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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
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.

Research Article
Copyright © Cambridge University Press 1974



Bodmer, W. F. (1960). Discrete stochastic processes in population genetics. Journal of the Royal Statistical Society B 22, 218244.Google Scholar
Bodmer, W. F. & Felsenstein, J. (1967). Linkage and selection: theoretical analysis of the deterministic two locus random mating model. Genetics 57, 237265.Google ScholarPubMed
Bodmer, W. F. & Parsons, P. A. (1962). Linkage and recombination in evolution. Advances in Genetics 11, 1100.Google Scholar
Feller, W. (1951). Diffusion processes in genetics. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 227246.Google Scholar
Hill, W. G. (1968). Population dynamics of linked genes in finite populations. Proceedings of the XIIth International Congress of Genetics, vol. ii, pp. 146147.Google Scholar
Hill, W. G. (1969). Maintenance of segregation at linked genes in finite populations. Proceedings of the XIIth International Congress of Genetics, vol. iii (Japanese Journal of Genetics 44, supplement 1), pp. 144151.Google Scholar
Hill, W. G. & Robertson, A. (1968). Linkage disequilibrium in finite populations. Theoretical and Applied Genetics 38, 226231.CrossRefGoogle ScholarPubMed
Karlin, S. & McGregor, J. (1964). On some stochastic models in genetics. In Stochastic Models in Medicine and Biology (ed. Gurland, J.), pp. 245279. Madison: University of Wisconsin Press.Google Scholar
Karlin, S. & McGregor, J. (1972). Polymorphisms for genetic and ecological systems with weak coupling. Theoretical Population Biology 3, 210238.CrossRefGoogle ScholarPubMed
Kimura, M. (1956). A model of a genetic system which leads to closer linkage under natural selection. Evolution 10, 278287.CrossRefGoogle Scholar
Kimura, M. & Ohta, T. (1971). Theoretical aspects of population genetics. Monographs in Population Biology, no. 4. Princeton: Princeton University Press.Google Scholar
Levin, B. R. (1969). Simulation of genetic systems. In Computer Applications in Genetics (ed. Morton, N. E.), pp. 2846. Honolulu: University of Hawaii Press.Google Scholar
Lewontin, R. C. & Kojima, K. (1960). The evolutionary dynamics of complex polymorphisms. Evolution 14, 116129.Google Scholar
May, R. (1973). Stability in randomly fluctuating versus deterministic environments. American Naturalist 107, 621650.CrossRefGoogle Scholar
Norman, M. F. (1972). Markov processes and learning models. Mathematics in Science and Engineering, vol. 84. New York and London: Academic Press.Google Scholar
Ohta, T. & Kimura, M. (1969 a). Linkage disequilibrium due to random genetic drift. Genetical Research 13, 4755.CrossRefGoogle Scholar
Ohta, T. & Kimura, M. (1969 b). Linkage disequilibrium at steady state determined by random genetic drift and recurrent mutation. Genetics 63, 229238.Google ScholarPubMed
Ohta, T. & Kimura, M. (1971). Behaviour of neutral mutants influenced by associated over-dominant loci in finite populations. Genetics 69, 247260.Google Scholar
Robertson, A. (1970). The reduction of fitness from genetic drift at heterotic loci in small populations. Genetical Research 15, 257259.CrossRefGoogle ScholarPubMed
Roux, C. Z. (1974). Hardy-Weinberg equilibria in random mating populations. Theoretical Population Biology 5, 393416.CrossRefGoogle ScholarPubMed
Smith, C. A. B. (1969). Local fluctuations in gene frequencies. Annals of Human Genetics 32, 251260.CrossRefGoogle ScholarPubMed
Sved, J. A. (1968). The stability of linked systems of loci with a small population size. Genetics 59, 543563.Google ScholarPubMed
Sved, J. A. (1972). Heterosis at the level of the chromosome and at the level of the gene. Theoretical Population Biology 3, 491506.CrossRefGoogle ScholarPubMed
Sved, J. A. & Feldman, M. W. (1973). Correlation and probability methods for one or two loci. Theoretical Population Biology 4, 129132.CrossRefGoogle ScholarPubMed