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

  • Joseph Felsenstein (a1)

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.

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W. G. Hill & A. Robertson (1968). Linkage disequilibrium in finite populations. Theoretical and Applied Genetics 38, 226231.

R. May (1973). Stability in randomly fluctuating versus deterministic environments. American Naturalist 107, 621650.

C. A. B. Smith (1969). Local fluctuations in gene frequencies. Annals of Human Genetics 32, 251260.

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Genetics Research
  • ISSN: 0016-6723
  • EISSN: 1469-5073
  • URL: /core/journals/genetics-research
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