# Fixation Time for Competing Beneficial Mutations and Their Genomic Footprint

## TL;DR

This paper studies how beneficial mutations interact and spread in populations, showing how recombination can speed up their fixation and leave detectable genomic patterns.

## Contribution

A mathematical model is introduced to estimate fixation times of overlapping beneficial mutations and their genomic signatures.

## Key findings

- Interference between beneficial mutations is strongest when the initial frequency of the first mutation is below 0.1.
- Recombination can speed up fixation when the recombination rate exceeds a threshold.
- Strong interference leads to an excess of intermediate-frequency variants at neutral sites between selected loci.

## Abstract

Knowing how fast natural selection can act on changes in the environment is fundamental for understanding evolution. The time it takes for a beneficial mutation to spread through a natural population has been investigated thoroughly in the history of population genetics and evolutionary biology. In this study the focus is on the interaction between beneficial mutations during their way through a population. The traditional view has been that beneficial mutations occur sequentially such that there is at most one of them on a chromosome on its way through a population at a time. The question, however, is what happens when they overlap. Do they compete with each other? Another notion is that in some circumstances they may recombine with each other such that their chance to spread through a population is increased. A mathematical model is presented to estimate the time until two overlapping beneficial mutations recombine and go to fixation; i.e., sweep together through an entire population. These dynamics are then linked to characteristic genomic patterns that may be observed in DNA sequencing studies.

For a highly beneficial mutation A at locus 1 spreading in a very large population, we have analyzed the scenario that at a closely linked locus 2 a second beneficial mutant B arises before A has fixed. Under the assumptions that the fitness of B is greater than that of A and that A- and B-carrying chromosomes can recombine at some rate r, recombinants AB may form and eventually fix. We present explicit formulas for the fixation time of AB under additive fitness of the mutants as a function of the frequency X20  of A at the time when B is introduced. Our analysis suggests that the effect of interference between the beneficial mutations is most pronounced for small values of X20<0.1. Furthermore, we identify a threshold value for r, above which recombination speeds up fixation. Using published simulation data, we also describe the genomic footprint of competing beneficial mutations. At neutral sites between the two linked selected loci, an excess of intermediate-frequency variants may occur when interference is strong, i.e., X20 small. Finally, we discuss under which circumstances this scenario may be encountered in real sequences from recombining genomic regions.