Ricker Stock Recruitment Model Research Articles

Determining Optimal Stocking Rates Using a Stock–Recruitment Model: An Example Using Walleye in Northern Wisconsin

AbstractWe propose that stock–recruitment models can be used to estimate optimal stocking rates. Data to estimate the optimal stocking rates can be obtained in a relatively short amount of time by sampling similar populations over a few years. Whether the goal of stocking is endangered species recovery or supplementation of recreational fisheries, accurately determining the optimal stocking rate is of ecological and financial importance. As an example, we applied this approach using a Ricker stock–recruitment model to walleye Sander vitreus stocking in northern Wisconsin lakes. Using June stocking data and fall age‐0 survey data for 39 lakes over a 14‐year time period, we found that the stocking rate resulting in the greatest number of age‐0 walleyes was 60 age‐0 walleyes/ha. Similarly, using June stocking data and fall age‐1 survey data in 18 lakes over a 9‐year time period we found that the stocking rate resulting in the greatest number of age‐1 walleyes was 75 age‐0 walleyes/ha. About 16% of the variation in fall age‐0 walleye density was explained by the stocking rate, and 28% of the variation in fall age‐1 walleye density was explained by the stocking rate. Density‐dependent survival was apparent and significant, as low and high stocking densities resulted in lower age‐0 and age‐1 juvenile walleye densities. The lake surface area explained a significant amount of the residual variation in the age‐1 stock–recruitment relationship such that stocked walleyes generally survived at lower rates in large lakes than in small lakes, which may be due to a greater diversity of predators in larger lakes. Based on our analysis, we recommend stocking small fingerling walleyes at a rate of 75 fish/ha in northern Wisconsin lakes.

ABUNDANCE, DYNAMICS AND MORTALITY RATES OF THE DELAWARE BAY STOCK OF BLUE CRABS, CALLINECTES SAPIDUS

Abstract The Delaware Bay stock of blue crabs supports a bistate fishery in New Jersey and Delaware, with annual landings climbing through the 1980s and 1990s to almost 11 × 106 pounds (4,390 metric tons) in 1995 and then declining to a recent average of 7 × 106 pounds (2,796 metric tons) over the last 5 y. In Delaware, this fishery ranks as number one in value. Landings declines in 1996 spurred efforts to conduct a stock assessment, which is now updated annually. This assessment was based on: (1) a biomass-based minimum recruitment threshold from a Ricker stock-recruitment model fit to indices of relative abundance from a research trawl survey and (2) a catch-survey model incorporating observation and process error that produced annual estimates of absolute abundance, biomass, and fishing mortality rates from 1979 through 2002. Adult blue crab abundance estimates showed a positive trend over the period, ranging from 20 × 106 in 1979 up to 146 × 106 in 1993, with recent estimates between 70 × 106 and 97 ×...

Comparison of reference points estimated using a size-based method for two high-latitude crab species in the United States and Canada

We briefly reviewed the decision rules currently used for managing two major high-latitude crab stocks, snow crab (Chionoecetes opilio) and Dungeness crab (Cancer magister), in the United States and Canada and compared them with model-based reference points, harvest rate, and biomass proportion relative to virgin biomass, developed using species- and area-specific parameters. The model followed a size-based approach, which incorporated Beverton–Holt and Ricker stock–recruitment models and estimated mean and median reference points. The recruitment was also perturbed to generate distributions of reference points. The Beverton–Holt stock–recruitment model provided a lower harvest rate than that of the Ricker model. Harvest rates were lower for combined sexes spawning biomass than for female-only spawning biomass. Increasing the minimum size at first capture and decreasing the handling mortality resulted in increased harvest rates. Changes in fishery duration and timing of fishery open date did not change the harvest rate appreciably. The harvest rates for the Canadian snow and Dungeness crabs were mostly higher than those estimated for the Bering Sea and Southeast Alaska stocks. Reliable estimates of a number of life history parameters are lacking for both species, and hence, the results of this exercise need to be treated in a precautionary manner.

