Enhancing maximum sustainable yield in a multi-patch Rosenzweig–Macarthur model with symmetrical prey and asymmetrical predator migration

¹ Laboratory of Nonlinear Analysis and Applied Mathematics, Department of Mathematics, Faculty of Science, University of Tlemcen, 13000, Algeria
² UMMISCO, Sorbonne Université, Institut de Recherche pour le Dáveloppement, IRD, 93143 Bondy, France
³ Faculty of Mathematics, University of Sciences and Technology Houari Boumediene, Algiers, Algeria

^* Corresponding author: moussaouidz@yahoo.fr

Received: 23 July 2024
Accepted: 20 January 2025

Abstract

In this paper, we formulate a Rosenzweig–MacArthur (RM) predator–prey model incorporating the dispersal of both prey and predator among n discrete habitat patches. We assume that only the predator is harvested and not its prey, growing logistically on each site. Our aim is to investigate whether the total catch in a system of interconnected patches through migration can surpass the sum of the optimal catch from n isolated patches, known as the maximum sustainable yield (MSY). We start by revisiting some fundamental properties of the RM model examining the stability of its equilibrium points. We then analyze the MSY for a single patch, deriving conditions on the fishing effort required to achieve MSY. Next, we consider the MSY of the RM model for both separated and connected patches, and provide different answers to the aforementioned question for different cases. In the homogeneous case with symmetric movement of the prey between patches, we show that the total yield at MSY for the interconnected system is equivalent to the sum of the yields at MSY for each isolated patch. In contrast, in the heterogeneous case, we show that the total maximum sustainable yield for the connected patches can surpass the sum of the maximum sustainable yields for each isolated patch. Our analysis establishes the conditions under which one scenario is more favorable in terms of yield.