Optimal number ofsites in multi-site fisheries with fish stock dependent migrations - Ali Moussaoui; Pierre Auger; Christophe Lett (Mathematical Biosciences and Engineering)
We present a stock-effort dynamical model of a fishery subdivided intofishing zones. The stock corresponds to a fish population moving betweenthese zones, on which they are harvested by fishing fleets. We consider alinear chain of identical fishing zones. Fish movements between the zones,as well as vessels displacements, are assumed to take place at a faster timescale than the variation of the stock and the change of the fleet size. Thevessels movements between the fishing areas are assumed to be stockdependent, i.e. the larger the stock density is in a zone the more vesselstends to remain in it. We take advantage of these two time scales to derivea reduced model governing the dynamics of the total harvested stock and thetotal fishing effort. Under some assumption, we obtain either a stableequilibrium or a stable limit cycle which involves large cyclic variationsof the total fish stock and fishing effort. We show that there exists anoptimal number of fishing zones that maximizes the total catch atequilibrium. We discuss the results in relation to fish aggregating devices(FADs) fisheries.