the effect of host density on ectoparasite distribution

164

Ecology, 83(1), 2002, pp. 164–175q 2002 by the Ecological Society of America

THE EFFECT OF HOST DENSITY ON ECTOPARASITE DISTRIBUTION:AN EXAMPLE OF A RODENT PARASITIZED BY FLEAS

BORIS KRASNOV,1,3 IRINA KHOKHLOVA,2 AND GEORGY SHENBROT1

1Ramon Science Center, Jacob Blaustein Institute for Desert Research, Ben-Gurion University of the Negev,P.O. Box 194, Mizpe Ramon, Israel

2Wyler Department of Desert Agriculture, Jacob Blaustein Institute for Desert Research,Ben-Gurion University of the Negev, Beer Sheva, Israel

Abstract. The pattern of parasitism of the flea species Xenopsylla dipodilli and Nos-opsyllus iranus theodori on the desert rodent species Gerbillus dasyurus was studied totest the hypothesis that the relationships between flea abundance and host density conformto pre-existing models of R. M. Anderson and R. M. May, with the correction that thedensity of those host individuals that possess permanent burrows (residents) is substitutedfor the overall host density. It was predicted that: (1) the intensity of flea infestation wouldincrease in curvilinear fashion with increase of host density to a plateau that would beattained at a lower level of host density than would be expected from the basic model, and(2) the prevalence of flea infestation plotted against host density would be hump-shaped.The results indicated that intensity of flea infestation increased in either curvilinear fashionto an asymptote (for X. dipodilli) or linearly (for N. i. theodori) with increase of hostdensity. As host density increased, the prevalence of infestation changed either unimodally(X. dipodilli) or logarithmically (N. i. theodori). In addition, there was a positive relationshipbetween the mean number of fleas per host and the percentage of hosts infested. Both basicand corrected models describing the relationships between flea burden and host density fitthe observational data well. However, simulations of the fraction of resident hosts dem-onstrated that this parameter influences the relationship between host density and flea burdenonly when residents comprise #50% of all host individuals.

Key words: ectoparasite; flea burden; Gerbillus dasyurus; host density; Nosopsyllus iranus theo-dori; parasitism; rodent; Xenopsylla dipodilli.

INTRODUCTION

Unlike most free-living species, the geographicrange of parasites consists of a set of more or lessuniform inhabited ‘‘islands’’ or patches, represented bytheir host organisms, and the environment betweenthese patches is absolutely unfavorable. The distribu-tion of a parasite population across a host populationis characterized by their aggregation, or overdispersion.Most individuals of the overdispersed parasite occuron a few host individuals, while most host individualshave a only a few parasites or none at all (Andersonand May 1978, Poulin 1993). This particular distri-bution of parasite individuals among hosts has impor-tant consequences for different aspects of the evolu-tionary ecology of parasites. For example, overdisper-sion can explain the density dependence of the intensityof intraspecific competition (Shostak and Scott 1993)and the biased sex ratio (Morand et al. 1993) in par-asites.

The basic models of Anderson and May (Andersonand May 1978, May and Anderson 1978), implying theoverdispersed distribution of parasites, predicted that

Manuscript received 17 April 2000; revised 20 December2000; accepted 17 January 2001.

3 Present address: Ramon Science Center, P.O. Box 194,Mizpe Ramon 80600 Israel. E-mail: [email protected]

the mean number of parasites per infested host (parasiteburden or intensity of infestation) would increase in acurvilinear fashion to a plateau with increasing hostdensity (Dobson 1990). This is due to the increasedprobability that a parasite transmission stage wouldmeet a host. However, only a few empirical studies ofthis prediction have been conducted (Haukisalmi andHentonnen 1990, Arneberg et al. 1998). Another com-ponent of parasite abundance, namely, prevalence ofinfestation (percentage of infested hosts), was not con-sidered in the framework of the model of Anderson andMay (1978). Nevertheless, the prevalence of infestationcould be expected to increase with increasing host den-sity. The argument for this can be the same as that forthe intensity of infestation, namely, that under high hostdensity there is an increased probability that the par-asite transmission stage will be transmitted. Anotherexplanation follows metapopulation theory: parasitesinfesting different host individuals are analogous tofree-living organisms inhabiting discrete patches, andthe percentage of occupation of the latter increases withthe decrease of patch isolation (Thomas and Hanski1997). This correlation between host density and prev-alence of infestation has been supported by empiricalstudies (Arneberg et al. 1998).

Most studies related to parasite evolutionary ecologyand host–parasite relationships were made on endo-

January 2002 165HOST DENSITY AND ECTOPARASITE DISTRIBUTION

PLATE 1. Wagner’s gerbil (Gerbillus dasyurus). Photo by G. Shenbrot.

