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Uncorrelated genetic drift of gene frequencies and linkage disequilibrium in some models of linked overdominant polymorphisms

Published online by Cambridge University Press:  14 April 2009

Joseph Felsenstein
Joseph Felsenstein
Affiliation:
Department of Genetics, University of Washington, Seattle, Washington 98195
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For large population sizes, gene frequencies p and q at two linked over-dominant loci and the linkage disequilibrium parameter D will remain close to their equilibrium values. We can treat selection and recombination as approximately linear forces on p, q and D, and we can treat genetic drift as a multivariate normal perturbation with constant variance-covariance matrix. For the additive-multiplicative family of two-locus models, p, q and D are shown to be (approximately) uncorrelated. Expressions for their variances are obtained. When selection coefficients are small the variances of p and q are those previously given by Robertson for a single locus. For small recombination fractions the variance of D is that obtained for neutral loci by Ohta & Kimura. For larger recombination fractions the result differs from theirs, so that for unlinked loci r2 ≃ 2/(3N) instead of 1/(2N). For the Lewontin-Kojima and Bodmer symmetric viability models, and for a model symmetric at only one of the loci, a more exact argument is possible. In the asymptotic conditional distribution in these cases, various of p, q and D are uncorrelated, depending on the type of symmetiy in the model.

Type
Research Article
Information
Genetics Research , Volume 24 , Issue 3 , December 1974 , pp. 281 - 294
Copyright
Copyright © Cambridge University Press 1974

References

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