On the exact distribution of the numbers of alleles in DNA mixtures

When more than one individual contributes biological material to a forensic stain, the resulting DNA type is termed a DNA mixture. DNA mixtures occur frequently in forensic genetic casework, and in recent years, much research has been devoted to this subject. This paper presents a derivation of the exact distribution of the number of alleles for any number of profiles and investigated loci. The per locus number of observed alleles is of interest as it indicates the plausible range on the number of contributors. Hence, by specifying a prior distribution on the number of contributors, the locus distribution may be used to assess the number of contributors. Furthermore, the total number of alleles across all loci is used by some forensic geneticists to estimate the probability that an allele has failed to be detected (allelic drop-out).