parasites, mainly helminths. A host represents an ul-timate habitat for an endoparasite, providing it with aplace for living, foraging, and mating. Thus, hosts maybe considered as habitat patches for most endopara-sites. Unlike endoparasites, ectoparasites are influ-enced not only by characters of the host, but also bycharacters of their off-host environment, because theircontact with the host is usually intermittent. The rangeof off-host:on-host ratio of different ectoparasite taxais very broad, varying from almost constant occurrenceon the host lice (Anoplura), to sporadically attackinghost ticks (Ixodidae) and sand flies (Phlebotomidae).Fleas (Siphonaptera) take a median position in thisrange, alternating between periods when they occur onthe body of their host and periods when they occur inits burrow or nest. Fleas are permanent satellites ofhigher vertebrates, being most abundant and diverse onsmall burrowing mammals. The female flea of somespecies oviposits while on the host, but the eggs typ-ically drop off into the nest or burrow (e.g., Pectin-octenus pavlovskii, Leptopsylla segnis [Vasiliev 1961,cited by Vatschenok 1988]). Other species mate andoviposit both on-host and off-host (e.g., Xenopsyllacheopis). Nevertheless, in nearly all cases, larval andpupal development is entirely off-host. The larvae arenot parasitic (except for a single species, Uropsyllatasmanica [see Vatschenok 1988]) and feed on debrisand materials found in the burrow and/or nest of thehost. The larvae of the third instar spin a cocoon, cam-ouflaging it by adhering particles of the substrate.Therefore, the habitat patch of a flea should be con-sidered not only as a particular host, but rather as aparticular host with a particular burrow or nest in aparticular habitat. This complex host–habitat–parasiterelationship can change the expectations derived fromthe basic models.

Indeed, the increase of density in rodent populations,

particularly in solitary species, often results in a surplusof individuals that have no individual home ranges(Brandt 1992, Gliwicz 1992 and references therein). Intheory, these homeless individuals should not be pu-tative hosts for fleas, because they do not possess bur-rows that are necessary for flea reproduction and de-velopment of pre-imaginal stages. In turn, the densityof resident hosts is determined by the carrying capacityof the given habitat. For example, this carrying capacitycan be dependent on the number of available burrowsor places for burrowing, all else being equal. If the fleaburden increases in a curvilinear fashion to a plateauwith increasing host density, the breakpoint of thiscurve should be determined by the density of residenthosts rather than by the overall density of the hosts.Consequently, the flea burden should decrease with theproportion of resident individuals, under the same over-all abundance of the host and the same overall abun-dance of parasites. The plateau of the flea burden curveshould be lower than is expected from the basic model.

If the resident hosts alone support the flea popula-tion, the prevalence of infestation should increase withthe increase of host density, until the habitat becomessaturated with residents (e.g., all available burrows oc-cupied). Under higher host density, the prevalence offlea infestation should decrease, since the resident ro-dents would compose an ever-decreasing fraction ofthe overall host population. Thus, the prevalence offlea infestation plotted against host density is expectedto be hump-shaped.

The small gerbilline rodent, Gerbillus dasyurus(Wagner, 1842) (body mass is 20–24 g), occupies avariety of habitats in the Negev Highlands, Israel(Shenbrot et al. 1997; see Plate 1). The density of G.dasyurus varies across habitats, being highest in loesshills and lowest on gravel plains (Krasnov et al. 1996).The fraction of transient (nonresident) individuals

166 BORIS KRASNOV ET AL. Ecology, Vol. 83, No. 1

varies both among habitats and between years. Thisfraction reaches as high as 50% in high-density yearsin loess hills (Gromov et al. 2000) and is even higheron gravel plains, where the majority of individuals aretransient (Khokhlova et al. 1994). Young individualsof G. dasyurus have been observed mainly from Aprilto September, whereas the last pregnant females oc-curred in October (Shenbrot et al. 1997). This indicatesthat the spring and summer parts of breeding periodwere successful, while the pups of late autumn repro-duction tended not to survive. In addition, the dispersalof young gerbils occurred mainly in late spring andsummer (I. S. Khokhlova and B. R. Krasnov, unpub-lished data). Two types of burrows of G. dasyurus havebeen described (Shenbrot et al. 1997): (1) simple bur-rows of small depth, without nests, and (2) complex,deeper, burrows with a spherical nest made from driedplant material. It appears that resident individuals usecomplex burrows, whereas transients have to be sat-isfied with simple burrows, if any. We recorded fleasin complex burrows of G. dasyurus, whereas no fleaswere found in simple burrows (B. R. Krasnov and G.I. Shenbrot, unpublished data). Nevertheless, each bur-row of either type is occupied by one adult individual(Shenbrot et al. 1997).

G. dasyurus is parasitized mainly by two flea species,Xenopsylla dipodilli Smit, 1960, and Nosopsyllus ir-anus theodori Smit, 1960 (Krasnov et al. 1998, 1999).X. dipodilli occurs on G. dasyurus throughout the year,although the abundance of this flea in winter is ex-tremely low (Krasnov et al. 1997). In contrast with X.dipodilli, N. i. theodori is a winter flea. No imago hasbeen found on G. dasyurus between April and Decem-ber (Krasnov et al. 1997). Thus, these two fleas alter-nate on G. dasyurus. These flea species occur also onother rodents in the area (Krasnov et al. 1997, 1999).However, extremely low abundances and sporadicityof these fleas on rodents other than G. dasyurus suggestthat this has no any significant effect on the host–par-asite population dynamics.

We hypothesized that the relationships between fleaabundance and host density conform to the basic mod-els of Anderson and May (1978), with the followingcorrection: flea abundance is influenced by the abun-dance of resident hosts, rather than overall host density.We predicted that the intensity of flea infestation wouldincrease with an increase in host density in a curvilinearfashion to a plateau that would be attained at a lowerlevel of host density than expected from the basic mod-el. In addition, we predicted that the prevalence of fleainfestation plotted against host density would be hump-shaped. To test these predictions, we studied the patternof parasitism of the fleas X. dipodilli and N. i. theodorion G. dasyurus in the Negev desert.

