvae become large larvae at low temperatures sototal numbers of large larvae on all strata are re-duced At moderate and high temperatures pre-dictions of numbers of larvae on the head andwrapper leaves were more sensitive to changes inparameters affecting spatial dynamics

Effects of changing forecast temperatures onpredictions of accumulated feeding were muchgreater when the forecast temperatures were lowand less when the forecast temperatures were highthan at moderate temperatures Changing devel-opment rate parameters had a greater effect onaccumulated feeding at low temperatures butchanging feeding rate parameters had a greatereffect at high temperatures than at moderate tem-peratures Accumulated feeding was less sensitiveto changes in transition probabilities at low tem-peratures and more sensitive to changes in tran-sition probabilities at high temperatures than atmoderate temperatures

In general interactions between temperaturedevelopment and feeding rates as well as param-eters governing spatial effects were not evidentTypically the effect of changes in each of theseparameters was similar regardless of the value ofthe other parameters One interaction did occurWhen temperature was increased a negativechange in T ni development rate resulted in lesspredicted feeding on the head than when no changein T ni development rate was made In all othercases negative change in development rates re-sulted in higher predicted feeding on the head thanwhen development rates were not changed Re-gardless 5 changes in development rates for Tni resulted in lt3 differences in feeding on thehead so the effects of this interaction are not ofgreat importance Thus this analysis reinforced thesingle parameter analysis Feeding rates themselveswere changed in this analysis rather than the pa-rameters that govern them and accumulated feed-ing on the head and wrapper leaves was still moresensitive to changes in development rate and tem-perature

5o

middot5 0

Feeding on Heed

-5Feeding on Wrapper Leaves

o 10

Larvae on Head

middot10

b5b4b3b2bl858483a281

middot20l( Change in

-20 middot10 0 10 Change in Larvae on Wrapper leaves

II2l

~toa0gtatoten

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

SDElA rapae g2

g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

October 1990 Hoy ET AL INTRAPLANTMOVEMENTANDECONOMICTHRESHOLDS 1593

~

SDELT nJ g2

9d

~

SDElA rapae g2

g1C

) SDEL

P XYlostella ~~

-30 -20 -10 o

o Effect of a +10 changebull Effect of a -10 change

10 20 30 -10 o 10 20 30 Change in

Transition prob A rapaeP xylostella

Initial larval distributionInitial ages T ni

A rapae) T ni

Age movement starts A rapaeP xylostella

Hours of sunshineTemperatures

-100

Change In

Feeding on Head

oFeeding on Head

Feeding on Wrapper Leaves

-40 -20 0 20 40 60Feeding on Wrapper Leaves

80

Fig 11 Percentage of change in predicted accumulated area of feeding on the head and wrapper leaves asa result of changing model parameters by + and -10

The sensitivity analyses suggest some importantimplications for use of the model First becausethe model was quite sensitive to initial age distri-bution and temperatures a user should exercisegreat care in collecting data for inputs Samplingfor pests should be intensive enough to estimatethe age distribution of each species accurately Fur-

thermore because the insects within an instar areassumed to be uniformly distributed in age withinthe instar erroneous predictions could be made iflarval ages are more synchronous (eg all smalllarvae are within a few hours of eclosion) Insectsin the field are usually not highly synchronous intheir development because of different times of

o Effect of a +10 changebull Effect of a -10 change

Feeding Rates

T ni ) ~~ hl

A rapae ) ~~ hl

P xylostella ) ~~ hl

-30 -20 -10 0 10 20 Change in Feeding on Head

30 40 -20 -10 0 10 20 30 40Feeding on Wrapper leaves

Fig 12 Percentage of change in predicted accumulated area of feeding by Lepidoptera on cabbage headsand wrapper leaves after a + or -10 change in feeding rate parameters

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

1594 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

oviposition and individual variation in develop-ment rate Insecticides however can create moresynchrony in larval ages by killing some life stagesand not others Errors are also likely to occur be-cause of erroneous weather forecasts and extendedforecasts from the National Weather Service couldbe inaccurate enough to result in such errorsWeather forecasts used should be as recent as pos-sible and as specific as possible to the local areabeing simulated in the model

A second consideration is that predictions ofnumber of larvae of a given species on a givenstratum may be less precise than predictions ofaccumulated feeding because the predictions ofnumber of larvae on a given stratum are moresensitive to changes or imprecision in model pa-rameters Managers should be more concerned withpredicted feeding anyway because this is the vari-able that determines value of the crop In makingdecisions predictions of feeding should be stressedas the most robust indicator of economic damageand the output variable for which the model ismost robust The predictions of number of larvaecan be used to support decisions based on predic-tions of feeding damage and perhaps to help targetthe most damaging species when selecting an in-secticide or other treatment

