Estimating Time‐Varying Productivity and Reference Points: A Case of North Sea Demersal Fish Stocks

Abstract

The productivity of marine fish populations determines both maximum sustainable yield (MSY) and resilience to exploitation. While biological reference points like MSY and depend on species traits and population density, they are also influenced by environmental variability and ecological interactions. However, commonly used models, such as stock–recruitment and surplus production models (SPMs), often assume constant productivity and reference points over time, potentially overlooking important ecosystem changes. We conducted a semi‐systematic literature review to identify covariate‐free approaches for modelling time‐varying productivity in marine populations. Based on this, we developed a continuous‐time stochastic SPM framework that allows both the intrinsic growth rate () and carrying capacity () to vary and co‐vary over time. Simulation experiments showed that time‐varying models, especially those with correlated changes in and , significantly improved estimation accuracy while retaining robust convergence. As a case study, we applied this model to seven commercially important demersal fish stocks in the North Sea. Results revealed a 56% average decline in MSY over four decades, with roundfish showing greater declines than flatfish. Temporal patterns in productivity correlated with environmental variables such as bottom temperature and salinity, indicating potential drivers. Our findings provide evidence of long‐term productivity declines in North Sea demersal stocks and offer a covariate‐free method for reconstructing historical reference points. This work underscores the need for adaptive management strategies that account for shifting productivity regimes under ongoing environmental change.

Bibliographic Information