Fisheries Research 94 (2008) 304–314

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Fisheries Research

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Modeling the sustainability of lake trout fisheries in easternWisconsin waters of Lake Superior

Julie L. Nielanda,∗,1, Michael J. Hansena, Michael J. Seiderb, Jonathan J. Derobac

a University of Wisconsin-Stevens Point, College of Natural Resources, 800 Reserve Street, Stevens Point, WI 54481, USAb Wisconsin Department of Natural Resources, Lake Superior Office, 141 South Third Street, Box 589, Bayfield, WI 54814, USAc Michigan State University, Department of Fisheries and Wildlife, 13 Natural Resources Building, East Lansing, MI 48824, USA

a r t i c l e i n f o

Article history:Received 15 November 2007Received in revised form 12 July 2008Accepted 15 July 2008

Keywords:Lake troutSalvelinus namaycushLake SuperiorHarvestSustainabilitySimulation model

a b s t r a c t

Lake trout Salvelinus namaycush stocks in Lake Superior collapsed in the 1950s due to overfishing and sealamprey Petromyzon marinus predation. Stocks were rehabilitated through stocking, sea lamprey control,and fishery regulation, but concern over lake trout population sustainability still exists because commer-cial and recreational fishing demand is high relative to productivity, and the currently accepted 42% totalannual mortality rate has not been tested for sustainability. Our objective was to estimate the maximumsustainable (i.e., likely not to cause extirpation) fishing mortality and total annual mortality rates for laketrout in eastern Wisconsin waters of Lake Superior. We developed a dynamic, age-structured popula-tion model to predict future lake trout abundance. The simulation model included parameter uncertaintyand autocorrelated process error in the stock–recruitment relationship and in sea lamprey mortality,and accounted for assessment and implementation error. We used mean abundance, mean total annualmortality rate, mean catch for the commercial and recreational fisheries, and probability of decline asperformance metrics to evaluate a range of commercial and recreational fishing mortality rates and dif-ferent assessment and implementation errors. Increasing assessment error led to undesirable outcomes(e.g., low mean abundance). However, varying implementation error had almost no effect on performancemetrics. Increased commercial fishing had larger effects on performance metrics than recreational fish-ing. Combinations of commercial and recreational fishing mortality rates corresponding to total annual

mortality rates of approximately 40% may be sustainable, and so the currently accepted 42% total annualmortality rate is also likely sustainable. However, we recommend that the amount of assessment error be

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. Introduction

Lake trout Salvelinus namaycush were historically important inhe Great Lakes as top predators in the fish community and aspredominant species to the fishing industry. Native Americansrst harvested lake trout for subsistence and trade, and Europeanseveloped commercial and recreational fisheries as they settled the

reat Lakes basin in the late 1700s and early 1800s (Lawrie andahrer, 1972; Goodier, 1989; Hansen, 1999). Commercial fisheriesxpanded and effort shifted to previously unexploited grounds astocks were depleted (Lawrie and Rahrer, 1972; Goodier, 1989;

∗ Corresponding author at: 317 Clifford Street, Lansing, MI 48912, USA.el.: +1 715 630 4150; fax: +1 517 432 1699.

E-mail address: nielandj@msu.edu (J.L. Nieland).1 Present address: Michigan State University, Department of Fisheries and Wildlife,3 Natural Resources Building, East Lansing, MI 48824, USA.

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165-7836/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.fishres.2008.07.005

spawner abundance be avoided through the use of threshold managementing quotas be closely monitored and enforced.

© 2008 Elsevier B.V. All rights reserved.

ansen et al., 1995). Beginning in the late 1800s, advances in tech-ology, including steam tugs, motor boats, hydraulic gill-net lifters,nd nylon gill nets, made harvest more efficient. Lake trout abun-ance was already reduced in the lower Great Lakes, Ontario andrie by 1900, rebounded slightly in the 1920s, only to collapse in the930s and 1940s (Christie, 1973; Cornelius et al., 1995; Elrod et al.,995). Lake trout abundance was also declining in the upper Greatakes, but yield was sustained through increased fishing effort (Hilet al., 1951; Pycha and King, 1975) until 1935 in Lake Huron, 1943n Lake Michigan, and 1950 in Lake Superior (Baldwin et al., 1979).he invasion of sea lampreys Petromyzon marinus put even moretrain on the already declining lake trout stocks. The combinationf overfishing and sea lamprey predation drove lake trout to extir-

ation by 1962 in all of the Great Lakes except remote areas in Lakeuron and Lake Superior (Berst and Spangler, 1973; Lawrie, 1978;ycha, 1980).

