Relationships Among Sires in Estimating Genetic Variance

A method to account for relationships among sires in estimating covariance among paternal half-sibs and heritability is described. The reduction in sum of squares from fitting sire effects after eliminating all other effects in the model is divided by the sum of products of elements of the matrix of coefficients after absorption and elements of the matrix of relationships among sires rather than by the trace of the matrix of coefficients. The method requires computation of relationships that for many sires may be difficult