GREAT LAKES FISHERY COMMISSION Project Completion Report 1

Transcription

1 GREAT LAKES FISHERY COMMISSION 2009 Project Completion Report 1 A Model Based Evaluation of How Stocking Oncorhynchus Influences the Fish Communities of Lakes Huron and Ontario by: Travis O. Brenden 2 and James R. Bence 2 2 Quantitative Fisheries Center Department of Fisheries and Wildlife Michigan State University East Lansing, Michigan October Project completion reports of Commission-sponsored research are made available to the Commission s Cooperators in the interest of rapid dissemination of information that may be useful in Great Lakes fishery management, research, or administration. The reader should be aware that project completion reports have not been through a peer-review process and that sponsorship of the project by the Commission does not necessarily imply that the findings or conclusions are endorsed by the Commission. Do not cite findings without permission of the author.

2 ABSTRACT: We developed offshore fish community models for lakes Huron and Ontario to forecast the potential consequences to changes in Pacific salmonid Oncorhynchus stocking policies by the states of New York and Michigan and the province of Ontario. The Lake Huron forecasting model included Chinook salmon Oncorhynchus tshawytscha, lake trout Salvelinus namaycush, steelhead Oncorhynchus mykiss, walleye Sander vitreus, and burbot Lota lota as predators; the Lake Ontario forecasting model included Chinook salmon, lake trout, steelhead, Atlantic salmon Salmo salar, brown trout Salmo trutta, and coho salmon Oncorhynchus kisutch as predators. Alewife Alosa pseudoharengus and rainbow smelt Osmerus mordax were the primary prey species for both models. Evaluated stocking policies ranged from a complete cessation in stocking of all Pacific salmonids to a doubling of the average stocking rate. Policies were evaluated using metrics that captured the desire to have high, stable catches of lake trout and Chinook salmon and large sizes of Chinook salmon. The susceptibility of alewife and rainbow smelt populations being driven to low adult abundance levels was also measured for the policy evaluations simulations. We found that for Lake Huron decreases in Pacific salmonid stocking rates were predicted to increase biomass and fishery yield of lake trout and age-3 Chinook salmon spawning weights throughout the lake; additionally, recreational yield of Chinook salmon was predicted to increase in the Main Basin of Lake Huron. Biomass of alewife and rainbow smelt biomass also increased with decreases in Pacific salmonid stocking rates; however, even with a complete cessation of all Pacific salmon stocking, there still remained a high probability of prey abundance declining to below threshold levels as a result of presumably high wild recruit of Chinook salmon. The fish community of Lake Ontario was relatively unaffected by changes in Pacific salmon stocking policies because of higher prey productivity and presumably low wild recruitment of Chinook salmon. The results for both lakes Huron and Ontario were sensitive to assumptions about predator wild recruitment, predator search efficiencies, and scaling of prey stock-recruitment relationships. These sensitivities should be kept in mind in any proposed changes in Pacific salmonid stocking rates. PRESS RELEASE: Title: Consequences of Different Pacific Salmon Stocking Policies on Lakes Huron and Ontario Beginning in the mid 1960s, Great Lakes state and provincial fishery management agencies undertook a major initiative to rehabilitate lakes Huron, Ontario and Michigan by stocking hatcheryreared Pacific salmonids Oncorhynchus spp. to reduce densities of exotic pelagic prey fishes and establish recreational fisheries. Although stocking of Pacific salmon is widely credited as having played a major role in the reduction of alewife and rainbow smelt densities in the lakes, the continuation of the stocking program has become controversial. Concerns about possible predatorprey imbalances and adverse effects on native species have resulted in calls to discontinue Pacific salmon stocking. As part of a project funded by the Great Lakes Fishery Commission, researchers with the Quantitative Fisheries Center at Michigan State University constructed fish community models for lakes Huron and Ontario that allowed the consequences of changes in Pacific salmonid stocking policies to be forecasted. Stocking policies that were explored ranged from a complete cessation of stocking by all states and provinces bordering the lakes to a doubling of the stocking rate. The forecasting models incorporated the best available information regarding wild recruitment of predators in the lakes, as well as the relationships between numbers of young prey produced by differing densities of adult fish. Additionally, the evaluations of stocking policies implicitly incorporated major uncertainties in the dynamics of predator and prey populations and the interactions between predators and preys. The researchers found that for Lake Huron decreases in Pacific salmonid stocking rates were 2

3 predicted to increase biomass and fishery yield of lake trout and age-3 Chinook salmon spawning weights throughout the lake; additionally, recreational yield of Chinook salmon was predicted to increase in the Main Basin of Lake Huron. Biomass of alewife and rainbow smelt biomass also increased with decreases in Pacific salmonid stocking rates; however, even with a complete cessation of stocking, there still remained a high probability of prey abundance declining to below threshold levels as a result of presumably high wild recruit of Chinook salmon. For Lake Ontario, the researchers found that the fish community was relatively unaffected by changes in Pacific salmonid stocking policies. Unlike Lake Huron, wild recruitment of Chinook salmon on Lake Ontario is believed to have declined over time, and previously instituted stocking cuts on Lake Ontario have likely helped to prevent the imbalance between predator and prey populations. The researchers caution, however, that the results of their stocking policy predictions were sensitive to assumptions about wild recruitment of predators and the ability of predators to search for prey within the lakes; the sensitivity of stocking policies to these hard-to-measure quantities should not be ignored when evaluating possible changes in Pacific salmonid stocking rates in the lakes. SUMMARY STATEMENT: Objective 1) Estimate or summarize a time-series of abundances of salmonines and other top-level piscivores of the offshore waters in lakes Huron and Ontario. A time-series of abundance estimates for lake trout and Chinook salmon in lakes Huron and Ontario were obtained through statistical catch at age (SCAA) models. Abundance estimates from lake trout in the Main Basin were obtained from existing SCAA models used to develop total annual catch limits for Lake Huron. We developed new SCAA models for lake trout in Lake Ontario and Chinook salmon in Lake Huron, and refined a pre-existing Chinook salmon SCAA model in Lake Ontario. There was insufficient information to develop SCAA models for other top-level piscivores in the lakes (e.g., steelhead, Coho salmon, walleye); consequently, timeseries estimates of abundance were obtained using a simple estimation approach based on assumed levels of survival and wild reproduction obtained from the literature. The SCAA model developed for Chinook salmon in Lake Huron encompassed the years 1968 to 2004 and fish of ages 0 to 5. The SCAA model used the following types of data: recreational harvest (total numbers) from Michigan DNR and Ontario MNR creel surveys and charter boat reports, fishery effort (total number of angler hours), recreational harvest age-compositions (proportions at each age [summing to 1.0 for a year]), similar age-compositions restricted to mature fish only sampled during July and August (late enough to allow maturity stage to be identified but not so late that scale degeneration became critical), numbers returning to the Swan Creek Weir by year class, and weight-at-age (mean weight in kg for each age and year). The developed SCAA model included features such as time-varying recreational fishery catchabilities, recreational selectivities that were a function of weight at age, maturation mortality rates that were a function of weight at age, and time-varying age-0 natural mortality rates. The SCAA model predictions of Chinook salmon abundance indicated that abundance peaked in the late 1980s but has since declined (Fig. 1). Predicted recreational harvests from the SCAA model were similar to creel survey measurements. Based on research conducted by J. Johnson, Michigan Department of Natural Resources, there has been a dramatic increase in wild reproduction of Chinook salmon since the 1990s (Fig. 1). SCAA model predictions of age-0 natural mortality have also increased since the 1990s (Fig. 1), which is why increases in wild reproduction have not resulted in larger recreational harvests or Swan Creek Weir returns The SCAA model developed for lake trout in Lake Ontario encompassed the years 1985 to 2007 and fish of ages 1 to 15+. The SCAA model used the following types of data: recreational harvest (total number) from New York DEC and Ontario MNR creel surveys with adjustments for those portions of the lake not regularly surveyed, recreational harvest length compositions, 3

4 recreational harvest composition of coded-wire tagged lake trout, U.S. Geological Survey, New York DEC, Ontario MNR fishery independent surveys, and a cooperative U.S. Geological Survey and New York DEC juvenile trawl survey. Sea lamprey induced mortality on lake trout was calculated externally from the SCAA model. The developed SCAA model included features such as time-varying recreational fishery catchabilities and age-1 natural mortality rated and assumed measurement errors occurred in recreational catch and effort observations. The SCAA model predicted that there had been a nearly 80% decline in total abundance of lake trout between 1985 and 2007 (Figure 2). Predicted harvest of lake trout from the SCAA model was very similar to observed harvest levels in most years, the few exceptions occurred in the mid 1980s and early 1990s (Figure 2). An increase in age-1 natural mortality rates of appears to have been a major factor in abundance declines of lake trout in the lake. The SCAA model estimated that age-1 natural mortality rates of lake trout had risen from an average of 0.23 in the late 1980s to an average of 1.95 between 2003 and 2007 (Figure 2). The refined SCAA model for Chinook salmon in Lake Ontario encompassed the years 1985 to 2007 and fish of ages to 1 to 4. The SCAA model used data from New York DEC and Ontario MNR creel surveys and age-composition of fish returning to the Salmon and Credit rivers. Like lake trout abundance in Lake Ontario, SCAA model predictions of Chinook salmon abundance declined over time, as have recreational harvest predictions (Fig. 3). Recreational harvest predictions from the SCAA model were close to actual measurements (Fig. 3). Based on the findings of Connerton et al. (2009), declines in Chinook salmon abundance have been caused largely by a decrease in wild reproduction; proportion of wild-origin Chinook salmon in Lake Ontario is estimated to have declined from 84 to 45% between 1989 and 2002 (Fig. 3). Objective 2) Estimate a time series of predator consumption rates for lakes Huron and Ontario. Predator consumption was calculated using a multi-species Type-II functional response, which is a saturating functional response that assumes predator consumption at certain prey densities reaches an asymptote because at some point prey handling time limits consumption. Parameterization of the functional response was completed during the calibration phase of the forecasting model development. The functional response was parameterized so that predicted growth rates of predators were similar to observed growth rates, and so that predicted growth rates under an assumption of overly abundant prey matched what might be expected under such circumstances. In the simulation model consumption was converted into predator growth based on an assumed gross conversion efficiency (GCE) that depended both on fish size and ration. This function that related GCE to fish ration and size was parameterized to be consistent with estimates of gross conversion efficiencies (GCEs) for predators obtained by using the Wisconsin Bioenergetics model to estimate growth across a wide range of ration-levels and preliminary sizes of fish. For the MB of Lake Huron, mean consumption for the period of 1973 to 2005 was estimated at 15.5 kilotons (kt) for lake trout, 2.9 kt for Chinook salmon, 4.0 kt for steelhead, 0.3 kt of walleye, and 2.1 kt for burbot. For the NC/GB of Lake Huron, mean consumption for the period of 1973 to 2005 was estimated at 3.7 kt for lake trout, 3.4 kt for Chinook salmon, 4.5 kt for steelhead, and 0.24 kt for burbot. The lower than expected estimates of consumption for Chinook salmon was due to very high estimates of age-0 natural mortality that were predicted during the calibration process. For Lake Ontario, mean consumption for the period of 1985 to 2005 was estimated at 6.6 kt for lake trout, 93.1 kt for Chinook salmon, 2.4 kt for steelhead, 0.5 kt for Atlantic salmon, 5.8 kt for brown trout, and 0.2 kt for coho salmon. Objective 3) Develop fish community models for lakes Huron and Ontario that will allow predictions 4

