Inserting it back to the correlation coefficient formula, we have: r=4p2+pq(π1+2π2)−4p22pq=π12+π2 The probability that a randomly selected allele from one relative is IBD with a randomly selected allele from another relative, called kinship coefficient Φ, is equal to Φ = π2(1/2) + π1(1/4) (Malécot, 1948; Lange 1997). The correlation coefficient r is twice the value of kinship coefficient: r = 2Φ. The same relationship was derived more tediously in, e.g., (Broman, 2001) without using the ITO matrices.
