Discrete Time Optimal Harvesting of Fish Populations with Age Structure

Abstract

We consider an optimal fishery harvesting problem using an age-structured population model with nonlinear recruitment. The motivating example is Atlantic Cod. The goal is to maximize the profit (total gain) of fishing. We seek to find the optimal harvesting strategy for each age class, but also to find the optimal net size. Using the extension of Pontryagin’s Maximum Principle to discrete systems, we are able to derive the necessary conditions and the characterizations for the optimal harvesting strategies. Numerical simulations for both Beverton-Holt and Ricker recruitment functions are provided.

Keywords

• optimal harvesting
• discrete model
• age structure