5 of how changes in plantings of hatchery-reared Pacific salmonids would influence the fish community. The forecasting models that were constructed for lakes Huron and Ontario were lake-wide stochastic simulation models that projected predator abundance, consumption, and growth and prey recruitment and abundance. The forecasting models operated on monthly, rather than annual, time steps, which permitted more accurate tracking of those events that occurred more or less continuously throughout the year. Using a monthly time step was particularly beneficial for modeling prey consumption by predators, which is affected by relative sizes of predators and prey which can change substantially during the course of a season. The Lake Huron forecasting model included Chinook salmon, lake trout, steelhead, walleye, and burbot as predators; the Lake Ontario forecasting model included Chinook salmon, lake trout, steelhead, Atlantic salmon, brown trout, and coho salmon as predators. Alewife and rainbow smelt were the primary prey species for both models. Population models for the key predators in the lakes were age-based with age ranges that reflected those observed in the lakes. Population models for the prey species were length-based. The forecasting model for Lake Ontario consisted of a single spatial unit, while the model for Lake Huron consisted of two separate spatial units: the Main Basin (MB) and North Channel/Georgian Bay (NC/GB). For lake trout, the MB of Lake Huron was subdivided into three sub-basins (North, Central, and South) so that the forecasting model matched up with existing SCAA assessment models. Walleye were assumed to only occur in the MB of Lake Huron. The forecasting models were constructed to include options for reading in predator and prey recruitment levels, which allowed for the forecasting model to be used to directly estimate consumption for a predator abundance time series. The forecasting models were also constructed with the ability to impose zero prey recruitment levels for a period of time, which can be useful for exploring how the lakes will respond to a crashed prey base. Objective 4) Describe, compare, and interpret model predictions within each lake for different Pacific salmon stocking scenarios. We evaluated eight different Pacific salmon stocking policies to determine how different policies would affect the lakes Huron and Ontario fish communities. The policies that we evaluated were: average of stocking rate, increase of the average by 50%, increase of the average by 100%, decrease of the average by 33%, decrease of the average by 50%, cessation of stocking by all agencies, cessation of stocking by the Ontario Ministry of Natural Resources, and cessation of stocking by the Ontario Ministry of Natural Resources while accounting for Michigan s and New York s response to Ontario s policy. Policies were evaluated based on the following performance metrics that were either time averaged or were the percentage of years that a performance variable was below a designated threshold during a 25-year simulation: biomass of lake trout, Chinook salmon, alewife, and rainbow smelt, the average recreational and commercial harvest and yield of lake trout and Chinook salmon, the absolute annual variation in recreational and commercial harvest of lake trout and Chinook salmon, the probability that alewife and rainbow smelt adult abundances declined below abundance threshold values set for the species, how often alewife and rainbow smelt adult abundances declined below abundance threshold values for each simulation run, the probability that alewife and rainbow smelt adult abundances declined below abundance threshold value for at least three consecutive years, and how often alewife and rainbow smelt adult abundances declined below abundance threshold values for at least three consecutive years during each simulation run. These performance metrics were chosen because they captured the desire to 5

6 have high stable catches of lake trout and Chinook salmon, large sizes of Chinook salmon, and the susceptibility of alewife and rainbow smelt to being driven to low abundance levels. The effect that certain assumptions made in the lakes Huron and Ontario forecasting models on relative performance of the different stocking policies was explored by conducting a sensitivity evaluation of several key variables in the forecasting models. These key variables included natural mortality rates of predators and prey, predator wild recruitment levels, and predator search efficiencies and prey stock-recruitment scalars. We found that for Lake Huron decreases in Pacific salmonid stocking rates were predicted to increase biomass and fishery yield of lake trout and age-3 Chinook salmon spawning weights throughout the lake; additionally, recreational yield of Chinook salmon was predicted to increase in the Main Basin of Lake Huron. Biomass of alewife and rainbow smelt biomass also increased with decrease in Pacific salmonid stocking rates; however, even with a complete cessation of all Pacific salmon stocking, there still remained a high probability of prey abundance declining to below threshold levels as a result of presumably high wild recruit of Chinook salmon. The fish community of Lake Ontario was relatively unaffected by changes in Pacific salmon stocking policies because of higher prey productivity and presumably low wild recruitment of Chinook salmon. Objective 5) Compare model predictions for all scenarios between lakes Huron and Ontario. There were substantial differences between lakes Huron and Ontario in the effects of alternative Pacific salmonid stocking policies. Whereas the fish community of Lake Ontario was predicted to be relatively unaffected by either increases or decreases in Pacific salmonid stocking rates, the Lake Huron fish community was predicted to be more strongly affected by changes in stocking. Perhaps the most notable difference between lakes Huron and Ontario was that even if all stocking of Pacific salmonids was stopped, there still was a strong possibility that adult abundance of prey fish could drop below threshold levels on Lake Huron. This difference was likely a consequence of lower prey productivity and higher wild recruitment of Chinook salmon in Lake Huron than in Lake Ontario. The results for both lakes Huron and Ontario were sensitive to assumptions about predator wild recruitment, predator search efficiencies, and scaling of prey stock-recruitment relationships. These sensitivities should be kept in mind in any proposed changes in Pacific salmonid stocking rates. 6

7 Fig. 1. Statistical catch at age model (SCAA) results for Chinook salmon from the Main Basin of Lake Huron over the period of 1968 to The top, middle, and bottom panels provide estimated abundance for age-1 and older and age-3 and older, recreational harvest predictions (solid line) and creel survey (black circles) estimates, wild reproduction SCAA inputs (solid line) and age-0 natural mortality estimates (dashed line). 7

8 Fig. 2. Statistical catch at age model (SCAA) results for lake trout from Lake Ontario over the period of 1985 to The top panels shows predicted abundance of age-1 and older lake trout from Lake Ontario. The middle panel compares SCAA model predictions (solid line) and creel survey (black circles) estimates of recreational harvest. The bottom panel compares SCAA model CPUE predictions (solid line) and actual CPUE measurements from the cooperative USGS and NYDEC juvenile lake trout trawl survey. Also shown on the bottom panel are SCAA model predictions of lake trout age-1 natural mortality. 8

9 Fig. 3. Statistical catch at age model (SCAA) results for Chinook salmon from Lake Ontario over the period of 1985 to Shown are predictions of age-1 and older lake trout (top panel), a comparison of model predictions (solid line) and creel survey (black circles) estimates of recreational harvest (middle panel), and estimated levels of recruitment from wild reproduction (solid line, from Connerton et al. 2009) and stocking (dashed line) used as SCAA model inputs (bottom panel). 9

10 APPENDIX: DRAFT OF A MANUSCRIPT INTENDED FOR EVENTUAL SUBMISSION TO ECOLOGICAL MODELLING Model-Based Evaluation of How Stocking Pacific Salmonids Influences the Fish Communities of Lakes Huron and Ontario Travis O. Brenden*,1 and James R. Bence 2 Quantitative Fisheries Center Department of Fisheries and Wildlife Michigan State University East Lansing, Michigan USA *Corresponding author 1 - brenden@msu.edu; Phone: ; Fax: bence@msu.edu; Phone: ; Fax: Key words: Lake Huron, Lake Ontario, Pacific salmon, Oncorhynchus spp., stocking, stochastic simulation 10

11 Introduction The Laurentian Great Lakes of North America is the largest freshwater system in the world, with a total surface area of more than 200,000 square kilometers (Beeton et al. 1999). The five lakes that make up this system (lakes Erie, Huron, Michigan, Ontario, and Superior) have each been subjected to a variety of disturbances, including invasion of exotic species (e.g., zebra mussels Dreissena polymorpha, sea lamprey Petromyzon marinus, alewife Alosa pseudoharengus, rainbow smelt Osmerus mordax), overharvest of native fisheries, and poor water quality stemming from eutrophication and pollution (Madenjian et al. 2002; Mills et al. 2003; Dobiesz et al. 2005). By the mid 1960s, lakes Michigan, Huron, and Ontario, in particular, were considered to be in ecological and management crises. Native apex piscivores, lake trout Salvelinus namaycush, Atlantic salmon Salmo salar, and burbot Lota lota, were scarce or had been completely extirpated (Berst and Spangler 1972; Christie 1972; Hansen 1999; Mills et al. 2003). Although naturally reproducing stocks of steelhead Oncorhynchus mykiss and pink salmon Oncorhynchus gorbuscha were present as a result of purposeful or inadvertent introductions prior to the 1960s, they exerted relatively low predatory pressure on prey fishes (Kocik and Jones 1999). As a result, small exotic pelagic species, alewife and rainbow smelt, dominated the offshore fish communities of the lakes (O Gorman and Stewart 1999). Although commercial fisheries did exist for alewife and rainbow smelt (Brown et al. 1999), these species were considered to be of low fishery value and to be the cause of numerous problems, including suppressing recruitment of native fish species, clogging of water intake systems, and degrading beach quality due to large-scale intermittent die-offs (Tanner and Tody 2002). Beginning in the mid and late 1960s, state and provincial fishery management agencies undertook a major initiative to rehabilitate the Great Lakes by stocking hatchery-reared Pacific salmonids Oncorhynchus spp. to reduce densities of pelagic prey fishes and establish recreational fisheries (Berst and Spangler 1972; Tanner and Tody 2002; Mills et al. 2003). Although several species of Pacific salmonids were experimented with, Chinook salmon Oncorhynchus tshawytscha soon dominated the stocking programs of most agencies due to the species fast growth rates, high angling quality, low production cost, and high rate of alewife predation (Hansen and Holey 2002; Mills et al. 2003). By the early 1970s, large numbers of Chinook salmon were being stocked into lakes Huron, Michigan, and Ontario (Madenjian et al. 2002; Mills et al. 2003; Dobiesz et al. 2005). By the mid 1980s, stocking of Chinook salmon exceeded 11

12 that of all other Oncorhynchus species combined (Kocik and Jones 1999; Hansen and Holey 2002). Roughly coincident to this widespread stocking of Pacific salmonids, large numbers of hatchery-reared lake trout were being stocked into the Great Lakes in an effort to reestablish selfsustaining populations. To date self-sustaining lake trout populations have only been established in Lake Superior (Hansen 1999; Bronte et al. 2003) and in an isolated embayment of Georgian Bay in Lake Huron (Reid et al. 2001), however, stocked lake trout remain an important component of the fish communities of lakes Huron, Michigan, and Ontario. The reestablishment of apex predators profoundly affected the Great Lakes. In addition to creating economically important recreational fisheries (Bence and Smith 1999), mortality rates of pelagic prey species were substantially increased, which helped alleviate some of the environmental problems caused by high pelagic prey densities. On Lake Michigan, where the food-web consequences of Pacific salmonid stocking have been the most studied, the increase in predator abundance is thought to have been a major cause for the decline in alewife abundance during the 1970s (Stewart et al. 1981; Jones et al. 1993; Holey et al. 1998; Hansen and Holey 2002; Madenjian et al. 2005). Despite the seemingly positive benefits of the Pacific salmonid stocking programs, by the late 1970s concerns were already being expressed as to whether the abundance of offshore piscivores in lakes Huron, Michigan, and Ontario might exceed prey production capacity (Stewart et al. 1981; Jones et al. 1993). A commercial trawl fishery that had developed for alewife on Lake Michigan was restricted in the 1970s and 1980s out of concern that harvest might reduce prey availability to predators (Brown et al. 1999). In the late 1980s and early 1990s, Chinook salmon abundance in Lake Michigan declined sharply due to a massive die-off that was attributed to a stress-induced outbreak of bacterial kidney disease caused by declining abundance of alewife (Holey et 1998; Hansen and Holey 2002). On lakes Huron and Ontario, recent declines in growth and condition of Chinook salmon (Eckert 2006; He and Bence 2007; He et al. 2008; Bence et al. 2008a) and reduced abundances of alewife and rainbow smelt in annual prey assessments (Madenjian et al. 2008; Riley et al. 2008; Walsh et al. 2008a,b) have exacerbated concerns about possible predator-prey imbalances in these systems. Development of economically and socially important recreational fisheries for Pacific salmon on the Great Lakes, combined with the strong possibility that sustaining these fisheries is incompatible with low alewife abundance, has substantially complicated management of Great Lakes fisheries (Goddard 2002; Hansen and Holey 2002). There is a diversity of views as to the 12

