Two-locus identity coefficients in pedigrees

This paper proposes a solution to a long-standing problem concerning the joint distribution of allelic identity by descent between two individuals at two linked loci. Such distributions have important applications across various fields of genetics, and detailed formulas for selected relationships appear scattered throughout the literature. However, these results were obtained essentially by brute force, with no efficient method available for general pedigrees. The recursive algorithm described in this paper, and its implementation in R, allow efficient calculation of two-locus identity coefficients in any pedigree. As a result, many existing procedures and techniques may, for the first time, be applied to complex and inbred relationships. Two such applications are discussed, concerning the expected likelihood ratio in forensic kinship testing, and variances in realized relatedness.