How can the stock recruitment relationship of the Barents Sea capelin (Mallotus villosus) be improved by incorporating biotic and abiotic factors?

We studied whether incorporation of terms for environmental factors (temperature, herring and 0-group cod) into the stock recruitment functions for the Barents Sea capelin (Mallotus villosus) would increase the ability to predict recruitment. We also investigated the effects of alternative estimates of the capelin spawning stock (SSB) and juvenile herring on model predictability. By using nonlinear regression, the modified Beverton–Holt and Ricker stock recruitment models were fitted to time series of capelin spawning stock, capelin recruitment, juvenile herring, 0-group cod and temperature from 1973 to 2000. The modified Beverton–Holt model with a term for juvenile herring fit capelin recruitment data well. Inclusion of terms for temperature and 0-group cod abundance did not significantly improve the model fit. The best model predicts an almost proportional relationship between the spawning stock and the capelin recruitment when the abundance of juvenile herring is high.

How can the stock recruitment relationship of the Barents Sea capelin (Mallotus villosus) be improved by incorporating biotic and abiotic factors?

We studied whether incorporation of terms for environmental factors (temperature, herring and 0-group cod) into the stock recruitment functions for the Barents Sea capelin (Mallotus villosus) would increase the ability to predict recruitment. We also investigated the effects of alternative estimates of the capelin spawning stock (SSB) and juvenile herring on model predictability. By using nonlinear regression, the modified Beverton–Holt and Ricker stock recruitment models were fitted to time series of capelin spawning stock, capelin recruitment, juvenile herring, 0-group cod and temperature from 1973 to 2000. The modified Beverton–Holt model with a term for juvenile herring fit capelin recruitment data well. Inclusion of terms for temperature and 0-group cod abundance did not significantly improve the model fit. The best model predicts an almost proportional relationship between the spawning stock and the capelin recruitment when the abundance of juvenile herring is high.

Recruitment Dynamics of the 1971–1991 Year‐Classes of Lake Trout in Michigan Waters of Lake Superior

AbstractIn the 1950s, populations of lake trout Salvelinus namaycush in Lake Superior collapsed because of excessive exploitation and predation by sea lampreys Petromyzon marinus. Restoration began in the 1950s with the stocking of juvenile, hatchery‐reared lake trout and controls on fisheries and sea lampreys. Partial restoration was declared in 1996 because wild fish made up most of the populations in many areas, especially in Michigan waters, so stocking was dramatically curtailed in most areas. We evaluated the production of age‐7 lake trout (recruits) by age‐8 and older wild and stocked parental lake trout (spawners). Using Ricker stock–recruitment models, we also evaluated the effects of large‐mesh (114‐mm stretch measure) gill‐net effort on wild lake trout recruitment in Michigan waters of Lake Superior during 1970–1998. In general, the density of wild lake trout spawners increased, whereas that of stocked lake trout spawners decreased in all management areas investigated. The density of recruits was best described by the combined density of wild and stocked parents, which suggested similar reproductive contributions for both. Recruitment rates declined significantly with increasing spawner density in four of the five management areas and suggested that carrying capacities were reached and exceeded, which may serve as an indicator of population restoration. We conclude that both wild and stocked lake trout have contributed to the recruitment of lake trout in Michigan waters of Lake Superior. Large‐mesh gill‐net fishing effort varied in all Michigan management areas but did not account for the significant variation in wild lake trout recruitment. We conclude that levels of large‐mesh gill‐net fishing effort during 1970–1998 were not having an appreciable effect on wild lake trout recruitment in Michigan waters of Lake Superior.

