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Population Dynamics of Lake Ontario Lake Trout during1985–2007Travis O. Brenden a , James R. Bence a , Brian F. Lantry b , Jana R. Lantry c & Ted Schaner da Quantitative Fisheries Center, Department of Fisheries and Wildlife, Michigan StateUniversity, 153 Giltner Hall, East Lansing, Michigan, 48824, USAb U.S. Geological Survey, Lake Ontario Biological Station, 17 Lake Street, Oswego, New York,13126, USAc New York State Department of Environmental Conservation, Cape Vincent Fisheries Station,541 East Broadway, Post Office Box 292, Cape Vincent, New York, 13618, USAd Ontario Ministry of Natural Resources, Lake Ontario Management Unit, 41 Hatchery Lane,Rural Route 4, Picton, Ontario, K0K 2T0, Canada

Available online: 29 Nov 2011

To cite this article: Travis O. Brenden, James R. Bence, Brian F. Lantry, Jana R. Lantry & Ted Schaner (2011): PopulationDynamics of Lake Ontario Lake Trout during 1985–2007, North American Journal of Fisheries Management, 31:5, 962-979

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North American Journal of Fisheries Management 31:962–979, 2011C© American Fisheries Society 2011ISSN: 0275-5947 print / 1548-8675 onlineDOI: 10.1080/02755947.2011.635241

ARTICLE

Population Dynamics of Lake Ontario Lake Trout during1985–2007

Travis O. Brenden* and James R. BenceQuantitative Fisheries Center, Department of Fisheries and Wildlife, Michigan State University,153 Giltner Hall, East Lansing, Michigan 48824, USA

Brian F. LantryU.S. Geological Survey, Lake Ontario Biological Station, 17 Lake Street, Oswego, New York 13126, USA

Jana R. LantryNew York State Department of Environmental Conservation, Cape Vincent Fisheries Station,541 East Broadway, Post Office Box 292, Cape Vincent, New York 13618, USA

Ted SchanerOntario Ministry of Natural Resources, Lake Ontario Management Unit, 41 Hatchery Lane,Rural Route 4, Picton, Ontario K0K 2T0, Canada

AbstractLake trout Salvelinus namaycush were extirpated from Lake Ontario circa 1950 owing to commercial and recre-

ational fishing, predation by sea lampreys Petromyzon marinus, and habitat degradation. Since the 1970s, substantialefforts have been devoted to reestablishing a self-sustaining population through stocking, sea lamprey control, andharvest reduction. Although a stocking-supported population has been established, only limited natural reproductionhas been detected. Since the 1990s, surveys have indicated a continuing decline in overall abundance despite fairlystatic stocking levels. We constructed a statistical catch-at-age model to describe the dynamics of Lake Ontario laketrout from 1985 to 2007 and explore what factor(s) could be causing the declines in abundance. Model estimatesindicated that abundance had declined by approximately 76% since 1985. The factor that appeared most responsiblefor this was an increase in age-1 natural mortality rates from approximately 0.9 to 2.5 between 1985 and 2002. Thelargest source of mortality for age-2 and older fish was sea lamprey predation, followed by natural and recreationalfishing mortality. Exploitation was low, harvest levels being uncertain and categorized by length rather than age.Accurate predictions of fishery harvest and survey catch per unit effort were obtained despite low harvest levels byusing atypical data (e.g., numbers stocked as an absolute measure of recruitment) and a flexible modeling approach.Flexible approaches such as this might allow similar assessments for a wide range of lightly exploited stocks. Themechanisms responsible for declining age-1 lake trout survival are unknown, but the declines were coincident withan increase in the proportion of stocked fish that were of the Seneca strain and a decrease in the overall stocking rate.It is possible that earlier studies suggesting that Seneca strain lake trout would be successful in Lake Ontario are nolonger applicable given the large ecosystem changes that have occurred subsequent to invasion by dreissenid mussels.

Lake trout Salvelinus namaycush were extirpated fromLake Ontario circa 1950 as a result of commercial andrecreational fishing, predation by sea lampreys Petromyzonmarinus, and habitat degradation (Christie 1973; Elrod et al.

*Corresponding author: brenden@msu.eduReceived January 19, 2011; accepted July 6, 2011

1995). Although stocking of young lake trout was conductedfrom the early 1950s through the mid-1960s, plantings wereeventually discontinued because survival of age-3 and olderfish remained low owing to persisting high rates of sea lamprey

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POPULATION DYNAMICS OF LAKE ONTARIO TROUT 963

predation and bycatch in the Canadian commercial fisheryfor lake whitefish Coregonus clupeaformis (Schneider et al.1983; Elrod et al. 1995). In the early 1970s, efforts to restorelake trout populations were resumed primarily through closureof commercial fisheries, stocking of juveniles, and reductionof sea lamprey populations through lampricide treatment oflamprey-producing tributaries (Elrod et al. 1995). The ultimategoal of these restoration efforts has been the reestablishmentof a self-sustaining population to the point where the speciesis once again the dominant hypolimnetic predator in the lake(Stewart et al. 1999). Although some wild reproduction has beendetected (Owens et al. 2003), wild recruitment to the fisheryhas been limited (Lange and Smith 1995; Schaner et al. 2007).Consequently, the current Lake Ontario lake trout populationdepends heavily on continued stocking of hatchery-rearedfish.

Since 1973, the number of lake trout stocked annually hasranged from approximately 66,000 to more than 2.3 millionyearling equivalents. From 1985 to 1992, number stockedaveraged over 1.9 million yearling equivalents, but in 1993,stocking was reduced because of concerns regarding possiblepredator–prey imbalances (Jones et al. 1993) and since hasaveraged approximately 0.9 million. Despite a fairly staticstocking rate in recent years, both fishery-dependent andfishery-independent surveys have indicated an overall declinein abundance (Lantry and Eckert 2009; Lantry and Lantry2009). The exact cause for this decline is not presently known,but it nevertheless suggests that the goal of reestablishinga self-sustaining lake trout population remains a distanttarget.

Zimmerman and Krueger (2009) recommended several areasof research to aid in the reestablishment of native deepwaterfishes, including lake trout, in the Laurentian Great Lakes.Among these recommendations were the identification oflife history bottlenecks and the examination of populationor metapopulation dynamics, including the documentationof patterns in population abundances. Such information wasdeemed beneficial as it would help identify realistic expecta-tions for reestablished populations and potential obstacles toreestablishment. The purpose of this research was to quantifyand examine trends in abundance and population dynamicsof Lake Ontario lake trout. Our approach was to integratestocking, fishery, and survey data with information on recoveryof fish bearing coded wire tags (CWTs) by developing andfitting a statistical catch-at-age (SCAA) assessment model.This approach to assessment is also known more generallyas an integrated approach (Fournier and Archibald 1982;Deriso et al. 1985; Methot 1990). This enabled us to estimatevarious sources of mortality for both juvenile and adult laketrout, which we then compared with prescribed managementtargets. Our overarching goal was to identify what factors weremost likely inhibiting reestablishment of a self-sustaining anddominant lake trout population in Lake Ontario

METHODS

Data CollectionStocking.—Essentially all recruitment of Lake Ontario lake

trout comes from stocking of hatchery-reared fish. Numbers offish stocked into Lake Ontario were obtained from the NewYork State Department of Environmental Conservation (NYS-DEC) and the Ontario Ministry of Natural Resources (OMNR).In both New York and Ontario jurisdictional waters, althoughspring yearlings have been the primary stocked life stage, fall fin-gerlings also have been stocked periodically. Numbers stockedas fall fingerlings were converted to yearling equivalents by mul-tiplying number stocked by an assumed survival rate of 40%based on a survival estimate from Elrod et al. (1988). Whileactual survival of fingerlings has likely varied over time, suchvariation was accounted for in the SCAA model by allowingannual variation in age-1 natural mortality rates.

Since 1980, the majority (≈80%) of fish that have beenstocked in New York jurisdictional waters of Lake Ontario havebeen tagged with CWTs. Fish captured in fishery-independentsurveys have been routinely scanned for these tags since CWTfish have been at large, and age-composition of these recoveriesprovides the most accurate information on fish age (Elrod et al.1995). We separately kept track of the number of New Yorkstocked fish to predict survey catch per effort (CPE) and agecomposition for fish bearing these CWTs, under the assumptionthat CWT-bearing fish followed the same demographics as otherfish. Although OMNR also used to stock lake trout tagged withCWTs, we did not incorporate OMNR CWT fish in the SCAAmodel as that tagging was discontinued in 1997.

