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The reduction in fixation probability caused by substitutions at linked loci

Published online by Cambridge University Press:  14 April 2009

N. H. Barton
N. H. Barton
Affiliation:
Institute of Cell, Animal and Population Biology, University of Edinburgh, Kings' Buildings, Edinburgh EH9 3JT, UK
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The probability of fixation of a mutation with selective advantage s will be reduced by substitutions at other loci. The effect of a single substitution, with selective advantage , can be approximated as a sudden reduction in the frequency of the favourable allele, by a fraction w = 1 −(s/S)r/s (where r is the recombination rate). An expression for the effect of a given sequence of such catastrophes is derived. This also applies to the ecological prxoblem of finding the probability that a small population will survive, despite occasional disasters. It is shown that if substitutions occur at a rate Δ, and are scattered randomly over a genetic map of length R, then an allele is unlikely to be fixed if its advantage is less than a critical value, Scrit = (π2/6)(2ΔS/(Rlog(S/s))). This threshold depends primarily on the variance in fitness per unit map length dueto substitutions, var(W)/R = 2ΔS/R. With no recombination, the fixation probability can be calculated for a finite population. If Δ > s, it is of the same order as for a neutral allele ( ≈ Δ/(2N(Δ−s))), whilst if , fixation probability is much higher than for a neutral allele, but much lower than in the absence of hitch-hiking . These results suggest that hitch-hiking may substantially impede the accumulation of weakly favoured adaptations.

Type
Research Article
Information
Genetics Research , Volume 64 , Issue 3 , December 1994 , pp. 199 - 208
Copyright
Copyright © Cambridge University Press 1994

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