13 role of Pacific salmonids in the Great Lakes; Kocik and Jones (1999) aptly described this diversity of views as extending along a continuum from an enhancement to a restoration view. At the enhancement end, the Great Lakes are viewed as dysfunctional ecosystems, where Pacific salmonids are a central management concern, and continued stocking is necessary to enhance the value of the system. At the restoration end, the focus is on rehabilitation of native species, and the prominence of Pacific salmonids in the Great Lakes is viewed as inconsistent with long-term objectives. Some favoring the restoration view nevertheless argue that stocking of Pacific salmonids has served a restoration function by reducing alewife abundance, which has promoted the recovery of some native fishes (Eshenroder and Burnham-Curtis 1999; Madenjian et al. 2008; Bence and Mohr 2008). Other restoration advocates have emphasized negative attributes of stocking Pacific salmonids (e.g., disease transmission, agonistic interactions with lake trout) and argued for a complete cessation of stocking (Crawford 2001). Somewhat counter-intuitively, those supporting management primarily for Pacific salmonids have sometimes found themselves suggesting intermediate levels of stocking between these alternative restoration approaches. Understanding how predators influence prey dynamics is critical for rational management of fishery communities (Tsou and Collie 2001; Essington et al. 2002; Wiese et al. 2008). Clearly, different perceptions as to the influence of Pacific salmonids on Great Lakes fish communities can lead to different stocking policy recommendations, even in cases of mutually agreed upon management objectives. Evaluating the effects of different Pacific salmonid stocking policies is complicated not only by the size and economic importance of the systems, which makes direct experimentation difficult, but also by the substantial uncertainty with regards to factors that influence the consequences of stocking, such as natural recruitment of apex predators, survival rates of stocked fish, and the relationship between stock abundance and recruitment of important prey. The purpose of this research was to conduct a model-based evaluation of how different Pacific salmonid stocking policies might affect the fish communities of lakes Huron and Ontario. We were particularly interested in exploring how key uncertainties in our understanding of the dynamics of predator and prey populations and the interactions between predators and preys population affected the outcomes of the different stocking policies. Past experience has shown that it is important to account for such uncertainties when evaluating different management options for fishery systems as they often lead to different management 13

14 actions being recommended than when key uncertainties are ignored (Walter 1986; McAllister and Pikitch 1997; Sainsbury et al. 1997; Robb and Peterman 1998; Haeseker et al. 2003; Deroba and Bence 2008; Irwin et al. 2008). 1.1 Relationships to Existing Models Models for exploring predator consumption of prey have previously been developed for both lakes Huron (Dobiesz 2003) and Ontario (Jones et al. 1993; Rand et al. 1993; Koonce and Jones 1994; Jackson 1996, 1997; Rand and Stewart 1998; Murry et al. in press), and for a generalized salmon-alewife system based on Lake Michigan (Fenichel et al. in press). For the most part, the primary intent of these models have been to compare historic and current estimates of predator consumption in relation to prey productivity (Rand et al. 1993; Rand and Stewart 1998; Murry et al. in press), although in some cases the models have been used to forecast possible consequences to changes in stocking policies (Jones et al. 1993; Dobiesz 2003, Fenichel et al. in press). The models constructed by Jackson (1996, 1997) were primarily used to track bioaccumulation of PCBs in piscivorous fish in Lake Ontario, although in the case of Jackson (1997) the model was used evaluate how different stocking policies could influence PCB uptake in predator fish. The models developed by Rand et al. (1993), Rand and Stewart (1998), Dobiesz (2003), and Murry et al. (in press) were classic bioenergetic models in the sense that the models estimated predator consumption based on observed predator growth rates while accounting for energy losses due to excretion, egestion, metabolism, and specific dynamic action (Hartman and Hayward 2008). Generally, bioenergetic models do not attempt to dynamically model prey populations, which limits their usefulness for exploring how prey stocks may be affected by changes in predator abundance. Conversely, the models of Jones et al. (1993), Koonce and Jones (1994), and Jackson (1996, 1997) were true system models in that both predator and prey components, as well as interactions (e.g., consumption) between predators and prey, were modeled dynamically (Caron-Lormier 2009). Fenichel et al. (in press) modeled a simplified biological system using a deterministic framework, but included dynamic behavioral responses of anglers. The system model constructed by Jones et al. (1993) and Koonce and Jones (1994) for Lake Ontario, which also served as the basis for the models constructed by Jackson (1996, 1997), included lake trout, Chinook salmon, steelhead, coho salmon Oncorhynchus kisutch, and 14

15 brown trout Salmo trutta as predator species and alewife, rainbow smelt, and slimy sculpin Cottus cognatus as prey species. Predator population dynamics were largely controlled by assumed known recruitment and mortality rates, with total mortality composed of fishing, maturation, and other natural mortality components. Fishing mortality was assumed to vary proportionally to fishing effort, whereas maturation schedules and other natural were assumed constant (Jones et al. 1993). For prey species, recruitment was modeled through Shepard stockrecruitment functions, which accounted for overcompensation at high spawner abundances. Mortality of prey fish consisted of predation mortality, which was determined jointly from predator and prey abundances through a Type-II functional response, and other natural mortality. Predator growth was calculated by multiplying predator consumption estimates by gross conversion efficiency (GCE) estimates, which is the fraction of consumed biomass that is converted to growth. For the Jones et al. (1993) model, GCEs were assumed to be constant across age classes of a predator. Koonce and Jones (1994) also modeled salmonid-prey interactions in Lake Michigan, and this model was subsequently modified and updated (Szalai et al. 2008, Jones and Bence in press). Most importantly, the modified model directly incorporated uncertainty in key parameter values using a Decision Analysis (DA) approach, which allowed the propagation of these uncertainties through the simulations so that they influenced the outcomes of different management decisions. Our modeling approach for evaluating the consequences of Pacific salmonid stocking on lakes Huron and Ontario was similar to that used by Jones et al. (1993) and Koonce and Jones (1994) for lakes Ontario and Michigan in that we attempted to dynamically model both predator and prey components of the systems. We used a Type-II functional response to calculate predator consumption of prey and a production-based approach for converting predator consumption to growth. Compared to the Jones et al. (1993) and Koonce and Jones (1994) Lake Ontario model, our simulation models incorporated an improved understanding of predator bioenergetics and new information on wild recruitment of Chinook salmon in both lakes. Our simulation models also benefitted from improved age-structured assessment of major predators on both lakes, which aided in the parameterization of our forecasting models. Additionally, our simulation models operated at a monthly, rather than annual time step, which better allowed for incorporating knowledge of how predator-prey relative sizes influenced interactions. The 15

16 influence of key uncertainties was propagated through following a DA approach similar to that previously used on Lake Michigan 1.2 Study Systems Lake Huron is the second largest of the Laurentian Great Lakes (Figure 1) in surface area and the fourth largest lake in the world (Beeton et al. 1999). Although Lake Huron is hydrologically connected to Lake Michigan through the Straits of Mackinac, the lakes are typically regarded as two separate systems for management purposes. Lake Huron receives outflow from Lake Superior via the St. Marys River and empties into Lake St. Clair through the St. Clair River. With the exception of Saginaw Bay and several nearshore areas, Lake Huron is generally regarded as oligotrophic (Dobiesz et al. 2005). Lake Huron is bordered by the State of Michigan and the Province of Ontario. The fisheries of the lake are jointly managed by Michigan, Ontario, and several Native American and First Nation tribes that border the lake. These Native American and First Nation tribes signed treaties in the1800s that ceded territories to the U.S. and Canadian governments, but which retained the rights for tribal and aboriginal members to fish within historical fishing grounds. These aboriginal fishing rights, as well as the recognition that Native American and First Nation tribes have an obligation to participate in the protection and management of the fishery resources, have been repeatedly recognized by state, provincial, and federal courts since the late 1970s (Brown et al. 1999). As previously stated, the Lake Huron fish community was considered to be in a highly disturbed state by the 1970s (Berst and Spangler 1972). Rainbow smelt and alewife were first observed in Lake Huron in 1925 and 1933 (Smith 1970; Berst and Spangler 1972), and by the 1970s they accounted for more than 60% of catch by weight in bottom-trawl prey assessments (Argyle 1982). Sea lamprey, which were first observed in Lake Huron in the 1930s, were at pest levels in the 1980s, and are believed to have played a major role in reducing abundances of several native species, including lake trout and lake whitefish Coregonus clupeaformis. Although efforts to control sea lamprey have resulted in reduced abundance of spawning-phase sea lamprey, abundance and sea-lamprey marking rates remain above target levels in Lake Huron (Bence et al. 2008a). 16

17 By the 1970s, historically important fishes in Lake Huron, such as lake trout, burbot, walleye, cisco, lake whitefish, and bloater were greatly reduced in abundance (Dobiesz et al. 2005). These declines are largely believed to have resulted from a combination of overfishing, sea lamprey predation, and competition/predation with alewife and rainbow smelt, although the relative roles that these factors played in native fish declines are a matter of debate. In an effort to reduce alewife and rainbow smelt densities in Lake Huron, both Michigan and Ontario experimented with stocking Pacific salmonids as a way to elevate predation mortality on these prey fish. More than 200,000 Kokanee salmon Oncorhynchus nerka were introduced by Ontario in 1964 (Berst and Spangler 1972). Michigan began stocking coho salmon in 1968, followed by Chinook salmon in By 1992, almost 16 million fish, including Pacific salmonids, lake trout, brown trout, and walleye, were being stocked annually in Lake Huron (Dobiesz et al. 2005). Since 1994, declines in abundance indices for a number of prey species in Lake Huron have been observed, including alewife, rainbow smelt, bloater, ninespine stickleback, and slimy sculpin (Riley et al. 2008). Possible causes for these declines include elevated predation rates due to an overabundance of predators in the system, as well as ecological consequences from invasion of exotic species (Riley et al. 2008). The declines of alewife and rainbow smelt on Lake Huron are believed to have had some positive consequences. For example, emerald shiner Notropis atherinoides, which are native to Lake Huron and historically have been an important prey source for several native predators in the lake, have increased in abundance since 2004 (Schaeffer et al. 2008), following a very large decline in alewife abundance that occurred that year. Increased natural reproduction of lake trout and walleye in Lake Huron are also believed to be a consequence of this reduced alewife abundance. Madenjian (2008) argued that there is strong evidence that recruitment of many native species in the Great Lakes is adversely impacted by alewife. Although the smallest of the Laurentian Great Lakes in surface area, Lake Ontario still ranks as the seventeenth largest lake in the world (Beeton et al. 1999). It is the easternmost of the Great Lakes (Figure 1), receiving outflow from Lake Erie via the Niagara River and Welland Canal and emptying into the St. Lawrence River. Lake Ontario is bordered and managed cooperatively by the State of New York and the Province of Ontario (Figure 1). Like Lake Huron, Lake Ontario is generally regarded as oligotrophic (Mills et al. 2003). 17