Fishery harvest and effort.—Both the NYSDEC and OMNRannually assess a portion of the recreational fisheries that occurwithin their respective jurisdictional waters. In New York juris-dictional waters, boat angler harvest is assessed through a directcontact creel survey that covers the open-lake fishery in LakeOntario’s main basin, from the Niagara River in the westernend of the lake to Association Island in the eastern end of thelake. The NYSDEC fishing boat survey is conducted from Aprilthrough September and uses boat trips as the primary unit offishing effort. The survey has a stratified random design basedon expected fishing boat use at different access points (i.e., chan-nel type) and by day type. Additional information on the designof the NYSDEC fishing boat survey can be found in Stewartet al. (2003) and Lantry and Eckert (2009).

Because the NYSDEC fishing boat survey is concentratedin the main portion of New York’s jurisdictional waters, it wasnecessary to adjust estimated harvest to account for fishing oc-curring in the eastern outlet basin. The eastern outlet basin isthe only portion of New York waters excluded from the fishingboat survey; however, it does support a lake trout fishery. Creelsurveys of the recreational fishery in the eastern outlet basinof New York’s jurisdictional waters were conducted in 1998and 2003 during the summer months. The estimated harvest in

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964 BRENDEN ET AL.

the eastern outlet basin was 2,658 and 4,134 fish, respectively(McCullough and Einhouse 2004). In these same years, the es-timated harvest in the main basin was 11,862 and 4,711 fish,respectively (Eckert 1999, 2004). Based on these harvest esti-mates, we multiplied the NYSDEC fishing boat survey harvestestimates by 1.551, the mean ratio of the sum of the main basinand eastern outlet basin lake trout harvests to the main basinharvest for the 2 years when both creel surveys were conductedby NYSDEC.

Boat angler effort and harvest in Ontario jurisdictional wa-ters of Lake Ontario are measured through a stratified randomaccess point survey. Surveys are conducted from April throughSeptember and are stratified by day, season, and geographic area(Stewart et al. 2003). Within each geographic area, anglers areinterviewed at one or two high-effort ramps, effort and harvestsubsequently being expanded based on boat trailer counts at allaccess sites. The OMNR did not conduct its fishing boat surveyin 1996, 2006, or 2007. Ontario recreational harvest and effortfor 1996, and for 2006 and 2007, were linearly interpolated fromthe 1995 and 1997 and the 2005 and 2008 measurements, re-spectively. Additional information on the design of the OMNRfishing boat survey can be found in Stewart et al. (2003) andOMNR (2006).

The OMNR fishing boat survey is primarily concentrated inthe western portion of Ontario’s jurisdictional waters of LakeOntario’s main basin. As a result, it was necessary to adjustharvest estimates to account for fishing occurring in the east-ern basin, which is where most lake trout harvest in Ontariojurisdictional waters is thought to occur. Harvest of lake troutin the eastern basin portion of Ontario jurisdictional waters wasassessed in 1987 and 1992. Estimated harvest in these yearswas 12,200 and 10,560 fish, respectively (Elrod et al. 1995).In these same years, the estimated lake trout harvest in thewestern portion of Ontario’s waters was 8,391 and 2,997 fish(OMNR 2006). Based on these harvest estimates, we multipliedthe OMNR fishing boat survey harvest estimates by a factor of3.489, which again is the mean ratio of the sum of the westernmain basin and eastern basin lake trout harvests to the westernmain basin harvest for the 2 years when both creel surveys wereconducted by OMNR. Biological data collected as part of thecreel surveys in Ontario and New York were used to calculatethe observed length composition of the recreational harvests foreach year.

In our assessment modeling, we assumed that the recreationalfisheries were the only fishery removals from the Lake Ontariolake trout stock. While there is no directed commercial fisheryon lake trout, there is some bycatch from the lake whitefish com-mercial fishery that occurs in Ontario jurisdictional waters. Thisbycatch has not regularly been recorded, and those familiar withthe fishery believe it to be substantially less than recreationalharvests. Thus, although the data do not exist to include thiscomponent, we do not believe our inability to include it hassubstantially biased our results.

Fishery-independent surveys.—Since 1984, the U.S. Geolog-ical Survey (USGS) and NYSDEC have cooperated in an adultgill-net survey of lake trout within New York’s jurisdictionalwaters. This survey is conducted in September and consists ofsampling randomly placed transects within 14–17 geographicareas distributed throughout New York’s jurisdictional waters.Gill nets have consisted of nine 15.2-m × 2.4-m panels of 51-to 151-mm mesh in 12.5-mm increments. (Elrod et al. 1995;Lantry and Lantry 2009). Four nets per transect are fished par-allel to depth contours beginning at the 10–12◦C isotherm andproceeding deeper at 10-m depth increments. From this com-bined survey, a stratified CPE is calculated using four depthstrata (Elrod et al. 1995; Lantry and Lantry 2009), which weused as a data source for the SCAA assessment. The surveycatches are routinely scanned for the presence of CWTs, andconsequently we also used the similarly calculated CPE of NewYork stocked lake trout bearing CWTs in the SCAA modeling.Length has been recorded for all fish counted in this survey,from which proportions of captured fish in 25.4-mm length-classes were calculated for comparison with model predictions.For CWT fish, proportions at age, rather than proportions atlength, were calculated and compared with model predictions.Given that New York started stocking CWT fish in 1980 andsurvey fish have been routinely scanned for CWTs since thattime, these age compositions were available for each year overthe period covered by the assessment model.

Since 1992, the OMNR has assessed adult lake trout pri-marily through a community index gill-net program, which isconcentrated in the eastern portion of Ontario’s jurisdictionalwaters. The community index gill-net program generally is con-ducted from late June or early July to mid or late September ineach year. Between two and eight nets are sampled at each siteat depths generally ranging from 7.5 to 27.5 m. Gill nets havegenerally consisted of ten 15.2-m × 2.4-m panels of 38- to151-mm mesh in 12.5-mm increments. For assessing trends inthe lake trout population, the OMNR uses surveys conductedfrom July through September, at water temperatures less than12◦C, and at depths less than 80 m. Using these criteria to sub-set the data, mean CPEs for Kingston Bay and open-water areaswere calculated by averaging over all sets and depths. An over-all CPE was then calculated by averaging the Kingston Bay andopen-water mean CPEs. Length was recorded for all countedfish and proportions in 25.4-mm length-classes were calculatedfor each year using the same subset of the data.

Juvenile survey.—Since 1980, the USGS and NYSDEC havecooperated in a bottom trawl survey that targets age-2 fish as amethod for indexing early survival. The trawl survey is con-ducted from mid-July to early August, and generally at 14locations distributed uniformly along the southern shore andwithin the eastern basin of New York’s jurisdictional waters. Onelocation in Ontario’s jurisdictional waters off the mouth of theNiagara River is also assessed. From 1980 to 1996, trawling wasconducted with a 12-m headrope trawl at 5-m depth intervals,

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POPULATION DYNAMICS OF LAKE ONTARIO TROUT 965

beginning at the 15◦C isotherm and progressing into deeper wa-ter until few or no additional lake trout were captured. Becauseof fouling of the gear by dreissenid mussels, the trawling gearwas replaced in 1997 with a 3-in-1 trawl (18-m headrope, 7.6-mspread) equipped with roller gear along the footrope (O’Gormanet al. 2000). Because of an abrupt shift in the depth distributionof juveniles to deeper waters (O’Gorman et al. 2000) during themid-1990s, the sampling protocol for the trawl survey was mod-ified in 1998 by decreasing sampling effort at depths less than55 m and increasing effort at depths greater than 70 m, and byalternating sampling depths at approximately 5-m incrementsbetween adjacent sites and years (Lantry and Lantry 2009). Thesurvey data are summarized as the total catch of age-2 lake troutfor each year per 500,000 yearling-equivalent lake trout stockedin the year previous to the survey.

Statistical Catch-at-Age ModelingStatistical catch-at-age models consist of a population sub-

model that projects abundances at age of the modeled populationand an observation submodel that predicts observable quantities(e.g., recreational harvest, survey CPE) from the projected abun-dances at age. Abundances at age were modeled for the timeperiod of 1985 to 2007 and ages 1–15, the last age-class beingan aggregate group that included all fish ages 15 and older. Be-cause Ontario and New York recreational fishery harvests weremeasured by length-group, length-classes (177.8–965.2 mm in25.4-mm increments) of lake trout were also incorporated inthe SCAA model. Definitions of parameters and variables usedin equations for the population and observation submodels inthe main text are presented in Table 1. A full description of themodels, and a table of all variables and parameters is presentedin the appendix.

