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.
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