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

SUMMARY For large population sizes, gene frequenciespandqat two linked over-dominant loci and the linkage disequilibrium parameterDwill remain close to their equilibrium values. We can treat selection and recombination as approximately linear forces onp, qandD, 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, qandDare shown to be (approximately) uncorrelated. Expressions for their variances are obtained. When selection coefficients are small the variances ofpandqare those previously given by Robertson for a single locus. For small recombination fractions the variance ofDis 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 ofp, qandDare uncorrelated, depending on the type of symmetiy in the model.