A novel mathematical framework for pedigree-based calculation of Y-STR match probabilities

Y-chromosomal short tandem repeat (Y-STR) markers are routinely used in forensic casework to identify male donors of biological traces left at crime scenes, particularly in sexual assault cases. However, the evidential value of a match between the Y-STR profile of a trace and a potential donor, usually a crime suspect, is difficult to quantify, and the common albeit inappropriate practise to equate Y-STR match probabilities with Y-STR profile frequencies estimated from population databases has been subject to scientific debate for decades. As a solution to this long-standing problem, we suggest an alternative approach to the calculation of Y-STR match probabilities that involves splitting the group of potential donors other than the suspect into two: (i) his close male relatives (termed his 'pedigree') and (ii) all other males. While an upper limit to the match probability is easily calculated for the second group, it is computationally challenging to derive for the first. We therefore developed a mathematical framework that uses importance sampling to reconstruct and evaluate the Y-STR profiles of untyped members of the suspect's pedigree by way of simulation. Extensive testing with elementary pedigrees of different structure and complexity confirmed that both, the framework and its Python-based software implementation yield match probability estimates that approximate well the correct analytical results, depending upon the number of simulations performed. Our methodology thus facilitates a more appropriate and valid solution to the long-standing problem of interpreting Y-STR profile matches in forensic casework.