Genotypic covariance matrices and their inverses for models allowing dominance and inbreeding

Abstract

Summary - Dominance models are parameterized under conditions of inbreeding. The properties of an infinitesimal dominance model are reconsidered. It is shown that mixedmodel methodology is justifiable as normality assumptions can be met. Tabular methods for calculating genotypic covariances among inbred relatives are described. These methods employ 5 parameters required to accommodate additivity, dominance and inbreeding. Rules for calculating inverse genotypic covariance matrices are presented. These inverse matrices can be used directly to set up the mixed-model equations. The mixed-model methodology allowing for dominance and inbreeding provides a powerful framework to better explain and utilize the observed variation in quantitative traits.