Mixtures with relatives: a pedigree perspective

DNA mixture evidence pertains to cases where several individuals may have contributed to a biological stain. Statistical methods and software for such problems are available and a large number of cases can be handled adequately. However, one class of mixture problems remains untreated in full generality in the literature, namely when the contributors may be related. Disregarding a plausible close relative of the perpetrator as an alternative contributor (identical twin is the most extreme case) may lead to overestimating the evidence against a suspect. Existing methods only accommodate pairwise relationships such as the case where the suspect and the victim are siblings, for example. In this paper we consider relationships in full generality, conveniently represented by pedigrees. In particular, these pedigrees may involve inbreeding, for instance when the parents of an individual of interest are first cousins. Furthermore our framework handles situations where the opposing parties in a court case (prosecution and defence) propose different family relationships. Consequently, our approach combines classical mixture and kinship problems. The basic idea of this paper is to formulate the problem in a way that allows for the exploitation of currently available methods and software designed originally for linkage applications. We have developed a freely available R package, euroMix based on another package, paramlink, and we illustrate the ideas and methods on real and simulated data.