Robustness and management performance of MSY reference points derived from the hockey-stick stock-recruitment model under structural uncertainty

The hockey-stick (HS) stock recruitment relationship (SRR) has been widely used as an empirical alternative to conventional SRRs such as the Beverton–Holt (BH) and Ricker (RI) models. However, the management performance and risks associated with estimating maximum-sustainable-yield (MSY) reference points (RPs) based on HS remain insufficiently understood. This study first defines deterministic and stochastic MSY RPs under the HS model and provides an overview of their properties. We then conduct simulation experiments to investigate the bias and management consequences that arise when MSY RPs are estimated from the HS model (HS-derived MSY RPs) rather than from the true SRR (e.g., BH) across a range of biological and stochastic parameters, with particular focus on scenarios with insufficient data contrast. Our results show that HS-derived MSY RPs tend to exhibit higher bias but lower variance than MSY RPs derived from the true SRR. Management strategy evaluation simulations further reveal that management procedures combining HS-derived MSY RPs with adaptive model learning and some precautionary measures gradually reduce this bias and achieve average spawning biomass and yield that are comparable to those obtained under management based on the true BH SRR. We also show that the management effectiveness of the precautionary measures depends on life-history traits and recruitment variability. These findings indicate that although HS-derived MSY RPs may be biased and require cautious use, combining them with appropriate precautionary measures allows management to remain robust while limiting variability and yield losses. This broadens the range of management options that are available for supporting sustainable fisheries management.