Fishery managers took steps to preserve and revive remain-ng lake trout stocks. Although several morphotypes of lake trout

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nce occurred in the Great Lakes, rehabilitation efforts focused onhe lean lake trout because commercial and recreational lake troutsheries targeted this morphotype (Eschmeyer and Phillips, 1965;awrie and Rahrer, 1973; Pycha and King, 1975). Several lake troutopulations remained in Lake Superior. Therefore, a rehabilitationlan was developed first for that lake to restore recruitment, reduceotal mortality, and sustain reproducing lake trout stocks capablef supporting annual yields of 2 million kg (LSLTTC, 1986; Hansen,996). The strategy was to increase recruitment by stocking and toeduce mortality by controlling sea lamprey abundance and regu-ating fisheries. Rehabilitation in Lake Superior began in 1947 withhe stocking of hatchery-reared juveniles (Lawrie and Rahrer, 1972,973; Lawrie, 1978; Hansen et al., 1995). Chemical control of seaamprey was implemented in 1958 and helped reduce sea lampreybundance by 86% in 1962 (Smith et al., 1974). Fisheries for lakerout were closed in 1962 to give lake trout a reprieve from fish-ng pressure (Pycha and King, 1975). Management agencies latereopened restricted recreational and commercial fisheries as lakerout stocks began to recover (Hansen et al., 1995). In Wiscon-in waters, two refugia were also designated to protect lake troutSwanson and Swedberg, 1980; Hansen et al., 1995). The Lake Supe-ior Technical Committee (LSTC) set the sustainable limit of totalnnual mortality for lake trout at 42%, based on the work of Healey1978) (LSLTTC, 1986), but how this limit was intended to apply ton age-structured population was not made explicit.

Results of rehabilitation efforts varied among jurisdictions andreas of the lake. Abundance of wild lake trout from unknownarentage generally increased during 1970–1992 (Hansen, 1990;ansen et al., 1994b), but abundance of stocked lake troutecreased despite relatively consistent stocking rates (Hansen etl., 1994a,b). An early stock–recruitment analysis indicated thattocked lake trout contributed to recruitment more than wild lakerout (Hansen et al., 1995), but subsequent analyses indicated thatild and stocked lake trout contributed equally to recruitment inichigan waters (Richards et al., 2004) and wild lake trout drove

ecruitment in Wisconsin and Minnesota waters (Corradin et al.,008). Survival of the 1963–1986 year-classes of stocked lake troutas limited by large-mesh gill-net fishing in Michigan and Wiscon-

in waters and by wild lake trout predation in Minnesota watersHansen et al., 1996). In contrast, survival of wild lake trout dur-ng 1970–1998 was not substantially limited by large-mesh gill-netshing effort in Michigan waters (Richards et al., 2004). Survival ofild and stocked lake trout is likely regulated by different forces

ecause catchability of stocked and wild lake trout differs, possiblyue to differences in bathymetric distribution (Krueger et al., 1986).urther analysis of historical and modern lake trout abundance inichigan waters indicated that wild lake trout stocks were more

bundant during 1984–1998 than during 1929–1943 (Wilberg etl., 2003).

Studies suggested that lake trout rehabilitation goals had beenet, and stocking was halted in most areas of Lake Superior byarch 1996 (Hansen, 1996). However, fisheries must be carefully

egulated because lake trout are still in high demand in commercialnd recreational fisheries and stock abundance must be accuratelystimated to set harvest quotas, which are divided among stategencies and several Lake Superior Bands of Chippewa Indians.

Agencies currently set quotas without knowing if the currentlyccepted 42% total annual mortality rate is sustainable. Our objec-ive was to estimate the maximum sustainable fishing and totalnnual mortality rates (defined as those rates which will likely not

ause extirpation) for lake trout in eastern Wisconsin waters of Lakeuperior to address this issue. We developed an age-structured,ensity-dependent model to simulate long-term effects of vari-us commercial and recreational harvest allocations. The modelocused on the wild lean lake trout morphotype because this mor-

L

arch 94 (2008) 304–314 305

hotype is the most highly sought by commercial and recreationalsheries, and because stocking was discontinued in our study area

n 1996 and wild lake trout drive recruitment (Corradin et al.,008).

. Methods

.1. Study area

The U.S. and Canadian waters of Lake Superior are divided intoake trout management units (Fig. 1). Our study focused on the east-rn Wisconsin management unit known as WI2, which has a surfacerea of 4474 km2 and includes the 22 Apostle Islands. This manage-ent unit contains two fish refugia: the Gull Island Shoal refuge hassurface area of 336 km2, and the Devils Island Shoal refuge has a

urface area of 283 km2. No commercial or recreational fishing isermitted in the refugia.

.2. Overview of simulations and basic population modeltructure

A stochastic simulation model was built to predict future lakerout abundance in the eastern Wisconsin waters of Lake Supe-ior. The simulation model was parameterized using the estimatesf abundance-at-age, selectivity, natural mortality, total instanta-eous mortality, and fully selected sea lamprey mortality (ages–15+2) during 1980–2004 from a statistical catch-at-age (SCAA)odel for lake trout in non-refuge portions of the eastern Wis-

onsin waters of Lake Superior (Linton et al., 2007; Wisconsintate-Tribal Technical Committee, unpublished data).

