On the Analysis of Weak Two-locus Viability Selection and Quasi-linkage Equilibrium

Abstract

A model of weak two-locus viability selection, defined by ordinary differential equations, is analyzed. The weak selection is considered as a perturbation of the model without selection. Using the perturbation theory, the estimation of the coefficient D of linkage disequilibrium was determined in terms of usual concepts of the mean effects in quantitative genetics and in terms of singular perturbation theory in mathematics. The results obtained generalize the ones found by Kimura (for two diallelic loci) in the case of multiple alleles and allow standardizing the analysis of weak effects of systematic factors of microevolution in population genetics.