METHODS

Study area

The study was conducted in the Ramon erosioncirque, Negev Highlands, Israel. The Ramon erosion

cirque is an area of about 200 km2 and is situated atthe southern boundary of the Negev Highlands (308359N, 348459 E). The diverse habitats represented in theRamon cirque, range from sandy dunes in the north-eastern parts of the cirque to sandstone rocks on therims. The climate is characterized by hot, dry summers(mean daily air temperature of July is 348C) and rel-atively cold winters (mean daily temperature of Januaryis 12.58C). There is a sharp decrease in annual rainfallfrom 100 mm on the north rim to 56 mm in the bottomof the cirque.

Rodent trapping and flea collection

Rodents were trapped on seven 1-ha plots from sum-mer 1992 until summer 1993 and on 16 1-ha plots fromsummer 1994 until summer 1995. The first seven plotswere sampled every 2–3 mo. Other plots were sampledevery 6 mo. Plots were selected to represent the mainsubstrate and vegetation gradients. Each plot was sam-pled during 3–5 consecutive days, using 50 Shermanlive traps (Sherman Traps, Tallahasse, Florida, USA)placed in a grid at 5 3 5 stations, with two traps perstation and an interval of 20 m between stations. Theoverall density of G. dasyurus was evaluated as theminimal number of individuals known to be alive. Anindividual was considered resident if it was capturedeither: (1) at least once in each of three consecutivetrapping periods, each 2–3 mo apart (in 1992–1993),or (2) at least once in each of two consecutive trappingperiods, each 6 mo apart (in 1994–1995). This deter-mination of resident vs. transient status can producesome bias toward finding transients. In other words,we could erroneously attribute the transient status toresident gerbil (e.g., if it died by some unknown rea-sons during the study period) but could not erroneouslyattribute the resident status to transient gerbil. How-ever, the individual composition of G. daysurus pop-ulations has been shown to be very stable (Shenbrot etal. 1997), suggesting that this potential bias could beconsidered negligible.

We collected fleas from each individual rodent onlywhen it was captured the first time. The animal’s furwas combed thoroughly, using a toothbrush over awhite plastic bath, and fleas were carefully collected.Each rodent was sexed, weighed, marked by toe clip-ping, and released. In total, 657 gerbils were captured,and 945 X. dipodilli and 320 N. i. theodori were col-lected.

The models

We used the models presented by Anderson and May(1978), May and Anderson (1978), Grenfell (1992),and Arneberg et al. (1998). These models describe thedynamics of populations of host (H ) and parasite (P).The main assumptions of the basic models are that: (1)host population growth is density dependent, given thatthere is no parasite-induced reduction of host repro-duction, (2) hosts are long-lived, relative to their par-


TABLE 1. Description of the parameters of the basic model (adapted from Anderson and May1978, Dobson 1990, Arneberg et al. 1998).

Parameter Description

a Instantaneous birth rate of host (per host per unit time)b Instantaneous death rate of host due to causes other than parasite (per

host per unit time)a Instantaneous host death rate due to parasite influence (per host per unit

time)b Instantaneous rate of host reproduction reductions due to parasite influ-

ence (per host per unit time)Ã Severity of density dependence in host population growthl Instantaneous birth rate of parasite transmission stages (per parasite per

unit time) (the transmission stage for fleas is the adult imago)m Instantaneous death rate of parasites due to either natural or host induced

(e.g., autogrooming) causesH0 Transmission efficiency constant, varying inversely with the proportion of

parasite transmission stages that infest individuals of the host popula-tion (see Anderson and May [1978] for further explanations)

k Parameter of the negative binomial distribution, varying inversely withthe degree of overdispersion; it measures the degree of aggregation ofthe parasites within host population

asites, and (3) the frequency of parasites within hostsfollows the negative binomial distribution.

The basic model utilizes the following equations:

dH5 (a 2 b 2 ÃH )H 2 (a 1 b)P (1)

dt

dP lPH5 2 (b 1 ÃH 1 a 1 m)P

dt H 1 H0

2(k 1 1)P2 (a 1 m) . (2)

kH

The parameters of the model are presented in Table 1.The model assumes that a parasite induces mortalityof a host (Anderson and May 1978, May and Anderson1978). However, Arneberg et al. (1998) argued that thepositive relationship between host density and parasiteabundance would also be expected when parasites haveno pathogenic effects. Although the negative influenceof flea parasitism on the fitness of a rodent host hasbeen reported for Synosternus cleopatrae on Gerbillusandersoni allenbyi (Lehmann 1992), no effect of fleainfestation on body conditions or on the survival of G.dasyurus was found (Krasnov et al. 1997).

Thus, given that fleas neither induce host mortalitynor reduce host reproduction, a 5 b 5 0 is assumed.Further, we assumed that the dynamics of fleas is in-fluenced by the density of those host individuals thatare resident and have permanent burrows (S ). This den-sity is limited by the carrying capacity of the habitat,for example, by the number of available burrows. Inaddition, only resident host individuals reproduce. Fur-thermore, we assume that all host individuals are equal-ly susceptible to parasitism by fleas, and thus, the trans-mission of fleas from individual to individual, or fromburrow to burrow, can be performed by both resident

and transient host individuals. This transmission canoccur either when individuals visit alien burrows orthrough direct contact between host individuals (Kras-nov and Knyazeva 1983). Consequently,

dH5 (a 2 ÃS)S 2 bH (3)

dt

2dP lPS (k 1 1)P5 2 (b 1 ÃS 1 m)P 2 m . (4)

dt H 1 H kH0

The parasite burden (M ) is the mean number of par-asites per infested host, so the rate of changes in par-asite burden is

dM dP /H5

dt dt

lMS m(k 1 1)25 2 (b 1 ÃS 1 m)M 2 M

H 1 H k0

2S S2 a M 1 Ã M 1 bM. (5)

H H

At equilibrium (dH/dt 5 dp/dt 5 dM/dt 5 0),

lS S S kM 5 2 m 2 a 2 1 2 ÃS .1 2[ ][ ]H 1 H H H m(k 1 1)0

(6)

Eq. 6 was applied for X. dipodilli in spring and summer.N. i. theodori occurs on its host during the period whenhost does not reproduce (a 5 0). Consequently, thisequation for N. i. theodori was transformed as

lS S kM 5 2 m 1 2 ÃS . (7)1 2[ ][ ]H 1 H H m(k 1 1)0

Hereafter, Eqs. 6 and 7 are referred to as ‘‘corrected’’models. They are collapsed into the equations of thebasic model, if S 5 H.