Finally these analyses suggest two areas in whichadditional work to improve the model would bemost useful transition probabilities for P xylostellaand A rapae and the microclimate submodelChanging transition probabilities for P xylostellaand A rapae had large effects on predicted numberof larvae on the head and wrapper leaves Thevalues used for these matrices reflect our obser-vations and descriptions in the literature of move-ment by larvae of these species Qualitatively thematrices fit these observations well but each tran-sition probability was not estimated quantitativelyTemperature affects not only the direction ofmovement by T ni but also the overall probabilityof movement (Hoy et al 1989) Temperature couldaffect movement of the other two species as wellwith the same proportion of larvae that do movegoing to a given stratum but different proportionsof larvae moving at different temperatures Tech-niques developed to model movement as a functionof environmental conditions for T ni may be usefulfor the other two species

Temperature itself within the canopy has beenrepresented with a simple descriptive model Thisdescription is based on an understanding of theenergy budget within a crop canopy but that en-ergy balance can itself be modeled more mechanis-tically Unfortunately a more mechanistic treat-ment would require consideration of more weatherconditions Specifically heat loss due to convectionwould require estimates of wind speed and evap-orative heat loss would require estimates of am-bient humidity Because these cannot be predictednearly as reliably as temperature they were notincluded in this first version of the model However

given the sensitivity of the model to temperaturemaking use of whatever predictions are availablein a more sophisticated and mechanistic microcli-mate model may improve reliability of predictionsof numbers of larvae on given plant strata andpredicted area of feeding on those strata

Conclusions

The simulation model described here has al-lowed us to estimate the importance of intraplantspatial dynamics in determining when and howmuch damage will occur on the marketable partsof a crop We have learned from the model thatthese dynamics have an important effect on theamount of damage incurred on the marketable partsof the plant resulting from a given combination ofpopulation densities of pest species and environ-mental conditions We maintain that these effectsare important enough to warrant the use of a morecomplex model than the static threshold populationdensity in making management decisions for thesystem we have studied

A manager using this model would supply aweather forecast and results of a field sample togenerate predictions of feeding damage If mini-mal or no damage is forecast on the head andwrapper leaves for the next 7 d no treatmentswould be applied to the crop If unacceptable levelsof feeding were forecast during the 7-d period themanager would look at the output for each day todetermine when unacceptable levels were forecastto appear Until the manager has gained some ex-perience in using the model a conservative limitfor allowable damage would probably be used Atreatment usually an insecticide application wouldbe applied to reduce the pest population beforethe damage is forecast to appear Fine tuning ofthe timing of this application that would considerweather schedule of other farm operations andchanging age structure of the pest population andresulting effectiveness of the insecticide is possiblebetween the time the forecast is made and the timethe unacceptable damage is forecast to appear Ifthe weather during this period is different fromthe forecast the model could be rerun with theupdated weather forecast for even more preciseinformation

We rely on the manager to decide what level ofdamage is unacceptable and to devise reasonablemanagement strategies accordingly Our experi-ence has been that individual farmers have theirown guidelines for acceptability developed throughyears of experience in marketing their productDespite attempts to standardize quality guidelinesconsiderable variation seems to exist in what in-dividual buyers are willing to accept with accom-panying variation in what they are willing to payNo one understands these guidelines better thanthe buyer and seller because the understanding iscreated between these two The sellers in this case

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

October 1990 Hoy ET AL INTRAPLANT MOVEMENT AND ECONOMIC THRESHOLDS 1595

are also the pest managers who must plan aheadto meet the guidelines for the market chosen fortheir crop

Use of the model in its present form is limitedto an extent by the form of the output the averagearea of feeding on a cabbage head and wrapperleaves Percentage of marketable heads which themanager is more interested in depends on the meanand variance of feeding area on these plant partstherefore this version of the model does not predictthe variable percentage of marketable heads thatwould allow direct calculation of expected cost ofthe pest infestation The model incorporates onlyintra plant spatial dynamics of pests and their feed-ing damage interplant dynamics would also haveto be addressed to predict interplant distributionof damage This prediction is possible but willrequire additional research or computing One wayto predict percentage of marketable heads wouldbe to run the simulation separately for each of thesampled cabbage plants using the individual plantcounts as inputs The percentage of plants havingless than a given amount of damage could then beestimated This would require considerable addi-tional computing Another possibility would be toestimate empirically a relationship between themean and variance of feeding area if such existsThe variance and percentiles for given levels ofdamage could then be estimated as a function ofthe mean

