Harvesting Optimal Policy in Three Species Food Chain Model As an Optimal Control Problem with Path Constraints

Abstract

In this paper, we address the issue of harvesting prey and intermediate predators in a tritrophic food chain. Our approach is based on a model that characterizes the interactions among the three species. We assume that the intermediate predator has alternative food sources (it is a generalist), while the top predator relies solely on the intermediate predator (it is a specialist). This model has been previously explored in the literature, but representing the harvesting effort as a scalar control variable. In this study, we treat it as a vector variable, offering a more comprehensive representation, particularly relevant for terrestrial species hunting. Our primary objective is to determine optimal harvesting policies that ensure the persistence of all three species. To achieve this, we formulate the problem as an optimal control problem with a finite horizon and path constraints. We present a numerical example solved using ICLOCS2.