Extinction time distributions of populations and genotypes

TL;DR

This paper investigates the distributions of extinction times in populations, exploring various scenarios and stochastic influences, and proposes criteria for classifying systems based on their extinction dynamics.

Contribution

It provides a comprehensive survey of extinction time distributions across different population dynamics and introduces criteria for distinguishing underlying extinction mechanisms.

Findings

Gumbel distribution as a universal asymptotic for extinction times

Criteria for classifying systems based on extinction dynamics

Analysis of demographic and environmental stochasticity effects

Abstract

In the long run, the eventual extinction of any biological population is an inevitable outcome. While extensive research has focused on the average time it takes for a population to go extinct under various circumstances, there has been limited exploration of the distributions of extinction times and the likelihood of significant fluctuations. Recently, Hathcock and Strogatz [PRL 128, 218301 (2022)] identified Gumbel statistics as a universal asymptotic distribution for extinction-prone dynamics in a stable environment. In this study, we aim to provide a comprehensive survey of this problem by examining a range of plausible scenarios, including extinction-prone, marginal (neutral), and stable dynamics. We consider the influence of demographic stochasticity, which arises from the inherent randomness of the birth-death process, as well as cases where stochasticity originates from the more pronounced effect of random environmental variations. Our work proposes several generic criteria that can be used for the classification of experimental and empirical systems, thereby enhancing our ability to discern the mechanisms governing extinction dynamics. By employing these criteria, we can improve our understanding of the underlying mechanisms driving extinction processes.