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.

SNP allele calling of Illumina Infinium Omni5-4 data using the butterfly method.

We introduce a within-sample SNP calling method, called the "butterfly method", that improves the quality of SNP calling with the Illumina Infinium Omni5-4 SNP Kit. This was done by improving how no-calls are determined from allele signal intensities. High confidence of SNP allele calling is extremely important in forensic genetics and clinical diagnostics. This paper is accompanied by two open-source R packages, omni54manifest and snpbeadchip that make SNP calling easy by helping with bookkeeping and giving easy access to meta-information about the SNPs typed with the Illumina Infinium Omni5-4 Kit (including chromosome, probe type, and SNP bases). We compared the results from our method with those obtained with the Illumina GenomeStudio software (which does not provide sample and SNP specific genotype probabilities or other quality measures), and with whole-genome sequencing (WGS). Given the signal intensities, the SNP calling quality was optimised using a threshold for the a posteriori probability of a SNP belonging to a SNP cluster. By lowering the a posteriori probability threshold for no-calls, we obtained a higher call rate than GenomeStudio. Using a higher a posteriori probability threshold, we achieved a higher concordance with the WGS data than GenomeStudio. Our method had SNP call and concordance rates with WGS data of approximately 99%.

Inference of admixed ancestry with Ancestry Informative Markers.

Analysis of Ancestry Informative Markers (AIMs) is of interest to forensic geneticists for the purpose of assessing the origin of individuals. Often AIMs are used to produce investigative leads for potential suspects in crime cases and identification in missing persons mass disaster cases. We have previously suggested to assess the origin of the profile of interest by a likelihood ratio test on Fisher's exact test. The likelihood ratio test assesses the likelihood of the data under two competing hypotheses, where the null hypothesis assume common origin of the profile of interest and those in a specified population. However, in the case of a profile of an individual of admixed ancestry, there is an increased risk that the profile will be rejected in the constituting populations. The likelihood ratio test approach is extended by allowing for profile admixture implying the profile of interest is a mixture of profiles from two populations. The Expectation-Maximisation (EM) algorithm is used to handle the ambiguity of allocation of alleles at heterozygous markers. To demonstrate the approach, admixed profiles are simulated using AIMs genotypes in eight global meta populations.

Stutter analysis of complex STR MPS data.

Stutters are common and well documented artefacts of amplification of short tandem repeat (STR) regions when using polymerase chain reaction (PCR) occurring as strands one or more motifs shorter or longer than the parental allele. Understanding the mechanism and rate by which stutters are created is especially important when the samples contain small amounts of DNA or DNA from multiple contributors. It has been shown that there is a linear relationship between the longest uninterrupted stretch (LUS) and the stutter ratio. This holds if there is only a single type of stutter variant. However, with massively parallel sequencing (MPS), we see that alleles may create different stutters corresponding to stuttering of different parts of the parental allele. This calls for a refinement of the LUS concept. We analysed all uninterrupted stretches, here called blocks, and identified the block from which the stutter originated. We defined the block length of the missing motif (BLMM) as the length of the identified block. We found that the relationship between the stutter ratio and BLMM was linear using a simple system of recurrence relations. We found that the mean square error decreased by a factor up to 17.5 for compound and complex autosomal markers when using BLMM instead of LUS.

Weight of the evidence of genetic investigations of ancestry informative markers.

Ancestry-informative markers (AIMs) are markers that give information about the ancestry of individuals. They are used in forensic genetics for predicting the geographic origin of the investigated individual in crime and identification cases. In the exploration of the genogeographic origin of an AIMs profile, the likelihoods of the AIMs profile in various populations may be calculated. However, there may not be an appropriate reference population in the database. The fact that the likelihood ratio (LR) of one population compared to that of another population is large does not imply that any of the populations is relevant. To handle this phenomena, we derived a likelihood ratio test (LRT) that is a measure of absolute concordance between an AIMs profile and a population rather than a relative measure of the AIMs profile's likelihood in two populations. The LRT is similar to a Fisher's exact test. By aggregating over markers, the central limit theorem suggests that the resulting quantity is approximately normally distributed. If only a few markers are genotyped or if the majority of the markers are fixed in a given population, the approximation may fail. We overcome this using importance sampling and show how exponential tilting results in an efficient proposal distribution. By simulations and published AIMs profiles, we demonstrate the applicability of the derived methodology. For the genotyped AIMs, the LRT approach achieves the nominal levels of rejection when tested on data from five major continental regions.

YfilerⓇ Plus population samples and dilution series: stutters, analytic thresholds, and drop-out probabilities.

