Using reproductive values to define optimal harvesting for multisite density-dependent populations: example with a marine reserve

Abstract

A new method for determining optimal harvest from age-structured populations with a density-dependent stock-recruit relationship is presented. The theoretical optimal harvest comes from removing the age-class with the smallest ratio of reproductive value to weight. The method is derived from considering the sensitivity of equilibrium egg production to harvest using results for density-dependent Leslie matrices. The method holds in both single- and multi-site contexts and is derived for both Ricker and Beverton–Holt recruitment functions. I illustrate the method for a one-site model of Arcto-Norwegian cod (Gadus morhua) and obtain the same optimal strategy as previous methods, namely that age-class 6 should be harvested 45%. Including age-specific selectivities, the best constrained yields occur at a harvest rate of 11% on ages 5–12. This yield is 73% of the theoretical optimum. I considered the same model when a reserve is established and found that high transfer rates out of the reserve (where spawners attain a higher fecundity) produced greater yields that were 86% of the one-site (no reserve) yield. Also, if overfishing occurs at 1.5 and 2.0 times the optimal level in the one-site case, then most yields from the reserve model are greater than those from the one-site model.