Stochastic dynamics of ecological populations subjected to environmental perturbations

The stochastic logistic model is widely used to capture random fluctuations arising from birth-death processes in ecological populations. We use this model to study the impact of environmental perturbations that may occur naturally or as a consequence of population harvesting. In our model formulation, environmental perturbations occur randomly as per a Poisson process, and the perturbations result in each individual dying with a certain probability of death. Moment closure schemes are employed to derive expressions for the mean and variability in population numbers. Moreover, to quantify the impact of population extinction in our model we compute the probability of extinction using the Finite State Projection (FSP) numerical method. Our analysis shows that rare environmental perturbations with a high probability of death lead to overall larger random fluctuations and extinction risk as compared to frequent perturbations with a low probability of death. Finally, we formulate the problem in the context of population harvesting to find the optimal harvesting rate that maximizes the cumulative yield.