Optimal exploitation of a multi-species community☆

Abstract We consider the problem of exploiting a multi-species ecological community in such a way as to maximize the discounted present value, ∫ ∞ 0 e −pt R (x,h) dt , where R(x, h) is the net revenue obtained by harvesting stocks represented by the population vector x at rates given by the harvest vector h. When the system obeys x=f(x)−h and two mild conditions hold on f and R, we reduce the determination of the optimal equilibrium state and exploitation strategy to the determination of the maximum of a simple scalar function of x. As an example, the method is applied to a generalized multi-species logistic model of a community.