Population submodel.—Modeled abundances at age werecomputed using the exponential population model

Ny+1,a+1 = Ny,a exp(−Zy,a

). (1)

We assumed that initial abundance of age-1 lake trout in eachyear was equal to the number of yearling-equivalent fish stockedin that year. Abundances at ages 2–13 for the initial year (1985)were estimated as parameters, while initial abundances for ages14 and older lake trout population were set to 0 given that recentstocking attempts were begun in 1973.

Total mortality was partitioned into four components: naturalmortality, sea lamprey-induced mortality, New York recreationalfishing mortality, and Ontario recreational fishing mortality, rep-resented as

Zy,a = My,a + MSLy,a+

∑f

Ff,y,a. (2)

Instantaneous natural mortality of age-1 lake trout was assumedto vary annually, and rates were estimated as freely varying

TABLE 1. Description of equation symbols.

Symbol Description

a Indicator variable for age-class (1–15 + )y Indicator variable for year (1985–2007)f Indicator variable for fishery (NY recreational = 1,

ONT recreational = 2, NY survey = 3, ONTsurvey = 4, NY juvenile survey = 5)

q Catchabilityσ2 Standard dispersion parameter for objective function

data componentsN AbundanceZ Total instantaneous mortalityM Instantaneous natural mortalityMSL Instantaneous sea lamprey-induced mortalityF Instantaneous recreational fishing mortalitys SelectivityH Model-estimated recreational fishery harvestI Model-estimated adult gill-net survey CPEU Model-estimated juvenile trawl survey adjusted catchλ Dispersion scalar for negative log-likelihood

componentsE Recreational fishery effort

parameters. It was necessary to set age-1 natural mortality in2007 equal to that of 2006 as there was insufficient informationto estimate this mortality component itself. We did not attempt toestimate M for age-2 and older fish as part of the formal SCAAmodel estimation process as this is generally difficult owing toconfounding with other mortality sources (Hilborn and Walters1992; Quinn and Deriso 1999). Rather, we set M for age-2 andolder fish equal to 0.15, which is close to the rates that havebeen estimated for other lake trout populations within the GreatLakes basin (Shuter et al. 1998; Sitar et al. 1999; Linton et al.2007).

Sea lamprey induced-mortality was calculated external fromthe SCAA model using methods described in Bence et al. (2003),Rutter and Bence (2003), Linton et al. (2007), and the ap-pendix. Briefly, sea lamprey marking rates observed on sur-viving lake trout sampled in the USGS–NYSDEC and OMNRfishery independent surveys were converted to sea lamprey in-stantaneous mortality based on length-class-specific proportion-alities. Length-class specific mortality rates were converted toage-specific rates based on an age–length key.

New York and Ontario recreational fishing mortalities wereassumed to be products of annual fishing effort, age-specificselectivities, and year-specific catchabilities, expressed as

Ff,y,a = qf,ysf,aEf,y . (3)

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966 BRENDEN ET AL.

Year-specific catchabilities were modeled using a random walkprocess, which allows for year-to-year changes in catchabilitybut penalizes large changes (see appendix). Wilberg and Bence(2006) advocated the use of this approach as a default for model-ing fishery catchability based on simulation results. Recreationalfishery selectivity was first modeled as a function of length, theresults being converted to age-based selectivity. This approachwas adopted because size-based regulations (slot limits) havebeen used to manage the recreational fishery harvest of laketrout in New York waters. More specifically, length-based selec-tivity in the absence of size regulations was obtained as gammafunction of length, and then these selectivities were adjusted forany slot limit that was in effect for that year and fishery (seeappendix). Both the parameters of the gamma functions andthe adjustments were estimated during fitting of the assessmentmodel.

Observation submodel.—Age-specific harvests for the NewYork and Ontario recreational fisheries were calculated for eachyear using the Baranov catch equation

Hf,y,a = Ff,y,a

Zy,a

Ny,a

[1 − exp(−Zy,a)

]. (4)

Age-specific harvests were then converted to length-class-specific harvests by allocating the age-specific harvests basedon an assumed length distribution for each age, and summingfor each length-class over the ages (see appendix). Total an-nual harvest and proportions harvested in each length-class werethen calculated for comparison with the corresponding observedquantities.

Predicted CPEs by age for the combined USGS–NYSDECadult gill-net survey and the OMNR community index gill-netsurvey were calculated as

If,y,a = sf,aqf Ny,a exp

(− 8

12Zy,a

), (5)

thus predicting that CPE would be proportional to abun-dance adjusted for within-year mortality occurring prior to thesurvey (late summer), with proportionality depending on a con-stant overall catchability and age-specific selectivity. Catcha-bility was estimated and selectivity was modeled as a gammafunction with estimated parameters. As with recreational har-vest, these predictions were then converted to length-specificpredicted CPEs (see appendix), and total predicted CPE andproportions by length-classes were calculated for comparisonwith observed quantities.

In addition to predicting gill-net survey CPEs for the entire at-large population of lake trout in Lake Ontario, we also predictedage-specific CPE of CWT lake trout for the combined USGS–NYSDEC adult gill-net survey. These predictions were equal tothe age-specific predictions for the entire population, multipliedby the fraction of each stocked cohort of lake trout that weretagged with CWTs (see appendix). Again, totals and proportionswere calculated for comparison with observed data.

Catch per 500,000 stocked yearling-equivalent lake trout dur-ing the combined USGS–NYSDEC juvenile lake trout trawl sur-vey was predicted as proportional to the estimated abundance ofage-2 lake trout divided by the number of yearling-equivalentlake trout stocked in the previous year (multiplied by 500,000),expressed as

Uy = 500,000 × q5,yNy,2

Ny−1,1. (6)

A separate catchability was estimated for each of three timeblocks (before 1992, 1993 through 1996, and after 1996), thetime blocks being chosen to account for the change in trawl con-figuration that occurred in 1997 and for the decreased samplingefficiency of the original trawl configuration after dreissenidmussels became widely established in Lake Ontario in the early1990s (see appendix).

Model fitting.—The SCAA model was programmed in ADModel Builder (ADMB Project 2009). Model parameters wereestimated by highest posterior density estimation (also referredto as maximum penalized likelihood) using a quasi-Newton op-timization algorithm and AD Model Builder default terminationcriteria. Upper and lower bounds were specified for all param-eters to help keep the optimization algorithm from flat parts ofthe likelihood surface. These bounds were chosen to representvalues above or below which would be considered implausi-ble. No parameters were estimated to be at their bounds, andmoderate changes to the bounds did not influence results. Theobjective function for the SCAA model consisted of the sumof 13 components being either negative log-likelihood compo-nents or negative log-prior (penalty) components (Table A.2).These components were based on assumed probability distribu-tions. We assumed lognormal distributions for the seven totalannual harvest or total annual CPE data sources (Table A.2). Inthe random walk model, the fishery catchability in one year wasmultiplied by year-specific deviation to obtain the catchability inthe next year (see appendix). The log-prior (penalty) componentassociated with the random walks assumed that these year-to-year multiplicative changes were lognormally distributed forboth the New York and Ontario recreational fisheries. We as-sumed that the five proportions-at-length or proportions-at-agedata sources behaved as though they resulted from a measuredor aged subsample that followed a multinomial distribution(Table A.2).

The weighting of individual data sources or penalty com-ponents in terms of their overall effect on model fits is one ofthe most difficult aspects of SCAA modeling (Quinn and De-riso 1999). For components based on a lognormal distribution,squared deviations (e.g., between an observed and predictedvalue) on a log scale were weighted inversely by the lognormaldispersion parameter. We represented this dispersion factor forthe ith data source by σ2/λi, where σ2 is a “standard dispersionparameter” and λi represent how far the dispersion parame-ter for a particular data source deviates from this “standard.”Thus, a λ equal to 1.0 implies that the dispersion parameter

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POPULATION DYNAMICS OF LAKE ONTARIO TROUT 967

for a data source is equal to the standard dispersion parame-ter, while λ equal to 0.5 implies that the dispersion parameterfor a data source is twice the standard. We estimated σ2 dur-ing the fitting of the assessment model, the λs being fixed atprespecified values. We used an iterative approach for settingλs whereby we initially designated λs for data sources basedon our perception of the reliability of the data sources, thencalculating how closely these assumed dispersions matched theSCAA model mean squared error for the different sources. Wethen adjusted the λs based on the discordance between the as-sumed dispersions and fitted SCAA model residual estimates,until the assumed dispersions and fitted SCAA model residualestimates were approximately equal or were reasonable giventhe data source. Negative log-likelihood components for multi-nomial components were weighted by the effective sample size,which was the number of fish for which ages or lengths wereused in constructing the annual compositions or 100 for samplesizes larger than 100.

