Cooperation dilemma in finite populations under fluctuating environments

TL;DR

This paper introduces a new analytical approach to study how fluctuating environmental factors influence the likelihood of cooperation fixation in populations, revealing that extrinsic noise can significantly promote cooperation.

Contribution

The authors develop a semiclassical method to analyze rare fixation events under environmental fluctuations, extending previous population genetics models to include extrinsic noise effects.

Findings

Extrinsic noise can greatly increase cooperation fixation probability.

Environmental fluctuations can alter the dependence of fixation probability on population size.

The approach provides insights into how extrinsic factors promote cooperation in evolutionary dynamics.

Abstract

We present a novel approach allowing the study of rare events like fixation under fluctuating environments, modeled as extrinsic noise, in evolutionary processes characterized by the dominance of one species. Our treatment consists of mapping the system onto an auxiliary model, exhibiting metastable species coexistence, that can be analyzed semiclassically. This approach enables us to study the interplay between extrinsic and demographic noise on the statistics of interest. We illustrate our theory by considering the paradigmatic prisoner's dilemma game whose evolution is described by the probability that cooperators fixate the population and replace all defectors. We analytically and numerically demonstrate that extrinsic noise may drastically enhance the cooperation fixation probability and even change its functional dependence on the population size. These results, which generalize earlier works in population genetics, indicate that extrinsic noise may help sustain and promote a much higher level of cooperation than static settings.