Overdispersion in allelic counts and θ-correction in forensic genetics

We present a statistical model for incorporating the extra variability in allelic counts due to subpopulation structures. In forensic genetics, this effect is modelled by the identical-by-descent parameter θ, which measures the relationship between pairs of alleles within a population relative to the relationship of alleles between populations (Weir, 2007). In our statistical approach, we demonstrate that θ may be defined as an overdispersion parameter capturing the subpopulation effects. This formulation allows derivation of maximum likelihood estimates of the allele probabilities and θ together with computation of the profile log-likelihood, confidence intervals and hypothesis testing. In order to compare our method with existing methods, we reanalysed FBI data from Budowle and Moretti (1999) with allele counts in six US subpopulations. Furthermore, we investigate properties of our methodology from simulation studies.