Evolution of continuous variation: direct approach through joint distribution of genotypes and phenotypes.

Abstract

The evolutionary dynamics of the joint distribution of genotypes and phenotypes is studied. The model, originally devised to study the joint effects of Mendelian and other types of transmissions, provides results of interest also to the theory of direct Mendelian transmission with natural selection. Assuming bivariate normal distributions, in the latter case genotypic and phenotypic means and variances, and genotype-phenotype correlation can be expressed recursively as functions of the parameters for the selection, environmental and mutation variance. Equilibria and rates of approach for these moments are calculated. In the presence of selection the heritability, defined as the ratio of expected genotypic to expected phenotypic variance after selection, is greater than that before selection by a predictable amount and that it can be greater than unity.