# The probability of fixation of a favoured allele in a subdivided population

Barton NH. 1993. The probability of fixation of a favoured allele in a subdivided population. Genetics Research. 62(2), 149–158.

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Abstract

In a stably subdivided population with symmetric migration, the chance that a favoured allele will be fixed is independent of population structure. However, random extinction introduces an extra component of sampling drift, and reduces the probability of fixation. In this paper, the fixation probability is calculated using the diffusion approximation; comparison with exact solution of the discrete model shows this to be accurate. The key parameters are the rates of selection, migration and extinction, scaled relative to population size (S = 4Ns, M = 4Nm, Λ = 4Nλ); results apply to a haploid model, or to diploids with additive selection. If new colonies derive from many demes, the fixation probability cannot be reduced by more than half. However, if colonies are initially homogeneous, fixation probability can be much reduced. In the limit of low migration and extinction rates (M, Λ 1), it is 2s/{1 + (Λ/MS)(1 −exp(−S))}, whilst in the opposite limit (S 1), it is 4sM/{Λ(Λ + M)}. In the limit of weak selection (M, Λ 1), it is 4sM/{Λ(Λ + M)}. These factors are not the same as the reduction in effective population size (Ne/N), showing that the effects of population structure on selected alleles cannot be understood from the behaviour of neutral markers.

Publishing Year

Date Published

1993-10-01

Journal Title

Genetics Research

Acknowledgement

This work was supported by grants from the SERC (GR/H/09928) and NERC (GR/3/8002), and by the Darwin Trust of Edinburgh. Thanks are due to B. Nürnberger for convincing me that population structure does reduce fixation probability, to M. Whitlock for discussions on calculations of effective population size, and to W. G. Hill, P. Keightley and the anonymous referees for their comments.

Volume

62

Issue

2

Page

149 - 158

ISSN

IST-REx-ID

### Cite this

Barton NH. The probability of fixation of a favoured allele in a subdivided population.

*Genetics Research*. 1993;62(2):149-158. doi:10.1017/S0016672300031748Barton, N. H. (1993). The probability of fixation of a favoured allele in a subdivided population.

*Genetics Research*. Cambridge University Press. https://doi.org/10.1017/S0016672300031748Barton, Nicholas H. “The Probability of Fixation of a Favoured Allele in a Subdivided Population.”

*Genetics Research*. Cambridge University Press, 1993. https://doi.org/10.1017/S0016672300031748.N. H. Barton, “The probability of fixation of a favoured allele in a subdivided population,”

*Genetics Research*, vol. 62, no. 2. Cambridge University Press, pp. 149–158, 1993.Barton, Nicholas H. “The Probability of Fixation of a Favoured Allele in a Subdivided Population.”

*Genetics Research*, vol. 62, no. 2, Cambridge University Press, 1993, pp. 149–58, doi:10.1017/S0016672300031748.**All files available under the following license(s):**

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