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

  • Joseph Felsenstein (a1)
Summary
SUMMARY

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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Bodmer W. F. (1960). Discrete stochastic processes in population genetics. Journal of the Royal Statistical Society B 22, 218244.
Bodmer W. F. & Felsenstein J. (1967). Linkage and selection: theoretical analysis of the deterministic two locus random mating model. Genetics 57, 237265.
Bodmer W. F. & Parsons P. A. (1962). Linkage and recombination in evolution. Advances in Genetics 11, 1100.
Feller W. (1951). Diffusion processes in genetics. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 227246.
Hill W. G. (1968). Population dynamics of linked genes in finite populations. Proceedings of the XIIth International Congress of Genetics, vol. ii, pp. 146147.
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.
Hill W. G. & Robertson A. (1968). Linkage disequilibrium in finite populations. Theoretical and Applied Genetics 38, 226231.
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.
Karlin S. & McGregor J. (1972). Polymorphisms for genetic and ecological systems with weak coupling. Theoretical Population Biology 3, 210238.
Kimura M. (1956). A model of a genetic system which leads to closer linkage under natural selection. Evolution 10, 278287.
Kimura M. & Ohta T. (1971). Theoretical aspects of population genetics. Monographs in Population Biology, no. 4. Princeton: Princeton University Press.
Levin B. R. (1969). Simulation of genetic systems. In Computer Applications in Genetics (ed. Morton N. E.), pp. 2846. Honolulu: University of Hawaii Press.
Lewontin R. C. & Kojima K. (1960). The evolutionary dynamics of complex polymorphisms. Evolution 14, 116129.
May R. (1973). Stability in randomly fluctuating versus deterministic environments. American Naturalist 107, 621650.
Norman M. F. (1972). Markov processes and learning models. Mathematics in Science and Engineering, vol. 84. New York and London: Academic Press.
Ohta T. & Kimura M. (1969 a). Linkage disequilibrium due to random genetic drift. Genetical Research 13, 4755.
Ohta T. & Kimura M. (1969 b). Linkage disequilibrium at steady state determined by random genetic drift and recurrent mutation. Genetics 63, 229238.
Ohta T. & Kimura M. (1971). Behaviour of neutral mutants influenced by associated over-dominant loci in finite populations. Genetics 69, 247260.
Robertson A. (1970). The reduction of fitness from genetic drift at heterotic loci in small populations. Genetical Research 15, 257259.
Roux C. Z. (1974). Hardy-Weinberg equilibria in random mating populations. Theoretical Population Biology 5, 393416.
Smith C. A. B. (1969). Local fluctuations in gene frequencies. Annals of Human Genetics 32, 251260.
Sved J. A. (1968). The stability of linked systems of loci with a small population size. Genetics 59, 543563.
Sved J. A. (1972). Heterosis at the level of the chromosome and at the level of the gene. Theoretical Population Biology 3, 491506.
Sved J. A. & Feldman M. W. (1973). Correlation and probability methods for one or two loci. Theoretical Population Biology 4, 129132.
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Genetics Research
  • ISSN: 0016-6723
  • EISSN: 1469-5073
  • URL: /core/journals/genetics-research
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