Mean Extinction Time in Predator-Prey Model

A basic predator-prey (Lotka-Volterra) system exhibits marginal stability on the deterministic level. Intrinsic demographic stochasticity destroys this stability and drives the system toward extinction of one or both species. We analytically calculate the mean extinction time of such a system and investigate its scaling with the system’s parameters. This mean extinction time, measured in number of population cycles, scales as the square root of the size of the smaller population and as the minus three halves power of the size of the larger population. The analytic results are fully confirmed by Monte-Carlo simulations.