The Yfiler Ⓡ Plus Amplification Kit amplifies 27 Y chromosomal small tandem repeat (STR) markers. The kit has five-fluorescent dye chemistry and the improved PCR buffer system of modern STR kits. We validated the kit for accredited investigations of crime scene samples by a thorough study of kit dynamics and performance. We determined dye-dependent analytical thresholds by receiver operating characteristics (ROC) and made a customised artefact filter that includes theoretical known artefacts by use of previously analysed population samples. Dilution series of known male DNA and a selection of crime scene samples were analysed with the customised thresholds and artefact filters. The Yfiler Ⓡ Plus Amplification Kit was sensitive giving full profiles down to 70 pg of male DNA. The balances between the fluorescent dyes as well as between loci were very good. The kit was able to produce full Y-STR profiles from crime scene samples containing small amounts of male DNA and large amounts of female DNA (although unspecific reactions were evident for very unbalanced mixtures). A decrease in the drop-out rate was found for both the dilution series and population samples, as well as a small increase in the drop-in rate for population samples, using the customised threshold and artefact filters compared to company-provided thresholds and artefact filters. The additional drop-ins were all of a nature that would be detected by inspection of the results. For the crime scene samples, large amounts of female DNA complicated the analysis by causing drop-ins of characteristic female DNA artefacts. Even though the customised analytical threshold in combination with the custom-made artefact filters gave more alleles, crime scene samples still needed special attention from the forensic geneticist.

The multivariate Dirichlet-multinomial distribution and its application in forensic genetics to adjust for subpopulation effects using the θ-correction.

In this paper, we discuss the construction of a multivariate generalisation of the Dirichlet-multinomial distribution. An example from forensic genetics in the statistical analysis of DNA mixtures motivates the study of this multivariate extension. In forensic genetics, adjustment of the match probabilities due to remote ancestry in the population is often done using the so-called θ-correction. This correction increases the probability of observing multiple copies of rare alleles in a subpopulation and thereby reduces the weight of the evidence for rare genotypes. A recent publication by Cowell et al. (2015) showed elegantly how to use Bayesian networks for efficient computations of likelihood ratios in a forensic genetic context. However, their underlying population genetic model assumed independence of alleles, which is not realistic in real populations. We demonstrate how the so-called θ-correction can be incorporated in Bayesian networks to make efficient computations by modifying the Markov structure of Cowell et al. (2015). By numerical examples, we show how the θ-correction incorporated in the multivariate Dirichlet-multinomial distribution affects the weight of evidence.

Identifying the most likely contributors to a Y-STR mixture using the discrete Laplace method.

In some crime cases, the male part of the DNA in a stain can only be analysed using Y chromosomal markers, e.g. Y-STRs. This may be the case in e.g. rape cases, where the male components can only be detected as Y-STR profiles, because the fraction of male DNA is much smaller than that of female DNA, which can mask the male results when autosomal STRs are investigated. Sometimes, mixtures of Y-STRs are observed, e.g. in rape cases with multiple offenders. In such cases, Y-STR mixture analysis is required, e.g. by mixture deconvolution, to deduce the most likely DNA profiles from the contributors. We demonstrate how the discrete Laplace method can be used to separate a two person Y-STR mixture, where the Y-STR profiles of the true contributors are not present in the reference dataset, which is often the case for Y-STR profiles in real case work. We also briefly discuss how to calculate the weight of the evidence using the likelihood ratio principle when a suspect's Y-STR profile fits into a two person mixture. We used three datasets with between 7 and 21 Y-STR loci: Denmark (n=181), Somalia (n=201) and Germany (n=3443). The Danish dataset with 21 loci was truncated to 15 and 10 loci to examine the effect of the number of loci. For each of these datasets, an out of sample simulation study was performed: A total of 550 mixtures were composed by randomly sampling two haplotypes, h1 and h2, from the dataset. We then used the discrete Laplace method on the remaining data (excluding h1 and h2) to rank the contributor pairs by the product of the contributors' estimated haplotype frequencies. Successful separation of mixtures (defined by the observation that the true contributor pair was among the 10 most likely contributor pairs) was found in 42-52% of the cases for 21 loci, 69-75% for 15 loci and 92-99% for 10 loci or less depending on the dataset and how the discrete Laplace model was chosen. Y-STR mixtures with many loci are difficult to separate, but even haplotypes with 21 Y-STR loci can be separated.

Cluster analysis of European Y-chromosomal STR haplotypes using the discrete Laplace method.

