Rare events in population genetics: Stochastic tunneling in a two-locus model with recombination

TL;DR

This paper investigates how finite population size and recombination influence the time it takes for a population to acquire a beneficial double mutation, revealing non-monotonic and exponential growth patterns in escape times.

Contribution

It introduces a detailed analysis of stochastic tunneling in a two-locus model, highlighting the effects of recombination and population size on escape times.

Findings

Escape times are highly variable in small populations due to demographic noise.

Mean escape time exhibits a non-monotonic dependence on recombination rate.

Beyond a critical recombination rate, escape times grow exponentially with population size.

Abstract

We study the evolution of a population in a two-locus genotype space, in which the negative effects of two single mutations are overcompensated in a high fitness double mutant. We discuss how the interplay of finite population size, $N$, and sexual recombination at rate $r$ affects the escape times $t_\mathrm{esc}$ to the double mutant. For small populations demographic noise generates massive fluctuations in $t_\mathrm{esc}$. The mean escape time varies non-monotonically with $r$, and grows exponentially as $\ln t_{\mathrm{esc}} \sim N(r - r^\ast)^{3/2}$ beyond a critical value $r^\ast$.