TABLE 2. Parameters of frequency distribution of X. dipo-dilli and N. i. theodori on G. dasyurus

Flea species N s2/X̄ Mo k

Negativebinomial

x2 P

X. dipodilliN. i. theodori

945320

7.253.79

0.530.51

0.390.51

29.0518.9

0.270.45

Note: See Statistical processing for explanation of param-eters.

TABLE 3. Parameters of the corrected and basic model when fitted to the observed burden ofX. dipodilli or N. i. theodori in relation to density of G. dasyurus.

Flea Model

Varianceexplained

(%) R H0 Ã m

X. dipodilli

N. i. theodori

BasicCorrectedBasicCorrected

71.569.781.583.0

0.840.810.900.91

3.6 6 1.03.4 6 1.8

17.6 6 1.919.1 6 1.2

24.9 6 2.6

29.6 6 1.8

9.2 6 0.78.7 6 1.23.7 6 0.83.1 6 0.7

Note: The Ã term is not present in the basic model (because S 5 H).

We assigned values of the birth rate of G. dasyurus(a 5 2) based on our data both from field observations(on average, two litters per breeding female per repro-duction period, 1.4:1 male:female ratio, 60% repro-ductively active adult females; Shenbrot et al. 1997)and from laboratory breeding (on average, four pups/litter; I. S. Khokhlova and B. R. Krasnov, unpublisheddata). No data are available on birth rate of transmis-sion stages either of X. dipodilli or N. i. theodori.Therefore, we used data on congeneric species, namely,Xenopsylla cheopis (Samarina et al. 1968), Xenopsyllaconformis (Vatschenok 1988; B. R. Krasnov and I. S.Khokhlova, unpublished data), and Nosopsyllus con-similis (Alekseev 1961, Vatschenok 1988). We calcu-lated the birth rate of flea transmission stages based onthe rate of oviposition per female per breeding season,given that survival of pre-imaginal stages is 80%. Thus,l was considered to be equal to 100 for X. dipodilli,and 140 for N. i. theodori. Parameters H0, Ã, and mwere estimated from the model-fitting procedures (seeStatistical processing).

Analysis of the model concentrated on the variationin flea burden and prevalence of infestation with chang-es in the fraction of resident host individuals under thesame overall density. We simulated changes in thisfraction from 5% to 100% with a 5% step.

Statistical processing

Whether the negative binomial can be used as a mod-el for the distribution of X. dipodilli and N. i. theodorion G. dasyurus was tested using the NEGBINOM com-puter software (Krebs 1989). The acceptance of the nullhypothesis that the negative binomial distribution fitsthe data was performed using a chi-square test. In ad-dition, three measures of aggregation were calculated:(1) k of the negative binomial distribution, (2) variance-

to-mean ratio s2/X̄, and (3) standardized Morisita indexMo (Krebs 1989) using the NEGBINOM program.

We applied least-squares estimation procedures viathe quasi-Newton algorithm for fitting the models ofthe relationships between host density and flea burden.In addition, we used regression analysis for the de-scription of the relationships between both flea burdenand prevalence of flea infestation, and both overall hostdensity and density of resident hosts. Samples with G.dasyurus density ,2 were excluded from the analysesof prevalence of infestation. Model simulations for X.dipodilli were analyzed using a nonlinear estimation ofthe breakpoint of piecewise linear regression. Thosefor N. i. theodori were analyzed using linear regression.All these calculations were performed with the statis-tical package STATISTICA (StatSoft, 1995).

RESULTS

Flea distribution among host individuals

Distributions of both flea species on G. dasyuruswere aggregated. The aggregation is indicated by thevalues of the standardized Morisita index of dispersion,the variance-to-mean ratio and k for negative binomial(Table 2). The negative binomial model successfullyfit the observed frequency distribution of both X. di-podilli and N. theodori on G. dasyurus in spring–sum-mer and winter, respectively (Table 2).

The effect of host density on flea burden

The burden of X. dipodilli (Mobs) on G. dasyurusincreased in a curvilinear fashion to a plateau withincrease in host density. This relationship could be de-scribed significantly by logarithmic fit Mobs 5 0.4 10.73logH (F1,34 5 80.45, r2 5 0.69, P , 0.001). Changein host density was accompanied by a rapid change inflea burden until the former attained ;20 individuals/ha. Further increase in host density did not causechange in flea burden. Both corrected and basic modelsdescribed this relationship well (Table 3, Fig. 1), yield-ing similar values for the parameters H0 and m.

Manipulation of the fraction of host residents whileholding all other parameters constant, produced a num-ber of curves (Fig. 2). It may be envisaged that thebasic and corrected models differed from one anotherwhen the fraction of residents was $50%. The break-point of the piecewise linear regressions of flea burden


FIG. 1. Dependence of X. dipodilli burden on density ofG. dasyurus (observed, triangles and solid line; expected fromcorrected model, circles and dashed line; expected from basicmodel, diamonds and bold dashed line).

