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Linkage disequilibrium due to random genetic drift*

  • Tomoko Ohta (a1) and Motoo Kimura (a1)
  • DOI:
  • Published online: 01 April 2009

The behaviour of linkage disequilibrium between two segregating loci in finite populations has been studied as a continuous stochastic process for different intensity of linkage, assuming no selection. By the method of the Kolmogorov backward equation, the expected values of the square of linkage disequilibrium z2, and other two quantities, xy(1 − x) (1 − y) and z(1 − 2x) (1 − 2y), were obtained in terms of T, the time measured in Ne as unit, and R, the product of recombination fraction (c) and effective population number (Ne). The rate of decrease of the simultaneous heterozygosity at two loci and also the asymptotic rate of decrease of the probability for the coexistence of four gamete types within a population were determined. The eigenvalues λ1, λ2 and λ3 related to the stochastic process are tabulated for various values of R = Nec.

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W. G. Hill & A. Robertson (1968). Linkage disequilibrium in finite populations. Theor. Appl. Genet. 38, 226231.

M. Kimura (1955). Solution of a process of random genetic drift with a continuous model. Proc. natn. Acad. Sci. U.S.A.41, 144150.

M. Kimura (1956). A model of a genetic system which leads to closer linkage by natural selection. Evolution 10, 278287.

M. Kimura (1957). Some problems of stochastic processes in genetics. Ann. Math. Statist. 28, 882901.

M. Kimura (1963). A probability method for treating inbreeding systems, especially with linked genes. Biometrics 19, 117.

M. Kimura (1964). Diffusion models in population genetics. Jour. Applied Probability, 1, 177232.

M. Kimura & J. F. Crow (1963). The measurement of effective population number. Evolution 17, 279288.

R. C. Lewontin & K. Kojima (1960). The evolutionary dynamics of complex polymorphisms. Evolution 14, 458472.

T. Ohta (1968). Effect of initial linkage disequilibrium and epistasis on fixation probability in a small population, with two segregating loci. Theor. Appl. Genet. 38, 243248.

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Genetics Research
  • ISSN: 0016-6723
  • EISSN: 1469-5073
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