The fixation probability and time for a doubly beneficial mutant

TL;DR

This paper analyzes the probability and time for a doubly beneficial mutant to fix in a population, considering the effects of recombination and large selection coefficients.

Contribution

It provides a convergence result for the fixation probability and time of the double mutant under specific beneficial conditions and recombination.

Findings

Fixation probability converges for large selection coefficients.

Fixation time is characterized under recombination.

Double beneficial mutants can successfully fix under certain conditions.

Abstract

For a highly beneficial mutant $A$ entering a randomly reproducing population of constant size, we study the situation when a second beneficial mutant $B$ arises before $A$ has fixed. If the selection coefficient of $B$ is greater than the selection coefficient of $A$, and if $A$ and $B$ can recombine at some rate $\rho$, there is a chance that the double beneficial mutant $AB$ forms and eventually fixes. We give a convergence result for the fixation probability of $AB$ and its fixation time for large selection coefficients.