An Approach to Quantifying Scientific Uncertainty in West Coast Stock Assessments Groundfish & CPS Subcommittees

Quantifying scientific uncertainty in estimating an appropriate catch level for a fish stock is challenging. Multiple sources of error can easily be identified, including measurement error that is conditioned on the adopted model, model specification error, forecast error, and uncertainty about overall stock productivity. In addition, there are without doubt other unknown factors that will negatively influence the precision of scientific advice on catch levels. Notwithstanding these difficulties, the Magnuson-Stevens Act (MSA) as amended in 2007 requires the Scientific and Statistical Committees (SSCs) of the Regional Fishery Management Councils to provide an acceptable biological catch (ABC) recommendation. According to the revised National Standard 1 Guidelines, ABCs must account for scientific uncertainty in estimates of overfishing limits (OFLs). Moreover, the ABC is the catch level that annual catch limits (ACLs) may not exceed. While many sources of uncertainty exist, the focus here is on quantification of statistical measurement error and model specification error, particularly the latter. While not all inclusive, the study of these two factors is feasible using the information that is currently available. They are also likely to include the dominant sources of scientific uncertainty in the development of scientific advice with respect to catch levels at the Pacific Fishery Management Council for groundfish and coastal pelagic species. Although full Bayesian integration through MCMC calculations is a preferred method of estimating measurement error " within " a stock assessment, an insufficient number of studies have successfully achieved that type of analysis. Consequently, we report the first order approximate estimates of the standard error on terminal biomass from stock assessments that are calculated by inverting 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 retrospective variation among multiple assessments of the same stock. Results show that for 17 groundfish and coastal pelagic species the mean of the coefficient of variation on terminal biomass is 18%. This represents the average amount of statistical measurement error within assessments conducted for the PFMC. In contrast, the average coefficient of variation ascribable to model specification error (i.e., among assessment variation) is 37%, which is the greater of the two sources of uncertainty. Given these results, if only this source of variation is considered, and the probability of overfishing is fixed at 0.40, an appropriate buffer on the overfishing catch level is to reduce the harvest by …