A Quantitative Approach to Prior Setting for Relative Biomass (B/k) in CMSY++: Application to Snow Crabs (Chionoecetes opilio) in Korean Waters

Snow crabs (Chionoecetes opilio), a commercially valuable species in Korean waters, have been managed under the Total Allowable Catch (TAC) system since 2002. However, stock assessment has been limited due to difficulties in estimating key ecological traits such as growth, maturity, and mortality. In this study, the Bayesian Schaefer Model (BSM), implemented within CMSY++ framework, was applied to assess the stock status of snow crabs in Korean waters. BSM requires catch and abundance index data, such as catch per unit effort (CPUE) or biomass, as well as prior information on species resilience and relative biomass (B/k). To improve the reliability of B/k priors, we developed a method to calculate them quantitatively using fishery data, sales amounts, and biological information, unlike the qualitative assumptions on stock and fishing conditions proposed in previous research. Two standardized CPUE indices with differing temporal trends in recent years were used as abundance indices. To address the structural uncertainty associated with these divergent trends, we applied a grid-based approach by treating each CPUE index as an independent model scenario and integrating the posterior distributions. A total of 12,000 posterior estimates (6000 per index) were generated through the BSM and used to construct a Kobe plot. Results indicate that the current biomass is slightly above the level supporting maximum sustainable yield, and fishing mortality slightly below the optimal level, suggesting that the stock is healthy and sustainably exploited. Future research should aim to establish a systematic framework for developing quantitative B/k priors to enhance stock assessment accuracy.