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 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 the coefficient of variation can be substantial even in very large populations. Th...