FIG. 3. Values of the breakpoint of piecewise linear re-gression (triangles) and the threshold of establishment (cir-cles), calculated for simulation curves of X. dipodilli burden–G. dasyurus density in dependence on the simulated per-centage of resident host individuals.

FIG. 2. Relationships between X. dipodilli burden and G.dasyurus density produced by manipulation of the fraction ofhost residents from 5% to 100%, while holding all other pa-rameters constant.

FIG. 4. Dependence of N. i. theodori burden on densityof G. dasyurus (observed, triangles and solid line; expectedfrom corrected model, circles and dashed line; expected frombasic model, diamonds and bold dashed line).

against host density changed logarithmically with a dif-ferent fraction of residents attaining a plateau whenthis fraction achieved 50–60% (F1,18 5 2247.5, r2 50.99, P , 0.001; Fig. 3). In addition, the describedsimulation demonstrated that the threshold of estab-lishment (the minimal size of host population necessaryto sustain a parasite population) was higher when therewas a lower (5–30%) fraction of residents in a hostpopulation (F1,18 5 38.2, r2 5 0.69, P , 0.001; Fig.3). Furthermore, X. dipodilli burden decreased weakly,albeit significantly, with an increase in the observedpercentage of resident G. dasyurus (F1,34 5 19.8, r2 50.35, P , 0.001). In contrast with X. dipodilli, theburden of N. i. theodori increased linearly with an in-crease in G. dasyurus density (F1,20 5 85.8, r2 5 0.8,P , 0.001). As was the case with X. dipodilli, bothcorrected and basic models fit this pattern well (Table3, Fig. 4).

The results of the manipulation of the fraction ofresident hosts while holding all other parameters con-stant are presented in Fig. 5. Again, the basic and cor-

rected models differed from one another when the frac-tion of residents exceeded 50%. The higher the residentfraction, the faster was the rate of change in flea burden,indicated by the value of the slope of linear regression,until the fraction of residents attained 50–60% (F1,18

5 73.4, r2 5 0.80, P , 0.001; Fig. 6). As was the casefor X. dipodilli, the threshold of N. i. theodori estab-lishment was greater with a lower fraction of residentsin a host population (F1,18 5 16.8, r2 5 0.77, P , 0.001;Fig. 6). The observed flea burden was correlated neg-atively with the observed percentage of resident gerbils(F1,20 5 19.7, r2 5 0.49, P , 0.001).

The effect of host density on flea prevalence

Prevalence of infestation by X. dipodilli changed un-imodally with an increase in overall density of G. das-yurus. The fraction of infested gerbils peaked at a den-sity of 20 individuals/ha, whereas it was lower underboth lower and higher gerbil density (Fig. 7). This re-lationship can be described by the equation PI 5 50.1


FIG. 5. Relationships between G. dasyurus density andN. i. theodori burden produced by manipulation of the fractionof host residents from 5% to 100% while holding all otherparameters constant.

FIG. 7. Relationship between the density of G. dasyurusand prevalence of infestation by X. dipodilli, calculated forresident gerbils only (triangles and dashed line) and for bothresident and nonresident gerbils (circles and solid line).

FIG. 6. Values of the slope of linear regression (triangles)and threshold of establishment (circles) calculated for sim-ulation curves of X. dipodilli burden–G. dasyurus density independence on the simulated percentage of resident host in-dividuals.

FIG. 8. Relationship between the density of G. dasyurusand prevalence of infestation by N. i. theodori, calculated forresident gerbils only (triangles and dashed line) and for bothresident and nonresident gerbils (circles and solid line).

1 3.15H 2 0.1H2, where PI is prevalence of infestationand H is host density (F2,30 5 26.8, r2 5 0.62, P ,0.001). Prevalence of X. dipodilli infestation plottedagainst density of resident hosts was also hump-shaped,with a peak of prevalence at 12–13 individuals/ha (Fig.7). The curve of prevalence against resident densitywas steeper than the curve of prevalence against overalldensity, and fitted the equation PI 5 36.0 1 8.6S 20.36S2, where S is density of resident individuals (F2,30

5 20.9, r2 5 0.58, P , 0.001). Coefficients of thesetwo regressions differed significantly (t 5 3.64 and t5 3.95, P , 0.01). The prevalence of infestation re-sponded weakly, albeit significantly, to the fraction ofresident individuals in the host population being higherwith a greater percentage of residents (F1,31 5 9.6, r2

5 0.23, P , 0.001).Prevalence of infestation by N. i. theodori increased

logarithmically with an increase in host density (F1,20

5 16.8, r2 5 0.46, P , 0.001; Fig. 8). The same wastrue for the relationship between the prevalence of in-festation and the density of resident hosts (F1,20 5

25.41, r2 5 0.56, P , 0.001; Fig. 8). Although thesetwo regressions did not differ significantly (t 5 0.45for intercepts and t 5 0.29 for slopes), the density ofresident hosts seemed to be a better predictor of prev-alence of infestation than overall host density (notehigher r2 values). In contrast with X. dipodilli, no cor-relation was found between prevalence of infestationby N. i. theodori and the fraction of resident individualsin the host population (F1,20 5 0.76, P . 0.3).

