Relatedness calculations for linked loci incorporating subpopulation effects

Often the loci in forensic multiplexes are selected to avoid linked loci. However linked loci have occurred in some recent commercially available multiplexes. Previously formulae have been given for both joint and conditional match probabilities for some relationships that did not account for subpopulation effects [1] and [2]. In this paper we extend these works to include a subpopulation correction of the form first suggested by Balding and Nichols [3]. We extend the work to grandparent/grandchild, first cousin, uncle/nephew and half uncle/nephew relationships and apply these to two different populations and STR multiplexes. Our model assumes that the two people have no relationship other that the one specified. That is, we assume their parents are neither related nor themselves inbred. The multiplications inherent in these formulae also assume that there is no linkage disequilibrium at the subpopulation level for these loci. We found that when taking into account linkage the match statistic decreases for all relationships, with siblings having the greatest effect. However, the effect was less than a factor of two decrease in match statistic.