18 Lake Ontario was the first of the Great Lakes to be invaded by sea lamprey and alewife (Mills et al. 1993), although it is possible that sea lamprey were native to the lake (Waldman et al. 2004). Rainbow smelt were first detected in Lake Ontario in the late 1920s, although like sea lamprey there is some question as to whether rainbow smelt are native to the lake (Duggan et al. 2003). Alewife were first detected in Lake Ontario in 1873 (Mills et al. 1993), and by 1890 they were already considered to be abundant and were experiencing periodic die-offs (Smith 1995; O Gorman and Stewart 1999). Historically important piscivores in Lake Ontario, including lake trout and Atlantic salmon, were believed to have been completely extirpated from the system by the late 1800s (Atlantic salmon) and 1950s (lake trout). Efforts to restore these species have had only limited successes. Despite widespread stocking of lake trout since the 1970s, only limited natural reproduction has been detected (Lange and Smith 1995; Mills et al. 2003; Lantry et al. 2007). Stocking of Atlantic salmon in Lake Ontario was initiated in 1983, but several factors, including thiamine deficiency as a result of consuming alewife and limited access to suitable spawning habitat, are believed to possibly limit restoration of this species. Initially, coho salmon were stocked by New York and Ontario as a means to reduce the abundance of prey in the lake. Coho salmon were first stocked by New York in 1968 and Ontario in 1969 (Stewart and Schaner 2002). Ontario continued to primarily stock coho salmon through the late 1970s, whereas New York switched to stocking primarily Chinook salmon by Chinook salmon were first stocked by New York in 1969 and by Ontario in 1971 (Stewart and Schaner 2002). Stocking of Chinook salmon peaked in 1984 at 4.2 million fish, which on a per area basis was the highest stocking intensity of all the Great Lakes (Kocik and Jones 1999). In 1993, the stocking rate of Chinook salmon was reduced to 2.1 million fish, which was an approximate 40% decrease from the 1992 stocking rate. In 1994, the stocking rate of Chinook salmon was reduced to 1.5 million fish, which was an approximate 30% decrease from the previous year s stocking rate. Since 1997, the mean annual stocking rate of Chinook salmon in Lake Ontario has been approximately 2.0 million fish. 2. Methods 2.1. Overview of forecasting models 18

19 The forecasting models that were constructed for lakes Huron and Ontario were lakewide stochastic simulation models that projected predator abundance, consumption, and growth and prey recruitment and abundance. The forecasting models operated on monthly, rather than annual, time steps, which permitted more accurate tracking of those events that occur more or less continuously throughout the year. Using a monthly time step was particularly beneficial for modeling prey consumption by predators because predator and prey sizes can change substantially during the course of a season, which can strongly influence predation rates. The Lake Huron forecasting model included five key predators: lake trout (LKT), Chinook salmon (CHK), steelhead (STH), burbot (BBT), and walleye (WAE). The Lake Ontario forecasting model included six key predators: LKT, CHK, STH, Atlantic salmon (ATS), brown trout (BRT), and coho salmon (COS). For both lakes Huron and Ontario, alewife (ALE) and rainbow smelt (RBS) were the primary prey species; however, two additional prey groups were also included in the models: benthic (BEN) and other pelagic (PEL). These additional prey groups functioned as alternative sources of prey for predators in the event that ALE and RBS were driven to low abundances. The BEN and PEL prey categories were intended to represent aggregates of species and were not intended to be representative of particular types of prey. The BEN and PEL prey groups were considered to consist of populations that were vulnerable to predation and refuge populations that were not vulnerable to predation. The refuge populations were assumed to consist of constant abundances of fish, of which a fraction migrated to the vulnerable population at the beginning of each year but which were immediately replaced by additions to the refuge population. The refuge populations served as source populations for the BEN and PEL prey groups, which prevented the prey groups from being driven to extinction as a result of high predatory demand. Lake whitefish (LWF), sea lamprey (LAM), and double-crested cormorants (COM) Phalacrocorax auritus were also included in each of the forecasting models. These species were not modeled dynamically; rather, their annual abundances were model inputs. Sea lamprey were included in the models as an additional source of mortality for LKT; LWF were included in the models as an alternative source of prey for LAM. Double-crested cormorants were an alternative source of predation on prey populations and thus competed with other predators in the lakes. Population models for the key predators in the lakes were age-based with age ranges that reflected those observed in the lakes (Table 1). Population models for the prey species were 19

20 length-based and consisted of 10 length bins ranging from 0 to 250 mm for ALE and RBS (Table 1). Only a single length bin was used for the BEN and PEL prey groups. For the BEN prey group, all fish were assumed to be 150 mm, while for the PEL prey group all fish were assumed to be 100 mm. The forecasting model for Lake Ontario consisted of a single spatial unit, while the model for Lake Huron consisted of two distinct spatial units that applied to all predator and prey groups: the Main Basin (MB) and North Channel/Georgian Bay (NC/GB). For LKT, the MB of Lake Huron was further subdivided into three sub-basins (North, Central, and South) so that the forecasting model matched existing statistical catch as age stock assessment (SCAA) models. Walleye were assumed to only occur in the MB of Lake Huron. The lakes Huron and Ontario forecasting models were programmed in Microsoft Excel using the Visual Basic for Applications (VBA) programming language. Data inputs for the Lake Huron model were read in from accompanying Excel worksheets. Data inputs for the Lake Ontario model were read in from a separate Microsoft Access database. Simulation run outputs of the forecasting models were stored in Excel worksheets, which were added to the workbooks that housed the VBA code of the forecasting models. Detailed descriptions of how predator and prey recruitment, post-recruitment abundance dynamics, consumption, and growth were modeled are presented in ensuing sections. Parameter definitions and descriptions are in Table Recruitment For predators, new recruits to initial ages were calculated in the beginning of each year prior to mortality, predation, or growth. Salmonid recruits came from two sources: stocking and wild reproduction. For LKT, CHK, STH, COH, ATS, and BRT, annual stocking numbers (fingerlings for CHK, yearlings for LKT, STH, COH, ATS, and BRT) were model inputs. For LT in the MB of Lake Huron, the calculation of annual stocking numbers to the three sub-basins followed that of Rutter (2004). Numbers of yearling-equivalent LKT stocked at each of ten locations around the MB were model inputs. These numbers were then multiplied by a stocking matrix that distributed stocked fish to the various sub-basins of the MB. For all stocked predators, numbers of stocked fish were multiplied by basin-specific, post-stocking survival rates to obtain the numbers of recruits produced from stocking in each year. 20

21 The treatment of wild recruitment differed among the predator species. For CHK, STH, COH, ATS, BRT, and BBT, wild recruitment in each year were normally distributed random deviates with the means and standard deviations of the distributions as forecasting model inputs Pr (, ) R N μσ. The number of wild recruits produced each year was assumed to be independent from those produced in previous years. Standard deviations for the distributions were set equal to 10% of the distribution means. Wild recruitment of walleye in the MB of Lake Huron was a model input and was assumed to be constant. Although wild reproduction of LKT has been detected in both lakes Huron and Ontario (Reid et al. 2001; Riley et al. 2007; Lantry and Lantry 2007; Bence et al. 2008a), for the purposes of this study we assumed that no wild reproduction of LKT occurred in the lakes. There is evidence of growing levels of natural reproduction of lake trout in Lake Huron. If this continues to increase then including wild lake trout in projections would become warranted, although the actual sequence of wild recruitment in relationship to lake conditions is clearly highly uncertain. Recruitment of ALE and RBS was modeled with Ricker stock-recruitment functions with log-normally distributed errors bpyy,, bpy, bpyy,, β b, pysb, py, y εb, py, y R = α S e e (Eq ) Py ( 0, σ ) ε N. Like predator wild recruitment, prey recruitment was also assumed to be independent among years. Prey spawning stock abundance for predicting recruitment levels was calculated by multiplying the abundance of fish in each length category at the start of the year by the proportion of mature fish in each length category and summing across length categories S = N p. (Eq ) bpyy,, bpyly,,, bpyl,, l To capture the variability in timing of when new recruits were vulnerable to predation, 1/12 of the predicted recruits produced in a year were added to the first length bin in each month of the year. The stock-recruitment functions for ALE and RBS were parameterized using relative abundances from bottom trawl surveys that the U.S. Geological Survey (USGS) Great Lakes Science Center (GLSC) have conducted on lakes Huron and Ontario since the 1970s. For Lake 21

22 Huron, we used data collected during a fall survey, while for Lake Ontario we used data collected during a spring survey. Descriptions of the lakes Huron and Ontario surveys, including methods for standardizing catches at trawls of different depths and for changes in trawling gear are provided in O Gorman and Schneider (1986), O Gorman et al. (1997, 2004), and Riley et al. (2008). From the Lake Huron trawl survey, we calculated annual weighted mean catch per ha of age-0 and adult ALE and RBS for the time period of 1973 to 2005 (no sampling was conducted in 2000, thus data for this year were not available). From the Lake Ontario trawl survey, we calculated annual weighted mean catch per ha of age-1 and adult RBS for the time period of 1978 to For both lakes, weighting of trawl CPUE was by hectares with each depth stratum that trawl surveys were conducted. Length-frequency information of ALE and RBS collected as part of the trawl surveys were used to partition total catch into size-based age classes. For Lake Huron ALE, we assumed that fish 100 mm in length or smaller were age 0, and that fish greater than 150 mm in length were adults (i.e., spawning stock). For Lake Huron RBS, we assumed that fish 90 mm in length or smaller were age 0 and that fish greater than 140 mm in length were adults. For Lake Ontario RBS, we assumed that fish 75 mm in length or smaller were age 0 and that fish greater than 100 mm in length were adults. To parameterize the Ricker stock-recruitment function for Lake Ontario ALE, we used CPUE of age-1 and adult (greater than 150 mm) ALE presented in O Gorman et al. (2004) from the USGS GLSC Lake Ontario spring bottom trawl survey conducted between 1978 and In addition to ALE CPUE, O Gorman et al. (2004) also presented data for several environmental variables (number of degree days between May and July of each year, a measure of winter duration, and a predation index) and postulated several stock-recruitment models that incorporated these environmental covariates. Using the data presented, we fit linearized Ricker stock-recruitment functions to each of the models postulated in O Gorman et al. (2004). We then averaged the parameter coefficients across the stock-recruitment models. This model averaging was conducted by weighting parameter estimates from each model by the associated Akaike Information Criteria weights corrected for small sample sizes (Burnham and Anderson 2002). The resulting model-averaged stock recruitment function was R ln = S DD WD E-07PI (Eq ) S 22

23 where R was the CPUE of age-1 ALE, S was the CPUE of adult ALE, DD was number of degree days from May to July, WD was a measure winter duration, and PI was a predation index. Using Equation 2.2.3, we estimated CPUE of age-1 ALE in the absence of predation by setting predation index values to zero and predicting recruitment using the data presented in O Gorman et al. (2004). We used these predicted CPUEs of age-1 ALE in the absence of predation and the observed CPUE of adult ALE presented in O Gorman et al. (2004) to parameterize the stockrecruitment function for ALE for the Lake Ontario forecasting model (parameterization described below). The parameters of the Ricker stock-recruitment function for lakes Huron and Ontario ALE and RBS were fit using the linearized version of the function and a Bayesian inference approach. Diffuse, uniform priors were assigned to all parameters of the linearized Ricker stockrecruitment functions [ln(α), β, and σ Py ]. The joint posterior probability distribution of the parameters were obtained using the Metropolis-Hastings algorithm as implemented in AD Model Builder (Otter Research 2001) to generate chains for the Markov chain Monte Carlo (MCMC) calculations. The MCMC chains were run for 3,000,000 cycles; the chains were thinned by sampling every 300 th cycle. The first 1,000 samples of the saved chains were discarded as a burn-in so that inferences were based on a chain of 9,000 values that remained after the original chain was thinned and the burn-in period dropped. Trace plots and chain autocorrelation functions were examined to identify any unusual structure in the posterior distributions (Thiebaux and Zweiers 1984), which we did not detect. Because relative abundance estimates were not available for the NC/GB of Lake Huron, we assumed that the parameters of the stockrecruitment functions for the NC/GB of Lake Huron were the same as those for the MB. Preliminary scaling of the parameterized stock-recruitment models for ALE and RBS to absolute abundances was based on hydroacoustic estimates of abundance for Lake Huron ALE and RBS (D. Warner, USGS GLSC, unpublished data) and Lake Ontario RBS (T. Schaner, Ontario Ministry of Natural Resources, unpublished data). For Lake Huron, there were three years (1997, 2004, 2005) of hydroacoustic abundance estimates available for scaling the trawl estimates; for Lake Ontario, nine years ( ) of hydroacoustic abundance estimates were available. Despite the limited availability of data, we believed that this was the best available information for scaling trawl relative abundances to absolute abundances. The hydroacoustic surveys conducted on Lake Huron included surveys the NC/GB, so basin specific scalars were 23