The simulation model forecasted performance metrics (Section.6) for a range of commercial and recreational fishing mortalityates to identify the maximum sustainable fishing and total annualortality rates. We evaluated (a) the same commercial and recre-

tional fishing mortality rates, (b) a recreational mortality rate nearecent levels (0.01), varying the commercial rate, and (c) a commer-ial mortality rate near recent levels (0.02), varying the recreationalortality rate (Table 1). The simulations included assessment and

mplementation error (Irwin et al., this issue; Punt et al., 2008), andhe sensitivity of the results was evaluated to different values forach source of error. For each set of fishing mortality rates, assess-ent error, and implementation error, 1000 simulations were run

or 200 years.The initial abundances at age (i.e., in year zero) for each simula-

ion were set based on the results from the SCAA model for 2004.bundance N at age j in each subsequent year i was then predicted:

i+1,j+1 = Nij e−Zij ; (1)

here Zij was the age and year specific total instantaneous mor-ality rate (the sum of instantaneous natural mortality rate M,he instantaneous sea lamprey mortality rate Lij, the commer-ial instantaneous fishing mortality rate FKij, and the recreationalnstantaneous fishing mortality rate FRij). M was estimated in theCAA model as a constant for all ages (M = 0.1649 yr−1; Linton etl., 2007; Wisconsin State-Tribal Technical Committee, unpublishedata). Lij, FKij, and FRij are the product of fully selected mortality ratesnd selectivity, SLj, SKj, and SRj (Fig. 2; Linton et al., 2007; Wisconsin

ij = SLjLi,15+; FKij = SKjFKi,8; FRij = SRjFRi,7. (2)

2 +denotes an aggregate group of all fish greater than or equal to the given age.

306 J.L. Nieland et al. / Fisheries Research 94 (2008) 304–314

F oted ba

2

aw

L

wld

N

ε

ε

aw

N

tioawiaiattpites1

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cvtType-II functional response (Gotelli, 2001). The parameters deter-mining sea lamprey predation (�, �L, �L) were estimated using aBayesian approach applied to data from the SCAA for 1983–2004,with uniform priors imposed on all parameters (Appendix A).

ig. 1. Lake trout management areas in Lake Superior. U.S. management areas are denreas are marked using only numbers.

.3. Sea lamprey mortality sub-model

Lij was modeled as a density-dependent function of lake troutbundance, but at low lake trout densities sea lamprey mortalityas held constant:

i,15+ ={�N−1

Li,4+ eεLi ifNi,4+ ≥ 100,0000.45 otherwise

(3)

here � was the instantaneous sea lamprey mortality rate whenake trout abundance is zero, NLi,4+ was the mean lake trout abun-ance across all ages weighted by sea lamprey selectivity:

Li,4+ =∑15+

j=4 SLjNij(1 − e−Zij )

Zij. (4)

Li was temporally autocorrelated process error:

Li+1 = �LεLi + �i; �i ∼ N(0;�2L ), (5)

nd �L was the level of autocorrelation. The value for εLi for 2005as drawn from the stationary distribution3:(

0;�2L

1 − �2L

). (6)

The instantaneous sea lamprey mortality rate on age-15+ lakerout was used to calculate the fully selected sea lamprey mortal-ty rate because sea lampreys have been shown to select larger,lder fish (Swink, 1991, 2003). The exponent in Eq. (3) was fixedt −1 because preliminary attempts to estimate it simultaneouslyith other parameters resulted in values less than −1, which are

mplausible for a Type-II functional response (Gotelli, 2001). Thessumption that the sea lamprey mortality rate was (on average)nversely related to lake trout abundance reflects the biologicalssumption that individual sea lamprey are saturated and feed athe same maximal rate over the range of lake trout densities, andhat sea lamprey abundance will be held relatively constant byopulation control. This assumption is consistent with available

nformation, but the sea lamprey feeding rate would be expected

o decline below some lake trout abundance as they will becomencounter rate limited. Consequently, sea lamprey mortality waset to a constant value when lake trout abundance fell below00,000 (approximately the lowest observed value for NLi,4+). This

3 The initial values in the first year for other autocorrelated error terms, describedelow, were defined similarly.

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y state: Michigan - MI, Minnesota - MN, and Wisconsin - WI. Canadian management

orresponds to an assumption that the number of attacks by indi-idual sea lamprey on lake trout was directly proportional to lakerout abundance at these lower lake trout abundances, similar to a

ig. 2. Age-specific selectivity for sea lamprey, the commercial gill-net fisheries, andhe recreational angling fisheries for lake trout in eastern Wisconsin waters of Lakeuperior during 1980–2004.

