Time to fixation in the presence of recombination

TL;DR

This paper develops an analytical approach to determine the fixation time in a recombining haploid population, revealing how epistasis and recombination rate influence evolutionary dynamics.

Contribution

It introduces a new analytical method to calculate fixation time considering various epistasis types in a recombining population.

Findings

Fixation time decreases with high recombination under negative epistasis.

Fixation time increases with recombination under positive epistasis.

Fixation time diverges near a critical recombination rate in compensatory mutations.

Abstract

We study the evolutionary dynamics of a haploid population of infinite size recombining with a probability $r$ in a two locus model. Starting from a low fitness locus, the population is evolved under mutation, selection and recombination until a finite fraction of the population reaches the fittest locus. An analytical method is developed to calculate the fixation time $T$ to the fittest locus for various choices of epistasis. We find that (1) for negative epistasis, $T$ decreases slowly for small $r$ but decays fast at larger $r$ (2) for positive epistasis, $T$ increases linearly for small $r$ and mildly for large $r$ (3) for compensatory mutation, $T$ diverges as a power law with logarithmic corrections as the recombination fraction approaches a critical value. Our calculations are seen to be in good agreement with the exact numerical results.