Finally our sensitivity analysis has suggested partsof the model that further research could improveGiven the insensitivity of model output to some ofthe parameters it may be possible to simplify someaspects of the model for management use Sensi-tivity analysis also provided an indication of theprecision required in sampling fields to obtain pestpopulation density estimates for model inputs Thislevel of precision may require more sampling effortthan is currently expended Although our valida-tion analysis examined the predictive capabilitiesof the model the costs and benefits of using it fordecision making should stilI be estimated and com-pared to current practice Construction and anal-ysis of the model in its present form however haveyielded important new insights into intraplant spa-tial dynamics of insect pests and how those dy-namics affect the relationship of pest populationdensity to crop damage

Acknowledgment

We thank Gary W Fick for his assistance with thiswork and Robert C Seem for patient help with weathermonitoring equipment We are also grateful to DavidW Onstad and Stephen E Naranjo for thorough andhelpful reviews of an earlier draft of the manuscriptThis work is part of a thesis submitted by Casey W Hoyto the Cornell University Graduate School in partial ful-fillment of the requirements for the degree of Doctor ofPhilosophy

References Cited

Andaloro J T C W Hoy K B Rose J P Tette ampA M Shelton 1983a A review of cabbage pestmanagement in New York from the pilot project tothe private sector 1978-1982 New York Food andLife Science Bulletin 105 New York State Agricul-tural Experiment Station Cornell University Ithaca

Andaloro J T K B Rose A M Shelton C W Hoyamp R F Becker 1983b Cabbage growth stagesNew York Food and Life Science Bulletin 101 NewYork State Agricultural Experiment Station CornellUniversity Ithaca

Bishop Y M M S E Fienherg amp P W Holland1975 Discrete multivariate analysis MIT PressCambridge Mass

Boldt P E K D Biever amp C M IgnolJo 1975Lepidopteran pests of soybeans consumption of soy-bean foliage and pods and development time J EconEntomo 68 480-482

Butler G D Jr A G Hamilton amp A C Bartlett1975 Development of the dark strain of cabbagelooper in relation to temperature Environ Entomo4 619-620

Butler G D Jr R E Stinner amp G L Greene 1976Application of a thermodynamic model for the de-velopment of larvae of the cabbage looper (Lepidop-tera Noctuidae) at fluctuating temperatures FlaEntomo 59 165-169

Cartwright B J V Edelson amp C Chambers 1987Composite action thresholds for the control of lepi-dopterous pests on fresh-market cabbage in the lowerRio Grande valley of Texas J Econ Entomol 80175-181

Chalfant R B W H Denton D J Schuster amp R BWorkman 1979 Management of cabbage cater-pillars in Florida and Georgia by using visual damagethresholds ] Econ Entomo 72 411-413

Chen C amp W Suo 1978 Influence of temperature onthe development and feeding amount of diamond-back moth larvae on cauliflower Plant Prot Bull 20224-231

1982 Influence of temperature on development andleaf consumption of three caterpillars on cauliflowerPlant Prot Bull 24 131-141

Chua T H amp B H Lim 1979 Distribution patternof the diamondback moth Plutella xylostella (Lepi-doptera Plutellidae) on choy-sum plants Z AngewEntomol 88 170-175

Given B B 1944 The relative food consumption ofdiamond-back moth and white butterfly larvae NZ Sci Tech 26(A) 195-197

Goudriaan J 1973 Dispersion in simulation modelsof population growth and salt movement in the soilNeth J Agric Sci 21 269-281

Greene G L W G Genung R B Workman amp E GKelsheimer 1969 Cabbage looper control in Flor-ida-a cooperative program J Econ Entomo 62798-800

Harcourt D G 1963 Biology of cabbage caterpillarsin eastern Ontario Proc Entomo Soc Ont 93 61-75

1966 Major factors in survival of the immature stagesof Pieris rapae (L) Can Entomo 98 653-662

Harcourt D G R H Backs amp L M Casso 1955Abundance and relative importance of caterpillarsattacking cabbage in eastern Ontario Can Entomo87 400-406

Hardy J E 1938 Plutella maculipennis Curt its

1596 ENVIRONMENTAL ENTOMOLOGY Vol 19 no 5

natural and biological control in England Bull Ento-mol Res 29 343-372

Harper J D 1973 Food consumption by cabbageloopers infected with nuclear polyhedrosis virus JInvertebr Patho 21 191-197

Hoy C W amp A M Shelton 1987 Feeding responseof Artogeia rapae (Lepidoptera Pieridae) and Trich-oplusia ni (Lepidoptera Noctuidae) to cabbage leafage Environ Entomo 16 680-682

Hoy C W C Jennison A M Shelton amp J T An-daloro 1983 Variable intensity sampling a newtechnique for decision making in cabbage pest man-agement J Econ Entomol 76 139-143

Hoy C W C E McCulloch C A Shoemaker amp AM Shelton 1989 Transition probabilities forTrichoplusia ni (Lepidoptera Noctuidae) larvae oncabbage as a function of microclimate EnvironEntomo 18 187-194

