Resonant Activation of Population Extinctions

Understanding the mechanisms governing population extinctions is of key importance to many problems in ecology and evolution. Stochastic factors are known to play a central role in extinction, but the interactions between a population's demographic stochasticity and environmental noise remain poorly understood. Here, we model environmental forcing as a stochastic fluctuation between two states, one with a higher death rate than the other. We find that in general there exists a rate of fluctuations that minimizes the mean time to extinction, a phenomenon previously dubbed "resonant activation." We develop a heuristic description of the phenomenon, together with a criterion for the existence of resonant activation. Specifically the minimum extinction time arises as a result of the system approaching a scenario wherein the severity of rare events is balanced by the time interval between them. We discuss our findings within the context of more general forms of environmental noise, and suggest potential applications to evolutionary models.