24 able to be developed for the lake. Preliminary scaling of the Lake Ontario ALE stockrecruitment functions to absolute abundance was based on an areal expansion of trawl swept area. We chose to use an areal expansion for Lake Ontario ALE rather than a hydroacoustic expansion as this is what has typically been done to develop absolute abundance estimates of ALE on the lake (Jones et al. 1993; Murry et al. in press) and because of concerns that the hydroacoustic surveys do not yield accurate estimates of absolute abundance (T. Schaner, Ontario Ministry of Natural Resources, personal communication). Recruitment for the BEN and PEL prey groups (vulnerable populations only) was modeled with Beverton-Holt stock-recruitment functions with log-normally distributed errors R bpyy,, α S = 1 + β S Py ( 0, σ ) ε N. bpy, bpyy,, bpy, bpyy,, e ε bpyy,, (Eq ) We chose to use Beverton-Holt stock recruitment functions for the BEN and PEL prey groups as these represented aggregates of prey species, which we believed were less likely to suffer overcompensation at high spawner abundance. Spawning stock abundance was defined as the total abundance of fish in the vulnerable populations. Unlike ALE and RBS recruitment, new recruits were added to the benthic and other pelagic prey groups as a single pulse at the beginning of each year. An additional source of recruitment for the benthic and other pelagic prey groups was migration from the refuge population. At the beginning of each year, a fraction of the refuge population migrated from the refuge population to the vulnerable population and thus became available to predators. The fraction of prey migrating to the vulnerable populations from the refuge populations were model inputs and were assumed to not vary temporally Post-recruitment abundance dynamics Monthly predator abundance at age surviving in a basin to the start of the next month, was calculated as bpraym,,,, + 1 bpraym,,,, Z bpraym,,,, N = N e. (Eq ) At the beginning of each year, it was assumed that there was some limited exchange of CHK and STH between the MB and NC/GB of Lake Huron. To account for this we first calculated the 24

25 numbers that survived in a basin to the end of the last month of the previous year using equation These became N, the number in the basin in the first month of the following month prior to any movement. A fraction of these fish were then moved to the other basin, with the rest of the fish remaining in the current basin, leading to abundance in a basin after movement of: ( 1 ) ( ) N = N Θ + N Θ b b (Eq ) bpray,,,,1 bpray,,,,1 bpra,, b, pray,,,1 b, pra, In Lake Ontario accounting for immigration or emigration of predators was not necessary because the lake was modeled as a single basin. For LKT in the MB of Lake Huron, there was not assumed to be any exchange of fish among the sub-basins. The components of total mortality differed by species and lake. For Lake Huron WAE and BBT, Z was not separated into any components. For CHK, STH, ATS, BRT, and COH, Z was assumed to consist of natural and recreational fishing mortality components Z = M + F. (Eq ) REC bpraym,,,, bpraym,,,, bpraym,,,, These species were also assumed to experience a pulse of maturation mortality related to spawning activities. Maturation mortality rates for all species were age specific. For STH, ATS, BRT, and COH, maturation mortality was assumed to occur in the 12 th month of each year, thus the abundance of these species at the beginning of a year was calculated as ( 1 ) Z bpray,,,,12 bpray,,, 1,1 bpray,,,,12 bpra,, N + = N e Mat. (Eq ) For CHK, maturation mortality was assumed to occur in the 9 th month of each year, thus the abundance of CHK in the 10 th month of each year was calculated as ( 1 ) Z bchkay,,,,9 bchkay,,,,10 bchkay,,,,9 bchkay,,, N = N e Mat. (Eq ) Age-specific maturation mortality rates for STH, ATS, BRT, and COH were forecasting model inputs and were assumed to be constant. For CHK, maturation mortality rates were predicted quantities based on model-calculated weights at age and thus could vary temporally. Maturation mortality was predicted as a logistic function of weight at age using the equation Mat bchk,, a, y = 1+ 1 ( 1, ba, ( WbCHKay,,,,9 δ 2, ba, )) e δ (Eq ) where the parameters of Equation were both basin and age specific For CHK, unique sets of parameters was assumed to apply to age-1 age 2 and 3 in Lake Ontario, and age 2 to 4 in Lake Huron. For both lakes, maturation mortality of age-0 CHK was assumed to be zero. For 25

26 Lake Huron, maturation mortality of age-5 CHK was assumed to equal one, as was maturation mortality for age-4 CHK in Lake Ontario. The parameters of the CHK maturation mortality function were estimated as part of the most recent SCAA stock assessment models for lakes Huron and Ontario. When fitting the CHK SCAA models, diffuse, uniform priors were assigned to the parameters of the maturation mortality functions. The joint posterior probability distribution of the parameters was obtained using a similar approach to that described for the ALE and RBS stock recruitment relationships. Markov chain Monte Carlo sampling was used to approximate the joint posterior probability distribution of the model parameters. The MCMC chains were run for 9,000,000 cycles, with thinning of the chain at every 900 th cycle. The first 1,000 samples of the chain were discarded as a burn-in. Trace plots and chain autocorrelation functions were again used to identify any unusual structure in the posterior distributions (Thiebaux and Zweiers 1984), which we did not detect. We again needed to assume that the parameters of the maturation mortality function that was estimated for the MB of Lake Huron also applied to NC/GB as data were not available to separately parameterize a maturation mortality function for this part of the lake. For Lake Huron lake trout, Z was separated into natural, recreational fishing, and commercial fishing mortality components Z = M + F + F. (Eq ) REC COM blktaym,,,, blktaym,,,, blktaym,,,, blktaym,,,, A commercial fishery for LKT on Lake Ontario has not existed since the species were extirpated from the lake in the 1960s (Lange and Smith 1995; Brown et al. 1999); thus Z for Lake Ontario LKT was only separated into natural and recreational fishing components (Equation 2.3.3). In the MB of Lake Huron, commercial and recreational fisheries were modeled by sub-basin. Thus when performing a stocking policy evaluation for Lake Huron, separate estimates of fishing effort, catchability, and selectivity (described below) needed to be input for each sub-basin. Although LKT did not experience maturation mortality, they were assumed to suffer a pulse of sea lamprey mortality in the 9 th month of each year. Thus, the abundance of lake trout in the 10 th month of each year was calculated as LAM Z M blktay,,,,9 bay,, blktay,,,,10 blktay,,,,9 N = N e e. (Eq ) 26

27 Sea lamprey induced mortality on LKT was determined based on the per sea lamprey attack rate of LKT (described in Section 2.4) and the probability of a LKT surviving a sea lamprey attack (Eshenroder and Koonce 1984; Bence et al. 2003) ( 1 ) M = A P. (Eq ) LAM LAM bay,, bay,, bay,, The probability of a surviving a sea lamprey attack was assumed to be a logistic function of weight at age and was estimated based on the laboratory work of Swink (2003) by 1 =. (Eq ) + e P bay,, W blktay,,,,9 1 Recreational and commercial fishing mortalities were assumed to be products of annual fishing effort, age-specific selectivities, catchabilities, and estimates as to the fraction of annual fishing effort that occurred in each month F = q s E f (Eq ) REC REC REC REC REC b, pr, a, y, m b, pr b, pr, a b, pr, y b, pr, m F = q s E f (Eq ) COM COM COM COM COM baym,,, a y m For LKT, STH, ATS, BRT, and COH, the fisheries were assumed to operate continuously throughout the year so f REC and f COM were set to 1/12 for all months. For CHK recreational fishing, fishing effort was assumed to be more seasonally varying. The values of f REC for CHK fishing effort in Lake Huron were obtained from the most recent SCAA stock assessment model for the species. For Lake Ontario, the values of f REC for CHK were calculated from monthly fishing effort estimates measured through annual fishing surveys conducted by the New York State Department of Environmental Conservation and the Ontario Ministry of Natural Resources. For most predators and ages, natural mortality rates were forecasting model inputs and were assumed to be constant. The one exception to this was natural mortality of age-0 CHK, which was assumed to be a function of the biomass of CHK and LKT in relation to the biomass of ALE biomass. The equation used to predict age-0 CHK natural mortality was M ρ LKT CHK ( B + B ) 1, b b, y b, y bchk,,0, y = ALE 1+ ρ2, bbb, y. (Eq ) Estimation of age-0 CHK natural mortality in the lakes Huron and Ontario forecasting models was done at the start of each year prior to any changes in abundance or growth. The biomass calculations did however include the number of recruits that were to be added to both the predator and prey populations in that particular year. 27

28 Parameterization of Equation was based on a time series of age-0 natural mortality estimates that were estimated via random walk as part of the most recent SCAA stock assessment model for CHK in the MB of Lake Huron. Biomass estimates of LKT and CHK for parameterizing Equation were also taken from the most recent Lake Huron SCAA stocks assessment models for these species. The ALE biomass estimates were derived as part of the calibration process for the Lake Huron forecasting model (see Section 2.6). The potential distribution of parameters for Equation were obtained by Bayesian inference using similar methods to those described for prey stock-recruitment relationships and the maturation mortality function for CHK. Because we lacked time-series estimates of age-0 CHK natural mortality for both the NC/GB of Lake Huron and Lake Ontario, we assumed that the mortality function parameterized for the MB of the Lake Huron applied to these other basins as well. Annual recreational harvest of predators was predicted using the Baranov catch equation REC REC bpraym,,,, bpray,,, bpraym,,,, m Zbpraym,,,, Zbpraym,,,, ( 1 ) F H = N e. (Eq ) Commercial harvest of LKT in Lake Huron was similarly predicted. Annual recreational and commercial yield was predicted by including monthly weight at age of harvested predators in Equation Because prey populations were length based, the calculation of monthly prey abundance was somewhat different from that of predator abundance. It was necessary to account for prey growing into and out of each length category each month. For all but the smallest and largest length categories, monthly prey abundance was calculated as Z ( 1 ) ( ) Zbpylym,,,, bpyl,, 1, ym, bpylym,,,, + 1 bpylym,,,, bpyl,, bpyl,, 1, ym, bpyl,, 1 N = N e T + N e T (Eq ) For the largest length category, monthly prey abundance was calculated as ( ) Zbpyl,,, ym, Zbpyl,, 1, ym, bpylym,,,, + 1 bpylym,,,, bpyl,, 1, ym, bpyl,, 1 N = N e + N e T, (Eq ) while for the smallest length category monthly prey abundance was calculated as Z R bpy ( ),,1, ym, bpyy N,, bpy,,1, ym, + 1 = Nbpy,,1, ym, e 1 Tbpy,,1 +. (Eq ) 12 The fraction of fish in a length category that grew into the next largest length category was calculated using the approach described in Rogers-Bennett and Rogers (2006). This entailed fitting von Bertalanffy growth models to ALE and RBS length at age data and determining for 28

29 each length category what minimum size of fish would grow into the next length category based on the predicted growth of various length of fish within the length category. As an example, if we fit a growth model for one of the species and determined from this fitted model that within the 30 to 50 mm length group only 45 mm and larger fish were predicted to attain 50 mm within one month, than the fraction of fish that grew into the 50 to 75 mm length category from the 30 to 50 mm length category was 25% and the fraction of fish that remained in the 30 to 50 mm length category was 75%. For prey species, Z was separated into natural and predation mortality components Z = M + O. (Eq ) bpylym,,,, bpylym,,,, bpylym,,,, Natural mortality rates for all prey types and length categories were forecasting model inputs and were assumed constant. Total predation mortality exerted on a particular prey type and length category was the sum over all predator types (including double-crested cormorants) and age classes of the per predator consumption rate of each predator type and age class (described in Section 2.4) multiplied by the ratio of the predator type and age class density to prey type and length category density O A D b, pr, a, py, l, y, m b, pr, a, y, m bpylym,,,, =. (Eq ) pr a Dbpylym,,,, For LKT in the MB of Lake Huron, estimating total predation mortality on each prey type and length class required weighted averaging of the instantaneous attack rates from each sub-basin with the weights set to the amount of habitat area in each sub-basin Consumption The total amount of prey consumed by a predator was calculated using a Type-II multispecies functional response. This is a saturating functional response that assumes a predator s consumption rate asymptotes at high prey densities because consumption handling time at some point limits consumption. The per predator instantaneous consumption rate of each predator type and age class on each prey type and length category was calculated as A bprapylym,,,,,, = 1 φ + D D bprapyl,,,, pylym,,, φ W b, pr, a, py, l py, l, y, m py, l CMAX py l pr, a, y, m. (Eq ) 29

