No shortcut solution to the problem of Y-STR match probability calculation

Abstract

Match probability calculation is deemed much more intricate for lineage genetic markers, including Y-chromosomal short tandem repeats (Y-STRs), than for autosomal markers. This is because, owing to the lack of recombination, strong interdependence between markers is likely, which implies that haplotype frequency estimates cannot simply be obtained through the multiplication of allele frequency estimates. As yet, however, the practical relevance of this problem has not been studied in much detail using real data. In fact, such scrutiny appears well warranted because the high mutation rates of Y-STRs and the possibility of backward mutation should have worked against the statistical association of Y-STRs. We examined haplotype data of 21 markers included in the PowerPlex(®)Y23 set (PPY23, Promega Corporation, Madison, WI) originating from six different populations (four European and two Asian). Assessing the conditional entropies of the markers, given different subsets of markers from the same panel, we demonstrate that the PowerPlex(®)Y23 set cannot be decomposed into smaller marker subsets that would be (conditionally) independent. Nevertheless, in all six populations, >94% of the joint entropy of the 21 markers is explained by the seven most rapidly mutating markers. Although this result might render a reduction in marker number a sensible option for practical casework, the partial haplotypes would still be almost as diverse as the full haplotypes. Therefore, match probability calculation remains difficult and calls for the improvement of currently available methods of haplotype frequency estimation.

Keywords: Entropy; Interdependence between Y-STRs; PowerPlex(®)Y23; Product rule.