Abstract

Environmental variability has a strong influence on marine fish stocks. Thus, management and harvest policies based on deterministic indicators, such as maximum sustainable yield (MSY), may be inappropriate facing such uncertainties. In this study, we investigate the long-term behavior of a single-species fishery, whose stock is harvested by several fleets and affected by variability in the recruitment. The dynamics of this population is modeled by a discrete-time stochastic age-structured model. In this context, we introduce the concepts of maximum expected, log expected, and harmonic expected sustainable yield, as biological reference points. We illustrate these concepts with a case study of the Patagonian toothfish fishery in Chile and Argentina. Via Monte-Carlo simulations, we verify that high levels of variability have a negative effect on all these maximum expected reference points, which suggests the need to be more cautious when large levels of variability on recruitment impact the fishery. Our simulations show that the deterministic MSY may not be attained in the presence of environmental noise, and therefore its use may lead to a failure of management strategies or rebuilding plans. Recommendations for Resource Managers For sustainable harvest, proper accounting of stochasticity in recruitment dynamics is necessary. For high levels of volatility, the use of deterministic reference points to develop regulations, such as maximum sustainable yield (MSY), may lead to overexploitation and even a possible extinction of the fishery. We extend the MSY to the stochastic age-structured framework by means of maximum expected stationary yield, maximum expected log-sustainable yield, and maximum expected harmonic sustainable yield, which can be used as precautionary reference points. These three maximum expected yields and their respective optimal fishing mortalities decrease when the variability of fish recruitment increases. This stresses the need to be more cautious in presence of volatility.