Sojourn times and fixation dynamics in multi-player games with fluctuating environments

Joseph W. Baron; Tobias Galla

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arXiv · 1612.05530

Sojourn times and fixation dynamics in multi-player games with fluctuating environments

Joseph W. Baron·Tobias Galla

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Abstract

We study evolutionary multi-player games in finite populations, subject to fluctuating environments. The population undergoes a birth-death process with absorbing states, and the environment follows a Markovian process, resulting in a fluctuating payoff matrix for the evolutionary game. Our focus is on the fixation or extinction of a single mutant in a population of wildtypes. We show that the nonlinear nature of fitnesses in multi-player games gives rise to an intricate interplay of selection, genetic drift and environmental fluctuations. This generates effects not seen in simpler two-player games. To analyse trajectories towards fixation we analytically calculate sojourn times for general birth-death processes in populations of two types of individuals and in fluctuating environments.

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Joseph W. Baron, Tobias Galla. 2016-12-16. Sojourn times and fixation dynamics in multi-player games with fluctuating environments. https://arxiv.org/abs/1612.05530

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