30 The instantaneous attack rate of each predator type and age class on each prey type and length category was a function of a predator s search efficiency, size preference of prey, and habitat overlap with prey φ = γ L SP HO. (Eq ) bprapylym,,,,,, bpr, bpraym,,,, bprapylym,,,,,, bprpy,, As in Jones et al. (1993), the size preference of a predator depended on its length relative to that of it prey and was calculated as SP bprapylym,,,,,, = exp ( ) 2 bprapylym,,,,,, (Eq ) Equation was a bell-shaped function that peaked at a preference of 1 at a prey to predator length ratio of When calculating the instantaneous consumption rates for LKT in the subbasins of the Lake Huron MB, we assumed that the density of prey was equal to the density of prey in the MB. Predator maximum consumption rate was assumed to be a power function of predator length CMAX ϕ ( L ) 2,, bpr bpraym,,,, = ϕ1, bpr, bpraym,,,,. (Eq ) Preliminary estimates of the parameters for Equation were obtained from Fish Bioenergetics 3.0 (Hanson et al. 1997). These preliminary parameter values were later adjusted as part of the model calibration process (see Section 2.6). Habitat overlap values were set on the perception of the degree of spatial and temporal overlap between predator and prey species (Koonce and Jones 1994). The habitat overlap values ranged from zero, indicating that a predator was unable to eat a given prey type, to one, indicating that the predator consumed a given prey type at the rate predicted by its functional response. We adjusted instantaneous consumption rates for some predators and age categories to reflect feeding that we were not able to track in our forecasting models. For CHK, we assumed that 100% of the diet of age-0 fish consisted of invertebrates until fish reached 200 mm in length, at which point they switched to complete piscivory. Age-0 CHK were assumed to grow at a set rate of g per month until they were able to make the switch to piscivory. For STH, we assumed that 50% of the diets of age-1 fish and 25% of the diets of age-2 and older fish consisted of invertebrates. For COH, we assumed that 25% of the diets of all ages consisted of 30

31 invertebrates. For WAE, we assumed that 50% of the diets of all ages came from nearshore areas, which we did not consider to be part of our forecasting model. Double-crested cormorants had their own multispecies Type-II functional response in the forecasting models A COR bpylym,,,, = 1 + py τ υ τυ l D D b b, py, l b, py, l, y, m W b b, py, l b, py, l, y, m b, py, l Cor CMAX. (Eq ) Double-crested cormorant effective search rates, preference for particular prey types and length categories, and maximum annual consumption rates were forecasting model inputs and were assumed to be constant. Sea lamprey also had their own multispecies Type-II functional response in the forecasting models, which predicted the number of sea lamprey attacks on LKT A LAM blktay,,, Tψ D = 1 + H ψ pr b b, pr, a b, LAM, y a D pr bpra,, bpray,,,,9. (Eq ) This functional response predicted the number of LAM attacks on LKT, and was a function LAM and available host densities, LAM feeding season length, and LAM effective search rates. Yearly sea lamprey abundance by basin was a forecasting model input. For the MB of Lake Huron, sea lamprey abundance was an input for each sub-basin, although there was allowed to be some exchange of LAM between the sub-basin at the start of each year. Although LAM were assumed to only be a mortality source for LKT, both CHK and LWF were assumed to be available as hosts and thus were included in the calculations of attacks on LKT. Although LAM mortality on lake trout was approximated as a mortality pulse in the 9 th month of year, the number of attacks depended on feeding season length and handling times. Parameterization of Equation followed that of Rutter (2004). Effective search rates were assumed to be a logistic function of host length ψ bpra,, = 1+ e ϑ ϑ1, b. (Eq ) b( Lb pr a ϑ b) 2,,, 3, Effective search rates for LWF and CHK and Chinook were adjusted from the values predicted by Equation using species-specific adjustment factors estimated by Rutter (2004). Monthly consumption of each prey type and length category by each predator type and age class were obtained using the Baranov catch equation with per predator instantaneous 31

32 consumption rates (Equations and 2.4.5) serving the role fishing mortality does when estimating catch rather than consumption A C = N e W (Eq ) bprapylym,,,,,, Z,,,,,,,,,,,,,, (1 bpylym b pr a py l y m b py l y m ) b, py, l Zbpylym,,,, Total consumption of a particular predator type and age class was then calculated by simply summing consumption across prey types and length categories C = C. (Eq ) bpraym,,,, bprapylym,,,,,, py l For those predators and age classes for which we adjusted consumption rates due to feeding in areas or on items not accounted for in the forecasting models, consumption was readjusted so that projected growth of fish was not affected. 2.5 Growth With the exception of new recruits and the first year and month of the forecasting model, weight and length at age of predators were modeled dynamically. Predator growth in each month of the forecasting model was estimated based on the monthly consumption of predators and the estimated gross conversion efficiency (GCE) of the predator (Ney 1990). Gross conversion efficiency is a measure of a fish s ability to convert ingested biomass into new tissue (i.e., growth). Because GCE is known to vary among different species of fish, as well by size, age, and amount consumed, we constructed a set of models that predicted GCE for each predator type based in its age, weight at the start of the month, and the fraction of maximum consumption that a predator consumed in a month. For age-0 CHK in Lake Huron, the model that was used to predict GCE was GCE ( η η W ) RatbCHK,,0, ym, ( η3, bchk,,0 + η4, bchk,,0 WbCHK,,0, ym, ) = + b, CHK,0, y, m 1, b, CHK,0 2, b, CHK,0 b, CHK,0, y, m ( ) (( 4, bchk,,0 4, bchk,,0 WbCHK,,0, ym, )( RatbCHK,,0, ym, ( 3, b,,0 4,,,0,,0,, ))) CHK +η b CHK W b CHK y m e η + η η For all other predators and ages, GCE was predicted from the equation GCE ( η η W ) = + bpraym,,,. 1, bpra,, 2, bpra,, bpraym,,,, ( 3, bpra,, 4, bpra,, Wbpraym,,,, )( Ratbpraym,,,, ( 5, bpra,, 6, bpra,, Wbpraym,,,, )) 1 e η + η η + η, (Eq ) (Eq ) where the fraction of maximum consumption that a predator consumed was calculated simply by 32

33 679 Rat bpraym,,,, C bpraym,,,, = (Eq ) CMAX bpraym,,,, with CMAX divided by 12 to reflect the fact that consumption was calculated monthly in our forecasting models. The data used to parameterize Equations and were obtained by using Fish Bioenergetics 3.0 (Hanson et al. 1997) to estimate predator growth under a wide range of ration levels and initial sizes. Physiological parameters for running the bioenergetics models were taken from Hanson et al. (1997) and Dieterman et al. (2004). Because physiological parameters were not available for ATS or BBT, we assumed that the GCE equations parameters for ATS were the same as those for STH, and that the GCE parameters for BBT were the same as those for LKT. Temperature inputs for running the bioenergetics models for lakes Huron and Ontario predators were taken from several sources (Dobiesz 2003; Stewart and Bowlby 2009; R. Bergstedt, USGS GLSC, unpublished data). Model parameters for Equations and were fit in SAS using PROC NLIN. Monthly growth of predators by weight was calculated by multiplying predator consumption levels by GCE predictions C W = GCE + W. (Eq ) bpraym,,,, bpraym,,,, + 1 bpraym,,,, bpraym,,,, Nbpraym,,,, Length was predicted using the equation L 1 W ζ 2, bpr, bpraym,,,, bpraym,,,, = ζ 1, bpr,. (Eq ) It should be noted that Equation was a simple algebraic rearrangement of the allometric growth model for a predator W ζ ( L ) 2,, bpr bpraym,,,, = ζ1, bpr, bpraym,,,,. (Eq ) 2.6 Calibration Prior to conducting the stocking policy evaluations, we calibrated the lakes Huron and Ontario forecasting models using SCAA stock assessment model predictions of LKT and CHK abundance and harvest at age, creel survey estimates of harvest of STH, ATS, BRT, and COH, and observations of weights of age of all predator species obtained from a variety of sources. 33

34 The calibrations were conducted by reading-in the best available time-series of historical CHK, LKT, ALE, and RBS recruitment levels and adjusting forecasting model parameters until predictions of predator abundance and harvest levels and growth rates matched those of these other data sources. The primary parameters that were adjusted during the calibration process included predator and prey natural mortality rates, the scalars used to adjust prey stockrecruitment relationships to absolute abundances, parameters of each predator s maximum consumption rate function, the length-based scalar of each predator s effective search area, predator-prey habitat overlap values, commercial and recreational catchabilities of predators, and parameters of the age-0 CHK natural mortality function (for Lake Ontario only). The primary goal of the calibration process was for the simulation model to approximate the data from these other sources, rather than to exactly reproduce their results. Exact reproduction of results was not possible even for SCAA model predictions of abundance and harvest of LKT and CHK as the SCAA models included complexities (e.g., time-varying catchabilities, time-varying selectivities) that were not incorporated in the structure of our forecasting models, and some forecasting quantities allow for annual stochastic variation during projections but were set to fixed values for all years during calibration. An additional aspect of the calibration was to evaluate what the forecasting models predicted in terms of predator growth if prey abundance was not limited. For this part of the calibration process, we multiplied ALE recruitment levels by a factor of 1,000 and used the forecasting model to predict predator growth rates. Our desire was for predicted weights to be near, but not exceed, record weights of the species from the lakes. 2.7 Stocking Scenarios After calibration, we used our constructed forecasting models to investigate the implications of several Pacific salmonid stocking policies on the fish communities of lakes Huron and Ontario. We evaluated the following Pacific salmonid stocking policies: Policy 1: average of the Pacific salmonid stocking policy Policy 2: 33% decrease in the average of the Pacific salmonid stocking policy Policy 3: 50% decrease in the average of the Pacific salmonid stocking policy Policy 4: 50% increase in the average of the Pacific salmonid stocking policy 34

35 Policy 5: 100% increase in the average of the Pacific salmonid stocking policy Policy 6: no stocking of Pacific salmonids by any agency Policy 7: no stocking of Pacific salmonids by Ontario and the average of Michigan s and New York s Pacific salmonid stocking policy Policy 8: no stocking of Pacific salmonids by Ontario while accounting for Michigan s and New York s anticipated response to Ontario s stocking policy change. To conduct our evaluation for Policy 8, we interviewed administrators with the Michigan Department of Natural Resources and the New York State Department of Environmental Conservation who had management authority over lakes Huron and Ontario and asked them what, if any, stocking program changes they would recommend if Ontario stopped stocking Pacific salmon. From these interviews, we determined that for Lake Huron a cessation of stocking by Ontario would result in either no change in Michigan s stocking program, which is the same as Policy 7, or else Michigan stocking program would be increased to a level that would offset Ontario s stocking cut. Thus, if Ontario s stocking levels represented 10% of the total number of Pacific salmonids stocked in Lake Huron, then stocking by Michigan would be increased by 10%. Although this change in Michigan s stocking program would result in the same number of fish stocked as Policy 1, the consequences may be different as the stocking rate in the MB of Lake Huron would be higher since normally Ontario would have stocked some of these fish in the NC/GB. For Lake Ontario, we found that a cessation in the Pacific salmonid stocking program by Ontario would have no affect on New York s stocking program (Policy 7). While the administrator we interviewed acknowledged that there may be some pressure for New York to increase Pacific salmon stocking if Ontario cut its stocking program, a change in New York s Pacific salmon stocking program would necessitate a reduction in stocking of some other species (e.g., BRT, ATS) because of limited hatchery space, which in turn would be met with resistance by angler groups. Each Pacific salmonid stocking policy was run over a 25 year time horizon, which based on previous work from Lake Michigan, was a sufficient time span to compare stocking policies (Szalai et al. 2008, Jones and Bence in press). Each stocking policy was repeated 1,000 times to account for model uncertainty. When conducting these simulations, yearly inputs values for variables such as recreational and commercial fishery effort, LAM, COM, LWF abundance 35

