The effect of varying the number of contributors on likelihood ratios for complex DNA mixtures

Interpretation of DNA mixtures with three or more contributors, defined here as high order mixtures, is difficult because of the inevitability of allele sharing. Allele sharing complicates the estimation of the number of contributors, which is an important parameter to assess the probative value. Consequently, these mixtures may not be deemed suitable for interpretation and reporting. In this study, we generated three-, four- and five-person mixtures with little or no drop-out and with varying levels of allele sharing. For these DNA mixtures we computed likelihood ratios (LRs) using the LRmix model, and always using persons of interest that are true contributors. We assessed the influence of different scenarios on the LR, and used (1) the true or an incorrect number of contributors, (2) zero, one or two anchored individuals and (3) an equal number of contributors under Hp and Hd or an extra contributor under Hd. It was shown that the LR varied considerably when the hypotheses used an incorrect number of contributors, especially when individuals were anchored under the hypotheses. Overall, when analysing high order mixtures, there may occur a transition from LR greater than one to less than one if an incorrect number of contributors is conditioned. This is a result of allele sharing among the multiple contributors rather than allele drop-out, since this study only utilised samples with little or no drop-out.