Tamtam Proceedings - lamsin

Bioeconomical fishing model 5411. IntroductionThe overexploitation of marine resources and the continuous high pressure on fishstocks leads inexorably to their extinction and to a global and worrying decrease in thelevel of catch. For example, in [6], authors study the evolution of Brittany’s industrialfleets and show an important decrease of their overall fishing power in the eighties forsaithe, cod, haddock and whiting in the West of Scotland area. An other important case isalso that of the pelagic resources, which represent 75 percent of the Atlantic fish stock inNorth-West Africa (see [8]). In Morocco, drastic fluctuations of abundance have been observedfor sardines and other pelagic during the last fifty years. This situation interpellatesthe responsible of fishery management, for making appropriate decisions, as controllingthe repartition of the fleets on different fishing zones, in order to avoid a potential slumpin the sector, and the aim of this work is to study the optimal spatial distribution of thefishing effort in a multi fishing zone, and to give some efficient management measures, bycontrolling the displacement of the fleets between the fishing zones, in order to increasethe total activity.In section 2, we present the complete fishing activity model on three zones. It consistsin a system of six ordinary differential equations governing the three local fishing stocksand the three fishing efforts on three adjacent fishing zones. We assume two time scales: afast one associated to the quick movements between different zones, and a slow one whichcorresponds to the growth of fish populations and the variation of the fleets revenue. Thegrowth of the fish is related to the natural demography rate (with Allee effect) less themortality rate due to the fishery, whereas the fishery fleet’s growth is function of the profitgenerated by the activity, which could be interpreted as an investment. We recall that wetake advantage of the two time scales to reduce the complete models by use of aggregationmethods (one can see the review article on aggregation techniques by Auger and Bravo dela Parra [1]). The analysis of the corresponding aggregated model leads to a level of totalsustainable fishing activity function of the spatial distribution of the fishing effort. That isthe spatial distribution could be chosen in order to maximize this total equilibrium level.Section 3 is devoted to a discussion/conclusion.2. The 3 fishing zones modelThe complete model: We consider a fish population harvested by a fishing fleet.Fishing boats are allowed to exploit the resource on three fishing zones. Let N(t) bethe fish population density at time t: N(t) = (n 1 (t), n 2 (t), n 3 (t)) T . n 1 (t) (resp. n 2 (t)and n 3 (t)) is the fish population density on fishing area 1, (resp. 2 and 3), at time t.Similarly, the fishing effort is subdivided into three components on each fishing zone:E(t) = (E 1 (t), E 2 (t), E 3 (t)) T . E i (t) is the fishing effort on fishing area i (i = 1, 2, 3),TAMTAM –Tunis– 2005