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.4. Stock–recruitment sub-model

Recruitment Ni+5,4 was modeled using the Ricker stock–ecruitment relationship (Ricker, 1975):

i+5,4 = ˛Ni,8+ e−ˇNi,8+ eεNi (7)

here ˛ was the number of recruits produced by each spawn-ng adult lake trout at low population abundance, Ni,8+ was thebundance of age-8+ lake trout, ˇwas the instantaneous decline inecruitment as parental abundance increased, and εNi was temporalutocorrelated process error:

Ni+1 = �NεNi + ςi; ςi ∼ N(0;�2N); (8)

nd�N was the level of autocorrelation. Our index of parental abun-ance assumed knife-edge maturity at age-8. Age-4 lake trout weresed to index recruitment because age-4 was the first age-classhen lake trout are recruited to large-mesh gill nets, and dataere not available to estimate abundance at ages younger than

ge-4. Recruitment was lagged by five years to account for theime between when age-8+ lake trout spawned and when age-4ake trout recruited to the gill-net fishery. The parameters (˛, ˇ, �N,N) of the stock–recruitment relationship were estimated using aayesian approach with uniform priors for all parameters except ˛,hich was assigned a lognormal prior (Appendix A).

.5. Assessment and implementation error

The simulation model included assessment and implementationrror in a manner similar to that of Irwin et al. (this issue) and Puntt al. (this issue). Assessment error was modeled as a year-specificognormal random deviation common to all ages, with first-orderutocorrelation:

ˆ ij = Nij eε i−�2

/2

; (9)

here Nij was the assessed abundance with error and ε i was theutocorrelated error:

i= � ε i−1

+ωi; ωi ∼ N(0;�2 ); (10)

nd � was the level of autocorrelation.Assessment error also affected the target catch that managers

et for each fishery because target catches, CKi for commercial and

ioas(

able 1cenarios that define assessment error (� and � ) and implementation error (� and ��n the eastern Wisconsin waters of Lake Superior

ssessment and implementation error

cenario Parameters

� � �

aseline scenario 0.700 0.223 0.000cenario 1 0.000 0.000 0.000cenario 2 0.700 0.536 0.000cenario 3 0.700 0.223 0.000cenario 4 0.700 0.223 0.200cenario 5 0.000 0.000 0.000cenario 6 0.700 0.536 0.200

ach scenario of assessment and implementation error was simulated for each combinati

arch 94 (2008) 304–314 307

˜Ri for recreational fisheries, were set by applying the desired levelf fully selected fishing mortality, FK and FR, to assessed abundancei.e., Nij) rather than actual abundance. For the commercial fishery:

˜Ki =

∑15+j=4 FKijNij(1 − e−Zij )

Zij; (11)

here FKij and FRij were the product of the desired fully selectedshing mortality rates and SKj and SRj, respectively, and:

˜ij =M + Lij + FKij + FRij. (12)

The fully selected fishing mortality rates that would result in thearget catch being removed when applied to actual abundance, FKind FRi, were found numerically using Newton–Raphson iterations.e set a maximum on FKi and FRi of 3.0 because CKi and CRi were

ometimes unachievable.Implementation error was included in each fishery as an inde-

endent lognormal error:

Kij = SKjFKi ei−�2/2; i ∼ N(0;�2

); (13)

here FKij was the actual commercial fishing mortality rate appliedo the actual abundance. Equations and distributional assumptionsor the recreational fishery were similar to those for the commercialshery except that K was replaced by R, and the variance defineds �2

�. Actual catch for each fishery, CKi for commercial and CRi forecreational, was then calculated, e.g.:

Ki =∑15+

j=4 FKijNij(1 − e−Zij )

Zij. (14)

or the baseline scenario, � , � , and �� were set to values similaro those for another Great Lakes fishery (Irwin et al., 2008; Table 1). was set to zero for the baseline scenario because we assumed

s usually below the target catch, and so we have no data to supportur assertion. The sensitivity of the results to the values chosen forssessment and implementation error was evaluated by runningeveral other scenarios with different values for � , � , ��, and �Table 1).

), and commercial and recreational fishing mortality rates simulated for lake trout

Fishing mortality rates

Commercial (yr−1) Recreational (yr−1)

��

0.100 0.00 0.000.100 0.10 0.100.100 0.20 0.200.000 0.30 0.300.200 0.40 0.400.000 0.70 0.700.200 0.02 0.01

0.04 0.010.10 0.010.20 0.010.40 0.010.70 0.010.02 0.050.02 0.100.02 0.200.02 0.400.02 0.70

on of fishing mortality rates.

