On identification problems requiring linked autosomal markers

This paper considers identification problems based on DNA marker data. The topics we discuss are general, but we will exemplify them in a simple context. There is DNA available from two persons. There is uncertainty about the relationship between the two individuals and a number of hypotheses describing the possible relationship is available. The task is to determine the most likely pedigree. This problem is fairly standard. However, there are some problems that cannot be solved using DNA from independently segregating loci. For example, the likelihoods for (i) grandparent-grandchild, (ii) uncle-niece and (iii) half-sibs coincide for such DNA data and so these relations cannot be distinguished on the basis of markers normally used for forensic identification problems: the likelihood ratio comparing any pair of hypotheses will be unity. Sometimes, but not in the examples we consider, other sources of DNA like mtDNA or sex chromosomes can help to distinguish between such equally likely possibilities. Prior information can likewise be of use. For instance, age information can exclude alternative (i) above and also indicate that alternative (iii) is apriori more likely than alternative (ii). More generally, the above problems can be solved using linked autosomal markers. To study the problem in detail and understand how linkage works in this regard, we derive an explicit formula for a pair of linked markers. The formula extends to independent pairs of linked markers. While this approach adds to the understanding of the problem, more markers are required to obtain satisfactory results and then the Lander-Green algorithm is needed. Simulation experiments are presented based on a range of scenarios and we conclude that useful results can be obtained using available freeware (MERLIN and R). The main message of this paper is that linked autosomal markers deserve greater attention in forensic genetics and that the required laboratory and statistical analyses can be performed based on existing technology and freeware.