Incorporating Uncertainty into Fishery Models

Bayesian Approaches to the Analysis of Uncertainty in the Stock Assessment of Pacific Halibut

Ana M. Parma

doi: https://doi.org/10.47886/9781888569315.ch8

Abstract.—The uncertainty associated with estimates of stock size is increasingly acknowledged in the provision of management advice. Estimated variances, however, are usually small compared with the variability of abundance estimates for any given year produced by successive assessments, especially when changes in the assessment methods are introduced. Of all the different kinds of uncertainty, uncertainty in the specification of the model structure is often the most significant source of assessment errors in some closely monitored fisheries. Recent changes in Pacific halibut assessments illustrate this problem. A separable catch-at-age model used since the mid-1980s performed very poorly in retrospective analyses, initially overestimating biomass and then underestimating it in the 1990s. The latter has been attributed to trends in catchability at age associated with a remarkable decrease in halibut growth rate over the last 15 years. A new model was developed which replaced the assumptions of constant catchability and selectivity made in the old model by a more flexible and realistic treatment of observation and process variability. The change in model structure resulted in estimates of present biomass more than double the previous estimates. While retrospective performance of the new model is much improved, major uncertainties still remain. In particular, the relative importance of size and age effects in determining catchability of the setline surveys is difficult to discern from the data. Two extreme models, one based on the assumption that survey selectivity is a function of size and the other based on the assumption that survey selectivity at age is constant, have been formulated to incorporate this uncertainty. In this paper, Bayesian methods are used to evaluate the uncertainty around abundance estimates and short-term forward projections, including the uncertainty due to alternative possible model structures. The posterior distributions of parameters of interest under each of the two models are approximated by Markov Chain Monte Carlo methods, and the support given to the models by the data is evaluated by computing their integrated likelihoods. While far from a complete representation of all sources of model uncertainty, the analysis illustrates how uncertainty in model choice, in addition to the standard parameter uncertainty, can be incorporated in risk computations.