The mean and variance of the number of alleles is E[x] = 2p, Var[x] = 2pq, and the joint probability E[xsib1, xsib2] can be calculated by the Li-Sacks conditional probability given the identity-by-descent (IBD) status (Li and Sacks, 1954; Li 1998; Li and Reich 2000; Dai and Weeks, 2006). The three Li-Sacks matrices (the so called ITO matrices) are the probability of the second relative to have one of the genotypes given the genotype of the first relative, and given the IBD status between the two relatives: IBD=2IBD=1IBD=0I=(100010001),T=(pq0p/21/2q/20pq),O=(p22pqq2p22pqq2p22pqq2).