The European Y-chromosomal short tandem repeat (STR) haplotype distribution has previously been analysed in various ways. Here, we introduce a new way of analysing population substructure using a new method based on clustering within the discrete Laplace exponential family that models the probability distribution of the Y-STR haplotypes. Creating a consistent statistical model of the haplotypes enables us to perform a wide range of analyses. Previously, haplotype frequency estimation using the discrete Laplace method has been validated. In this paper we investigate how the discrete Laplace method can be used for cluster analysis to further validate the discrete Laplace method. A very important practical fact is that the calculations can be performed on a normal computer. We identified two sub-clusters of the Eastern and Western European Y-STR haplotypes similar to results of previous studies. We also compared pairwise distances (between geographically separated samples) with those obtained using the AMOVA method and found good agreement. Further analyses that are impossible with AMOVA were made using the discrete Laplace method: analysis of the homogeneity in two different ways and calculating marginal STR distributions. We found that the Y-STR haplotypes from e.g. Finland were relatively homogeneous as opposed to the relatively heterogeneous Y-STR haplotypes from e.g. Lublin, Eastern Poland and Berlin, Germany. We demonstrated that the observed distributions of alleles at each locus were similar to the expected ones. We also compared pairwise distances between geographically separated samples from Africa with those obtained using the AMOVA method and found good agreement.

Estimating Y-STR allelic drop-out rates and adjusting for interlocus balances.

Y chromosome short tandem repeats (Y-STRs) are valuable genetic markers in certain areas of forensic case-work. However, when the Y-STR DNA profile is weak, the observed Y-STR profile may not be complete--i.e. locus drop-out may have occurred. Another explanation could be that the stain DNA did not have a Y-STR allele that was detectable with the method used (the allele is a 'null allele'). If the Y-STR profile of a stain is strong, one would be reluctant to consider drop-out as a reasonable explanation of lack of a Y-STR allele and would maybe consider 'null allele' as an explanation. On the other hand, if the signal strengths are weak, one would most likely accept drop-out as a possible explanation. We created a logistic regression model to estimate the probability of allele drop-out with the Life Technologies/Applied Biosystems AmpFlSTR(®) Yfiler(®) kit such that the trade-off between drop-outs and null alleles could be quantified using a statistical model. The model to estimate the probability of drop-out uses information about locus imbalances, signal strength, the number of PCR cycles, and the fragment size of Yfiler. We made two temporarily separated experiments and found no evidence of temporal variation in the probability of drop-out. Using our model, we found that for 30 PCR cycles with a 150 bp allele, the probability of drop-out was 1:5000 corresponding to the average estimate of the probability of Y-STR null alleles at a signal strength of 1249 RFU. This means that the probability of a null allele is higher than that of an allele drop-out at e.g. 4000 RFU and the probability of drop-out is higher than that of a null allele at e.g. 75 RFU.

The discrete Laplace exponential family and estimation of Y-STR haplotype frequencies.

Estimating haplotype frequencies is important in e.g. forensic genetics, where the frequencies are needed to calculate the likelihood ratio for the evidential weight of a DNA profile found at a crime scene. Estimation is naturally based on a population model, motivating the investigation of the Fisher-Wright model of evolution for haploid lineage DNA markers. An exponential family (a class of probability distributions that is well understood in probability theory such that inference is easily made by using existing software) called the 'discrete Laplace distribution' is described. We illustrate how well the discrete Laplace distribution approximates a more complicated distribution that arises by investigating the well-known population genetic Fisher-Wright model of evolution by a single-step mutation process. It was shown how the discrete Laplace distribution can be used to estimate haplotype frequencies for haploid lineage DNA markers (such as Y-chromosomal short tandem repeats), which in turn can be used to assess the evidential weight of a DNA profile found at a crime scene. This was done by making inference in a mixture of multivariate, marginally independent, discrete Laplace distributions using the EM algorithm to estimate the probabilities of membership of a set of unobserved subpopulations. The discrete Laplace distribution can be used to estimate haplotype frequencies with lower prediction error than other existing estimators. Furthermore, the calculations could be performed on a normal computer. This method was implemented in the freely available open source software R that is supported on Linux, MacOS and MS Windows.

Population dynamics of filamentous bacteria in Danish wastewater treatment plants with nutrient removal.

Bulking and foaming are two frequently occurring operational problems in activated sludge wastewater treatment plants, and these problems are mainly associated with excessive growth of filamentous bacteria. In this study, a comprehensive investigation of the identity and population dynamics of filamentous bacteria in 28 Danish municipal treatment plants with nutrient removal has been carried out over three years. Fluorescence in situ hybridization was applied to quantify more than twenty probe-defined populations of filamentous bacteria that in total constituted a large fraction of the entire microbial community, on average 24%. Despite the majority being present within the flocs, they occasionally caused settling problems in most of the plants. A low diversity of probe-defined filamentous bacteria was found in the plants with Microthrix and various species belonging to phylum Chloroflexi (e.g., type 0803 and type 0092) as the most abundant. Few other filamentous probe-defined species were found revealing a large similarity between the filamentous populations in the plants investigated. The composition of filamentous populations was stable in each plant with only minor changes in relative abundances observed during the three-year study period. The relative composition of the different species was unique to each plant giving a characteristic "fingerprint". Comprehensive statistical analyses of the presence and abundance of the filamentous organisms did not reveal many correlations with a particular plant design or process parameter.