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.6. Performance metrics

Mean abundance, mean catch for commercial and recreationalsheries, mean total annual mortality rate, and probability ofecline were the performance metrics used to evaluate the sustain-bility of (desired) commercial and recreational fishing mortalityates, i.e., values for FK and FR. Mean abundance N4+ was the aver-ge abundance of age-4+ lake trout over the last 150 years i andimulations v:

¯ 4+ = 11000

×1000∑v=1

(1

150×

200∑i=51

15+∑a=4

Nij

)v

. (15)

Mean abundance of age-8+ lake trout N8+ and mean commercialnd recreational catch, CK and CR, respectively, were calculated inhe same way over ages, years, and simulations. Total annual mor-ality rate Ai was calculated using the fully selected sea lampreynd fishing mortality rates for each fishery:

i = 1 − e−(FKi,8+FRi,7+Li,15++M). (16)

This level of total annual mortality would only occur if fish wereully selected to all three sources of mortality at the same age, whichhey are not. Consequently, this method over-states the mortalityxperienced by any given age-group, but will also lead to conser-ative conclusions about what levels of mortality are sustainable.ean total annual mortality rate A was the average (over simula-

ions) total annual mortality rate over the last 150 years:

¯ = 1 ×1000∑(

1 ×200∑A

). (17)

1000v=1

150i=51

i

v

The probabilities of decline for age-4+ lake trout, Pdec4+, andge-8+ lake trout, Pdec8+, were the proportions of the 1000 sim-lations in which N4+ or N8+ was less than the average age-4+

nssa

ig. 3. Mean abundance of age-4+ lake trout in eastern Wisconsin waters of Lake Superioortality rates (FK and FR , respectively, in yr−1) and different amounts of assessment and

epresented by dashes. Values for scenarios 2, 4, and 6 are represented by dots.

arch 94 (2008) 304–314

r age-8+ abundance over the last three years included in theCAA model; 2,747,633 and 1,132,485, respectively. We used thesealues because lake trout rehabilitation goals for Lake Superiorave been met (Hansen, 1996), and we assumed that maintainingbundance near recent levels was desirable. The 95% probabilityntervals for mean abundance, mean catch for each fishery, and

ean total annual mortality rate were calculated using the 2.5- and7.5-percentiles for the 1000 simulations. A 95% confidence intervalas calculated for the probability of decline using the exact upper

nd lower 95% confidence limits for a binomial proportion (Zar,999).

. Results

Mean performance metrics and probability or confidence inter-als were nearly identical to those for the baseline scenario whenhe parameter determining the extent of variability in implemen-ation error was varied (scenarios 3 and 4; Figs. 3–9). Therefore, theesults of scenarios 3 and 4 were not considered any further.

Mean abundance of age-4+ lake trout, N4+, depended on thecenario and desired fishing mortality rates for each fishery. Inhe baseline scenario, N4+ was insensitive to FR and FK until FR =

˜K = 0.70 yr−1 (Fig. 3). For this scenario, N4+ remained insensitiveo FK until it reached 0.40 yr−1, after which N4+ declined when˜R = 0.01 yr−1 (Fig. 3). The same result was evident as FR was variednd FK was set to 0.02 yr−1, but N4+ only declined once FR reached.40 yr−1 (Fig. 3). N4+ was generally lower when FK was varied and

˜R was set to 0.01 yr−1 than when FR was varied and FK = 0.02 yr−1.

Mean abundance of age-8+ lake trout, N8+, depended on the sce-

ario and generally decreased as FR or FK increased. In the baselinecenario, N8+ decreased as FR = FK was increased (Fig. 4). For thiscenario, N8+ remained insensitive to FK until it reached 0.02 yr−1,fter which N8+ declined when FR = 0.01 yr−1. The same result was

r (with 95% probability interval) for a range of commercial and recreational fishingimplementation error. Values for the baseline scenario and scenarios 1, 3, and 5 are

J.L. Nieland et al. / Fisheries Research 94 (2008) 304–314 309

rtain t

edwvNw

a

Fig. 4. As for Fig. 3, except the results pe

vident as FR was varied, and FK was set to 0.02 yr−1, but N8+ onlyeclined once F reached 0.20 yr−1 (Fig. 4). N was generally lower

R 8+hen FK was varied and FR was set to 0.01 yr−1 than when FR was

aried and FK = 0.02 yr−1. The 95% probability intervals for N4+ and¯ 8+ included zero for nearly all combinations of FR and FK , except

hen FR and FK were set to zero (Figs. 3 and 4).

snwi

Fig. 5. As for Fig. 3, except the results pertai

o mean abundance of age-8+ lake trout.

Mean total annual mortality rate, A, depended on the scenarios well as on F and F . A increased to nearly 100% in the baseline

R K

cenario as FR = FK was increased to 0.70 yr−1 (Fig. 5). For this sce-ario, A remained insensitive to FK until it reached 0.20 yr−1 afterhich A increased when FR = 0.01 yr−1 (Fig. 5). A increased as FR

ncreased when FK = 0.02 yr−1 (Fig. 5). Increases in Awere greater

n to mean total annual mortality rate.

310 J.L. Nieland et al. / Fisheries Research 94 (2008) 304–314

perta

ww

dFpi

el

Fig. 6. As for Fig. 3, except the results

hen FR was set to 0.01 yr−1 and FK was increased, than when FKas set to 0.02 yr−1 and FR was increased (Fig. 5).

