Public goods games in populations with fluctuating size

TL;DR

This paper explores how fluctuating population sizes influence evolutionary game dynamics, revealing that cooperation can promote survival, but defectors tend to drive populations to extinction unless balanced by mutation and selection.

Contribution

It introduces a model of evolutionary game dynamics with variable population size, highlighting the complex interplay between cooperation, defection, and population survival.

Findings

Cooperators can enable long-term survival if selection is strong.

Defectors tend to drive populations to extinction without cooperation.

Selection can increase cooperator abundance but decrease their relative frequency.

Abstract

Many mathematical frameworks of evolutionary game dynamics assume that the total population size is constant and that selection affects only the relative frequency of strategies. Here, we consider evolutionary game dynamics in an extended Wright-Fisher process with variable population size. In such a scenario, it is possible that the entire population becomes extinct. Survival of the population may depend on which strategy prevails in the game dynamics. Studying cooperative dilemmas, it is a natural feature of such a model that cooperators enable survival, while defectors drive extinction. Although defectors are favored for any mixed population, random drift could lead to their elimination and the resulting pure-cooperator population could survive. On the other hand, if the defectors remain, then the population will quickly go extinct because the frequency of cooperators steadily declines and defectors alone cannot survive. In a mutation-selection model, we find that (i) a steady supply of cooperators can enable long-term population survival, provided selection is sufficiently strong, and (ii) selection can increase the abundance of cooperators but reduce their relative frequency. Thus, evolutionary game dynamics in populations with variable size generate a multifaceted notion of what constitutes a trait's long-term success.