Multi-species exploitation with evolutionary switching of harvesting strategies

In this paper, we propose a bioeconomic model which describes a fishery in which each of two noninteracting species is harvested by a given group of fishers during a defined time period. Then the Fishing Regulatory Authority allows each fisher to reconsider the harvesting decision at fixed (discrete) periods of time. The model derives from an Italian fisheries management experience in the Northern Adriatic Sea, where this kind of “self-adjusting” fishing policy has been proposed to regulate harvesting of two shellfish species. The proposed dynamic model assumes the form of a hybrid system, as the natural growth functions of the two species (in continuous time) are coupled with a discrete time adaptive system that regulates how agents switch from one harvesting strategy to the other period by period according to an evolutionary mechanism based on profit comparison. In order to obtain some insights into the basic mechanisms of the system, some relevant benchmark cases are analyzed before tackling (mainly numerically) the complete hybrid model. Our results suggest that, for proper sets of parameters, this kind of myopic and adaptive self-regulation may ensure a virtuous trade-off between profit maximization and resource conservation, driven by cost externalities and market pressure.