Calculation of the Paternity Index for the Alleged Father Related to the Child's Mother

To derive the paternity index (PI) calculation formula of the alleged father (AF) when the AF is a relative (parent/child, siblings, grandparent/grandchild, uncle/nephew, first cousins) of the child's biological mother. For the case when the AF is related to the child's biological mother, the existence of the relationship in the numerator and denominator hypothesis of PI was considered. The genotype frequency of the AF was calculated by using the frequency formula in which the mother's genotype was considered, while the random male in the denominator was substituted as another relative of the mother's same rank. The PI calculation formula was derived to eliminate the effect of the relationship between AF and the child's biological mother. When the AF and the biological mother have first, second and tertiary kinship, a more conservative PI was obtained from the PI calculation formula derived in this study compared with the PI calculation method which did not consider kinship. The calculation method provided in this study can eliminate the effect of the relation of the AF and mother on the PI in incest cases, to obtain more accurate and conservative identification conclusions.