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Resource Ecology and Ecosystem Modeling Program

Testing the Stability of the Suitability Coefficients from the Eastern Bering Sea Multispecies Virtual Population Analysis

Suitability coefficients are important for the estimation of predation mortality M2 in the multispecies virtual population analysis (MSVPA) and the multispecies forecasting model (MSFOR) models. Testing the assumption of the stability of the suitability coefficients is important to assess the robustness of the predictions made with MSFOR. We used different statistical methods to partially test this assumption. The comparison of the estimates from two different sets of data suggested that sample sizes greater than 200 reduce the differences between the two types of estimates. In a second approach, we contrasted the residual variances of partial data sets with the results from the fit of a combined data set. Results suggested a small effect (~10.8 %) of variation in stomach contents among years on suitability estimates. The comparison of the fitted means of the suitability coefficients associated with each predator species suggest that only 13 of the 50 pair-wise contrasts were significantly different (α = 0.05). In general, results suggested that the predator preferences and prey vulnerabilities remained stable over time. Therefore, MSFOR could be considered as a tool for providing advice to fisheries managers within a multispecies context.

By Jesús Jurado-Molina and Patricia Livingston

Incorporating Predation Interactions in a Statistical Catch-at-age Model for a Predator-prey System in the Eastern Bering Sea

Multispecies virtual population analysis (MSVPA) has been used to model groundfish predation interactions in the eastern Bering Sea. This model incorporates predation mortality, M2, into the virtual population estimation process. However, this model framework lacks the statistical assumptions now commonly used in single-species assessment modeling in which statistical fitting of parameters is accomplished by considering how errors enter into the model and multiple data sources are used to estimate parameters. In this work, a two-species system (walleye pollock and Pacific cod) was derived to incorporate the predation equations from MSVPA into a multispecies statistical catch-at-age model (MSM). The MSM is a complex model that estimates population numbers and predation mortality based on catch-at-age data, relative indexes of abundance, predator annual ration and predator stomach contents using estimation procedures for the statistical part and the predation mortality. MSM statistically estimates population parameters such as numbers at age and fishing mortality rates using either an optimization algorithm (Newton-Raphson for example) or Bayesian methods and an internal algorithm for the estimation of the predation mortality.

  Figure 1, see caption
Figure 1.  Comparison of estimates of average suitability coefficients for walleye pollock as predator from the multispecies virtual population analysis and the multispecies statistical model.

Results suggest that the multispecies statistical model reproduced most of the suitability coefficients (Fig. 1) and predation mortalities estimated by MSVPA and the adult population estimates from the single-species stock assessment. MSM also provides a measure of the uncertainty associated with these parameters, which is not available with the current MSVPA technology.

MSM is an important advancement in providing advice to fisheries managers because it incorporates the current tools used in stock assessment such as Bayesian methods and decision analysis into a multispecies context, helping to establish useful scenarios for management in the eastern Bering Sea. Future improvements to the model will include adding the full suite of groundfish predators presently modeled in the eastern Bering Sea MSVPA and incorporating stomach content data into the statistical estimation process.

By Jesús Jurado-Molina and Patricia Livingston


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