Optimal number of sites in artificial pelagic multisite fisheries

We present a mathematical model of artificial pelagic multisite fisheries. The model is a stock-effort dynamical model of a fishery subdivided into artificial fishing sites such as fish-aggregating devices (FADs) or artificial habitats (AHs). The objective of the work is to investigate the effects of the number of sites on the global activity of the fishery. We consider a linear chain of fishing sites in which fish are harvested by fishing vessels and a free stock that is unattached to the sites and not exploited. Fish movements between the sites and the free stock, as well as vessel displacements between the 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. We show that there exists an optimal number of fishing sites that maximizes the total catch at equilibrium. We finally extend the model to the situation in which both fish attached to the sites and fish in the free stock are exploited.