Fixation Probability for Competing Selective Sweeps

TL;DR

This paper analyzes how the probability of two beneficial mutations both fixing in a population depends on population size and recombination rate, especially when the second mutation confers a larger benefit, revealing a critical parameter $ ho N$.

Contribution

It introduces a new method for calculating the fixation probability of double mutants in large populations considering the impact of population size and recombination rate.

Findings

Fixation probability depends heavily on the product of population size and recombination rate.

For small $ ho N$, the probability of fixation for both mutations is nearly zero.

For large $ ho N$, the mutations' effects on each other are minimal.

Abstract

We consider a biological population in which a beneficial mutation is undergoing a selective sweep when a second beneficial mutation arises at a linked locus and we investigate the probability that both mutations will eventually fix in the population. Previous work has dealt with the case where the second mutation to arise confers a smaller benefit than the first. In that case population size plays almost no role. Here we consider the opposite case and observe that, by contrast, the probability of both mutations fixing can be heavily dependent on population size. Indeed the key parameter is $\rho N$, the product of the population size and the recombination rate between the two selected loci. If $\rho N$ is small, the probability that both mutations fix can be reduced through interference to almost zero while for large $\rho N$ the mutations barely influence one another. The main rigorous result is a method for calculating the fixation probability of a double mutant in the large population limit.