  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.