Biotic and Abiotic Factors Related to Rainbow Smelt Recruitment in the Wisconsin Waters of Lake Superior, 1978–1997

Lake Superior rainbow smelt ( Osmerus mordax) recruitment to 12–13 months of age in the Wisconsin waters of Lake Superior varied by a factor of 9.3 during 1978–1997. Management agencies have sought models that accurately predict recruitment, but no satisfactory models had previously been developed. In this study, modeling was conducted to determine which factors best explained recruitment variability. The Ricker stock-recruitment model derived from only the paired stock and recruit data accounted for 63% of the variability in recruitment data. The functional relationship that accounted for the greatest amount of recruitment variation (81%) included rainbow smelt stock size, May rainfall, and bloater ( Coregonus hoyi) biomass. Model results were interpreted to mean that recruitment was affected negatively by increased river flows from increased rainfall, and affected positively by the biomass of bloater, and those results were interpreted to mean that bloater mediated the effects of lake trout predation on rainbow smelt recruits. Model results were also interpreted to mean that stock size caused compensatory, density-dependent mortality on rainbow smelt recruits. Correlations observed here may be of value to managers seeking approaches to either enhance or control populations of this species, which is not indigenous to the Great Lakes.

Relationships between Bald Eagle Productivity and Dynamics of Fish Populations and Fisheries in the Wisconsin Waters of Lake Superior, 1983–1999

Bald eagle ( Haliaeetus leucocephalus) abundance declined in the 1950s and 1960s along the Wisconsin waters of Lake Superior, and were nearly absent along Wisconsin's Lake Superior shoreline. The population began to increase again between 1980 and 1983, and since then bald eagles nesting on islands along Wisconsin's Lake Superior shoreline (i.e., Apostle Islands) reproduced at a lower rate than have those nesting along the mainland shoreline of the lake and inland. Recent research indicated that bioaccumulation of toxic chemicals in the aquatic food chain no longer limits bald eagle reproduction there, and that productivity at island nests was lower than at mainland nests and inland nests as the result of low food availability. Management agencies have sought models that accurately predict productivity and explain ecological relationships, but no satisfactory models had previously been developed. Modeling was conducted here to determine which factors best explained productivity variability. The Ricker stock-recruitment model derived from only the bivariate breeding pair and productivity data explained only 1% of the variability in productivity data. The functional relationship that explained the greatest amount of productivity variation (83%) included the number of breeding pairs, burbot ( Lota lota) biomass, longnose sucker ( Catostomus catostomus) biomass, and commercial harvest of nontarget fishes. Model results were interpreted to mean that productivity was positively affected by populations of burbot and longnose sucker, which are important prey items, and by commercial fishermen feeding nontarget fish to bald eagles. Harvest of nontarget fishes by tribal fishermen and burbot and longnose sucker populations have not tended to change during the entire study period, although the burbot population has declined since 1991. Therefore, bald eagle productivity is not predicted to increase unless burbot, longnose sucker, or other preferred prey of bald eagles increases in the Apostle Islands.

Biotic and Abiotic Factors Related to Lake Herring Recruitment in the Wisconsin Waters of Lake Superior, 1984–1998

Lake Superior lake herring ( Coregonus artedi) recruitment to 13–14 months of age in the Wisconsin waters of Lake Superior varied by a factor of 5,233 during 1984–1998. Management agencies have sought models that accurately predict recruitment, but no satisfactory model had previously been developed. Lake herring recruitment was modeled to determine which factors most explained recruitment variability. The Ricker stock-recruitment model derived from only the paired stock and recruit data explained 35% of the variability in the recruitment data. The functional relationship that explained the greatest amount of recruitment variation (93%) included lake herring stock size, lake trout ( Salvelinus namaycush) population size, slimy sculpin ( Cottus cognatus) biomass, the interaction of mean daily wind speed in April (month of hatch) and lake herring stock size, and mean air temperature in April (when lake herring are 12-months old). Model results were interpreted to mean that lake herring recruitment was affected negatively by: slimy sculpin predation on lake herring ova; predation on age-0 lake herring by lake trout; and adult cannibalism on lake herring larvae, which was reduced by increased wind speed. April temperature was the variable that explained the least amount of variability in recruitment, but lake herring recruitment was positively affected by a warm April, which shortened winter and apparently reduced first-winter mortality. Stock size caused compensatory, density-dependent mortality on lake herring recruits. Management efforts appear best targeted at stock size protection, and empirical data implies that stock size in the Wisconsin waters of the lake should be maintained at 2.1–15.0 adults/ha in spring, bottom-trawl surveys.

