Fixation in finite populations evolving in fluctuating environments

TL;DR

This paper develops a general theory for fixation probabilities and times in finite populations evolving in environments that change according to a Markov process, revealing how environmental noise can enhance fixation chances.

Contribution

It introduces a comprehensive framework for understanding fixation in fluctuating environments and analyzes how environmental switching influences evolutionary outcomes.

Findings

Environmental switching can increase fixation probability beyond static environments.

Fast and slow environmental fluctuations have distinct effects on stationary distributions.

Dynamic environments can be exploited by mutants to increase fixation chances.

Abstract

The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death events. The rates of these events may vary in time depending on the state of the environment, which follows an independent Markov process. We develop a general theory for the fixation probability of a mutant in a population of wild-types, and for mean unconditional and conditional fixation times. We apply our theory to evolutionary games for which the payoff structure varies in time. The mutant can exploit the environmental noise; a dynamic environment that switches between two states can lead to a probability of fixation that is higher than in any of the individual environmental states. We provide an intuitive interpretation of this surprising effect. We also investigate stationary distributions when mutations are present in the dynamics. In this regime, we find two approximations of the stationary measure. One works well for rapid switching, the other for slowly fluctuating environments.