Mean commercial catch, CK , and recreational catch, CR, alsoepended on the scenario as well as on FR and FK (Figs. 6 and 7).or the baseline scenario, CK increased gradually from zero to aeak when FR = FK = 0.40 yr−1. When FR was set to 0.01 yr−1, CK

ncreased with FK until FK = 0.40 yr−1, after which CK declined. As

ab

mo

Fig. 7. As for Fig. 3, except the results perta

in to mean commercial fishing catch.

xpected, CK was insensitive to FR when FK was set to 0.02 yr−1. Theower 95% probability interval for CK included zero for all scenarios

nd values of FR and FK . The results for mean recreational catch, CR,ehaved as expected given changes to FR (Fig. 7).

The results for the baseline scenario and those with no assess-ent error (1 and 5) were similar. In contrast, A was similar to

r higher, and N4+ and N8+ were generally lower, than the base-

in to mean recreational fishing catch.

J.L. Nieland et al. / Fisheries Research 94 (2008) 304–314 311

lity of

lfec

at

0o

Fig. 8. As for Fig. 3, except the results pertain to the probabi

ine values for the scenarios with high assessment error (2 and 6)or all combinations of FR and FK (Figs. 3–5). CK and CR were gen-

rally lower for the scenarios with high assessment error for allombinations of FR and FK (Figs. 6 and 7).

The probability of decline for age-4+ lake trout, Pdec4+, decreaseds FR or FK increased, and the extent was scenario-dependent. Inhe baseline scenario, Pdec4+ decreased when FR = FK increased to

auR5a

Fig. 9. As for Fig. 3, except the results pertain to the probability of

decline of age-4+ lake trout (with 95% confidence interval).

.40 yr−1, but was higher and, at least 91%, for all other values of FRr FK (Fig. 8). When FR was set to 0.01 yr−1, Pdec4+ decreased slightly

s FK increased from 0.02 to 0.10 yr−1 and increased for higher val-es of FK . When FK was set to 0.02 yr−1, Pdec4+ was insensitive to FR.esults were similar for scenarios with no assessment error (1 and), except that Pdec4+ was generally less for all combinations of FRnd FK . For scenarios with high assessment error (2 and 6), Pdec4+

decline of age-8+ lake trout (with 95% confidence interval).

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as generally higher than the baseline values for all combinationsf FR and FK (Fig. 8).

The probability of decline for age-8+ lake trout, Pdec8+, increaseds FR or FK increased, and the extent of increase was slightlycenario-dependent. Pdec8+ increased to values equal to or near00% for all combinations of FR and FK above zero for the baselinecenario (Fig. 9). Results were similar for scenarios with no assess-ent error (1 and 5), while for scenarios with high assessment error

2 and 6) Pdec8+ was generally similar to or slightly higher than theaseline values (Fig. 9).

. Discussion

.1. Uncertainty and sources of error

This simulation model included assessment and implementa-ion error. Although this is not new (e.g., Eggers, 1993; Frederick andeterman, 1995; Hilborn et al., 2002), these sources of error haveften been ignored in studies evaluating the performance of man-gement strategies (Deroba and Bence, 2008). Studies that searchedor levels of fishing mortality (or other parameters required forther control rules, such as abundance thresholds) that performoptimally” for given objectives while including assessment andmplementation error are also rare (Deroba and Bence, 2008). Morerequently, control rule parameters, such as levels of fishing mortal-ty, that performed optimally without error are used in simulations

ith error (Deroba and Bence, 2008). In this analysis, we searchedver a discrete range of combinations of desired commercial andecreational fishing mortality rates so that a near-optimal combi-ation of rates could be identified for a given metric. This processhould lead to the selection of maximum sustainable fishing andotal annual mortality rates that are robust to sources of error andarameter uncertainty we included in our simulations.

We found that each performance metric moved toward an unde-irable state (e.g., low mean abundance) for most combinationsf fishing mortality rates with an increase in assessment error,mplying the need for more conservative strategies, as in othertudies (Frederick and Peterman, 1995; Katsukawa, 2004; Deroband Bence, 2008). The negative effect of assessment error mayave been caused by an asymmetric loss function, such that over-stimates of abundance that lead to fishing mortality rates higherhan desired are more costly than under-estimates of abundancehat lead to fishing mortality rates lower than desired (Fredericknd Peterman, 1995; Deroba and Bence, 2008). Consequently, theecreased mean abundance, catch, and increased probability ofecline when abundance is over-estimated and fishing mortality isigher than desired cannot be compensated for when abundance

s under-estimated and fishing mortality is lower than desired.imilar to our results, the harvest rate that maximized expectedresent value (measured in dollars) for Atlantic menhaden Brevoor-ia tyrannus decreased as assessment error increased (Fredericknd Peterman, 1995). Katsukawa (2004) found that control rulesore like constant fishing mortality rate were favored and the

ptimal level of fishing mortality decreased as assessment errorncreased when the objective was to simultaneously maximizeverage yield and minimum biomass. Assessment error for the WI2ake trout fishery has not been formally quantified, but inaccurateatch statistics and the relatively short assessed period on which

he SCAA model is based could potentially lead to large amountsf assessment error. Consequently, setting fishing mortality ratest more conservative (i.e., lower) levels might lead to better per-ormance in terms of mean abundance, catch, and probability ofecline.