A fuzzy logic model with genetic algorithm for analyzing fish stock-recruitment relationships

A new fuzzy logic model with a genetic algorithm is developed that overcomes some of the inherent uncertainties in the fish stock-recruitment process. This model is applied to stock-recruitment relationships for the Southeast Alaska pink salmon (Oncorhynchus gorbuscha) and the West Coast Vancouver Island Pacific herring (Clupea pallasi) stocks. In both examples, the annual mean sea surface temperature is used as an environmental intervention in the model. The fuzzy logic model provides the functional relationship between the number of fish spawners and the sea surface temperature that is used to reconstruct the historical fish recruitment time series and also to predict the number of fish that will recruit in the future. Globally optimized genetic learning algorithms are used to find the optimal values of the parameters for the fuzzy logic model. The results from this fuzzy logic model are compared with results from both a traditional Ricker stock-recruitment model and a recent artificial neural network model. These comparisons demonstrate the superior capability of the fuzzy logic model for addressing problems of uncertainty and vagueness in both the data and the stock-recruitment relationship. The fuzzy logic model approach is recommended as a useful addition to the analytical tools currently available for fish stock assessment and management.

Effects of Stocking Size and Rearing Method on Muskellunge Survival in Chautauqua Lake, New York

Abstract We examined the effects of rearing method and size at stocking on the survival of muskellunge Esox masquinongy in Chautauqua Lake, New York. Since 1961, changes in rearing methods have coincided with declining abundance of adult muskellunge. In particular, a change from pond rearing to trough rearing coincided with declining catches of adult muskellunge in pound nets. The decline was only partly reversed by changes from trough rearing to pond finishing of fingerlings. Changes in survival to age 5 from 1961 to 1996 indicated that both rearing method and stocking length significantly affected survival. Greater length at stocking resulted in higher survival rates. After accounting for length at stocking, survival was highest for pond-reared fingerlings, intermediate for pond-finished fingerlings, and lowest for trough-reared fingerlings. A modified Ricker stock–recruitment model indicated that survival of fingerlings declined over time. Increases in the adult stock of walleye Stizostedion vitrium si...

Investigation of density dependence in salmon spawner–egg relationships using queueing theory

A model based on queueing theory is presented to explain salmonid spawner–egg relationships caused by redd superimposition. The model incorporates carrying capacity, spawner arrival times, egg protection, preference of potential redd sites and accumulation of waiting spawners. Results show that the relationship described by the Beverton-Holt stock recruitment model produces a greater density dependent effect than just redd superimposition from random spawning. Whereas, the Ricker stock recruitment model produces similar results as the random spawning model at low spawner levels. A queueing model of waiting spawners explains reduced recruitment at high spawner levels similar to the Ricker model, but results are dependent on the assumptions made about the reduction in egg viability as spawning is delayed in waiting spawners. These results show, that when the carrying capacity and maximum rate of recruitment are fixed, the Ricker and Beverton-Holt models differ at both low and high spawner stock size. Therefore, the choice between Ricker and Beverton-Holt models should not depend only on the comparison of the comparison of recruitment at high spawning stock sizes. The model presented here is a good initial building block for a full life history model for salmonids or other species and similar techniques could be used for the other life history stages.

