Fixation in Evolutionary Games under Non-Vanishing Selection

TL;DR

This paper extends a WKB-based theoretical framework to analyze fixation probabilities and times in evolutionary games with non-vanishing selection, accurately capturing large fluctuations beyond weak selection limits.

Contribution

It generalizes existing theory to include non-vanishing selection, improving predictions of fixation metrics in evolutionary game models.

Findings

Accurately predicts fixation probabilities and times for large fluctuations.

Demonstrates the theory's effectiveness on cooperation dilemma models.

Outperforms Fokker-Planck approximation for finite selection intensity.

Abstract

One of the most striking effect of fluctuations in evolutionary game theory is the possibility for mutants to fixate (take over) an entire population. Here, we generalize a recent WKB-based theory to study fixation in evolutionary games under non-vanishing selection, and investigate the relation between selection intensity w and demographic (random) fluctuations. This allows the accurate treatment of large fluctuations and yields the probability and mean times of fixation beyond the weak selection limit. The power of the theory is demonstrated on prototypical models of cooperation dilemmas with multiple absorbing states. Our predictions compare excellently with numerical simulations and, for finite w, significantly improve over those of the Fokker-Planck approximation.