36 estimates were set equal to their averages. The values of all forecasting model parameters used in the stocking policy simulations are presented in the Appendix. 2.8 Incorporation of uncertainty We incorporated four main areas of uncertainty in our stocking policy evaluations: predator wild recruitment levels, the relationship between recruitment and spawning stock abundance in ALE and RBS, the relationship between CHK maturation mortality and growth, and the relationship between ALE, CHK, and LKT biomass and CHK age-0 natural mortality rates. Uncertainty in predator wild recruitment levels was incorporated in the simulation models by assuming that wild recruitment of each predator (except for WAE and LKT) in each year of each simulation run was a random variable drawn from a normal distribution with a specified mean and a standard deviation set to 10% of the distribution mean value. Probability theory suggests that any draw from such a distribution will have roughly a 95% change of the being within 20% of the mean. Thus, if we assumed a mean wild recruitment of 1 million fish, then in any given year we could expect wild recruitment (prior to post-stocking survival adjustments) to be within the range of 800,000 and 1,200,000 fish, which conceivably could have a large effect on the outcome of a particular stocking policy. The approach used to incorporate the other areas of uncertainty in the forecasting models was different from that taken with predator wild recruitment. As we previously described in Sections 2.2 and 2.3, the probability distributions for the parameters of the ALE and RBS stockrecruitment relationships, the CHK maturation mortality function, and the CHK age-0 natural mortality rate function were obtained by Bayesian inference; specifically, the joint posterior probability distributions of the parameters were approximated through MCMC sampling. These areas of uncertainty were incorporated in our simulation model by sampling from the resulting estimates of the joint posterior probability distribution of the parameters for each of the models. For each simulation run, a different set of model parameters were pulled from the thinned MCMC chains, which were among the data inputs for each of the forecasting models. For ALE and RBS stock-recruitment relationships, the joint posterior probability distributions included the standard deviation of the log-normal errors for the models. Thus, when predicting ALE and RBS recruitment, year-specific random errors were drawn from a normal distribution with a mean of zero and a standard deviation equal to the value drawn from the joint posterior probability 36

37 distribution. These year-specific random errors represented year-specific deviations from the conditional mean relationship of the stock-recruitment relationship. 2.9 Performance metrics Performance metrics that were used to evaluate the consequences of the various Pacific salmonid stocking policies were the average (over the 25 year time horizon) biomass of LKT, CHK, ALE, and RBS, the average recreational and commercial harvest and yield of LKT and CHK, the absolute annual variation in recreational and commercial harvest of LKT and CHK, the probability that ALE and RBS adult abundances declined below abundance threshold values set for the species, how often ALE and RBS adult abundances declined below abundance threshold values, the probability that ALE and RBS adult abundances declined below abundance threshold value for at least three consecutive years, and how often ALE and RBS adult abundances declined below abundance threshold values for at least three consecutive years. Alewife and rainbow smelt thresholds were set to 100 million and 500 million fish for the MB of Lake Huron MB, 5 million and 25 million fish for the NC/GB of Lake Huron, and 2 billion and 500 million fish for Lake Ontario. These thresholds were the lowest adult abundances of prey calculated from the calibrated forecasting models; thus, the performance statistics related to these thresholds measure the frequency that simulated prey populations drop to abundance levels below calibrated abundance levels. It should be noted that calibrated prey abundances are inexorably linked to assumptions about factors such as predator search efficiencies, scalars for prey stock-recruitment relationships, and predator maximum consumption rates. Thus, these absolute thresholds are only meaningful conditional on these assumptions. Thus, for example, if one were to presume different predator searching efficiencies, the thresholds could no longer be meaningfully tied to the estimates of prey fish abundance tied to real-world experiences during the historical period. Nevertheless, we do believe these thresholds are useful for evaluating policies, given that parameter changes that would change projections would similarly influence historical estimates of prey fish abundance. These performance metrics were chosen because they captured the desire to have high stable catches of LKT and CHK, large sizes of CHK, and the susceptibility of ALE and RBS to being driven to low abundance levels. It is important to note that desirable levels of several of these performance metrics depends on whether one sides with the enhancement or restoration 37

38 view concerning the role that Pacific salmonids play in the Great Lakes. We purposefully avoided making such value decisions and instead sought only to compare performance metrics across the different stocking policies Sensitivity analysis The effect that certain assumptions made in the lakes Huron and Ontario forecasting models on relative performance of the different stocking policies was explored by conducting a sensitivity evaluation of several key variables in the forecasting models. These key variables included natural mortality rates of predators and prey, predator wild recruitment levels, and predator search efficiencies and ALE and RBS stock-recruitment scalars. We evaluated the sensitivity of stocking policy performance by changing the values associated with these variables and re-running the stocking policy. The sensitivity of predator and prey natural mortality rates and predator search efficiencies and prey stock-recruitment scalars were explored in combination, as the influences of these variables were highly confounded. The values of the variables that we explored in our sensitivity evaluation were the following: 2.0 times predator natural mortality rates and 0.5 times prey natural mortality rates, 0.5 times predator natural mortality rates and 2.0 times prey natural mortality rates, 2.0 times predator wild recruitment levels, 0.5 time predator wild recruitment levels, 5.0 times predator search efficiency and 0.5 times prey recruitment scalar, and 0.2 times predator search efficiency and 2.0 times prey recruitment scalar. We did not perform separate forecasting model calibrations prior to conducting the sensitivity evaluation, which affected the values of the performance metrics that were obtained from running the simulations. However, the purpose of the sensitivity evaluation was only to compare whether the overall performance of the stocking policies remained similar and not to compare outputs from the various sensitivity scenarios. 3. Results and discussion 3.1 Calibration After calibration, the Lake Huron forecasting model was able to adequately approximate abundance, harvest, and growth of most predators. Despite the SCAA models for lake trout and Chinook salmon including far greater complexity than the Lake Huron forecasting model, 38

39 forecasting model predictions of abundance and harvest did not deviate substantially from SCAA model predictions. The largest difference in forecasting model predictions when compared to SCAA model prediction was for recreational harvest of Chinook salmon (Fig. 3). Part of the difficulty in matching these predictions came from using a deterministic equation in the forecasting model to predict age-0 natural mortality rates, which were estimated by random walk in the SCAA model. As stated previously, the intent of the calibration was for the forecasting model to only approximate the information from sources such as the CHK and LKT SCAA models and not to exactly reproduce their results. As a result, we were not overly concerned about the mismatch in recreational harvest predictions for the models, particularly since the CHK age-0 natural mortality rate function was one of the major areas of uncertainty we incorporated in our stocking policy evaluations. The Lake Huron forecasting model also was able to approximate observed weight at age of LKT and CHK (Fig. 3). The calibration of the Lake Ontario forecasting model also resulted in a fair approximation to the SCAA model predictions of LKT and CHK abundance and recreational harvest (Fig. 3). The largest deviation in forecasting model and SCAA model predictions was in CHK recreational harvest. This again was due to the far greater complexity of the SCAA model predictions. The forecasting model also reasonably approximated measurements of recreational harvests and weights at age of STH, BRT, and COH (Fig. 4). When an overabundance of prey was assumed in the lakes Huron and Ontario forecasting models, weights at age of predators were predicted to be upwards of 10 to 18 kg for CHK and LKT, 8 to 15 kg for STH, BRT, and COH, and 5 to 7 kg for BBT and WAE. These estimated growth rates were deemed reasonable given historical reports of predator sizes from the lakes. 3.2 Stocking policy evaluations For the MB of Lake Huron, there was substantial overlap in the distributions of the performance statistics among the evaluated Pacific salmonid stocking policies. Lake trout biomass and fishery yield (both recreational and commercial) were predicted to increase if stocking of Pacific salmonids was reduced from the average; the largest increases were predicted to occur with either a complete cessation of stocking by all agencies or at a 50% decrease in stocking rate by all agencies (Fig. 5). Under a complete cessation of Pacific salmon stocking, LKT biomass, recreational yield, and commercial was predicted to increase by 39

40 approximately 10% when compared to the average stocking rate, while a 50% decrease was predicted to result in a roughly 5 to 6% increase in LKT biomass, recreational yield and commercial yield. There was relatively little difference in the absolute annual variation of LKT commercial and recreational harvest among the stocking policies (Fig. 5), indicating that inter-annual variability in LKT harvest was relatively unaffected by Pacific salmonid stocking policies. Although CHK biomass was predicted to increase if Pacific salmonid stocking rates were increased, CHK recreational yield was predicted to decline when compared to the average stocking rate as a consequence of reduction in size (Fig. 5). Indeed, there was an inverse relationship between age-3 CHK spawning weight and Pacific salmon stocking rates, as stocking rates increase age-3 CHK spawning weight decreased. The median age-3 CHK spawning weight for the simulations was 5.75 kg at a 50% decrease in Pacific salmonid stocking rate, and 6.04 kg at a complete cessation of Pacific salmon stocking. Simulation medians of age- 3 CHK spawning weight were 5.01 kg at a 50% increase in Pacific salmonid stocking rates, and 4.51 kg at a 100% increase. There also was an inverse relationship between absolute annual variability in CHK recreational harvest and Pacific salmonid stocking rates. At the average stocking rate, median absolute annual variation was At a 50% decrease in the stocking rate, the median absolute annual variation was At a 100% increase in stocking, the median absolute annual variation was In terms of Lake Huron prey, there was an inverse relationship between ALE and RBS biomass and Pacific salmonid stocking rates (Fig. 6). At the average stocking rate, the median biomass of ALE and RBS from the simulation runs was and kt. Decreases in Pacific salmonids stocking rates of 33 and 50% were predicted to result in a 7 and 10% increase in ALE biomass and a 10 and 13% increase in RBS biomass. A complete cessation of Pacific salmonid stocking by all agencies was predicted to result in a 22% increase in ALE biomass and a 24% increase in RBS biomass. Conversely, a 50% increase in Pacific salmon stocking was predicted to decrease ALE and RBS biomass by 10 and 11%, while a 100% increase was predicted to decrease ALE and RBS by 21%. The fraction of simulation runs that resulted in adult ALE abundance declining below the threshold limit of 100 million fish ranged from 38 (complete cessation of stocking) to 65% (100% increase in stocking rate). The fraction of simulation runs that resulted in adult ALE abundance declining below the threshold limit of 100 million for 3 or more years ranged from 31 (complete cessation of stocking) to 58% (100% 40

41 increase in stocking rate). For RBS, the fraction of runs that resulted adult abundance declining below the threshold limit of 500 million fish ranged from 33 (complete cessation of stocking) to 62% (100% increase in stocking rate). The fraction of runs with adult RBS abundance declining below the threshold for 3 or more years ranged from 28 (complete cessation of stocking) to 56%. The number of years out of the 25 year time horizon that prey abundances dropped below threshold levels decreased with lower Pacific salmonid stocking rates. The average number of years that ALE abundance dropped below the abundance threshold was 3.5 years with a 50% decrease in Pacific salmonid stocking rates and was 2.7 years with a complete cessation of stocking. Conversely, the average number of years that ALE abundance dropped below the abundance threshold was 6.1 years if stocking rate was doubled. Qualitative patterns in performance statistics for the NC/GB of Lake Huron were similar to those observed for the MB. Biomass and yield of lake trout and CHK age-3 spawning weight were predicted to increase while CHK biomass was predicted to decrease with lower Pacific salmonid stocking rates (Fig. 7). Unlike the MB, however, CHK recreational yield was predicted to increase with higher Pacific salmonid stocking rate. For prey fish, ALE and RBS biomass were predicted to increase at lower stocking Pacific salmonid stocking rates, while the occurrence and duration of adult abundances declining below threshold levels was predicted to decrease (Fig. 8). This similarity in results between the basins of Lake Huron was largely the result of our assumption that the stock-recruitment relationships for prey in the NC/GB were the same as those for the MB. While this assumption may not be even approximately correct, we made it as a best guess given the lack of an alternative data source for parameterizing separate stock-relationships for prey populations in the NC/GB. Compared to the results of the Lake Huron stocking scenarios, the different Pacific salmonid stocking policies resulted in relatively small differences in performance metrics for Lake Ontario. Lake trout biomass, recreational yield, and absolute annual variation in recreational harvest differed by less than 1% when compared against the average stocking policy (Fig. 9). There was a positive relationship between Pacific salmonid stocking rates and CHK biomass and recreational yield, but there were very little differences in age-3 spawning weight among the different stocking policies. There also was a positive relationship between Pacific salmonid stocking rates and the absolute annual variation in CHK recreational harvest, with the greatest inter-annual variability observed when stocking rates were increased by 100% (Fig. 9). 41

