Tamtam Proceedings - lamsin

544 Mchich et al.3∑where r = r i νi∗3 , n = α + √ α 2 − 4rβ2ri=13∑fishing rates, we have: ã = a i νi ∗ µ ∗ i , ˜b =i=1and n = α − √ α 2 − 4rβ. For the global2r3∑3∑b i νi ∗ µ ∗ i and ˜c = c i µ ∗ i .For aggregation methods, we refer to [1, 2, 7]. The aggregated model is obtained byan approximation. It is valid when the small parameter is small enough (ε ã min(which means that a minimum of catchability is assured for the three fleets), then a simplecalculation shows that function E ∗ (ã, ˜b, ˜c) has a maximum for a spatial distribution ofthe fishing efforts chosen as follows: ã = ã min and ˜b = 2r ˜c. Therefore, the choice ofαa particular spatial distribution of the fishing effort allows to maximize the total fishingactivity. So, the optimal total sustainable fishing activity is given by: E ∗ = 1 ( α2ã min 4r −β)i=1TAMTAM –Tunis– 2005