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. The theoretical formulae give good approximations to
simulations for most parameter sets. The results have implications for
analyses of the effects of selective sweeps on variability at linked
sites. They reveal some areas that need further investigation, to
facilitate a full understanding of selective sweeps.