Resonant Activation of Population Extinctions

TL;DR

This paper investigates how stochastic environmental fluctuations influence population extinction times, revealing a resonant activation phenomenon where certain fluctuation rates minimize extinction time, with implications for ecology and evolution.

Contribution

It introduces a model demonstrating the existence of an optimal environmental fluctuation rate that minimizes population extinction time, expanding understanding of stochastic effects in population dynamics.

Findings

Existence of a fluctuation rate that minimizes extinction time.

Development of a heuristic description of resonant activation.

Application of findings to evolutionary models.

Abstract

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.