A novel recursive algorithm for the calculation of the detailed identity coefficients

Background

A recursive algorithm to calculate the fifteen detailed coefficients of identity is introduced. Previous recursive procedures based on the generalized coefficients of kinship provided the detailed coefficients of identity under the assumption that the two individuals were not an ancestor of each other.

Findings

By using gametic relationships to include three, four or two pairs of gametes, we can obtain these coefficients for any pair of individuals. We have developed a novel linear transformation that allows for the calculation of pairwise detailed identity coefficients for any pedigree given the gametic relationships. We illustrate the procedure using the well-known pedigree of Julio and Mencha, which contains 20 Jicaque Indians of Honduras, to calculate their detailed coefficients.

Conclusions

The proposed algorithm can be used to calculate the detailed identity coefficients of two or more individuals with any pedigree relationship.