Allelic drop-out probabilities estimated by logistic regression--further considerations and practical implementation.

We discuss the model for estimating drop-out probabilities presented by Tvedebrink et al. [7] and the concerns, that have been raised. The criticism of the model has demonstrated that the model is not perfect. However, the model is very useful for advanced forensic genetic work, where allelic drop-out is occurring. With this discussion, we hope to improve the drop-out model, so that it can be used for practical forensic genetics and stimulate further discussions. We discuss how to estimate drop-out probabilities when using a varying number of PCR cycles and other experimental conditions.

Analysis of matches and partial-matches in a Danish STR data set.

Over the recent years, the national databases of STR profiles have grown in size due to the success of forensic DNA analysis in solving crimes. The accumulation of DNA profiles implies that the probability of a random match or near match of two randomly selected DNA profiles in the database increases. We analysed 53,295 STR profiles from individuals investigated in relation to crime case investigations at the Department of Forensic Medicine, Faculty of Health Sciences, University of Copenhagen, Denmark. Incomplete STR profiles (437 circa 0.8% of the total), 48 redundant STR profiles from monozygotic twins (0.09%), 6 redundant STR profiles of unknown cause and 1283 STR profiles from repeated testing of individuals were removed leaving 51,517 complete 10 locus STR profiles for analysis. The number corresponds to approximately 1% of the Danish population. We compared all STR profiles to each other, i.e. 1.3×10(9) comparisons. With these large number of comparisons, it is likely to observe DNA profiles that coincide on many loci, which has concerned some commentators and raised questions about "overstating" the power of DNA evidence. We used the method of Weir [11,12] and Curran et al. [3] to compare the observed and expected number of matches and near matches in the data set. We extended the methods by computing the covariance matrix of the summary statistic and used it for the estimation of the identical-by-descent parameter, θ. The analysis demonstrated a number of close relatives in the Danish data set and substructure. The main contribution to the substructure comes from close relatives. An overall θ-value of 1% compensated for the observed substructure, when close familial relationships were accounted for.

Statistical model for degraded DNA samples and adjusted probabilities for allelic drop-out.

DNA samples found at a scene of crime or obtained from the debris of a mass disaster accident are often subject to degradation. When using the STR DNA technology, the DNA profile is observed via a so-called electropherogram (EPG), where the alleles are identified as signal peaks above a certain level or above a signal to noise threshold. Degradation implies that these peak intensities decrease in strength for longer short tandem repeat (STR) sequences. Consequently, long STR loci may fail to produce peak heights above the limit of detection resulting in allelic or locus drop-outs. In this paper, we present a method for measuring the degree of degradation of a sample and demonstrate how to incorporate this in estimating the probability of allelic drop-out. This is done by extending an existing method derived for non-degraded samples. The performance of the methodology is evaluated using data from degraded DNA, where cases with varying amounts of DNA and levels of degradation are investigated.

Identifying contributors of DNA mixtures by means of quantitative information of STR typing.

Estimating the weight of evidence in forensic genetics is often done in terms of a likelihood ratio, LR. The LR evaluates the probability of the observed evidence under competing hypotheses. Most often, probabilities used in the LR only consider the evidence from the genomic variation identified using polymorphic genetic markers. However, modern typing techniques supply additional quantitative data, which contain very important information about the observed evidence. This is particularly true for cases of DNA mixtures, where more than one individual has contributed to the observed biological stain. This article presents a method for including the quantitative information of short tandem repeat (STR) DNA mixtures in the LR. Also, an efficient algorithmic method for finding the best matching combination of DNA mixture profiles is derived and implemented in an on-line tool for two- and three-person DNA mixtures. Finally, we demonstrate for two-person mixtures how this best matching pair of profiles can be used in estimating the likelihood ratio using importance sampling. The reason for using importance sampling for estimating the likelihood ratio is the often vast number of combinations of profiles needed for the evaluation of the weight of evidence. Online tool is available at http://people.math.aau.dk/~tvede/dna/.

Estimating the probability of allelic drop-out of STR alleles in forensic genetics.

In crime cases with available DNA evidence, the amount of DNA is often sparse due to the setting of the crime. In such cases, allelic drop-out of one or more true alleles in STR typing is possible. We present a statistical model for estimating the per locus and overall probability of allelic drop-out using the results of all STR loci in the case sample as reference. The methodology of logistic regression is appropriate for this analysis, and we demonstrate how to incorporate this in a forensic genetic framework.