Optimal harvesting policy for the Beverton--Holt model.

Abstract

In this paper, we establish the exploitation of a single population modeled by the Beverton--Holt difference equation with periodic coefficients. We begin our investigation with the harvesting of a single autonomous population with logistic growth and show that the harvested logistic equation with periodic coefficients has a unique positive periodic solution which globally attracts all its solutions. Further, we approach the investigation of the optimal harvesting policy that maximizes the annual sustainable yield in a novel and powerful way; it serves as a foundation for the analysis of the exploitation of the discrete population model. In the second part of the paper, we formulate the harvested Beverton--Holt model and derive the unique periodic solution, which globally attracts all its solutions. We continue our investigation by optimizing the sustainable yield with respect to the harvest effort. The results differ from the optimal harvesting policy for the continuous logistic model, which suggests a separate strategy for populations modeled by the Beverton--Holt difference equation.