Implications of Using Identity-by-Descent versus Identity-by-State Matrices in Genetic Analyses

In pedigree based analyses, under additive gene action, the covariance matrix of the vector a of breeding values conditional of the pedigree P is proportional to the matrix A of additive relationships. This matrix is twice the matrix of identical-by-descent (IBD) probabilities. This conditional covariance of a given the pedigree P or given the matrix A of relationships is the basis for genetic analyses. When genotypes are available at the trait loci, it has been proposed that the matrix T of twice the identical-by-state (IBS) probabilities should be used in place of the A matrix. This implies that the conditional covariance matrix of a given T is proportional to T. We can show that this is only true when the gene frequencies at the trait loci is 0.5. Implications of this difference between IBD and IBS matrices will be discussed.