Fixation probabilities and hitting times under low levels of frequency-dependent selection

TL;DR

This paper derives approximations for fixation probabilities and hitting times in population genetics models with low frequency-dependent selection, extending key evolutionary game theory results to general diffusions.

Contribution

It extends the one-third rule and stochastic slowdown effects to general one-dimensional diffusions in population genetics.

Findings

Derived approximations for fixation probabilities and hitting times.

Extended the one-third rule to general diffusions.

Analyzed effects of stochastic slowdown in allele frequency dynamics.

Abstract

In population genetics, diffusions on the unit interval are often used to model the frequency path of an allele. In this setting we derive approximations for fixation probabilities, expected hitting times and the expected site-frequency-spectrum under small frequency-dependent selection. Specifically, we rederive and extend the one-third rule of evolutionary game theory (Nowak et al., 2004) and effects of stochastic slowdown (Altrock and Traulsen, 2009). Since similar effects are of interest in other application areas, we formulate our results for general one-dimensional diffusions.