mstaa

arch 94 (2008) 304–314

Our simulation model was not sensitive to the level of imple-entation error, which is consistent with other research on this

ubject (Sethi et al., 2005). For example, the optimal control rule foraximizing discounted yield was not affected by implementation

rror, although assessment error interacted with implementationrror in the study by Sethi et al. (2005). Our results did not revealn interaction between assessment and implementation error. Oneeason may be that Sethi et al. (2005) searched for an optimal con-rol rule and its parameters, whereas we only searched for optimalarameters within a single control rule (i.e., an optimal level of fish-

ng mortality for a constant fishing mortality rate control rule). Hade considered control rules other than constant fishing mortality

ate, our results may have been more consistent with those of Sethit al. (2005).

We attempted to incorporate parameter uncertainty and assess-ent and implementation error into our simulations, but fisheries

re dynamic systems and models are not 100% accurate. Further-ore, our model did not consider all possible sources of uncertainty

e.g., in natural mortality), and the SCAA model on which ourimulation was parameterized did not consider time-varying pop-lation parameters, such as catchability. Consequently, decisionsased on our work may be optimistic, and our analyses shoulde updated as new information becomes available. Furthermore,ur results should be interpreted cautiously because the lake troutshery in WI2 may be supplemented by the highly productivepawning grounds provided by the refugia in this managementnit.

.2. Summary and management implications

Combinations of fishing mortality rates that resulted in totalnnual mortality rates near 42% generally reduced mean age-8+bundance to about 50% of the unfished abundance. Maintainingpawner abundance in the range of 20–50% has been recommendeds a way to ensure replacement and attain a large portion of max-mum sustainable yield (Quinn et al., 1990; Clark, 1991; Fujiokat al., 1997; Booth, 2004). So, we conclude that the current 42%otal annual mortality rate limit is likely sustainable. To explic-tly avoid reaching low spawner abundances, however, managershould also consider placing minimum thresholds on spawnerbundance.

We also caution managers against using only age-4+ abun-ance as a measure of sustainability, because this metric onlyeflected changes in recruitment and not spawner numbers. Forhe baseline scenario, mean age-4+ abundances were relativelyimilar when there was no fishing mortality, when both recre-tional and commercial fishing mortality increased to 0.40 yr−1,nd when recreational mortality was held at recent levels and com-ercial mortality increased to 0.20 yr−1. These combinations of

shing mortality rates correspond to total annual mortality ratesimilar to or greater than the current limit of 42%, which suggestshat these rates may not cause a reduction in mean recruitmentFigs. 3 and 4). Mean age-8+ abundance, however, was reduced to7% of the unfished abundance when both fishing mortality ratesere set 0.40 yr−1, and 42% of the unfished level when recreationalortality was held at recent levels and commercial mortality

ncreased to 0.20 yr−1. So, even though recruitment may remainigh at the combination of fishing mortality rates described above,pawner numbers may decline, with the severity of decline depen-ent on the relative level of commercial and recreational fishing

ortality rates. We recommend that management decisions about

ustainable levels of total annual mortality rate and fishing mor-ality rates consider both age-4+ (recruit) and age-8+ (spawner)bundance, that threshold management strategies be considereds a way to avoid low spawner abundance, and that decisions also

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J.L. Nieland et al. / Fisherie

onsider the relative level of fishing mortality rates. Furthermore,shing mortality rates greater than the combinations describedbove would also generally result in less mean catch and meanotal annual mortality rates greater than 74%, and so should bevoided.

Probability of decline from mean age-4+ abundance in the lasthree years of the SCAA model was 74% or higher for all scenariosnd combinations of fishing mortality rates, and 88% or higher forean age-8+ abundance. In some areas of Lake Superior, abundance

n recent years is at or above levels before the fishery collapsedWilberg et al., 2003). Therefore, the high probability of decline,ven when there is no fishing, may be driven by our selectionf thresholds. Probability of decline for mean age-4+ abundancelso decreased as fishing mortality rate in one or both fisheriesas increased to a threshold where probability of decline then

ncreased. This result occurred because age-4+ abundance reflectedncreases in recruitment as spawner numbers (age-8+ abundance)eclined and moved recruitment toward the dome of the Rickertock–recruit relationship. Probability of decline for mean age-+ abundance, however, increased as fishing mortality rates were

ncreased. This result further supports our recommendation toonsider both age-4+ and age-8+ abundance when making man-gement decisions about sustainable mortality rates.

Declines in mean age-4+ and age-8+ abundance and increasesn total annual mortality rate were greater when recreational fish-ng mortality was held near recent levels and commercial fishing

ortality was increased compared to when commercial fishingortality was held near recent levels and recreational mortalityas increased. This result suggests that the commercial fishery mayave larger effects on the population than the recreational fish-ry, and ensuring that quotas for the commercial fishery are notxceeded may be crucial for sustainability. This result was likely aonsequence of fish entering the commercial fishery at a youngerge and remaining slightly more vulnerable at older ages than inhe recreational fishery (Fig. 2).

