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The treatment of short-tandem-repeat (STR) loci on the Y chromosome presentsspecial problems in the forensic analysis of DNA mixtures, chiefly but notexclusively relating to the linkage of Y-STR loci which precludes the use ofthe `product rule' for estimating Y-haplotype match probabilities. In recentpaper, Andersen and Balding(2017) estimated, via a population simulation model,the distribution of the number of haplotypes sharing a common profile over aset of Y-STR loci, and argued for its use as an alternative to estimatingY-haplotype match probabilities.  In this paper we present a sub-critical branching process model thatapproximates their population model, and show how to estimate the haplotypenumber distribution numerically using multivariate probability generatingfunctions. It is shown that the approximation provides a good fit to theirsimulations. The model is extended to propose a new framework for evaluatingthe weight-of-evidence of Y-STR haplotype mixtures, and it is illustrated withpublicly available data of a three person DNA mixture.

A sub-critical branching process model for application to analysing Y haplotype DNA mixtures