Use of the Elston-Stewart algorithm for the efficient calculation of exact pedigree-based Y-STR match probabilities

The formal assessment of a genetic match between a suspect and some biological trace material is one of the key tasks of forensic genetics, particularly in cases of sexual offence. The analysis of Y-chromosomal short tandem repeats (Y-STRs) has proven especially useful in this context. For a long time, however, calculating the probability of a perfect Y-STR profile match under the defense hypothesis that the suspect was not the trace donor posed a great challenge. This was due to the inherent uncertainty about the population of alternative donors, the so-called suspect population. We recently proposed to resolve this controversy by systematically favoring the suspect and considering his close male relatives as the suspect population. However, since the mathematical framework developed for this purpose was simulation-based, its practical application turned out increasingly difficult with increasing pedigree size. Here, we present an adaptation of the so-called Elston-Stewart algorithm, originally developed for the linkage analysis of human genetic diseases, to allow calculation of exact match probabilities in a time that scales linearly with pedigree size. The adapted algorithm was implemented in a publicly available software tool, and its correctness was verified by the comparison of its output with the correct, analytical results obtained for selected example pedigrees. The new implementation mostly outperforms the simulation-based solution, albeit with the important exception of Y-STRs present in multiple copies. Given the increasingly prominent role of such multicopy markers in forensic genetics, the complementary use of both approaches appears the most sensible strategy for the time being.