We found that 95% probability intervals for mean age-4+ andge-8+ abundance overlapped with zero for nearly all scenarios andombinations of desired commercial and recreational fishing mor-ality rates, except when both fisheries were closed. This variability

ay have been driven by large uncertainty in the parameters of thetock–recruitment and sea lamprey mortality relationships, bothf which were based on relatively few years of data over a limitedange of lake trout abundances. Uncertainty in these relation-hips and future management decisions could be reduced throughdaptive management techniques, such as passively continuing toollect more data through time, or active experimentation andanipulation of lake trout or sea lamprey abundance (Walters,

986).

cknowledgements

We thank the Wisconsin Department of Natural Resources Lakeuperior Office for making available the data used in this projectnd for sharing their knowledge of lake trout in Lake Superior. Wehank the Quantitative Fisheries Center at Michigan State Universityor their technical support and use of their resources. We thank Timinnett, Kevin Russell, Jim Bence, two anonymous reviewers, and

he guest editor, André Punt, who helped improve this manuscript.

his project was funded by the University of Wisconsin Sea Grantnstitute under grants from the National Sea Grant College Program,ational Oceanic and Atmospheric Administration (Project Num-er R/LR-95) and from the State of Wisconsin. This research wasompleted in partial fulfillment of the requirements for a Master ofcience degree at the University of Wisconsin-Stevens Point.

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arch 94 (2008) 304–314 313

ppendix A

.1. Sea lamprey mortality sub-model

The parameters for the sea lamprey mortality sub-model werestimated assuming that residuals about the fit to the data wereog-normally distributed:

L = n

2loge(�2

L ) + 1

2�2L

(n∑i=2

DL

); (A1)

here

L =(

loge

(Li,15+�N−1

Li,4+

)− �L loge

(Li−1,15+�N−1

Li−1,4+

))2

+ (1 − �2L )

(loge

(L1,15+�N−1

L1,4+

))2

; (A2)

nd n was the total number of observations (i.e., total number ofears) and Li,15+ and NLi,4+ were obtained from the SCAA model.

A different set of parameter values was used for each simula-ion by sampling from the joint posterior probability distributionbtained using Markov Chain Monte Carlo (MCMC) algorithm.ne thousand sets of parameter values (i.e., one for each simu-

ation) were generated by running the MCMC chain for 4 millionycles and sampling every 2000th cycle, discarding the first 1000amples as a burn-in to reduce the effect of the starting val-es on the MCMC results (Gelman et al., 2004). Trace plots andhain autocorrelation functions were examined to identify anynusual structure in the posteriors (Thiebaux and Zwiers, 1984).e also verified that the marginal posteriors for each parame-

er were not influenced by a long transient by also running aCMC simulation of 6 million cycles sampled every 3000 cycles,ith the first 1000 samples discarded as a burn-in. Lastly, we

ompared the means of the marginal posteriors with the maxi-um likelihood estimates (MLEs) to evaluate whether the posterior

istributions were sensitive to the uniform priors, which theyere not.

.2. Stock–recruitment sub-model

The parameters of the stock–recruitment sub-model were esti-ated based on the following negative loge-likelihood:

N = n

2loge(�2

N) + 1

2�2N

(n∑i=2

DN

); (A3)

here

N =(

loge

(Ni+5,4

˛Ni,8+ e−ˇNi,8+

)−�N loge

(Ni+4,4

˛Ni−1,8+ e−ˇNi−1,8+

))2

+ (1 − �2N)

(loge

(Ni+5,4

˛Ni,8+ e−ˇNi,8+

))2

; (A4)

nd n was the total number of observations.The prior assumed for the parameter ˛ was lognormal with

ean 2.09 and variance 0.18. The values for the mean and variancef this prior were selected based on results of a stock–recruitment

eta-analysis for Salmonidae (Myers et al., 1999).A different set of parameters was used for each simulation

y sampling from the joint posterior probability distributionbtained using the MCMC algorithm with the same characteristicsi.e., chain length, burn-in, etc.) as for sea lamprey mortality. The

3 es Rese

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R

B

B

B

C

C

C

C

D

E

E

E

F

F

G

G

GH

H

H

H

H

H

H

H

H

H

I

K

K

L

L

L

L

L

M

P

P

P

Q

R

R

S

S

S

S

S

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14 J.L. Nieland et al. / Fisheri

ame diagnostics (e.g., trace plots, comparison of means from theosteriors to MLEs, etc.) as for sea lamprey mortality were alsoxamined. Recruitment was capped at 1,600,000, about twice thatf the highest observed recruitment, to avoid unrealistic values.lthough arbitrary, recruitment in excess of this amount occurred

n less than 5% of samples from the posterior, so our results areikely robust to the cap.

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