The relationship between smolt density and fry density in salmonids

If the Ricker stock–recruitment model describes the relationship between egg density and survivor density at different stages of the life cycle, then the relationship between smolt density and fry density is not simple. Using data from a long‐term study (1966–1990) of a sea trout population Salmo trutta, the relationship between density of potential smolts and fry densities in late M ay/early June or late August/early September is shown to be a reflexed curve with zero origin, so that there are two smolt densities for each fry density. A linear relationship is obtained only when the exponential parameter in the Ricker model is constant for the different life Stages.

Estimating the parameters of the stock-recruitment model of Ricker from a yield-per-recruit model in data-limited situations

A simple method to estimate the parameters of the Ricker stock-recruitment model is described. The method is based on the Beverton and Holt yield per recruit model, as a function of fishing mortality, which can be used to describe the stock-recruitment relationship of an exploited stock even when the data are limited to 1 year of estimates for average biomass and fishing mortality, or, to describe virgin biomass (educated guess). Once the parameters are estimated, the surplus production and maximum sustainable yield can be established. The method is applied to Merluccius gayi of the central zone off Chile and Sardinops sagax off northern Chile. The application of the method is discussed.

Factors Affecting the Recruitment of Lake Whitefish in Two Areas of Northern Lake Michigan

Stock-recruitment and integrated recruitment models incorporating biotic and abiotic factors were developed for lake whitefish populations in northern Green Bay and the North Shore areas of Lake Michigan. Abundance and recruitment indices were calculated for the 1961-1985 year classes based on lake whitefish catch and effort data from the commercial fishery in each area. Previous research indicates that spawning stock abundance, winter ice cover, and spring temperatures are important in determining the egg and larval abundance and survival of lake whitefish. Therefore, spawning stock abundance, ice cover, winter wind velocity, and spring water and air temperature variables were used as model inputs in regression modeling. The biotic/abiotic recruitment model for northern Green Bay hindcasted lake whitefish recruitment as a function of spawning stock abundance and the number of days that ice cover exceeded 40% during egg incubation. This regression model (R 2 = 0.62) demonstrated improved hindcasting ability of historic recruitment when compared to the Beverton-Holt (R 2 = 0.37) or the Ricker (R 2 = 0.33) stock-recruitment models for the 1961-1985 cohorts. The biotic/abiotic recruitment model for the North Shore hindcasted lake whitefish recruitment as a function of average air temperature in May after larval emergence, the number of days that ice concentration exceeded 70% during egg incubation, and spawning stock abundance. The regression model (R 2 = 0.57) also demonstrated improved hindcasting ability of historical recruitment when compared with Beverton-Holt (R 2 = 0.09) or the Ricker (R 2 = 0.13) stock-recruitment models. Results of this study indicate that biotic/abiotic recruitment models were more successful in hindcasting recruitment than solely biologically based stock-recruitment relationships. Consideration of significant abiotic variables will be useful in the management of lake whitefish stocks in the Great Lakes by improving forecasts of recruitment.

Evaluating Forecasting Procedures for Predicting Pacific Herring (Clupea harengus pallasi) Recruitment in British Columbia

The ability of four forecasting methods to generate one-step-ahead forecasts of Pacific herring (Clupea harengus pillasi) recruitment is considered in this paper. Recruitment time series for five coastal stocks and various environmental time series are employed in the analyses. Information up to and including time t is employed to estimate the parameters of each model used to forecast recruitment in year t + 1. Parameter estimates are then updated after each time step with a total of seven one-step-ahead forecasts being generated by each model for each stock. The forecast errors are compared using the five criteria: (1) root mean squared error, (2) mean absolute deviation, (3) mean absolute percent error, (4) median absolute deviation, and (5) median absolute percent error. The results of the study indicate that time series models may provide better forecasts of recruitment for the Strait of Georgia/Johnstone Strait stocks than the other competing procedures. A Ricker stock–recruitment model that takes into account environmental data appears to produce marginally better forecasts for the Central Coast and Queen Charlotte Island stocks, while all models produced equally good/bad forecasts for the Prince Rupert district stocks.

