Covariance of inbred relatives with special reference to selfing

The covariance of inbred relatives from a population in linkage and identity equilibrium in the presence of dominance and epistasis is formulated using a similar procedure to that which B. S. Weir and C. C. Cockerham used to derive a general expression for the genotypic variance. An alternative model based on the description of a genotype in terms of the homozygotes of its constituent alleles is defined which leads to an equivalent set of 21 quadratic components, but when the relatives are descended from a common ancestor by selfing some confounding occurs and only 12 are necessary. This covariance can be subdivided into components arising among families at different levels of the hierarchy generated by a selfing series, and the component among descendants of distinct members of the base population has a different form from those arising at lower levels of the hierarchy. The 12 quadratic components together with an error variance can be estimated using the 20 statistics provided by analyses of variance and covariance of families generated by four generations of selfing.