Combining allele frequency uncertainty and population substructure corrections in forensic DNA calculations

TL;DR

This paper develops an improved approximation method for combining allele frequency uncertainty and population substructure corrections in forensic DNA calculations, enhancing accuracy in relatedness and mixture analyses.

Contribution

It introduces a new approximation that is exact for a single individual and closely matches previous models when combining two sources of uncertainty.

Findings

The approximation is exact for one individual.

Numerical tests show the approximation closely matches previous models.

Incorporating the approximation improves DNA mixture analysis accuracy.

Abstract

In forensic DNA calculations of relatedness of individuals and in DNA mixture analyses, two sources of uncertainty are present concerning the allele frequencies used for evaluating genotype probabilities when evaluating likelihoods. They are: (i) imprecision in the estimates of the allele frequencies in the population by using an inevitably finite database of DNA profiles to estimate them; and (ii) the existence of population substructure. Green and Mortera (2009) showed that these effects may be taken into account individually using a common Dirichlet model within a Bayesian network formulation, but that when taken in combination this is not the case; however they suggested an approximation that could be used. Here we develop a slightly different approximation that is shown to be exact in the case of a single individual. We demonstrate the closeness of the approximation numerically using a published database of allele counts, and illustrate the effect of incorporating the approximation into calculations of a recently published statistical model of DNA mixtures.