Quantitative character dynamics: Gametic model

Abstract

A gametic model of quantitative character dynamics is introduced that fills the gap between the two existing models: genic and zygotic/phenotypic. In this model, a gamete is treated as the elementary unit of evolution, all biological processes at the levels below gametic remain unspecified, and a gamete is characterized by its effect on the quantitative character rather than by the genotype. The hereditary and developmental processes are accounted for in a generalized form by gametogenetic and developmental functions defined for a pair of gametic effects representing an individual. A parameterization of these functions is suggested that imposes constraints on the heredity of quantitative characters similar to the constraints imposed by traditional genic models. It is shown that this parameterization can be derived for some polygenic additive models. General expressions for the dynamics of the mean and variance of additive quantitative characters are obtained, and the dynamics under random mating for sex-independent, sex-controlled, and sex-linked characters are considered. Comparisons with the dynamics predicted by genic models are made.