Dependence of Exploitation Rates for Maximum Yield and Stock Collapse on Age and Sex Structure of Chinook Salmon (Oncorhynchus tshawytscha) Stocks

In this paper we investigate the equilibrium behavior of an age- and sex-structured version of the Ricker stock–recruitment model specifically tailored to the complex nature of chinook salmon (Oncorhynchus tshawytscha) biology and fisheries. Conclusions from our analysis include the following. (1) Exploitation rates for maximum yield (umsy) and stock collapse (umax) depend strongly on a stock's maturity schedule, being lowest for a late-maturing stock and greatest for an early maturing stock. (2) Values of exploitation rates for umax overlap considerably with those for umsy, emphasizing the probability of stock collapse in fully exploited mixed stock fisheries. (3) Values of umsy and umax are independent of the value of the Ricker β parameter but depend directly on the Ricker α parameter, indicating that management research should focus on obtaining better estimates of α, contrary to recent suggestions in the literature. (4) Because they mature at older ages, female chinook suffer greater cumulative fishery removal rates than males and decline in abundance more rapidly as exploitation increases. Consequently, the use of sex-independent maturity schedules can give misleading estimates for umsy and umax. (5) Maximum changes in mean age of stocks that can be attributed to fishing up effects ranged from 0.32 to 0.81 yr. Many stocks appear already to have declined in mean age by this amount, further emphasizing the probability of impending collapse of some stocks.

Effects of Density-Dependent and Climatic Factors on American shad, Alosa sapidissima, Recruitment: A Predictive Approach

We developed environment-dependent stock–recruitment models for American shad, Alosa sapidissima, in the Connecticut River to forecast recruitment variability and measure density-dependent effects. These models were fitted to the 1966–78 stock–recruitment estimates and to May and June river flow, water temperature, and rainfall data shown previously to affect American shad year-class strength. We also attempted to validate the models by forecasting the 1979–84 year-classes based on juvenile indices, parent stock size, and hydrographic data for these years. The stock–recruitment models without environmental factors explained less than 3% of the recruitment variability, and none of the density-dependent exponents were statistically different from 0. The predictive capability of the Ricker stock–recruitment model improved dramatically (r2 = 0.90) when combined with mean May flows, June flows, and the number of American shad lifted over the Holyoke Dam. The density-dependent exponents of these multiple regression models were highly significant, indicating that density-dependent processes are hidden by climatically induced variability in recruitment. Two environment-dependent stock–recruitment models predicted 80–90% of the American shad recruitment variability from 1979–84.

Modification of the ricker stock recruitment model to account for environmentally induced variation in recruitment with particular reference to the blue crab fishery in Chesapeake Bay

A modification has been made to the simple Ricker stock recruitment model in order to account for density-independent mortality through fluctuating environmental conditions as well as density-dependent mortality. The modified model is applied to the blue crab fishery data from Chesapeake Bay, Maryland. The model results in a family of stock recruitment curves which assist in the understanding of a complex relationship between spawning stock and recruitment, thereby providing a better basis for recruitment prediction and fishery management. A management strategy for a fishery subject to fluctuating levels of recruitment is also discussed.

Adaptive Control of Fishing Systems

This paper discusses some formal techniques for deciding how harvesting policies should be modified in the face of uncertainty. Parameter estimation and dynamic optimization methods are combined for the Ricker stock-recruitment model to show how exploitation rates should be manipulated to give more information about the model parameters; in general, harvesting rates should be lower than would be predicted by the best fitting recruitment curve unless this curve predicts that the stock is very productive. A decision procedure is developed for comparing alternative stock-recruitment models; when applied to the Fraser River sockeye salmon (Oncorhynchus nerka), the procedure indicates that an experimental increase in escapements would be quite worthwhile. It appears that there is considerable promise for extending these methods and procedures to cases where the stock size is unknown and where fishing effort is poorly controlled.