Sensitivity and retrospective analyses.—Sensitivity analyseswere performed to determine whether model estimates weredisproportionately affected by some of the key assumptions thatwere made when configuring the SCAA model. The sensitivityof model estimates to the weightings of individual data sourceswas evaluated by increasing and decreasing the λs for each dataset fivefold and refitting the SCAA model. The sensitivity toassumed maximum effective sample sizes for estimating ageand length compositions of harvested and surveyed fish wasevaluated by increasing and decreasing the maximum threefoldand refitting the SCAA model. Similarly, we evaluated the sen-sitivity of model estimates to assumed natural mortality ratesfor age-2 and older lake trout, and the expansion factors used toexpand New York and Ontario recreational harvests to areas ofLake Ontario not normally covered during fishing boat surveysby increasing and decreasing these values threefold and refittingthe SCAA model. Sensitivity was evaluated based on deviationsof estimated total abundance, abundance of age-5 and older laketrout, estimates of age-1 M, and estimate of mean F for age-5and older fish from those obtained from the baseline data sourceweightings, maximum effective sample sizes, age-2 and olderM, and harvest expansion factors.

A retrospective analysis was conducted to determine whetherthe constructed SCAA model exhibited evidence of systematicbiases in model parameters or estimates by deleting a year ofdata from the SCAA model and refitting it (Mohn 1999); thiswas repeated until 6 years of data had been removed sequen-tially from the model. Retrospective patterns were examined forage-1 and older abundance, age-5 and older abundance, meaninstantaneous fishing mortality for age-5 and older fish, andinstantaneous natural mortality for age-1 fish.

RESULTS

Model FitsModel estimates of Ontario and New York recreational har-

vest matched very well with the observed temporal patterns

TABLE 2. Data sources or penalty components included in the model’s ob-jective function. For data sources or penalty components assumed to have alognormal distribution, the weighting factor (λ) is given; NA = not applicable.

Description λ

New York recreational fishery harvest 1.00Ontario recreational fishery harvest 1.00Combined USGS–NYSDEC adult gill-net survey CPE 0.75OMNR adult gill-net survey CPE 0.04Combined USGS–NYSDEC adult gill-net survey CPE

of CWT lake trout0.05

Combined USGS–NYSDEC juvenile trawl surveyCPE

0.03

New York recreational fishery catchability randomwalk deviations

1.00

Ontario recreational fishery catchability random walkdeviations

0.05

New York recreational fishery harvest lengthcomposition

NA

Ontario recreational fishery harvest length composition NACombined USGS–NYSDEC adult gill-net survey CPE

length compositionNA

OMNR adult gill-net survey CPE length composition NACombined USGS–NYSDEC adult gill-net CPE of

CWT lake trout age compositionNA

(Figure 1). There was also generally good agreement betweenestimated and observed CPE for the NYSDEC–USGS adult gill-net survey (Figure 1), although agreement was not as close asthat of the recreational harvest data sources as a result of thelower weighting assigned to the NYSDEC–USGS adult gill-netsurvey data source (Table 2). In terms of NYSDEC–USGS adultgill-net survey CPE for CWT lake trout, estimated CPE wasconsistently lower than that of observed CPE (Figure 1). Thisdiscrepancy was likely a result of the lower weighting assignedto this data source relative to that of CPE of the at-large laketrout population (Table 2). For the OMNR adult gill-net survey,the SCAA model underestimated CPE in years prior to 2000 andslightly overestimated CPE in years after 2000 (Figure 1). Onceagain, this poorer predictive performance was probably due atleast in part to the lower weighting assigned to this data source(Table 2), although part of the difficulty was also likely relatedto the OMNR survey indicating a steeper decline in lake troutabundance (97% decline) than the combined NYSDEC–USGSadult gill net survey.

The estimated mean length from the SCAA model did notsystematically differ from the observed mean length for the NewYork recreational fishery (Figure 2), nor did the estimated meanlength and age differ from the observed mean length and agefor the combined USGS–NYSDEC adult gill-net survey (Figure2). There did appear to be some systematic differences betweenobserved and estimated mean length for the Ontario recreationalfishery and OMNR adult gill-net survey (Figure 2). For theOntario recreational fishery, mean length was underestimatedby the SCAA model later in the time series. For the OMNR

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FIGURE 1. Model fits to recreational fishery harvest data (first row) and adult gill-net survey catch per effort (CPE; next two rows) in New York and Ontariowaters of Lake Ontario during 1985–2007 (1992–2007 for the Ontario survey). Model estimates are represented by solid lines and observed values by dots. Forthe New York adult gill-net survey, CPE is shown for both the at-large and coded-wire-tagged (CWT) lake trout populations.

adult gill-net survey, mean length was underestimated from thelate 1990s to early 2000s and was overestimated from 2004 to2007. The discrepancy between observed and estimated meanlengths for the OMNR adult gill-net survey was possibly duein part to low sample sizes causing this data source to haverelatively little influence on model fit; typically, fewer than 20fish were measured for length in recent years in the OMNR adultgill-net survey.

For the combined USGS–NYSDEC juvenile trawl survey,there was substantial interannual variability in observed adjustedcatch, particularly later in the time series (Figure 3), whichresulted from large fluctuations in catches at a few sites nearthe mouth of the Niagara River (B. F. Lantry, unpublished data).Despite this variability, the SCAA model appeared to adequatelypredict adjusted catch of the juvenile trawl survey, althoughthe model could not fully reproduce the observed variability inlater years since catchability for the survey was assumed to beconstant from 1997 to 2007.

Model EstimatesAccording to the fitted SCAA model, total estimated lake

trout abundance in Lake Ontario declined by approximately76% from a peak abundance of approximately 4.8 million fish inthe late 1980s and early 1990s to approximately 1.2–1.5 millionfish in 2006 and 2007 (Figure 4). Abundance of age-5 and olderlake trout experienced a similar rate of decline, with abundancedeclining from approximately 1.3 million fish in 1994 to 0.3million fish in 2007 (Table 3; Figure 4). The decline in lake troutrecreational fishery harvest was even more dramatic than thedecline in abundance, both New York and Ontario recreationalfishery harvest of lake trout having declined by more than 95%since the late 1980s.

Sea lamprey-induced mortality on lake trout generally com-prised the largest source of mortality for age-5 and older fish(Figure 5). Compared with both sea lamprey-induced mortal-ity and natural mortality, recreational fishing was a relativelyinsignificant source of mortality for lake trout in Lake

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FIGURE 2. Model fits to the mean length of lake trout in the recreational fishery harvest (first row) and adult gill-net surveys (second row) in New York andOntario waters of Lake Ontario during 1985–2007 (1992–2007 for the Ontario survey). Also shown are the results for the mean age of coded-wire-tagged (CWT)lake trout caught in the combined USGS–NYSDEC adult gill-net survey during 1985–2007. Model estimates are represented by solid lines and observed valuesby dots.

FIGURE 3. Model fits to the combined USGS–NYSDEC juvenile trawl surveycatch per effort (CPE) in Lake Ontario during 1985–2007. Model estimates arerepresented by solid lines and observed values by dots. Also shown are themodel estimates of instantaneous natural mortality for age-1 lake trout (dashedline).

FIGURE 4. Estimated abundance of age-1 and older (solid black line) and age-5 and older (solid gray line) lake trout in Lake Ontario during 1985–2007. Thedashed lines are 95% probability intervals that were obtained through likelihoodprofiling in AD Model Builder (ADMB Project 2009).

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TABLE 3. Model estimates of lake trout abundance at age (in thousands) at the beginning of the year during 1985–2007 in Lake Ontario.

Age

Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1985 1,713 653 556 521 564 168 0 0 0 0 0 0 0 0 01986 1,945 673 560 451 358 355 102 0 0 0 0 0 0 0 01987 2,032 693 579 467 325 234 223 63 0 0 0 0 0 0 01988 1,961 659 596 482 333 207 141 132 37 0 0 0 0 0 01989 2,001 533 567 503 367 248 151 101 93 26 0 0 0 0 01990 1,838 740 459 477 385 284 192 115 77 70 19 0 0 0 01991 2,034 567 637 386 351 272 201 136 82 54 49 14 0 0 01992 1,503 436 487 533 280 241 185 136 92 55 36 33 9 0 01993 1,147 441 375 413 420 216 186 143 105 71 42 28 25 7 01994 1,042 332 379 318 333 341 175 150 115 84 57 34 22 20 51995 1,028 241 286 320 253 269 276 142 121 92 67 45 27 18 201996 815 140 208 242 255 203 215 219 112 95 72 53 35 21 291997 973 159 120 176 192 201 158 165 167 85 72 54 39 26 381998 864 229 137 102 139 150 154 119 123 124 62 52 40 29 471999 939 108 197 116 81 108 114 115 88 90 90 45 38 29 542000 934 180 93 167 93 65 88 92 93 71 72 72 36 30 662001 954 99 155 79 132 73 50 66 68 68 51 52 52 26 692002 945 128 85 131 62 103 55 37 49 50 50 37 38 37 682003 910 79 110 73 106 51 84 45 30 39 40 40 30 30 842004 932 102 68 94 59 84 39 64 34 23 29 30 29 22 852005 685 102 88 58 76 47 65 30 49 26 17 22 22 22 802006 556 76 88 75 46 58 34 47 22 35 18 12 15 15 702007 901 140 65 75 60 36 44 25 34 16 25 13 8 11 60

Ontario, particularly in later years (Figure 5). Since themid-1990s, only around 5% of the total mortality for age-5 and older lake trout has been attributable to recreationalfishing.

