Modelling the dependence structure of Y-STR haplotypes using graphical models

Extending the discrete Laplace method: incorporating multi-copy loci, partial repeats and null alleles

The discrete Laplace method can be used to estimate the frequency of a Y-chromosomal STR haplotype using a random sample from the population. Two limitations of the method are the assumptions that each profile has exactly one allele at every locus and that this allele has an integer repeat number. We relax these assumptions to allow for multi-copy loci, partial repeats and null alleles. We show how the parameters to the extension of the model can be estimated by numerical optimisation using an off-the-shelf solver. Concordance with the discrete Laplace method is obtained when the data satisfy the more stringent assumptions of the original method. We also investigate the performance of the (extended) discrete Laplace method when used to assign match probabilities for haplotypes. A simulation study shows that as more loci are used, match probabilities are underestimated more severely. This is consistent with the hypothesis that the discrete Laplace method cannot model the matches that arise by being identical by descent (IBD). As the number of loci increases the fraction of matches that are IBD increases. Simulation provides support that the discrete Laplace can model those matches that arise from identity by state (IBS) only.

Weight of evidence of Y-STR matches computed with the discrete Laplace method: Impact of adding a suspect's profile to a reference database

The discrete Laplace method is recommended by multiple parties (including the International Society for Forensic Genetics, ISFG) to estimate the weight of evidence in criminal cases when a suspect's Y-STR profile matches the crime scene Y-STR profile. Unfortunately, modelling the distribution of Y-STR profiles in the population reference database is time-consuming and requires expert knowledge. When the suspect's Y-STR profile is added to the database, as would be the protocol in many cases, the parameters of the discrete Laplace model must be re-estimated. We found that the likelihood ratios with and without adding the suspect's Y-STR profile were almost identical with 1,000 or more Y-STR profiles in the database for Y-STR profiles with 8, 12, and 17 loci. Thus, likelihood ratio calculations can be performed in seconds if an established discrete Laplace model based on at least 1,000 Y-STR profiles is used. A match in a population reference database with 17 Y-STR loci from at least 1,000 male individuals results in a likelihood ratio above 10,000 in approximately 94% of the cases, and above 100,000 in approximately 82% of the cases. We offer free software accessible without restrictions to estimate a discrete Laplace model using a Y-STR reference database and subsequently to calculate likelihood ratios.

Assessing the Forensic Value of DNA Evidence from Y Chromosomes and Mitogenomes

Y chromosome and mitochondrial DNA profiles have been used as evidence in courts for decades, yet the problem of evaluating the weight of evidence has not been adequately resolved. Both are lineage markers (inherited from just one parent), which presents different interpretation challenges compared with standard autosomal DNA profiles (inherited from both parents). We review approaches to the evaluation of lineage marker profiles for forensic identification, focussing on the key roles of profile mutation rate and relatedness (extending beyond known relatives). Higher mutation rates imply fewer individuals matching the profile of an alleged contributor, but they will be more closely related. This makes it challenging to evaluate the possibility that one of these matching individuals could be the true source, because relatives may be plausible alternative contributors, and may not be well mixed in the population. These issues reduce the usefulness of profile databases drawn from a broad population: larger populations can have a lower profile relative frequency because of lower relatedness with the alleged contributor. Many evaluation methods do not adequately take account of distant relatedness, but its effects have become more pronounced with the latest generation of high-mutation-rate Y profiles.

Consistent estimation of Y STR haplotype probabilities

Many methods have been proposed to estimate Y-STR haplotype probabilities in a population, but no consensus has been achieved. In this paper a consistency principle for statistical models to provide such probabilities is proposed, in which it is required that the probability of a given haplotype profile on n loci cannot exceed that of any sub-haplotype matching on any n - 1 or fewer loci. If this consistency principle is violated by a Y haplotype probability model, then it could render the presentation of such probabilities highly problematic in a courtroom setting. We show, using publicly available datasets and two recently proposed graphical models for estimating probabilities of Y-STR haplotypes for illustration, that such violations can occur, and that the violations can in some instances be quite large. Some implications of this are discussed.

DNA commission of the International Society of Forensic Genetics (ISFG): Recommendations on the interpretation of Y-STR results in forensic analysis

Forensic genetic laboratories perform a large amount of STR analyses of the Y chromosome, in particular to analyze the male part of complex DNA mixtures. However, the statistical interpretation of evidence retrieved from Y-STR haplotypes is challenging. Due to the uni-parental inheritance mode, Y-STR loci are connected to each other and thus haplotypes show patterns of relationship on the familial and population level. This precludes the treatment of Y-STR loci as independently inherited variables and the application of the product rule. Instead, the dependency structure of Y-STRs needs to be included in the haplotype frequency estimation process affecting also the current paradigm of a random match probability that is in the autosomal case approximated by the population frequency assuming unrelatedness of sampled individuals. Information on the degree of paternal relatedness in the suspect population as well as on the familial network is however needed to interpret Y-chromosomal results in the best possible way. The previous recommendations of the DNA commission of the ISFG on the use of Y-STRs in forensic analysis published more than a decade ago [1] cover the interpretation issue only marginally. The current recommendations address a number of topics (frequency estimators, databases, metapopulations, LR formulation, triage, rapidly mutating Y-STRs) with relevance for the Y-STR statistics and recommend a decision-based procedure, which takes into account legal requirements as well as availability of population data and statistical methods.

A Nonparametric Bayesian Approach to the Rare Type Match Problem

The "rare type match problem" is the situation in which, in a criminal case, the suspect's DNA profile, matching the DNA profile of the crime stain, is not in the database of reference. Ideally, the evaluation of this observed match in the light of the two competing hypotheses (the crime stain has been left by the suspect or by another person) should be based on the calculation of the likelihood ratio and depends on the population proportions of the DNA profiles that are unknown. We propose a Bayesian nonparametric method that uses a two-parameter Poisson Dirichlet distribution as a prior over the ranked population proportions and discards the information about the names of the different DNA profiles. This model is validated using data coming from European Y-STR DNA profiles, and the calculation of the likelihood ratio becomes quite simple thanks to an Empirical Bayes approach for which we provided a motivation.