Age-structured assessment of three Aleutian fish stocks with predator-prey interactions Doug Kinzey School of Aquatic and Fishery Sciences University of Washington

Introduction Fisheries are embedded in a naturally interacting system of predators and prey. Predator-prey relationships are not explicitly considered in the formal, statistical procedures (single-species assessments) used to evaluate the status of most commercially-harvested populations, however. Nevertheless, management decisions about harvest levels and risks are often based on single-species assessments.

Single-species assessments Formal assessments are based on statistically complex models that may include age-structure and other details but consider interactions among species only indirectly. For instance, natural (non-fishing) mortality may enter these models as a single, constant value across all age classes, ie, an assumed 20 or 30% mortality per age class per year.

Objective The aim of this study is to: select a core group of populations for which individual assessments have been conducted that also interact as predators and prey, and for whom diet data are available as a time series; incorporate the predator-prey interactions into an age-based, statistical assessment of the populations simultaneously, and compare the outcomes between the single-species and multispecies versions of the models representing these populations.

Aleutian model The interaction among walleye pollock, Atka mackerel, Pacific cod and fisheries in the Aleutian Islands, Alaska, from was chosen for modeling. These are the basis of the three principle fisheries in the region. Single-species assessments are available for all three stocks from the NOAA Alaska Fisheries Science Center. An archived database of stomach samples collected since the 1970s from these and other Aleutian species is also maintained by the AFSC.

Aleutian chain

Ecosystem significance These three populations of fish comprise a central role in the food web of the Aleutian region. They are the main prey items of Steller sea lions and are important in the diets of many other mammal and seabird species. Competition with fisheries has been postulated as one component in the decline of Steller sea lions and several other fish-dependent predators in the region.

Existing models (single-species) Stock assessments: The pollock (Barbeaux et al 2003) and mackerel (Lowe et al 2003) assessments were age-based and produced using the “Amak” toolbox modeling software developed by Jim Ianelli at the Alaska Fisheries Science Center. The cod assessment (Thompson and Dorn 2003) was length-based and produced using the program “Synthesis”, developed by Rick Methot at the Northwest Fisheries Science Center.

Data for single-species models Used in likelihood components (the differences between model outputs and these data are minimized): Total fishery catches, Proportions at age from the fishery, some years Proportions at age from surveys, some years Biomass index from surveys, some years Considered known (used but not estimated by model): weight-at-age from the fishery, some years weight-at-age from surveys, some years maturity at age, some years

Data example: pollock proportions at age The pollock fishery shows a high proportion of older fish in the early 1990s that isn’t reflected in surveys.

Single-species calculations About 2,000 lines of Amak code (AD Model Builder) 27 main equations with interactions 84 estimated parameters for pollock and 351 for mackerel penalties on recruitment deviations and selectivity parameter estimates Pacific cod was assessed using a different model structure (Synthesis) This is already pretty complicated!

Single-species model output: numbers at age The assessments combine the various sources of information with the model structure to estimate such population features as numbers-at-age.

Multispecies model: diet data Prey proportions have been identified in over 8,000 individual stomachs from these three species caught in the Aleutians since the 1980s. 2,700+ Pacific cod stomachs 3,600+ walleye pollock stomachs 1,600+ Atka mackerel stomachs

Multispecies interactions Pollock and mackerel are the main prey of cod, comprising about 19% and 27% of total cod stomach contents, respectively, in Aleutian diet studies. Although probably of lesser importance than fisheries, cod are the main predators of adult pollock and mackerel, and are also among the major predators of juveniles of both species. To some extent, all three species can be predators of one another (including cannibalism) at various life stages.

Diet Reflects Prey Abundance The proportion of prey species in cod diets is partly a result of prey abundance. -Data provided by Ivonne Ortiz, University of Washington

Multispecies modeling approach Separate the parameter representing natural mortality in Amak into two sources (explicitly modeled and additional mortality). Add two likelihood components representing stomach proportions and total ration. Use the fit to diet data to select among alternative functional forms representing predation. Re-estimate original single-species parameters as well as new multispecies parameters in the expanded model.

Model comparisons Use the Markov Chain Monte Carlo algorithim to sample the posterior distributions of the model outputs in order to characterize the uncertainty around parameters of interest. Parameters of interest include numbers-at-age, productivity and natural mortality not accounted for by fishing or the three species included explicitly (the mortality potentially available to other predators).

Possible outcomes Single- and multispecies models could have similar estimates of central tendencies and variances for the parameters of interest. The two approaches could have similar estimates of central tendencies but different estimates of variances (differing uncertainty). The two approaches could produce different estimates of both central tendencies and variances.

Potential significance: fisheries Depending on the final outcomes, this study could suggest either: Conventional single-species assessments adequately represent population features of interest without requiring the addition of predator-prey interactions, or including predator-prey modeling and data on diets into the assessments changes the estimates of features of interest enough to warrant including these factors in future assessments.

Potential significance: other species If the combined mortality due to fisheries and the species included in the multispecies model is greater than the mortality estimated in the single-species assessments, this could imply a smaller source of prey for the predator species not included in the model. This modeling could also suggest changes in fishing mortality on particular ages/species of predatory fish that might increase the potential prey for other species in the ecosystem.

Acknowledgements Project funding is from the Washington Cooperative Fish and Wildlife Research Unit and the North Pacific Universities Marine Mammal Research Consortium. Alaska Fisheries Science Center Scientists Kerim Aydin, Jim Ianelli, Sandra Lowe, Steve Barbeaux and Grant Thompson are providing access to data and computer code. My advisor Dr André Punt and the Punt lab members at the University of Washington are furnishing discussion and ideas concerning statistical theory and practical aspects of natural resource modeling.