Stochastic models of population extinction

TL;DR

This paper reviews stochastic models of population extinction, highlighting how demographic and environmental stochasticity influence extinction times and pathways, with recent focus on environmental noise autocorrelation and advanced analytical tools from physics.

Contribution

It synthesizes recent advances in stochastic population models, emphasizing the impact of environmental noise structure and new analytical methods for understanding extinction dynamics.

Findings

Extinction time increases exponentially with population size due to demographic stochasticity.

Environmental noise autocorrelation ('color') significantly affects extinction probabilities.

Advanced physics-based tools improve predictions of extinction pathways.

Abstract

Theoretical ecologists have long sought to understand how the persistence of populations depends on biotic and abiotic factors. Classical work showed that demographic stochasticity causes the mean time to extinction to increase exponentially with population size, whereas variation in environmental conditions can lead to a power law scaling. Recent work has focused especially on the influence of the autocorrelation structure ("color") of environmental noise. In theoretical physics, there is a burst of research activity in analyzing large fluctuations in stochastic population dynamics. This research provides powerful tools for determining extinction times and characterizing the pathway to extinction. It yields, therefore, sharp insights into extinction processes and has great potential for further applications in theoretical biology.