Genetical Research

Research Article

Linkage disequilibrium due to random genetic drift*

Tomoko Ohtaa1 and Motoo Kimuraa1

a1 National Institute of Genetics, Mishima, Japan

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.

(Received June 21 1968)


* Contribution no. 691 from the National Institute of Genetics, Mishima, Shizuoka-ken, Japan.

† Supported by a post-doctoral fellowship from the Japan Society for the Promotion of Science.