ON THE OPTIMAL SIZE AND NUMBER OF RESERVES IN A MULTI-SITE FISHERY MODEL

Abstract

This paper addresses the problem of the optimal size and number of marine reserves to achieve maximum value in commercial fisheries. A simplified network planning situation is analyzed to optimize the size and number of marine reserves. We consider a general 2L-patch model of harvesting population dynamics with continuous time. Fish movements between the sites, as well as vessel displacements between the fishing sites, are assumed to take place at a faster time scale than the variation of the stock and the change of the fleet size. We take advantage of these two time scales to derive a reduced model governing the dynamics of the total fish stock and the total fishing effort. This reduced model is used to determine the optimal size and number of a marine reserves in order to maximize the catch at equilibrium. We show that the optimal number that maximizes the total fish catch at equilibrium depend intricately on the size of the reserve: A small number of reserves is optimal when the size of the reserve is higher and inverse.