American Society of Naturalists

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“How long does it take to fix a favorable mutation, and why should we care?”

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Brian Charlesworth (May 2020)

Read the Article (Just Accepted)

Evolutionary change under natural selection often involves the spread of a beneficial mutation in a gene throughout a population, replacing the ancestral state of the gene. In order to understand how evolution works, it is important to know how long it takes for this process to occur. This question was investigated by mathematical modeling early in the twentieth century. The results showed that the time involved is usually a relatively small multiple of the effect of the mutation on fitness, which helped to convince biologists of the importance of natural selection. If it had turned out that a new mutation would take millions of generations to spread to a high frequency within a population from a very low starting frequency, there would be serious doubts about natural selection as a cause of evolution.

But these results assumed that random fluctuations in the frequency of a mutation can be ignored, provided that the population size was large enough. When a mutation is either very rare or very common, however, such fluctations occur even in a very large population. Their effects can be determined by simple approximations, which yield formulae for both the mean and the amount of variability in the time taken for a mutation to spread through a population. While the classical results are still largely valid, the new findings have implications for contemporary work, in which researchers are trying to infer the action of selection from data on variation in DNA sequences among individuals within a species.


Abstract

The time taken for a selectively favorable allele to spread through a single population was investigated early in the history of population genetics. The resulting formulae are based on deterministic dynamics, leading to inaccuracies at allele frequencies close to zero or one. To remedy this problem, the properties of the stochastic phases at either endpoint of allele frequency need to be analysed. This paper uses a heuristic approach to determining the expected times spent in the stochastic and deterministic phases of allele frequency trajectories, for a model of weak selection at a single locus that is valid for inbreeding populations and for autosomal and sex-linked inheritance. The net fixation time is surprisingly insensitive to the level of dominance of a favorable mutation, even with random mating. Approximate expressions for the variance of the net fixation time are also obtained, which imply that there can be substantial stochastic effects even in very large populations. The accuracy of the approximations was evaluated by comparisons with computer simulations. The results reveal some areas that need further investigation, if a full understanding of selective sweeps is to be obtained, notably the possibility that fixations of slightly deleterious mutations may be affecting variability at closely linked sites.