Paternity index calculations when some individuals share common ancestry

Discrimination of half-siblings when maternal genotypes are known

Given the DNA profiles of two individuals and one parent (say the mother) of each, we present likelihood ratios (LRs) comparing the hypothesis that they have the same father with the hypothesis of unrelated fathers. If the individuals have the same mother, the problem is to distinguish full- from half-siblings, otherwise we are comparing a half-sibling relationship with unrelated. We simulate STR profiles at up to 60 loci, based on allele proportions observed at 15 loci in three populations, and use them to approximate misclassification rates both for binary classification (e.g. "half-sib" versus "unrelated"), and when a third "cannot say" category is included. We find that reliable inferences in the absence of the mothers' profiles require many more STR loci than the 10-25 loci that are currently routinely available. However, profiling the two mothers conveys more discriminatory power than profiling the same number of additional loci in the individuals themselves. Our likelihood ratio formulas include a theta (or Fst) adjustment to allow for the individuals concerned to have recent shared ancestry (coancestry), relative to the population from which the allele frequency database is drawn. We illustrate that using an appropriate value of theta can reduce the average misclassification rate.