A comprehensive functional form of the optimal harvest control rule for multiple fishery management objectives

For many of the world's fisheries, harvest control rules (HCRs) are the main tools for supporting decision-making. We previously clarified the optimal shape of the HCR to achieve multiple fisheries management objectives (maximising average catch, reducing variation in yields, and avoiding stock collapse) and ensure robustness to estimation errors in biomass by numerically estimating the optimal values of the 21 biological reference points (BRPs) comprised in the HCR. However, for actual management, a simple but comprehensive functional form to emulate the optimal HCR is desirable, as numerical HCR optimisation with many BRPs is time-consuming. Here, we introduced three objective utility functions ( U1– U3) representing HCR performance for composite management objectives: mean–variance utility functions, where the performance indicator for variation in yields is the standard deviation ( U1) or the annual average variance ( U2) of yields, and the constant relative risk aversion utility function ( U3). We derived two equations to emulate the optimal HCRs with three adjusting parameters corresponding to the management objectives and different magnitudes of estimation errors. These equations will help stakeholders discuss desired management strategies by showing expected catch and risk by adjusting the parameter values.