Interpreting forensic DNA mixtures: allowing for uncertainty in population substructure and dependence

We consider the assessment of deoxyribonucleic acid (DNA) profiles from biological samples containing a mixture of DNA from more than one person. The problem has been investigated in the context of likelihood ratios by Weir and co-workers under the assumption of independent alleles in DNA profiles. However, uncertainty about independence may arise from various factors such as population substructure and relatedness. This issue has received considerable attention in recent years. Ignoring this uncertainty may seriously overstate the strength of the evidence and therefore disadvantage innocent suspects. Taking this uncertainty into account, we develop a general formula for calculating the match probabilities of DNA profiles. Thus, we extend the result derived by Weir and co-workers to the dependence situation, which is often more to the benefit of the defendant in comparison with the simple product rule result based on an independence assumption. The effect of dependence of alleles on likelihood ratio estimates can be seen in the analysis of two real data sets.