Optimally managing oscillating predator-prey systems

Many interacting predator-prey populations have a natural tendency to exhibit persistent limit-cycle or damped oscillations, especially in the presence of environmental stochasticity. The restriction of habitats, and the resultant compression of ecosystems into small conservation reserves can induce these oscillations in previously stable predatorprey relationships. During the course of these oscillations, the abundance of both species regularly decreases to low levels. At these times, the inherent stochasticity of the environmentwill result in a high probability of species extinction. In these situations, actions should be taken by management authorities to stabilise the system and avoid extinction. In many practical cases, funding limitations restrict the actions available to managers, and so we assume that the only options available to a manager are to cull individuals from the two populations. Operating within these constraints, we show in this paper that strategic culling of organisms can greatly reduce the probability of a species becoming extinct. We use the mathematical technique of Stochastic Dynamic Programming to determine the optimal management strategy for these oscillation-prone populations. Application of the optimal strategy results in a much more persistent system, with only a small number of interventions being necessary. These methods can be applied to many different species, and can incorporate more complex system dynamics without a significant increase in computational time. The optimal strategies that result from our analyses offer general insights into how such systems should be managed.