In terms of selectivity patterns, the modeled recreational fish-ery and survey selectivity patterns were similar to those that havebeen estimated for other lake trout populations in the GreatLakes (Linton et al. 2007). There were slight differences in

FIGURE 5. Mean instantaneous mortality rates for age-5 and older lake trout in Lake Ontario during 1985–2007. The dashed horizontal lines indicate the totalannual mortality target range for lake trout identified by Schneider et al. (1983).

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FIGURE 6. Estimated selectivities of lake trout by age from the New York and Ontario recreational fishery and fishery-independent surveys during 1985–2007.Three selectivities are shown for the New York recreational fishery: that prior to the implementation of a slot limit (solid black line), that under the 635–762-mmslot limit (dashed black line), and that under the 686–762-mm slot limit (dashed gray line).

selectivities for both recreational fisheries and fishery-independent surveys between New York and Ontario (Figure6). Selectivities for older fish were generally less for the On-tario recreational fishery and survey than they were for the NewYork recreational fishery (at least when no length-based regu-lation was in effect) and survey. For the New York recreationalfishery, the length-based slot limit that went into effect in 1988helped to lessen exploitation for age-4 to age-15 lake trout, the635- to 762-mm slot limit that went into effect in 1988 andagain in 1993 doing a better job at protecting age-4 to age-10lake trout compared with the 686- to 732-mm slot limit (Figure6).

Model estimates of age-1 natural mortality rates have in-creased dramatically since the mid-1980s (Figure 3). In themid-1980s, age-1 natural mortality estimates were around 0.9,but by 2002 had increased to approximately 2.5. In terms of finiterates, this was an increase from 60% annual natural mortalityto 92%. Since their peak in 2002, age-1 natural mortality rateshave declined, but still on average have been near 1.9 (annualfinite rate ≈ 85%) since 2003 (Figure 3).

Sensitivity and Retrospective AnalysesThe SCAA model estimates were generally robust to as-

sumptions concerning the weighting of data source components,effective maximum sample sizes for estimating age and lengthcompositions, age-2 and older natural mortality rates, and recre-ational fishing harvest expansion factors. Threefold to fivefold

increases and decreases in these values did result in a range ofpoint estimates of overall and age-5 and older lake trout abun-dance, age-1 natural mortality rates, and mean age-5 and olderfishing mortality rates. For example, peak total abundance oflake trout varied between 3.7 and 8.6 million fish, while peakabundance of age-5 and older fish varied between 0.7 and 3.4million fish. Despite this variability, the qualitative conclusionsremained similar. That is, lake trout abundance (both overalland age-5 and older lake abundance) was estimated to have de-creased by approximately 70–80% since the early to mid-1990s,an overall decline in age-1 survival being the primary factorresponsible for this decline in abundance. Peak instantaneousnatural mortality rates for age-1 lake trout in our sensitivityanalyses ranged from 1.6 to 3.0 (finite rates = 80–95%).

There was no systematic retrospectivity evident in age-1 andolder abundance, age-5 and older abundance, mean instanta-neous fishing mortality for age-5 and older fish, or instantaneousnatural mortality for age-1 fish (Figure 7). Early in the time se-ries, it appeared that perhaps the SCAA model converged on asomewhat lower level of abundance of lake trout than in lateryears, although as was found with the sensitivity analyses theoverall pattern of decline in abundance remained similar to thatof the model fit with all available data. By 2003, abundances andmodel estimates were similar to those found when the SCAAmodel was fit to all available data, although there still remainedsome year-to-year scatter in abundance and parameter estimateswith no systematic pattern.

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FIGURE 7. Retrospective patterns for estimates of age-1 and older abundance (top-left panel), age-5 and older abundance (bottom-left panel), mean instantaneousfishing mortality for age-5 and older fish (top-right panel), and instantaneous natural mortality for age-1 fish (bottom-right panel). The terminal years of the dataincluded in the model refits are indicated by the different lines.

DISCUSSIONAlthough the restoration of self-sustaining lake trout popu-

lations in Lake Ontario has been somewhat contentious becausea restored population might compete with and subsequently af-fect the recreational quality of other fisheries (Lange and Smith1995), the reestablishment of the species as a dominant, hy-polimnetic predator remains a high-priority fish community ob-jective for the lake (Elrod et al. 1995; Stewart et al. 1999). One ofthe early barriers to restoration identified by Elrod et al. (1995)was inadequate numbers of spawning fish. The original intentfor the stocking program was to establish a population capableof producing recruitment levels equal to what was maintained bythe native population during periods of exploitation (Schneideret al. 1983). When stocking was first initiated, it was recognizedthat particular strains might be better adapted to surviving in thelake than others. Consequently, it was recommended that a va-riety of strains initially be stocked so that performance could beevaluated (Schneider et al. 1983). Stocking would then primar-ily be focused on those strains that performed well, the ultimategoal being the production of an “Ontario” strain of lake troutfrom those fish that successfully survived, matured, and repro-duced in the lake, which presumably would be best adapted forthe lake (Schneider et al. 1983; Marsden et al. 1993). More than10 different strains of lake trout were evaluated, several studiesindicating that Seneca strain fish had greater reproductive po-tential (Marsden et al. 1989, 1993; Grewe et al. 1994; Perkinset al. 1995). Additionally, adult Seneca strain fish were foundto have a lower chance of being attacked by sea lamprey and

a greater chance of surviving if an attack occurred (Schneideret al. 1996). Based on these strain comparisons, both Ontarioand New York began predominantly stocking Seneca strain laketrout in 1997.

The initial prospects for reestablishing a self-sustaining laketrout population were considered good owing to improving en-vironmental conditions, the ongoing efforts to suppress sea lam-prey densities, and the plans that were put in place for selectingan appropriate strain as the genetic basis for the restored popu-lations (Schneider et al. 1983; Elrod et al. 1995). More recently,the near-term outlook has been characterized as poor owing todeclining abundance of mature lake trout and low catches ofnaturally produced fish (Lantry et al. 2007). So what has gonewrong? Based on the results from this study, poor recruitmentof stocked fish, particularly in recent years, has led to an overalllow abundance of lake trout. Previous researchers have specu-lated that most of the mortality affecting lake trout recruitmentin Lake Ontario occurs within the first year of stocking (Elrodand Schneider 1992; Elrod et al. 1995). Our work sought toevaluate this hypothesis in a more quantitative way.

Our approach was to apply SCAA assessment methods. Atfirst consideration, this approach might have been dismissed asimpractical. Issues that we faced included low levels of harvestwith substantial uncertainty due to some areas of the lake beingirregularly sampled, the absence of age composition informationfor recreational fisheries, changes in length-based regulations(slot limits) leading to temporal changes in fishery selectiv-ity, possible changes in age-1 natural mortality (the focus of

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interest), and possible changes in natural mortality at older agesdue to sea lamprey predation. Under most conditions, attemptingto apply an SCAA model to a stock with such low rates of harvestwould prove difficult. We were able to move forward and ad-dress the other issues because we integrated data sources that areatypical to most SCAA applications, and tailored the model tothe system at hand. In particular, our SCAA model incorporatedan absolute measure of recruitment which allowed us to fit themodel and obtain robust estimates of temporal patterns. Giventhat recruitment at age 1 was essentially known and that we hada good time series of relative abundance for age 2 from the trawlsurvey, we could estimate natural time-varying mortality for age1. We were able to work around the absence of age–compositiondata for the fishery and the overall survey by making use of in-formation on a tagged subset of the at-large population as well asdata on length compositions together with information on lengthdistributions given age. This required that the model be adaptedto predict length compositions based on the model’s estimate ofthe population age composition. We similarly integrated infor-mation on sea lamprey marking to allow for temporal variationin natural mortality at older ages and modeled how slot limitregulations would influence selectivity. While the approachesused in this study for each model component were not uniqueto our work, our adaptable combination of the components isillustrative of the flexibility of SCAA and integrated modelingmore generally. For example, we have illustrated that the usualrequirement of absolute estimates of harvest combined with rel-atively high exploitation can be replaced with other absolutemeasures. Here we used absolute annual values of recruitment,but other estimates of absolute abundance (Methot 2009) orabsolute removals (e.g., by predators [Livingston and Methot1998; Hollowed et al. 2000; Moustahfid et al. 2009]) could alsofill this role. Thus, we suggest that assessment methods thathave become standard for highly exploited species might bemore widely adaptable to other species, which is of great im-portance given the increasing need to manage such stocks in thecontext of ecosystem management (Moustahfid et al. 2009).

