Linkage disequilibrium due to random genetic drift

Abstract

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 disequilibriumz2, and other two quantities,xy(1 −x) (1 −y) andz(1 − 2x) (1 − 2y), were obtained in terms ofT, the time measured inNeas unit, andR, 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, λ2and λ3related to the stochastic process are tabulated for various values ofR=Nec.