General Formulas for Calculating Commonly Used Kinship Index.

Objectives: To derive general formulas for calculating commonly used kinship index (KI).

Methods: By introducing the Kronecker symbol, the formulas used to calculate the same KI under different genotype combinations were summarized into a unified expression.

Results: The general formulas were successfully derived for KI in various case situations, including the paternity index, full sibling index, half sibling index, avuncular index, grandpaternity index, first-cousin index, and second-cousin index between two individuals without or with the mother being involved; grandpaternity index between grandparents and a grandchild without or with the mother being involved; half sibling index between two children with two mothers being involved; full sibling index among three children; and half sibling index among three children with no, one, or two mothers being involved.

Conclusions: The general formulas given in this study simplify the calculation of KIs and facilitate fast and accurate calculation through programming.