Our model adaptations allowed us to confirm that the declinein lake trout abundance in Lake Ontario was largely owing to anincrease in age-1 natural mortality, particularly in more recentyears. Although fishing and sea lamprey predation were impli-cated as factors that contributed to the initial extirpation of laketrout, neither of these factors presently appear to be problematic,at least when compared with early survival of stocked fish. Since1985, total annual mortality rates of age-2 and older lake trouthave been below targets specified by Schneider et al. (1983).Fishing mortality in particular constitutes only a small fractionof total mortality. As indicated by Lange and Smith (1995),many Lake Ontario anglers prefer fishing for other salmoninespecies and will only target lake trout when catch rates for otherspecies are low, which continues to be reflected in Lake Ontariocreel survey results (Lantry and Eckert 2010).

As previously indicated, Seneca lake trout have been the pri-mary strain stocked in both Ontario and New York jurisdictionalwaters of Lake Ontario since 1997. Although a causal relation-

ship cannot be established based on the results of our research,this increased reliance on Seneca strain lake trout, along with theincreases in age-1 natural mortality rates that we estimated, sug-gests that this strain may be less adapted to conditions in LakeOntario than previously thought. Comparison of the estimates ofage-1 natural mortality rates from this study with the proportionof yearling-equivalent lake trout stocked that were Seneca strainsuggests that as stocking has become dominated by this strainearly life survival has declined. When more than 35% of stockedyearling-equivalent lake trout have been Seneca strain, age-1 in-stantaneous natural mortality has averaged approximately 2.0.Conversely, when 35% or less of stocked yearling-equivalentlake trout have been Seneca strain, age-1 instantaneous naturalmortality has averaged approximately 1.2. Research conductedelsewhere on the Great Lakes has similarly indicated that Senecastrain lake trout can have low early life survival compared withother lake trout strains (McKee et al. 2004), although it remainsunclear as to what mechanisms may cause poor survival. IfSeneca strain lake trout do indeed have poor early life survivalin Lake Ontario, then relying on this strain to produce an adultspawning stock capable of sustaining the population throughnatural reproduction may not be the best management strategyto take even if the strain does have better reproductive potentialthan other strains, as suggested by Marsden et al. (1989, 1993),Grewe et al. (1994), and Perkins et al. (1995).

One reason why Seneca strain lake trout may not be per-forming as expected is that expectations were based on strainevaluations conducted prior to the invasion of dreissenid mus-sels, which are known to have had major ecosystem-level effectsthroughout the lake (Mills et al. 2003). Thus, it is difficult toknow definitively whether the characteristics that resulted in re-productive advantages for Seneca strain lake trout prior to dreis-senid mussel invasion are still advantageous. Given the changesthat have occurred in Lake Ontario, conducting new strain per-formance evaluations would likely prove beneficial to help guidefuture lake trout restoration efforts. Even if such evaluationsare conducted, restoration of lake trout populations may stillbe difficult to achieve owing to other restoration impediments,such as early mortality syndrome, predation of naturally pro-duced lake trout eggs and fry by alewife Alosa pseudoharengus(Krueger et al. 1995) and round goby Neogobius melanostomus(Chotkowski and Marsden 1999), and poor-quality spawninghabitat due to dreissenid mussel colonization and blooms of thebenthic filamentous algae Cladophora spp. (Lantry et al. 2007).

It should also be noted that the estimated increase in age-1natural mortality may be unrelated to lake trout strain and insteadbe a result of some other process. Indeed, examination of age-1natural mortality estimates in relation to the total number of laketrout that have been stocked in the lake suggests that stockingdensity could play a role in early survival, lower survival atlower densities of stocking suggesting that there could be a de-pensatory mechanism (such as predation) affecting survival ofstocked fish (Forney 1971). Another possible explanation is thatthe increase in natural mortality of age-1 lake trout is related tothe ecosystem-level changes that have occurred recently in Lake

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Ontario. One of the ecosystem-level changes that has occurredpostinvasion and expansion of dreissenid mussels is a majorrestructuring of zooplankton and macrobenthos communities(Johannsson et al. 2007), which may have affected feeding pat-terns of young lake trout (Elrod et al. 1993; Lantry et al. 2007).Between 1985 and 2007, predicted weight of 400-mm lake troutwas generally below the long-term average (except for some in-termittent periods between 1993 and 1998), but there was noapparent sustained decline in condition, which is perhaps whatone would expect if starvation was resulting in low survival. It isalso possible that predation on stocked lake trout by other preda-tors in Lake Ontario (including lake trout) may have increasedin recent years as a result of the ecosystem-level changes thathave recently occurred, stocking thus possibly serving almostas a supplemental feeding program for predators. Elrod et al.(1993) found a negative association between survival indices ofstocked fish and abundance of lake trout greater than 550 mm.Additionally, Dietrich et al. (2006) observed some instances ofpredation of stocked lake trout by adult conspecifics. Other dietstudies have shown no-to-very-little instances of predation onyoung lake trout by other predators (B. F. Lantry, unpublisheddata), although it is not clear whether these other studies wereconducted when predation on stocked lake trout would be ex-pected to occur. Part of the difficulty in clarifying which of theseor other factors are responsible for the increased age-1 naturalmortality rates of lake trout is that many of these factors (i.e.,increased reliance on Seneca-strain lake trout, lower stockingrates, ecosystem-level changes in Lake Ontario) have more orless occurred simultaneously, which makes it nearly impossibleto tease apart their relative contributions to the observed trendin mortality rates.

Our development of an SCAA model for Lake Ontario laketrout that integrated most of the existing data sources availablefor the species and system was beneficial in that it allowed ex-plicit estimation of age-specific abundances and mortality rates,which permitted us to examine trends in these variables andcomparisons with factors such as the proportion of lake troutstocked by strain. Nevertheless, data limitations forced us tomake a number of assumptions. Perhaps our biggest assumptionwas that the lake trout population consisted of a single, well-mixed population. Whether this is indeed the case or whetherthe stock was effectively a metapopulation consisting of severalsubstocks is unknown; however, it is doubtful that such detailcould have been incorporated into the SCAA model given avail-able data. Even attempting to develop SCAA models specific toNew York and Ontario would likely have proven difficult giventhe limited data. Research to explore this assumption would bebeneficial. More generally, assessment models built upon ourinitial effort will also likely prove beneficial in the future forevaluating the effects of strategies that are implemented to helpachieve lake trout restoration, and this argues for continued ef-forts to improve the assessment. For one, an expansion of ourSCAA model could be used to evaluate whether or not restora-tion goals such as those outlined in Schneider et al. (1983) havebeen met.

ACKNOWLEDGMENTSWe thank the Great Lakes Fishery Commission for providing

funding that allowed this work to be conducted. We additionallythank the many biologists and technicians, both past and present,who have participated in the assessment and management of theLake Ontario lake trout stock, and J. Markham, J. McKenna,Jr., S. Sitar, and one anonymous reviewer for reviewing earlierversions of this manuscript. This article is contribution 1657of the USGS Great Lakes Science Center and 2011-08 of theQuantitative Fisheries Center at Michigan State University. Ref-erence to trade names does not imply endorsement by the U.S.Government.

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Linton, B. C., M. J. Hansen, S. T. Schram, and S. P. Sitar. 2007. Dynamicsof a recovering lake trout population in eastern Wisconsin waters of LakeSuperior, 1980–2001. North American Journal of Fisheries Management 27:940–954.

Livingston, P. A., and R. D. Methot Jr. 1998. Incorporation of predation into apopulation assessment model of eastern Bering Sea walleye pollock. Pages663–678 in F. Funk, T. J. Quinn II, J. Heifetz, J. N. Ianelli, J. E. Powers, J. F.Schweigert, P. J. Sullivan, and C. I. Zhang, editors. Fishery stock assessmentmodels. Alaska Sea Grant College Program, University of Alaska, AKSG-98-01, Fairbanks, Alaska.

