How Long Does It Take to Fix a Favorable Mutation, and Why Should We Care?

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 formulas are based on deterministic dynamics, leading to inaccuracies at allele frequencies close to 0 or 1. To remedy this problem, the properties of the stochastic phases at either end point of allele frequency need to be analyzed. This article 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.