Derivation and Estimation of Variance and Covariance Components Associated with Covariance between Relatives under Sexlinked Transmission

Abstract

Kempthorne [1954] solved the general problem of partitioning the total genotypic variance and obtaining the genotypic covariance between relatives with arbitrary numbers of loci and alleles and with arbitrary dominance and epistasis. The chief objective of this study is to partition the total genotypic variances for male and female into their respective constituents, to construct the general structures of the covariances between two members of the same sex or different sexes with joint consideration of sexlinked and autosomal genes, to develop procedures for estimating the components of genetic variances and covariances from the analysis of variance and to derive the heritability estimators under the assumption of both sexlinked and autosomnal inheritance. Probability arguments will be used to derive the algebraic expressions for the covariances among relatives. The development refers to bisexual diploid organisms with males as the heterogametic sex. Throughout this paper the subscripts (superscripts) m and f will pertain to male and female respectively.