42 In terms of Lake Ontario prey, there were relatively minor differences in ALE and RBS biomass among the stocking policies (Fig. 10). The occurrence of adult ALE and RBS abundances dropping below threshold levels (ALE: 2 billion fish; RBS: 500 million fish) was also generally low across the different stocking policies. Even when the Pacific salmonid stocking rate was increased by 100%, adult ALE and RBS abundances dropped below threshold level in only 1.4% and 6.3% of the simulations that were conducted. Abundances below threshold values for at least 3 consecutive years occurred in only 0.1 (ALE) and 2.4% (RBS) of the simulated conducted under an assumed 100% increase in Pacific salmonid stocking rates. 3.3 Sensitivity analysis The results of our Pacific salmonid stocking policy evaluations were the most strongly affected by assumptions made regarding predator natural reproduction and the combination of predator search efficiencies and prey stock-recruitment scalars. For Lake Huron, the qualitative performance of the stocking policies remained largely unchanged. Decreases in stocking rates resulted in increases in LKT biomass, commercial and recreational yield, CHK age-3 spawning weight, ALE and RBS biomass, and decreases in the likelihood that ALE and RBS abundances dropped below threshold levels. For Lake Ontario, however, an increase in the assumed levels of predator natural reproduction levels and the combination of an increase in predator search efficiency and a decrease in the prey recruitment scalar resulted in ALE and RBS being more heavily affected by changes in Pacific salmonid stocking rates. Under these assumptions, the Lake Ontario results more closely mirrored those of Lake Huron. Namely, adult prey abundance became more susceptible to dropping below threshold values when stocking rates were increased. 3.3 Comparisons between lakes There were substantial differences between lakes Huron and Ontario in the effects of alternative Pacific salmonid stocking policies. Whereas the fish community of Lake Ontario was predicted to be relatively unaffected by either increases or decreases in Pacific salmonid stocking rates, the Lake Huron fish community was predicted to be more strongly affected by changes in stocking. Perhaps the most notable difference between lakes Huron and Ontario was that even if all stocking of Pacific salmonids was stopped, there still was a strong possibility that adult 42

43 abundance of prey fish could drop below threshold levels on Lake Huron. This difference appeared largely to be a consequence of lower prey productivity in Lake Huron compared to Lake Ontario, as even if wild recruitment of Chinook salmon was set to zero there still remained the possibility that prey abundance could be driven to below threshold levels. This lower level of productivity provides fishery managers a greater capacity to influence conditions on the fish community through implementation of different stocking policies. On Lake Ontario, the ability of fishery managers to elicit change in fish communities is far more limited. 3.4 Concluding remarks In this paper we have evaluated some of the consequences that would result from changes from status quo (as of 2005) stocking of Pacific salmonines in lakes Huron and Ontario. Overall changes in stocking over the range considered did not produce radical changes in prey fish communities. In Lake Huron this was because recruitment of wild Chinook salmon is an important predator in the system, whereas in Lake Ontario this results from the high productivity of prey stocks relative to the current level of prey fish consumption by predators. Nevertheless, in Lake Huron we find it likely that increases in stocking can lead to higher probabilities of low alewife conditions like those that have been seen in the lake since In contrast, it appears that substantially higher stocking of Pacific salmonines (or actions to improve the survival of stocked fish) would be necessary to have a substantial influence on the alewife population in Lake Ontario. Whether increases, decreases, or cessation of stocking of Pacific salmonines is advisable is a matter that depends critically on value judgments and goals for the ecosystem and fishery. There are those who value the lakes primarily for their ability to sustain fisheries for Chinook salmon, while others value rehabilitation of a fish community where native fishes are prominent (Eshenroder and Burnham-Curtis 1999; Crawford 2001). There is strong evidence for adverse effects of alewife on numerous native species (Smith 1964, 1968, 1970; Krueger et al. 1995; Madenjian et al. 2008). Recent events in Lake Huron support this view with substantial increases in wild recruitment of a suite of different native species following large declines in alewife abundance (Riley et al. 2007; Bence et al. 2008a; Fielder et al. 2008; Schaeffer et al. 2008). Consequently, and somewhat paradoxically, our results imply that increases in stocking, and in Lake Ontario perhaps massive increases outside the range we explored, would promote rehabilitation of native fish communities, whereas recovery or maintenance of Pacific salmon 43

44 fisheries would possibly be promoted by reductions in stocking in Lake Huron, and perhaps by avoiding massive increases in Lake Ontario. The differences between the prey productivity of Lakes Huron and Ontario are consistent with previous reports (O Gorman and Schneider 1986; Mason et al. 2001; Bence et al. 2008b), and our results suggest that the prey base in Lake Ontario is substantially more robust in the face of predation than some reports have suggested (Jones et al. 1993; Murry et al. in press). Our conclusion differ from Murry et al. (in press) who recently conducted a bioenergetics evaluation of Chinook salmon in Lake Ontario and concluded that salmonine predation in Lake Ontario may be pushing the limits of prey fish sustainability in Lake Ontario. The conclusions of Murry et al. (in press) were based on their findings that Chinook salmon consumed on average 22% of the alewife biomass in Lake Ontario over the period of 1989 and 2005, with a peak consumption of 44% of the alewife biomass in Although Murry et al. (in press) acknowledged that production to biomass ratios in alewife in the Great Lakes has been found to be greater than 1.0 (Brandt et al 1991; Rand et al. 1995), which means that more than 50% of Lake Ontario s alewife production would still be available, they believed that Lake Ontario salmonine predation pressure was excessive as a result of other predators in the system also consuming alewife. Our results however suggest that compared to Chinook salmon consumption, consumption of other predators is relatively minor and by accounting for Chinook salmon consumption the bulk of predatory pressure in Lake Ontario is accounted for. Further, by implicitly incorporating prey recruitment into our evaluations, we found that the production capacity of alewife in Lake Ontario was sufficiently great enough to buffer the population from any negative effects stemming from predation. We do readily acknowledge however that the Lake Ontario food web is presently in a state of flux due to invasion of dreissenid mussel and other exotic species (e.g., Hemimysis anamola, Neogobius melanostomus), which could be affecting the production capacity of Lake Ontario, and that our simulations may not fully integrate this lowered capacity. Acknowledgements We thank the Great Lakes Fishery Commission for providing funding for this research, and Emily Szalai and Weihai Liu for their assistance in programming the lakes Huron and Ontario forecasting models. This work was also supported by funding from the Michigan DNR, which included support from the U.S. Fish and Wildlife Sport Fish Restoration program. Successful completion of this project depended on the willingness of many individuals to share opinions, data, and knowledge. Our gratitude is extended to the following people: Tom Goniea, Ji He, Jim Johnson, Jory Jonas, Tammy Newcomb, Kurt Newman, Zhenming Su, Dan Bishop, Mike Connerton, Tom Eckert, Jana Lantry, Steve LaPan, Russ McCullough, Jim Bowlby, Gavin 44

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54 Table 1. Symbols and descriptions of variables used in the stochastic forecasting models for evaluating the effects of different Pacific salmonid stocking policies on lakes Huron and Ontario. Symbol Description Index variables Lake Huron: Main Basin, North Channel/Georgian Bay b Basin = Lake Ontario: Main Basin Lake Huron: LKT, CHK, STH, WAE, BBT pr Predator species = Lake Ontario: LKT, CHK, STH, ATS, BRT, COH py Prey species = ALE, RBS, BEN, PEL Lake Huron: (LKT), 0-5 (CHK), 1-5 (STH), (WAE), (BBT) a Predator age = Lake Ontario: (LKT), 0-4 (CHK), 1-5 (STH), 1-5+ (ATS), 1-5+ (BRT), 1-3 (COH) ALE and RBS: 0-30, 30-50, 50-75,..., mm l Prey length bin = BEN: 150 mm PEL: 100 mm y Year m Month State and control variables R Recruits S Spawning stock abundance p Proportion of prey fish mature in each length bin N Abundance at start of year prior to emigration or immigration N Abundance Θ Proportion of predator populations emigrating between basins Z Total instantaneous mortality rate M Instantaneous natural mortality rate excluding LAM-induced mortality M LAM Instantaneous LAM-induced mortality rate on LKT F REC Instantaneous recreational fishing mortality rate F COM Instantaneous commercial fishing mortality rate O Instantaneous predation-induced mortality on prey types Mat Finite maturation mortality rate W Weight of predator or prey L Length of predator or prey q REC Recreational fishery catchability q COM Commercial fishery catchability s REC Recreational fishery selectivity s COM Commercial fishery selectivity E REC Annual recreational fishing effort E COM Annual commercial fishing effort f REC Fraction of fishing effort occurring in each month Fraction of commercial effort occurring in each month f COM 54

55 B Biomass H REC Recreational fishery harvest H COM Commercial fishery harvest T Fraction of prey fish growing into the next largest length bin D Density A Per predator instantaneous consumption rate φ Instantaneous attack rate CMAX Per predator maximum annual consumption rate γ Length-based scalar of a predator s effective search area SP Predator s size preference for prey HO Predator-prey habitat overlap Length ratio between predator and prey A COR Instantaneous consumption rate of COM A LAM Number of LAM attacks on LKT τ COM effective search rates υ Prey preference of COM T Length of LAM feeding season ψ LAM effective search rate for potential hosts H LAM handling time in years P Probability of a LKT surviving a LAM attack C Predator consumption GCE Gross conversion efficiency of predators Structural and distributional parameters μ Mean of the normal distributions used to generate predator recruits σ Pr Standard deviation of the normal distributions used to generate predator recruits α Ricker and Beverton-Holt stock recruitment parameter β Ricker and Beverton-Holt stock recruitment parameter ε Ricker and Beverton-Holt stock recruitment parameter σ Py Standard deviation of the log-normal errors for the Ricker and Beverton-Holt stock recruitment models δ 1 CHK maturation mortality function parameter δ 2 CHK maturation mortality function parameter ρ 1 Age-0 CHK natural mortality function parameter ρ 2 Age-0 CHK natural mortality function parameter φ 1 Predator maximum consumption rate parameter φ 2 Predator maximum consumption rate parameter η 1 Predator GCE parameter η 2 Predator GCE parameter η 3 Predator GCE parameter η 4 Predator GCE parameter η 5 Predator GCE parameter η 6 Predator GCE parameter ζ 1 Predator allometric growth function parameter ζ 2 Predator allometric growth function parameter ϑ Asymptotic effective search rate for sea lamprey 1 55

56 1314 ϑ 2 ϑ 3 Shape parameter for logistic function of sea lamprey search rate Inflection point for logistic function of sea lamprey effective search rate 56

57 GB NC Ontario Michigan Ontario New York Lake Huron Lake Ontario Fig. 1. Maps of lakes Huron and Ontario and state and provincial boundaries for the lakes, which were the study systems for which forecasting models were constructed to explore fish community consequences to changes in Pacific salmonid stocking policies. 57