A General Linear Model for the Genotypic Covariance Between Relatives Under Assortative Mating*

A linear model for the genotypic covariance between relatives under assortative mating comprising the "classical linear model" and the model of "selective assortative mating" is proposed. The general conditions on the genetical and developmental mechanisms of quantitative characters, as well as on selection and the mating system, on which the model is based, are explicitly stated and discussed. A classification of different relationships is presented and it is shown that these conditions are sufficient to obtain the genotypic covariance between relatives only if the relationship is a combination of descendant-ancestor, full sib, Type 1 and Nth uncle-niece relationships. All the "traditional" relationships, i.e., those for which the covariances of the relatives have been obtained in the literature, fall into this category. These conditions also ensure that the regression of the individual's genotypic value on the genotypic value or phenotype of any of its ancestors is always linear.