Analysis of Trio Half Sibling Testing.

OBJECTIVES: To establish an analytical method for half sibling testing involving common three relatives' participation. METHODS: Based on the half sibling testing scenarios with the known biological mother, grandfather or uncle, and two unidentified controversial half siblings participating, two opposing hypotheses were set. Lineage reconstruction according to Mendel's law of heredity was carried out, and the calculation formula of the half sibling kinship index was derived. Verification of actual cases was carried out and the results were compared with duo half sibling testing. RESULTS: In the scenarios of the known biological mother, grandfather and uncle participating in half sibling testing, the kinship calculation formulae of 54, 91 and 99 genotype combinations for kinship index calculation were deduced respectively. The actual cases showed higher kinship indexes in trio half sibling testing compared with duo half sibling testing. CONCLUSIONS: It is beneficial to obtain more genetic information for family reconstruction and improvement of the strength of genetic evidence for half sibling testing by adding known relatives.

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.