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

TL;DR

This paper introduces a sub-critical branching process model to analyze Y-STR haplotype DNA mixtures, providing a new framework for forensic evidence evaluation that aligns well with previous simulation results.

Contribution

A novel sub-critical branching process model for Y-STR haplotype analysis, offering an alternative to population simulations and enabling new evidence evaluation methods.

Findings

Model fits well with existing simulation data

Provides a numerical method for haplotype distribution estimation

Proposes a new framework for forensic DNA mixture analysis

Abstract

The treatment of short-tandem-repeat (STR) loci on the Y chromosome presents special problems in the forensic analysis of DNA mixtures, chiefly but not exclusively relating to the linkage of Y-STR loci which precludes the use of the `product rule' for estimating Y-haplotype match probabilities. In recent paper, Andersen and Balding(2017) estimated, via a population simulation model, the distribution of the number of haplotypes sharing a common profile over a set of Y-STR loci, and argued for its use as an alternative to estimating Y-haplotype match probabilities. In this paper we present a sub-critical branching process model that approximates their population model, and show how to estimate the haplotype number distribution numerically using multivariate probability generating functions. It is shown that the approximation provides a good fit to their simulations. The model is extended to propose a new framework for evaluating the weight-of-evidence of Y-STR haplotype mixtures, and it is illustrated with publicly available data of a three person DNA mixture.