Population extinction in a fluctuating environment

TL;DR

This paper investigates how environmental noise influences the mean time to extinction of populations, using a stochastic birth-death model with colored Gaussian noise, revealing different population-size dependencies based on noise correlation.

Contribution

It introduces a path integral approach to evaluate mean time to extinction and identifies the impact of noise correlation on population extinction dynamics.

Findings

Mean time to extinction depends on noise correlation time.

Population-size dependence shifts from exponential to power law.

Limits of white and adiabatic noise are characterized.

Abstract

Environmental noise can cause an exponential reduction in the mean time to extinction (MTE) of an isolated population. We study this effect on an example of a stochastic birth-death process with rates modulated by a colored Gaussian noise. A path integral formulation yields a transparent way of evaluating the MTE and finding the optimal realization of the environmental noise that determines the most probable path to extinction. The population-size dependence of the MTE changes from exponential in the absence of the environmental noise to a power law for a short-correlated noise and to no dependence for long-correlated noise. We also establish the validity domains of the limits of white noise and adiabatic noise.