Genetic variance under assortative mating in the infinitesimal model

抄録

The genetic variance of a quantitative trait changes under assortative mating, where the phenotypes of the mates in the trait are correlated. The change is caused by build-up of linkage disequilibria generated due to the genetic similarity between mates. In this paper the change in the genetic variance under assortative mating is investigated using a genetic approach based on the infinitesimal model. Assuming that the genetic effect of each locus is of order n ^-1/2, where n is the number of loci involved, and formulating the choice of the mate as a selecting function, the linkage disequilibiria are evaluated under repeated cycles of assortative mating. The recursive formula for the genetic variance given by Bulmer (1980), based on the regression of the genetic value of offspring to those of the parents, is obtained by an alternative approach taking the linkage disequilibria into account. This approach can be applied to the case of multiple traits, where two or more traits are simultaneously involved in the assortative mating. A recursive formula for the genetic covariance matrix of multiple traits under assortative mating, which was given by Tallis and Leppard (1987b) based on a statistical approach, is derived using genetic arguments similar to the case of a single trait. It is shown that the equilibrium values of genetic variance of a trait under assortative mating involving the other traits along with the trait are different from those under assortative mating based on the trait alone. In a natural population it is expected that assortative mating is practiced for multiple traits. Thus, multiple traits should be jointly analyzed in research on assortative mating.