Relationships between flea burden andprevalence of infestation

The burden of X. dipodilli was not correlated withthe prevalence of infestation when the former was cal-culated as the mean number of fleas per infested gerbil(F1,30 5 0.1, P . 0.9). However, when this parameterwas substituted with mean number of fleas across allhosts, the relationship between flea abundance per host


and prevalence of infestation was significantly positive(F1,30 5 21.11, r2 5 0.41, P , 0.001). Furthermore, theprevalence of infestation of resident gerbils increasedsignificantly with the burden of X. dipodilli calculatedfor resident individuals only (F1,30 5 37.27, r2 5 0.55,P , 0.001). In order to test if these relationships weresampling artifacts, the sampling model of Hanski et al.(1993) was applied to our observational data. Thismodel explained only 32% of the variance in the frac-tion of uninfested gerbils across sampling sites. Thissuggests that the increase of the prevalence of infes-tation with the increase of flea burden cannot be con-sidered as sampling artifact.

A positive relationship has been found between theburden of N. i. theodori and the prevalence of infes-tation when the burden was calculated both for infestedgerbils and for all gerbils (F1,20 5 18.53, r2 5 0.48, P, 0.001, and F1,20 5 41.6, r2 5 0.68, P , 0.001 re-spectively). The intensity of infestation of resident G.dasyurus was an even better predictor of the prevalenceof infestation (F1,20 5 52.79, r2 5 0.73, P , 0.001).The sampling model explained only 44% of varianceof the fraction of uninfested gerbils across samplingsites.

DISCUSSION

The present study of patterns of flea parasitism onG. dasyurus produced the following answers to ques-tions we set out to address. The intensity of flea in-festation increases either in a curvilinear fashion to aplateau (for X. dipodilli) or linearly (for N. i. theodori)with an increase in host density. The difference be-tween overall host density and the density of residenthosts is important for the determination of parasite bur-den only if residents comprise ,50% of all hosts. Thepercentage of infested hosts changes either unimodally(X. dipodilli) or logarithmically (N. i. theodori) as hostdensity increases. There was a positive relationship be-tween the mean number of fleas per host and the per-centage of hosts infested. The answers were obtainedfrom the field data and from the analysis of a flea–rodent relationship model, incorporating among-hostfunctional differences that are important for flea re-production.

We recognize that in the real world, flea populationdynamics will be affected, among other factors, by abi-otic parameters (ambient temperature, relative humid-ity, etc.) that may directly influence flea reproductionand survival (especially during pre-imaginal develop-ment; B. R. Krasnov and I. S. Khokhlova, unpublisheddata). Nevertheless, our omission of the abiotic con-straints on the flea population dynamics is deliberate,since our main aim is to provide quantitative insightsinto the mechanisms by which hosts regulate parasitepopulations. Therefore, we excluded the concept of en-vironmental mediation of rodent–flea relationships tosimplify the manipulations. Such simplification eluci-dates predictions of biological concern.

Flea burden and host density

Our field data did not allow us to successfully dis-tinguish between the corrected and basic models ofhost–parasite dynamics. However, the manipulation ofthe fraction of host residents provided a set of curvesthat permitted us to discriminate between these models.

A positive relationship between host density and par-asite burden was expected from the increase of parasitetransmission rate under higher host densities (Andersonand May 1978, May and Anderson 1978, Arneberg etal. 1998). The greater the host density, the greater theprobability that each parasite individual or respectivetransmission state (egg, larva, or imago) will contacta host. Indeed, a positive correlation between parasiteburden and host density has been reported for bothendoparasites (Haukisalmi and Hentonnen 1990) andectoparasites (Zhonglai and Yaoxing 1997, 1998), al-though other studies did not support this prediction(Sorci et al. 1997).

The plateau attained by the curve of X. dipodilli bur-den with an increase in host density can be explainedmost easily by the limited carrying capacity of hostindividuals that can harbor a limited number of para-sites only. However, this suggests a negative impact ofparasites on hosts (Brown and Brown 1986, Lehmann1993). No indication of an effect of fleas on gerbil bodyconditions and survival was found (Krasnov et al.1997), and no effect was assumed in the present mod-els. Thus, the only possible explanation implicatinghost carrying capacity can be that this parasite thresh-old is very narrow, and that gerbil response to fleanumber is stepwise rather than gradual. Flea abundancebelow some threshold does not influence the health ofthe gerbil, whereas flea abundance above the thresholdis lethal. Consequently, the observed number of fleason every captured gerbil was below the threshold. Fur-thermore, the relationship between N. i. theodori andgerbil density was linearly positive, and there was noplateau under high gerbil density. In addition, the meannumber of fleas per infested rodent was higher for N.i. theodori than for X. dipodilli (mean 6 1 SE; 4.8 60.3 fleas/rodent vs. 2.7 6 0.1 fleas/rodent). This resultsuggests that the explanation of a plateau caused byhost mortality when flea intensity exceeds a specificthreshold is unsatisfactory.

An alternative explanation implies the heterogeneityof hosts in relation to burrows as habitats for successfulflea breeding, as well as the carrying capacity of hosthabitat. Flea populations can be established and main-tained on those host individuals that own burrows (res-idents), whereas homeless hosts can take part in fleatransmission but are unable to sustain fleas. As overallhost density increases, the number of residents attainsa particular level determined by the carrying capacityof host habitat. Further increases in host density resultin an increase in the number of nonresidents, while thenumber of residents remains stable. Because nonresi-


dent hosts do not participate in the siphonapteran lifecycle, the overall increase in host density after satu-ration of a habitat by residents has no effect on the fleaburden. This can also explain the absence of a plateauin the burden of N. i. theodori with a high density ofgerbils. In contrast to X. dipodilli, N. i. theodori is awinter flea, reproducing in periods when neither re-production nor dispersal of G. dasyurus occurs, so mosthost individuals in a given habitat are residents(Khokhlova et al. 1994, Shenbrot et al. 1997). If so,each habitat in each given period is saturated by res-idents, whereas transient homeless individuals are ab-sent. Thus, the flea burden increases linearly with hostdensity. Indeed, the mean percentage of individualsconsidered to be nonresidents was 17.4 6 3.1% non-resident individuals in spring–summer (when G. das-yurus was parasitized by X. dipodilli) and 3.1 6 1.1%nonresident individuals in winter (when G. dasyuruswas parasitized by N. i. theodori).

