# The reduction in fixation probability caused by substitutions at linked loci

Barton NH. 1994. The reduction in fixation probability caused by substitutions at linked loci. Genetical Research. 64(3), 199–208.

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Abstract

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 S0016672300032857inline1, 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 S0016672300032857inline2, fixation probability is much higher than for a neutral allele, but much lower than in the absence of hitch-hiking S0016672300032857inline3. These results suggest that hitch-hiking may substantially impede the accumulation of weakly favoured adaptations.

Publishing Year

Date Published

1994-12-01

Journal Title

Genetical Research

Volume

64

Issue

3

Page

199 - 208

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### Cite this

Barton NH. The reduction in fixation probability caused by substitutions at linked loci.

*Genetical Research*. 1994;64(3):199-208. doi:10.1017/S0016672300032857Barton, N. H. (1994). The reduction in fixation probability caused by substitutions at linked loci.

*Genetical Research*. Cambridge University Press. https://doi.org/10.1017/S0016672300032857Barton, Nicholas H. “The Reduction in Fixation Probability Caused by Substitutions at Linked Loci.”

*Genetical Research*. Cambridge University Press, 1994. https://doi.org/10.1017/S0016672300032857 .N. H. Barton, “The reduction in fixation probability caused by substitutions at linked loci,”

*Genetical Research*, vol. 64, no. 3. Cambridge University Press, pp. 199–208, 1994.Barton, Nicholas H. “The Reduction in Fixation Probability Caused by Substitutions at Linked Loci.”

*Genetical Research*, vol. 64, no. 3, Cambridge University Press, 1994, pp. 199–208, doi:10.1017/S0016672300032857 .