Identifying limit reference points for robust harvest control rules in fisheries management

Risk and uncertainty are intrinsic characteristics of natural resources that must be taken into account in their management. Harvest control rules (HCR) used to be the central management tool to control stock fisheries in an uncertain context. A typical HCR determines fishing mortality as a linear relationship of the biomass binding only when the biomass is above a critical risk value. Choosing the linear relationship and the risk value is a complex task when there is uncertainty because it requires a high level of data and an in-deep knowledge of the stock. This paper fully characterizes robust HCRs that explicitly include scientific uncertainty using the robust control theory approach. Our theoretical findings show that under uncertainty: i) Constant HCRs are not robust; ii) Robust HCRs show a steeper linear relationship between fishing mortality and biomass and a higher value of biomass to be consider at risk than non-robust HCRs. From the implementation viewpoint, we assume a three-sigma rule and show that robustness is achieved by selecting a fishing mortality such that its deviation from the fishing mortality target is twice the deviation of the biomass from the biomass target, and the critical value of the biomass (the point below which fishing should cease, or become as close to zero as possible) is half of the biomass associated with the maximum sustainable yield when this is the target.