Estimation of Y haplotype frequencies with lower order dependencies

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.

Interpretation of DNA data within the context of UK forensic science - investigation

This article is the second part of a review of the interpretation of DNA data in forensic science. The first part describes the evaluation of autosomal profile for criminal trials where an evidential weight is assigned to the profile of a person of interest (POI) and a crime-scene profile. This part describes the state of the art and future advances in the interpretation of forensic DNA data for providing intelligence information during an investigation. Forensic DNA is crucial in the investigative phase of an undetected crime where a POI needs to be identified. A sample taken from a crime scene is profiled using a range of forensic DNA tests. This review covers investigation using autosomal profiles including searching national and international crime and reference DNA databases. Other investigative methodologies described are kinship analysis; familial searching; Y chromosome (Y-STR) and mitochondrial (mtDNA) profiles; appearance prediction and geographic ancestry; forensic genetic genealogy; and body identification. For completeness, the evaluation of Y-STRs, mtDNA and kinship analysis are briefly described. Taken together, parts I and II, cover the range of interpretation of DNA data in a forensic context.

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.

Mutational data and population profiling of 23 Y-STRs in three Brazilian populations

Y-chromosomal STRs are important markers in forensic genetics, due to some peculiar characteristics. The absence of recombination makes them a useful tool to infer kinship in complex cases involving distant paternal relatives, or to infer paternal bio-geographic ancestry. The presence of a single copy, being transmitted from father to son, allow tracing mutational events in Y-STRs without ambiguity. For the statistical interpretation of forensic evidences based on Y-STR profiles, it is necessary to have estimates on both mutation rates and haplotype frequencies. In this work, 407 father-son duos from São Paulo and Rio de Janeiro states and 204 unrelated individuals from Manaus were analyzed. Haplotype frequencies and mutation rates for the Y-STRs from the PowerPlex Y23 commercial kit were estimated. Thirty-six mutations were observed in 15 of the 22 Y-STRs analyzed, for an average mutation rate of 3.84 × 10^-3 (95 % CI 2.69 × 10^-3 to 5.32 × 10^-3). All mutations in GAAA repeats occurred in alleles with 13 or more uninterrupted units. Mutations in GATA repeats were observed in alleles with 9-17 uninterrupted units. An analysis carried out in different father's age groups showed an increase of 2.48 times the mutation rate in the age group of 40-50 years, when compared to the 20-30 age group, in agreement with the described for autosomal STRs. A high haplotype diversity was found in the three Brazilian populations. Pairwise genetic distance analysis (F_ST) showed no significant differences between the three populations in this study, which were also close to populations with strong European influence. The highest distances among the Brazilian populations were with São Gabriel da Cachoeira, which has a high Native American ancestry.

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.