Optimally Managing Oscillating Predator-Prey Systems

During the course of these oscillations, the abundance of both species regularly decreases to low levels. At these times, the inherent stochasticity of the environment will 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.