Conditional Genotypic Probabilities for Microsatellite Loci

Modern forensic DNA profiles are constructed using microsatellites, short tandem repeats of 2-5 bases. In the absence of genetic data on a crime-specific subpopulation, one tool for evaluating profile evidence is the match probability. The match probability is the conditional probability that a random person would have the profile of interest given that the suspect has it and that these people are different members of the same subpopulation. One issue in evaluating the match probability is population differentiation, which can induce coancestry among subpopulation members. Forensic assessments that ignore coancestry typically overstate the strength of evidence against the suspect. Theory has been developed to account for coancestry; assumptions include a steady-state population and a mutation model in which the allelic state after a mutation event is independent of the prior state. Under these assumptions, the joint allelic probabilities within a subpopulation may be approximated by the moments of a Dirichlet distribution. We investigate the adequacy of this approximation for profiled loci that mutate according to a generalized stepwise model. Simulations suggest that the Dirichlet theory can still overstate the evidence against a suspect with a common microsatellite genotype. However, Dirichlet-based estimators were less biased than the product-rule estimator, which ignores coancestry.