Marsden, J. E., C. C. Krueger, P. M. Grewe, H. L. Kincaid, and B. May.1993. Genetic comparison of naturally spawned and artificially propagatedLake Ontario lake trout fry: evaluation of a stocking strategy for speciesrehabilitation. North American Journal of Fisheries Management 13:304–317.

Marsden, J. E., C. C. Krueger, and B. May. 1989. Identification of parentalorigins of naturally produced lake trout in Lake Ontario: application of mixed-

stock analysis to a second generation. North American Journal of FisheriesManagement 9:257–268.

Maunder, M. N., and G. M. Watters. 2003. A-SCALA: an age-structured statis-tical catch-at-length analysis for assessing tuna stocks in the eastern PacificOcean. Inter-American Tropical Tuna Commission Bulletin 22:433–582.

McCullough, R. D., and D. W. Einhouse. 2004. Eastern basin of LakeOntario creel survey, 2003. New York State Department of Environ-mental Conservation, Bureau of Fisheries, Lake Ontario Unit and St.Lawrence River Unit to the Great Lakes Fishery Commission’s Lake On-tario Committee, 2003 Annual Report, Section 22, Albany. Available:www.dec.ny.gov/docs/fish marine pdf/lorpt08sec02.pdf. (February 2010).

McKee, P. C., M. L. Toneys, M. J. Hansen, and M. E. Holey. 2004. Performanceof two strains of lake trout stocked in the midlake refuge of Lake Michigan.North American Journal of Fisheries Management 24:1101–1111.

Methot, R. D., Jr. 1990. Synthesis model: an adaptable framework for anal-ysis of diverse stock assessment data. International North Pacific FisheriesCommission Bulletin 50: 259–277.

Methot, R. D., Jr. 2009. Stock assessment: operational models in support offisheries management. Pages 137–165 in R. J. Beamish and B. J. Rothschild,editors. The future of fisheries sciences in North America. Springer Science,New York.

Mills, E. L., J. M. Casselman, R. Dermott, J. D. Fitzsimons, G. Gal, K. T. Holeck,J. A. Hoyle, O. E. Johannsson, B. F. Lantry, J. C. Makarewicz, E. S. Millard,I. F. Munawar, M. Munawar, R. O’Gorman, R. W. Owens, L. G. Rudstam,T. Schaner, and T. J. Stewart. 2003. Lake Ontario: food web dynamics ina changing ecosystem. Canadian Journal of Fisheries and Aquatic Sciences60:471–490.

Mohn, R. 1999. The retrospective problem in sequential population analysis: aninvestigation using cod fishery and simulated data. ICES Journal of MarineScience 56:473–488.

Moustahfid, H., J. S. Link, W. J. Overholtz, and M. C. Tyrell. 2009. The advan-tage of explicitly incorporating predation mortality into age-structured stockassessment models: an application for Atlantic mackerel. ICES Journal ofMarine Science 66:445–454.

O’Gorman, R., J. H. Elrod, R. W. Owens, C. P. Schneider, T. H. Eckert, andB. F. Lantry. 2000. Shifts in depth distribution of alewives, rainbow smelt,and age-2 lake trout in southern Lake Ontario following establishment ofdreissenids. Transactions of the American Fisheries Society 129:1096–1106.

OMNR (Ontario Ministry of Natural Resources). 2006. Lake On-tario fish communities and fisheries: 2005 annual report of theLake Ontario management unit. OMNR, Picton, Ontario. Available:www.glfc.org/lakecom/loc/mgmt unit/LOA%2006.01.pdf. (February 2010).

Owens, R. W., R. O’Gorman, T. H. Eckert, and B. F. Lantry. 2003. The offshorefish community in Lake Ontario, 1972–1998. Pages 407–441 in M. Munawar,editor. State of Lake Ontario: past, present, and future. Goodword Books, NewDelhi.

Perkins, D. L., J. D. Fitzsimons, J. E. Marsden, C. C. Krueger, and B. May.1995. Differences in reproduction among hatchery strains of lake trout ateight spawning areas in Lake Ontario: genetic evidence from mixed-stockanalysis. Journal of Great Lakes Research 21(Supplement 1):364–374.

Quinn, T. J., II, and R. B. Deriso. 1999. Quantitative fish dynamics. OxfordUniversity Press, New York.

Rutter, M. A., and J. R. Bence. 2003. An improved method to estimate sealamprey wounding rate on hosts with application to lake trout in Lake Huron.Journal of Great Lakes Research 29(Supplement 1):320–331.

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APPENDIX: STATISTICAL CATCH-AT-AGE MODELDETAILS

Population submodel.— Modeled lake trout abundancesat age were computed by the exponential model (equation1). As described in Methods, total instantaneous mortalityfor lake trout was partitioned into natural mortality, sealamprey-induced mortality, New York recreational fishingmortality, and Ontario recreational fishing mortality (equation2). Parameterization of natural mortality (exclusive of sealamprey) is described in Methods. Sea lamprey-inducedmortality on lake trout was calculated external from the SCAAmodel using methods described in Bence et al. (2003), Rutterand Bence (2003), and Linton et al. (2007). Briefly, we useda time-varying logistic model to predict the annual expectednumber of A1 sea lamprey wounds on lake trout as a functionof fish length. Observations of sea lamprey wounds on laketrout were taken from the NYSDEC and OMNR adult gill-netsurveys. The expected wounding rates from the parameterizedlogistic model were multiplied by a factor of 6.5 to expand theexpected wounding rate to include A2 and A3 marks (M. P.Ebener, Chippewa–Ottawa Resource Authority, personal com-munication). These expanded wounding rates were then used toestimate length-specific sea lamprey-induced mortality for laketrout larger than 420 mm (calculated at the midpoint of 20-mmlength intervals) on Lake Ontario lake trout using the equation

MSLy,l= Wy,l

(1 − pl

pl

).

The probability of a lake trout surviving a sea lamprey attackwas taken from the laboratory study conducted by Swink (1990).Length-specific sea lamprey-induced mortality rates were con-verted to age-specific mortality rates using an age–length key(Quinn and Deriso 1999). Because observations of sea lampreywounding rates were from surveys conducted in the late sum-mer and early fall, we assumed that the estimated age-specificsea lamprey-induced mortality applied to the year in whichthe observations were made. This is different than the assump-tion made when calculating sea lamprey-induced mortality onlake trout for Lakes Huron, Michigan, and Superior. For theseother lakes, estimated age-specific sea lamprey-induced mor-tality is assumed to apply to the year prior to when wounding

observations are made because sampling is conducted in thespring when sea lamprey are not parasitizing lake trout (Johnsonand Anderson 1980; Sitar et al. 1999; Bence et al. 2003).

New York and Ontario recreational fishing mortalities wereassumed to be products of annual fishing effort, age-specificselectivities, and year-specific catchabilities (equation 3).

The random walk model for year-specific catchabilitieswas

qf,y ={

qf,y ;qf,y−1 exp

(�f,y−1

);

for y = 1985for 1986 ≤ y ≤ 2007

�f,y−1 ∼ N(

0,σ2�f

).

Thus, qf,y and the �f,y−1 were model-estimated parameters.Note that exp (�f,y−1) are the multiplicative random walk devi-ations we refer to in Methods as being lognormally distributed.Length-based selectivity for the recreational fisheries, in the ab-sence of size regulations (slot limits), was estimated by gammafunctions (Quinn and Deriso 1999) of length (at the midpointsof 25.4-mm length-classes) using the formula

s∗f,l = L

αf

l exp (−βf Ll)

max(L

αf

l exp (−βf Ll)) .

