A meta-analytic approach to quantifying scientific uncertainty in stock assessments

Quantifying scientific uncertainty when setting total allowable catch limits for fish stocks is a major challenge, but it is a requirement in the United States since changes to national fisheries legislation. Multiple sources of error are readily identifiable, including estimation error, model specification error, forecast error, and errors associated with the definition and estimation of reference points. Our focus here, however, is to quantify the influence of estimation error and model specification error on assessment outcomes. These are fundamental sources of uncertainty in developing scientific advice concerning appropriate catch levels and although a study of these two factors may not be inclusive, it is feasible with available information. For data-rich stock assessments conducted on the U.S. west coast we report approximate coefficients of variation in terminal biomass estimates from assessments based on inversion of the assessment of the model’s Hessian matrix (i.e., the asymptotic standard error). To summarize variation “among” stock assessments, as a proxy for model specification error, we characterize variation among multiple historical assessments of the same stock. Results indicate that for 17 groundfish and coastal pelagic species, the mean coefficient of variation of terminal biomass is 18%. In contrast, the coefficient of variation ascribable to model specification error (i.e., pooled among-assessment variation) is 37%. We show that if a precautionary probability of overfishing equal to 0.40 is adopted by managers, and only model specification error is considered, a 9% reduction in the overfishing catch level is indicated.

Developing a growth-transition matrix for the stock assessment of the green sea urchin (Strongylocentrotus droebachiensis) off Maine

The green sea urchin (Strongylocentrotus droebachiensis) is important to the economy of Maine. It is the state’s fourth largest fishery by value. The fishery has experienced a continuous decline in landings since 1992 because of decreasing stock abundance. Because determining the age of sea urchins is often difficult, a formal stock assessment demands the development of a size-structured population dynamic model. One of the most important components in a size-structured model is a growth-transition matrix. We developed an approach for estimating the growth-transition matrix using von Bertalanffy growth parameters estimated in previous studies of the green sea urchin off Maine. This approach explicitly considers size-specific variations associated with yearly growth increments for these urchins. The proposed growth-transition matrix can be updated readily with new information on growth, which is important because changes in stock abundance and the ecosystem will likely result in changes in sea urchin key life history parameters including growth. This growth-transition matrix can be readily incorporated into the size-structured stock assessment model that has been developed for assessing the green sea urchin stock off Maine.