Local sensitivity of per-recruit fishing mortality reference points

We study the sensitivity of fishery management per-recruit harvest rates which may be part of a quantitative harvest strategy designed to achieve some objective for catch or population size. We use a local influence sensitivity analysis to derive equations that describe how these reference harvest rates are affected by perturbations to productivity processes. These equations give a basic theoretical understanding of sensitivity that can be used to predict what the likely impacts of future changes in productivity will be. Our results indicate that per-recruit reference harvest rates are more sensitive to perturbations when the equilibrium catch or population size per recruit, as functions of the harvest rate, have less curvature near the reference point. Overall our results suggest that per recruit reference points will, with some exceptions, usually increase if (1) growth rates increase, (2) natural mortality rates increase, or (3) fishery selectivity increases to an older age.