Extinction dynamics from meta-stable coexistences in an evolutionary game

TL;DR

This paper uses a classical mechanics approach to analyze how stochastic fluctuations cause the extinction of coexisting types in evolutionary games, revealing that abundance influences extinction likelihood and that the WKB method accurately predicts extinction sequences.

Contribution

It introduces a novel application of the WKB approximation to predict extinction trajectories in stochastic evolutionary game dynamics.

Findings

More abundant types tend to go extinct first.

Distance to extinction point does not predict extinction order.

WKB method accurately predicts which type goes extinct first.

Abstract

Deterministic evolutionary game dynamics can lead to stable coexistences of different types. Stochasticity, however, drives the loss of such coexistences. This extinction is usually accompanied by population size fluctuations. We investigate the most probable extinction trajectory under such fluctuations by mapping a stochastic evolutionary model to a problem of classical mechanics using the Wentzel-Kramers-Brillouin (WKB) approximation. Our results show that more abundant types in a coexistence can be more likely to go extinct first well agreed with previous results, and also the distance between the coexistence and extinction point is not a good predictor of extinction. Instead, the WKB method correctly predicts the type going extinct first.