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This paper mainly considers how the resource allocation affects the population of two species which are assumed to be in steady state under diffusion type of interaction. The problem is to control the intrinsic growth rate so as to optimize the net benefit. The optimal conditions are given and characterized. These optimal conditions are different from the results in [4,6]. Introduction Suppose  is a bounded domain in N R with 2 C  ;  and / n   denote respectively the Laplacian operator and the outward normal derivative. , i i B b and   1,2 i c i  are positive constants. In the conservation biology, allocation of resources often has a direct impact on the number of biological species. Assume that given a certain resource, how can we achieve the maximum benefits through the distribution of species in the environment? The question was first represented by Cantrell and Conser [1], also see [2]. The single-species spatial strategy model was constructed with Dirichlet, Robin or Neumann boundary conditions, respectively [3,4]. On the other hand, Leung and Stojanovic [5,6] studied the optimal harvesting of only one species. For optimal control of biological models, see [7,8]. Suppose there are two species in the environment. The species concentrations satisfy a preypredator Volterra-Lotka system under diffusion with Neumann boundary condition:

Optimal Control of the Growth Coefficient on a Prey-predator System