Can culling a threatened species increase its chance of persisting?

Many interacting predator-prey populations have a natural tendency to exhibit persistent limit-cycles or damped oscillations, especially in the presence of environmental stochasticity. The restriction of populations into small conservation reserves reduces the scale of ecosystems, and can induce cycling in previously stable predator-prey relationships. During the course of these cycles, the abundance of both predator and prey regularly decrease to low levels. At these times, environmental and demographic stochasticity may cause the extinction of one of the populations. Could culling one or both species at critical times reduce their probability of extinction? We use stochastic dynamic programming to determine the optimal management strategy for oscillation-prone species pairs. Remarkably, if the interventions are enacted at the appropriate time, infrequent culling of a small number of individuals significantly reduces the probability of extinction of the predator. Our approach can be applied to many different ecosystems, and can incorporate more complex system dynamics without a significant increase in computational time.