Since 1988, recreational harvest of lake trout in New Yorkwaters of Lake Ontario has been regulated through a slot limitregulation that prohibits harvest within the slot. From 1988 to1989, a 635- to 762-mm slot was in effect. In 1990, the slot waschanged to 686 to 762 mm. In 1993, the slot was changed back to635 to 762 mm. To account for the effects of these changing slotlimits on New York recreational fishery harvests, we estimatedselectivity as the product of what selectivity would be in theabsence of a slot limit (s∗) and a slot limit effect (ρ)

sf,l =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩

s∗f,l ; Ontario recreational harvest : all years; New

York recreational harvest : 1985−1987(no slot limit)

s∗1,lρ1,l ; New York recreational harvest : 1988−1989,

1993 + (635 to 762−mm slot limit)s∗

1,lρ2,l ; New York recreational harvest : 1990−1992(686 to 762−mm slot limit)

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POPULATION DYNAMICS OF LAKE ONTARIO TROUT 977

where

ρ1,l =⎧⎨⎩

1.0;φ1;φ2;

for Ll ≤ 622 mm or Ll ≥ 800 mmfor Ll = 648 mm or Ll = 775 mmfor Ll ≥ 673 mm and Ll ≤ 749 mm

and

ρ2,l =⎧⎨⎩

1.0;θ1;θ2;

for Ll ≤ 673 mm or Ll ≥ 800 mmfor Ll = 699 mm or Ll = 775 mmfor Ll ≥ 724 mm and Ll ≤ 749 mm

The parameters of these step functions(φ1,φ2,θ1,θ2

)were es-

timated as part of the model fitting process. The notion hereis that at lengths near the boundaries of the slot limits, anglersmay be more likely to retain a fish because of inaccurate lengthmeasurements of fish than they are of fish of lengths more in themiddle of the slot limit. Although slot limits have not been usedto manage lake trout recreational harvest in Ontario waters ofLake Ontario, we nevertheless estimated Ontario recreationalfishery selectivities as length-based so that both componentsof the lake trout recreational fishery were modeled similarly.The length-based selectivities were converted to age-based se-lectivities for the purpose of calculating recreational fishingmortalities by multiplying selectivities by a length–age matrixand summing across length-classes (Quinn and Deriso 1999),expressed as

sf,a =∑

l

�a,lsf,l .

The length–age matrix, which consisted of the proportions ofage a fish that were in length-class l, was derived by assuming thelengths of the fish in each age-class were normally distributed,the proportion of fish of age a in length-class l being a function ofthe mean length at age and the standard deviation of the length-at-age distribution. Mean length at age was predicted froma von Bertalanffy growth function with an asymptotic lengthof 803 mm, a Brody growth coefficient of 0.298, and an age atwhich length would theoretically be 0 of 0.127. Based on em-pirical examination of length-at-age distributions, we assumed aconstant coefficient of variation (SD/mean) for all age-classes of0.08 and calculated the corresponding standard deviation (0.08× mean). Thus, the proportion of fish of age a in length-class lfor the length–age matrix was calculated by subtracting the nor-mal cumulative distribution function at the lower end of eachlength-class from the cumulative distribution function value atthe upper end of the length-class, using the mean and standarddeviation appropriate for that age.

Observation submodel.— Age-specific harvests for the NewYork and Ontario recreational fisheries were calculated withthe Baranov catch equation (equation 4). Harvests for each25.4-mm length-class were then calculated by multiplying pre-dicted age-specific harvest by length–age matrix and summing

over the ages, calculated as

Hf,y,l =∑

a

Hf,y,a�a,l

(Quinn and Deriso 1999; Maunder and Watters 2003). Harvestproportions at length were calculated by dividing harvests foreach length bin by the total recreational harvests.

Catch per efforts by age for the combined USGS–NYSDECadult gill-net survey and the OMNR community index gill-netsurvey were calculated as the products of catchability, selec-tivity, abundances at age, and abundances at age adjusted toaccount for the fraction of total annual mortality that occurredbefore the surveys were conducted in late summer–early fall(equation 5). Selectivities for the adult gill-net surveys wereestimated as age-based gamma functions (Quinn and Deriso1999), expressed as

sf,a = aαf exp−βf a

max(aαf exp−βf a

) .

As with recreational harvest, survey catch for each 25.4-mmlength-catch class was calculated by multiplying estimated age-specific CPE by the proportion of age a fish that are in length-class l and summing over the ages, expressed as

If,y,l =∑

a

If,y,a�a,l .

Proportions at length of the gill-net surveys were calculated bydividing length-based CPEs by the overall survey CPEs.

In addition to calculating gill-net survey CPEs for the entireat-large population, we also calculated CPE of CWT lake troutfor the combined USGS–NYSDEC adult gill-net survey, whichwas simply the age-specific prediction of CPE for the entireat-large population in the survey multiplied by the fraction ofeach stocked cohort that were tagged with CWTs, calculatedas

I CWTy,a = I3,y,a cy−a+1

Catch per 500,000 stocked yearling-equivalent lake trout dur-ing the combined USGS–NYSDEC juvenile lake trout trawlsurvey was calculated by multiplying survey catchability andestimated abundance of age-2 lake trout, and dividing the re-sulting product by the number of yearling-equivalent lake troutstocked in the previous year (multiplied by 500,000; equation6). Catchability time blocks were used when estimating juve-nile trawl survey catches for reasons explained in the main text,expressed as

q5,y =⎧⎨⎩

γ1; for y < 1992γ2; for 1992 ≤ y < 1997γ3; for y ≥ 1997

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978 BRENDEN ET AL.

TABLE A.1. Description of equation symbols used in the analysis of lake trout population dynamics in Lake Ontario.

Symbol Description

Indicator variablesa Age-class (1–15 + )l Length-class (177.8 to 965.2 mm in 25.4-mm increments)Ll Midpoint of length-class class ly Year (1985–2007)f Fishery (NY recreational = 1, ONT recreational = 2, NY survey = 3, ONT survey = 4, NY juvenile survey = 5)

Estimated parametersN1985,2−13 Abundances at age in 1985 for age-2 to age-13 lake troutMy,1 Instantaneous natural mortality for age-1 lake troutq Catchabilityγ Catchability for USGS–NYSDEC juvenile trawl survey time blocks� Random walk deviations for catchabilityα Parameter for gamma selectivity functionβ Parameter for gamma selectivity functionφ Parameter for effect of 635–762-mm slot limit regulationθ Parameter for effect of 686–762-mm slot limit regulationσ2 Standard dispersion parameter for objective function data components

Calculated and assumed quantitiesN Abundancec Proportion of a stocked lake trout cohort tagged with CWTsZ Total instantaneous mortalityM Instantaneous natural mortalityMSL Instantaneous sea lamprey–induced mortalityF Instantaneous recreational fishing mortalityW Expected sea lamprey wounding ratep Probability of surviving a sea lamprey attacks∗ Selectivity prior to adjustment for slot limit effects Selectivityρ Step function for slot limit regulation� Age-to-length transition matrixH Model-estimated recreational fishery harvestP Model-estimated proportions at lengthI Model-estimated adult gill-net survey CPEI CWT Model-estimated adult gill-net survey CPE of CWT lake troutP CWT Model-estimated proportions at age of CWT lake trout in adult gill-net surveyU Model-estimated juvenile trawl survey adjusted catch� Negative log-likelihood componentλ Dispersion scalar for negative log-likelihood componentsNE Effective sample size of age- or length-estimated fish

Observed dataE Recreational fishery effortH Recreational fishery harvestP Proportions at lengthI Adult gill-net survey CPEICWT Adult gill-net survey CPE of CWT fishPCWT Proportions at age of CWT lake trout in adult gill-net surveyU Juvenile trawl survey adjusted catch

Distributional parametersµa Mean length at age predicted from a von Bertalanffy growth functionσl

a Standard deviation of length distribution for an age-classσ� Standard deviation for fishery catchability random walk deviations

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POPULATION DYNAMICS OF LAKE ONTARIO TROUT 979

TABLE A.2. Objective function equations for the Lake Ontario lake trout statistical catch-at-age model.

Equation Description

�Hf= nHf

loge

(σ√λHf

)+ 0.5

(λHf

σ2

) ∑y

[loge

(Hf,y

Hf,y

)2]

New York and Ontario recreational fisheryharvest

�If= nIf

loge

(σ√λIf

)+ 0.5

(λIf

σ2

) ∑y

[loge

(Iy

Iy

)2]

Combined USGS–NYSDEC and OMNR adultgill-net survey CPE

�ICWT = nICWT loge

(σ√

λICWT

)+ 0.5

(λICWT

σ2

) ∑y

[loge

(ICWTy

I CWTy

)2]

Combined USGS–NYSDEC adult gill-net surveyCPE of CWT lake trout

�U = nU loge

(σ√λU

)+ 0.5

(λU

σ2

) ∑y

[loge

(Uy

Uy

)2]

Combined USGS–NYSDEC juvenile trawlsurvey adjusted catch of age-2 lake trout

��f= n�f

loge

(σ√λ�f

)+ 0.5

(λ�f

σ2

)∑y

[loge

(�f,y

)2]

New York and Ontario recreational fisherycatchability random walk deviations

�Pf= −∑

y

NE,f,y

∑l

(Pf,y,l loge Pf,y,l

)New York and Ontario recreational fishery

harvest and combined USGS–NYSDEC andOMNR adult gill-net survey lengthcompositions

�P CWT = −∑y

NCWTE,y

∑a

(P CWT

y,a loge P CWTy,a

)Combined USGS–NYSDEC adult gill-net survey

age composition of CWT lake trout

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