Finally, it is possible that an increase in flea numberabove some threshold either arouses an irritation of agerbil’s skin and, consequently, excessive groomingactivity of a gerbil, or induces an immune response ofa gerbil to flea salivary gland-derived molecules (Wikel1996). Grooming activity of a host has been shown tobe one of the most significant host-induced mortalityfactors for ectoparasites (Marshall 1981), and is pos-itively correlated with the severity of infestation (Hin-kle et al. 1998). This is why the number of fleas on anindividual host does not exceed some threshold. Fur-thermore, in contrast to N. i. theodori, X. dipodilli hasno ctenidia that permit the flea to anchor itself withinhost fur, enabling it to resist the host’s grooming effort(Humphries 1967, Traub 1972). This can partly explainwhy the mean number of fleas per infested rodent washigher for N. i. theodori than for X. dipodilli.

Host immune responses can be also important inmodulating ectoparasite numbers. It has been reportedthat different taxa of blood-feeding arthropods, includ-ing fleas, stimulate a variety of host innate and specificacquired immune responses (Jones 1996, Wikel 1996).Consequently, host–ectoparasite associations are usu-ally characterized by development of some level ofacquired resistance, which could potentially limit thelevel of infestation. However, it is unknown whetherG. dasyurus is able to develop immune responses toflea infestation. Also, a higher level of N. i. theodoriinfestation in comparison with X. dipodilli infestationseems to contradict the explanation implying host im-mune response, given the absence of the plateau in theformer case and the presence of the plateau in the lattercase.

As mentioned previously, both basic and correctedmodels describing the relationships between flea bur-den and host density fitted the observation data well.However, the simulations of the fraction of residentsdemonstrated that this parameter influences the rela-tionship between host density and flea burden only

when residents comprise #50% of all host individuals.This was true for both flea species. The only possiblerole of nonresident hosts in flea dynamics is their effecton flea transmission, given that they do not support fleareproduction. It appears that when the percentage ofnonresidents is relatively low, they do not contributeheavily toward flea transmission, so their influence onflea dynamics and distribution is negligible (Khokhlovaand Knyazeva 1983). Thus, the introduction of a pa-rameter for nonresident density into the model does notproduce any significant shift in comparison with thebasic model. However, when the fraction in the hostpopulation is relatively high, their contribution to fleatransmission becomes significant. In such a case, amodel that takes this nonresident component into ac-count, should describe the observational data betterthan that which considers only the overall host density.The role of resident hosts in flea dynamics is also sup-ported by the fact that flea burden was correlated neg-atively with the percentage of resident gerbils, showingthat all flea individuals were distributed almost exclu-sively among resident hosts and did not occur on non-residents. In addition, the manipulation of the fractionof resident hosts demonstrated that the breakpoint ofthe flea burden vs. host-density curve is affected bythis fraction, thus conforming to our prediction, at leastin relation to X. dipodilli. The plateaux of the simulatedcurves of flea burden were lower with a lower fractionof resident hosts under the same overall host density.This also fits well with the hypothesis about the roleof resident hosts in flea distribution.

It is noteworthy that the threshold of establishment(the minimal size of a host population necessary tosustain a parasite population) was affected by the frac-tion of residents in the host population. The lower thepercentage of resident gerbils, the greater the numberof them necessary to maintain flea reproduction. Again,this is consistent with the assumption that only resi-dents support flea populations. For example, if it issurmised that the density of G. dasyurus is 2 individ-uals/ha, but both of them are residents, then this pro-duces two burrows for the reproduction of X. dipodilliwith a threshold of establishment equaling two. If thisis modified to assume that the density of G. dasyurusis 20 individuals/ha, but that only two are residents,this again produces two burrows for the reproductionof X. dipodilli, but the threshold of establishment nowequals 20. The same relationship between the fractionof resident hosts and threshold of establishment wasproduced by manipulations of the percentage of resi-dents for N. i. theodori. However, this pattern can beconsidered as a theoretical exercise only, because non-resident individuals comprise a very small proportionof overall gerbil population in the period when N. i.theodori occurs.

Flea prevalence and host density

Theoretically, the relationship between host densityand parasite prevalence is expected to be positive (at-


taining a plateau under high host density), given thatthere are no parasite extinction events across host in-dividuals. The explanation is that, once host densitybecomes high enough for all parasites to find a host, afurther increase in host density would be inconsequen-tial. However, field data on the relationship betweenflea prevalence and host density are contradictory. Forexample, the increase and stabilization of flea preva-lence around 100% with an increase in host densityhas been reported for Spermophilus richardsoni para-sitized by Opisocrostis bruneri and Oropsylla rupestris(Lindsay and Galloway 1997), whereas prevalence ofXenopsylla bantorum increased with the decrease indensity of its host, Arvicanthis niloticus (Schwan1986). Conversely, prevalence cannot be lower than aspecific eradication threshold (sensu Nee et al. 1997),because a minimum number of hosts is required for theparasite population to persist, analogous to a minimumnumber of patches for free-living animals (Nee 1994,Kareiva and Wennergren 1995, Hanski et al. 1996).

