The number of alleles in DNA mixtures with related contributors

The maximum allele count (MAC) across loci and the total allele count (TAC) are often used to gauge the number of contributors to a DNA mixture. Computational strategies that predict the total number of alleles in a mixture arising from a certain number of contributors of a given population have been developed. Previous work considered the restricted case where all of the contributors to a mixture are unrelated. We relax this assumption and allow mixture contributors to be related according to a pedigree. We introduce an efficient computational strategy. This strategy based on first determining a probability distribution on the number of independent alleles per locus, and then conditioning on this distribution to compute a distribution of the number of distinct alleles per locus. The distribution of the number of independent alleles per locus is obtained by leveraging the Identical by Descent (IBD) pattern distribution which can be computed from the pedigree. We explain how allelic dropout and a subpopulation correction can be accounted for in the calculations.