9781888569315-ch6
Incorporating Uncertainty into Fishery Models
A Stochastic Decision-Based Approach to Assessing the Status of the Delaware Bay Blue Crab Stock
Thomas E. Helser, Alexei Sharov, and Desmond M. Kahn
doi: https://doi.org/10.47886/9781888569315.ch6
Abstract.—Stock assessment methodology has increasingly employed statistical procedures as a means to incorporate uncertainty into assessment advice. Deterministic values of fishing mortality rates (Ft ) estimated from assessment models have been replaced by empirical distributions that can be compared with an appropriate biological reference point (FBRP) to generate statements of probability (e.g., Pr[Ft ≥ FBRP]) regarding the status of the resource. It must be recognized, however, that terminal year fishing mortality rates and the biological reference points to which they are compared are both estimated with error, which will impact the quality of decisions regarding the status of the stock. We propose a two-tier stochastic decision-based framework for a recently conducted stock assessment of the Delaware Bay blue crab stock that specifies not only the probability for the condition Pr(Ft ≥ FBRP), but also the statistical level of confidence (i.e., 90%) in that decision. The approach uses a mixed Monte Carlobootstrap procedure to estimate probability distributions for both the terminal year fishing mortality rate (Ft ) and the replacement fishing mortality rate, approximated by FMED as an overfishing definition. Probability density functions (PDFs) for Ft and FMED, generated using the mixed Monte Carlo-bootstrap procedure, show that recent fishing mortality rates (80% CI from 0.6 to 1.2) are generally below the FMED overfishing definition (80% CI from 0.9 to 1.6), with significant overlap in the PDFs. Using the PDFs, the stochastic decision-based approach then generates a probability profile by integrating the area under the Ft PDF for different decision confidence levels (e.g. 90%, 80%, 70%, etc.), which can be thought of as one-tailed α-probability from standard statistical hypothesis testing. For example, at the 80% decision confidence level (value of F corresponding to the upper 20% of the FMED PDF), Pr(Ft > FMED) is about 0.03. Thus, with high confidence (80%), we can state that the blue crab stock is not currently being overfished. This approach can be extended to decisions regarding control laws that specify both maximum fishing rate and minimum biomass thresholds.