Jackson C G G D Butler Jr amp D E Bryan 1969Time required for development of Voria ruralis andits host the cabbage looper at different temperaturesJ Econ Entomol 62 69-70

Jones R E amp P M lves 1979 The adaptiveness ofsearching and host selection behaviour in Pieris rapae(L) Aust J Eco 4 75-86

Kirby R D amp J E Slosser 1984 A compositeeconomic threshold for three lepidopterous pests ofcabbage J Econ Entomo 77 725-733

Leibee G L R B Chalfant D J Schuster amp R BWorkman 1984 Evaluation of visual damagethresholds for management of cabbage caterpillars inFlorida and Georgia J Econ Entomo 77 1008-1011

Manetsch T J 1976 Time-varying distributed de-lays and their use in aggregative models of largesystems IEEE Trans Syst Man Cybern SMC-6 No8 547-553

McEwen F L amp G E R Hervey 1960 Mass rearingthe cabbage looper Trichoplusia ni with notes onits biology in the laboratory Ann Entomo Soc Am23 229-234

Miner F D 1947 Life history of the diamondbackmoth J Econ Entomo 40 581-583

Morisak D J D E Simonet amp R K Lindquist 1984Use of action thresholds for management of lepidop-terous larval pests of fresh-market cabbage J EconEntomol 77 476-482

Onstad D W 1987 Calculation of economic-injurylevels and economic thresholds for pest managementJ Econ Entomo 80 297-303

Pedigo L P S H Hutchins amp L G Higley 1986Economic injury levels in theory and practice AnnuRev Entomol 31 341-368

Poston F L L P Pedigo amp S M Welch 1983Economic-injury levels reality and practicality BullEntomol Soc Am 29 49-53

Rahman M 1970 Effect of parasitism on food con-sumption of Pieris rapae larvae J Econ Entomol63 820-821

Richards O W 1940 The biology of the small whitebutterfly (Pieris rapae) with special reference to thefactors controlling its abundance J Anim Ecol 9243-288

Salinas P J 1984 Studies on the behavior of thelarvae of Plutella xylostella (Linnaeus) (LepidopteraPlutellidae) a world pest of cruciferous crops Normaland spacing behaviour Turrialba 34 77-84

Samson P R amp P W Geier 1983 Induction ofcrop damage by the cabbage white butterfly Pierisrapae (Lepidoptera Pieridae) on cabbage Prot Eco5 199-234

SAS Institute 1982 SAS users guide statistics SASInstitute Cary NC

Sears M K R P Jaques amp J E Laing 1983 Uti-lization of action thresholds for microbial and chem-ical control of lepidopterous pests (Lepidoptera Noc-tuidae Pieridae) on cabbage J Econ Entomol 76368-374

Shelton A M J T Andaloro amp J Barnard 1982Effects of cabbage looper imported cabbage wormand diamondback moth on fresh market and pro-cessing cabbage J Econ Entomo 75 742-745

Shelton A M M K Sears J A Wyman amp T CQuick 1983 Comparison of action thresholds forlepidopterous larvae on fresh-market cabbage J EconEntomol 76 196-199

Shorey H H L A Andres amp R L Hale 1962Biology of Trichoplusia ni (Lepidoptera Noctuidae)I Life history and behavior Ann Entomo Soc Am55 591-597

Smith C L amp Z Smilowitz 1976 Growth and de-velopment of Pieris rapae larvae parasitized byApanteles glomeratus Entomol Exp Appl 19 189-195

Stern V M 1973 Economic thresholds Annu RevEntomol 18 259-280

Stinner R E A P Gutierrez amp G D Butler Jr1974 An algorithm for temperature-dependentgrowth rate simulation Can Entomol 106 519-524

Tatchell G M 1981 The effects of a granulosis virusinfection and temperature on food consumption ofPieris rapae (Lepidoptera Pieridae) Entomophaga26 291-300

Theunissen J H den Ouden amp A K H Wit 1985Feeding capacity of caterpillars on cabbage a factorin crop lossassessment Entomol Exp Appl 39 255-260

Toba H H A N Kishaba R Pangaldan amp P V Vail1973 Temperature and development of the cab-bage looper Ann Entomol Soc Am 66 956-974

Wolfson J L 1982 Developmental responses of Pierisrapae and Spodoptera eridania to environmentallyinduced variation in Brassica nigra Environ Ento-mol 11 207-213

Workman R B R B Chalfant amp D J Schuster1980 Management of cabbage worms with twothresholds and five insecticidal sprays J Econ Ento-mol 73 757-760

Yamada H amp K Kawasaki 1983 The effect oftemperature and humidity on the development fe-cundity and multiplication of the diamondback mothPlutella xylostella Jpn J Appl Entomol Zool 2717-21

Received for publication 19 June 1989 accepted 18May 1990