Linkage equilibrium in multi-locus genotypic frequencies with mixed selfing and random mating

Abstract

The convergence to linkage equilibrium due to the recombination process is studied in a theoretical model of mixed selfing and random mating. The model assumes an arbitrary number of autosomal loci and considers genetic variation (two alleles at each locus) that is not subject to natural selection. The deviation from linkage equilibrium is given in terms of Bennett disequilibria that measure the deviation from Robbins proportions in the gametes, and these are generalized to disequilibrium measures that describe the deviation of genotypic frequencies from Hardy-Weinberg proportions. Alternatively, the derivation from linkage equilibrium is given in terms of linear measures of gametic and of genotypic disequilibrium. The convergence to linkage equilibrium is dominated by the convergence of the gametic frequencies to Robbins proportions, in that the convergence to the genotypic frequencies characteristic of partial selfing is comparatively rapid. At linkage equilibrium the genotypic frequencies deviate from the Hardy-Weinberg proportions, and the generalized disequilibrium measures describing the derviation from Hardy-Weinberg proportions are closely related to joint inbreeding coefficients for the loci.