Managing stochastic multispecies models

Qualitative properties of optimal policies for stochastic, multispecies harvesting models are described. Conditions that imply that a k-species model can be decomposed into k single species models are discussed. For a discrete, stochastic version of the Loth-Volterra models, it is shown that finding an optimal policy can be narrowed to finding the globally optimal harvest, and to using constraints developed on the partial derivatives of an optimal policy to accelerate computations. For a discrete stochastic mion of a comptition model developed by Silliman. it is proven that knowledge of the globally optimal harvest is sufficient to completely describe an optimal policy. Approximate policies that are easier to solve are suggested. The results suggest that an optimal harvesting policy will tend to simplify the ecosystem-that is harvest to low levels unwanted or less valuable species.