Mixture DNA profiles commonly appear in forensic genetics, and a large number of statistical methods and software are available for such cases. However, most of the literature concerns mixtures where the contributors are assumed unrelated and the genetic markers are unlinked. In this paper, we consider mixtures of linked markers and related contributors. If no relationships are involved, linkage can be ignored. While unlinked markers can be treated independently, linkage introduces dependencies. The use of linked markers presents statistical and computational challenges, but may also lead to a considerable increase in power since the number of markers available is much larger if we do not require the markers to be unlinked. In addition, some cases that cannot be solved with an unlimited number of unlinked autosomal markers can be solved with linked markers. We focus on two special cases of linked markers: pairs of linked autosomal markers and X-chromosomal markers. A framework is presented for calculation of likelihood ratios for mixtures with general relationships and with linkage between any number of markers. Finally, we explore the effect of linkage disequilibrium, also called allelic association, on the likelihood ratio.
Keywords: DNA mixtures; Forensics; Kinship; Likelihood ratio; Linkage; Linkage disequilibrium.