Another look at multiplicative models in quantitative genetics

Abstract

This paper reviews basic theory and features of the multiplicative model of gene action. A formal decomposition of the mean and of the genotypic variance is presented. Connections between the statistical parameters of this model and those of the factorial decomposition into additive, dominance and epistatic effects are also emphasized. General formulae for the genotypic covariance among inbred relatives are given in the case of linkage equilibrium. It is shown that neglecting the epistatic components of variation makes the multiplicative model a pseudo-additive one, since this approximation does not break the strong dependency between mean and variance effects. Similarities and differences between the classical polygenic 'additive-dominance' and the multiplicative gene action approaches are outlined and discussed. Numerical examples for the biallelic case are produced to illustrate that comparison.