Local sensitivity equations for maximum sustainable yield reference points

Quantitative fishery harvest strategies in many countries throughout the world are based on maximum sustainable yield (MSY) reference points (RPs); in particular, the fishing mortality rate that produces MSY (i.e. Fmsy) and the population biomass (Bmsy) that results from fishing at Fmsy. There is often great interest in the sensitivity of MSY RPs to their inputs and underlying assumptions. We perturb (i.e. ω) inputs to generate influence curves which we denote as Fmsy(ω) and Bmsy(ω) as functions of ω. We derive diagnostic equations for the slopes of Fmsy(ω) and Bmsy(ω) at the origin (i.e. no perturbation). These equations provide a conceptual understanding of how Fmsy and Bmsy will change in response to changes in inputs, which one does not get from a simple computational sensitivity analysis. We show that a leading factor determining the sensitivity of Fmsy is the amount of curvature in the equilibrium yield curve near Fmsy. Another leading factor affecting the sensitivity of Bmsy is if the stock–recruitment function indicates low density-dependence in recruitment productivity. With some exceptions, we find that Fmsy will increase if the body growth rate or asymptotic size increases, 2) proportions mature increase at younger ages, and 3) natural mortality rates decrease and the Ricker stock–recruitment function is used. If the fishery selectivity function of age is monotone increasing then Fmsy will also usually increase if peak selectivity is shifted to an older age. Usually the signs of the slopes for Bmsy and Fmsy are the same.