The prediction about the unimodal response of fleaprevalence to an increase in host density appeared tobe true for X. dipodilli, but not for N. i. theodori. Ifonly resident host individuals support the flea popu-lation, the prevalence of infestation increases with anincrease in host density until all resident individualsare infested and the habitat is saturated with residents(all available burrows are occupied or individual homeranges collapsed to minimal possible size). Under high-er host density, the prevalence of flea infestation de-creases, because the resident and infested gerbils com-pose an ever-decreasing fraction of the overall popu-lation. Conversely, for the above-mentioned reasons,flea prevalence plotted against resident host density isexpected to increase, reaching a plateau. This was notthe case; the curve of prevalence against resident den-sity was also hump-shaped, although steeper than thecurve of prevalence against overall density. An expla-nation for this result might be that flea reproductionand transmission have lower rates in comparison withreproduction and dispersal of gerbils. In other words,the rate of establishment of new patches (previouslyvacant or new burrows that are being occupied eitherby dispersing young gerbils or by transient adults) isfaster than the rate of their infestation. Consequently,it is probable that, under high host density, a fractionof resident hosts remains underused by the fleas, merelybecause they cannot keep pace with gerbil reproductionand dispersal. Indeed, the active breeding period of fleaXenopsylla hirtipes has been reported to fall behindactive breeding and dispersal of its main host, Rhom-bomys opimus, for 2–3 wk (Kiriakova et al. 1970). Inaddition, species of Xenopsylla have only 1–3 gener-ations/yr (Soldatkin et al. 1967 for X. gerbilli caspica,and Zolotova et al. 1978 for X. skrjabini), so the abovescenario is feasible.

The positive relationship between prevalence andhost density for N. i. theodori can be explained by the

above-mentioned discussion, namely that there is anincreased probability that the transmission stage istransmitted under high host density. The more distantlylocated the patches are (i.e., density is low), the lessfrequently they are occupied, due to greater difficultyof colonization (Hanski 1994). In the case of the fleaN. i. theodori, the number of habitat patches (hosts) ateach given location does not increase, so the absenceof an unimodal curve of prevalence plotted against hostdensity is to be expected.

Flea burden and flea prevalence

The relationship between flea burden and flea prev-alence is analogous to the intraspecific abundance–oc-cupancy relationship of free-living animals. The ex-istence of positive correlations between local densityand regional or geographic occupation have been re-ported for a variety of taxa (Gaston et al. 1997, Gaston1999 and references therein). Contrary to studies ofinterspecific abundance–occupancy relationships, abun-dance in the studies of intraspecific abundance–occu-pancy relationships is usually averaged across all (oc-cupied and unoccupied) sites (e.g., Kuno 1991 and ref-erences therein). These relationships have been foundto be positive, although contrary cases also have beenreported (Boecken and Shachak 1998). In general, anempirical relationship between the fraction of sites (orsamples) where a given species occurs and its meandensity can be modeled as a logistic curve (Gaston1999).

Intraspecific studies of parasite burden (equivalentof abundance) vs. parasite prevalence (equivalent ofpercentage occupancy or Diamond’s [1975] incidenceof a species) of a parasite species across individualhosts are related to relatively small scale (see Gaston1999). Thus, the model can be collapsed to its linearversion. Positive relationships have been repeatedly re-ported for helminth burden and prevalence (e.g., Bushand Holmes 1986, Haukisalmi and Hentonnen 1994).Analogous data for fleas have not been found.

The present results demonstrated that the burden ofboth fleas correlated positively with the prevalence ofinfestation, when it was calculated as the mean numberof fleas across all host individuals. These positive re-lationships could be sampling artifacts; the number ofpatches at which a species is recorded (prevalence)could be a positive function of the mean abundance ofthe species (burden) simply because locally rare speciesare more difficult to detect than are locally abundantspecies. However, this was not the case. The samplingmodel of Hanski et al. (1993) explained a relativelylow proportion of variance of the fraction of uninfestedgerbils across sampling sites, in spite of the small scaleof present considerations. The explanation for the pos-itive relationship between flea burden and prevalencemay be straightforward. The probability that a flea in-fests a new host individual (patch) is higher when theflea burden is higher. Flea colonization of new host


individuals is passive rather than active, and occurswhen host individuals come into direct contact withone another or visit each other’s burrows. It is clearthat the higher the flea abundance on a flea donor, thehigher the probability of infestation in a flea recipient.Moreover, fleas can infest nonresident hosts, but thesehosts are not able to support flea populations. Thisexplains why the intensity of infestation of residentgerbils was found to be the best predictor of the prev-alence of infestation. These results once more accen-tuate the effect of the density of resident host individ-uals on flea distribution.

ACKNOWLEDGMENTS

We thank M. Hastriter (Brigham Young University, Utah,USA), S. Medvedev and V. Vatschenok (both from ZoologicalInstitute RAS, St. Petersburg, Russia) for their help in fleaidentification. David Ward (Ben-Gurion University of the Ne-gev, Israel) and Neil Springate (Museum of Natural History,Great Britain) read an earlier version of the manuscript andmade helpful comments. We also thank J. S. Brown (Uni-versity of Illinois at Chicago, USA) and two anonymous ref-erees for their comments. Financial support during this studywas provided by Israel Ministry of Science, Israel Ministryfor New Immigrant Absorption and Local Council of MizpeRamon. This is publication no. 102 of the Ramon ScienceCenter.

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