A prey-predator fishery model with endogenous switching of harvesting strategy

We propose a dynamic model to describe a fishery where both preys and predators are harvested by a population of fishermenwho are allowed to catch only one of the two species at a time. According to the strategy currently employed by each agent, i.e. the harvested variety, at each time period the population of fishermen is partitioned into two groups, and an evolutionary mechanism regulates how agents dynamically switch from one strategy to the other in order to improve their profits. Among the various dynamic models proposed, the most realistic is a hybrid system formed by two ordinary differential equations, describing thedynamics of the interacting species underfishingpressure, andan impulsive variable that evolves in a discrete time scale, in order to describe the changes of the fraction of fishermen that harvest a given stock. The aim of the paper is to analyze the economic consequences of this kind of self-regulating fishery, as well as its biological sustainability, in comparisonwith other regulatory policies. Our analytic andnumerical results give evidence that in some cases this kind of myopic, evolutionary self-regulation might ensure a satisfactory trade-off between profit maximization and resource conservation. 2013 Elsevier Inc. All rights reserved.