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Mixture DNA profiles commonly appear in forensic genetics, and a large number of statistical methods and software are available for such cases. However, most of the literature concerns mixtures where the contributors are assumed unrelated and the genetic markers are unlinked. In this paper, we consider mixtures of linked markers and related contributors. If no relationships are involved, linkage can be ignored. While unlinked markers can be treated independently, linkage introduces dependencies. The use of linked markers presents statistical and computational challenges, but may also lead to a considerable increase in power since the number of markers available is much larger if we do not require the markers to be unlinked. In addition, some cases that cannot be solved with an unlimited number of unlinked autosomal markers can be solved with linked markers. We focus on two special cases of linked markers: pairs of linked autosomal markers and X-chromosomal markers. A framework is presented for calculation of likelihood ratios for mixtures with general relationships and with linkage between any number of markers. Finally, we explore the effect of linkage disequilibrium, also called allelic association, on the likelihood ratio.

Ideally for use in forensic analyses, genetic markers on the same chromosome should be more than 50 Mb in physical distance to ensure full recombination and thus independent inheritance. The forensic community has given attention to two STR markers, D12S391 and vWA, that are 6.3 megabases (Mb) apart on chromosome 12. Recent studies have shown no significant linkage disequilibrium between vWA and D12S391 in U.S. and worldwide populations, although genetic linkage has been identified. It is important to evaluate the impact of linkage effects on kinship analysis. In this study, we aimed to determine a more precise measurement of the recombination frequency between vWA and D12S391 based on a larger number of informative meiosis than has been studied previously. We estimated the recombination frequency (θ) to 0.089 (95% CI 0.044-0.158). Using pedigrees simulated under specific kinship scenarios where recombination was expected to affect the likelihood ratio (LR), we evaluated the impact on LR values of including or ignoring linkage between vWA and D12S391. For all pedigree scenarios considered, on average, LR values ignoring linkage were slightly underestimated than when linkage was considered. However, in the incest scenario considered, LR values could be overestimated up to 25-30 times when linkage was ignored. We demonstrate that the effect of ignoring linkage in the likelihood ratio calculation can be considerable. These results suggest that linkage should be considered during kinship analysis when vWA and D12S391 are tested for pedigrees where a recombination could impact the LR value., (Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.)

X-chromosomal markers in forensic genetics have become more widely used during recent years, particularly for relationship testing. Linkage and linkage disequilibrium (LD) must typically be accounted for when using close X-chromosomal markers. Thus, when producing the weight-of-evidence, given by a DNA-analysis with markers that are linked, the normally used product rule is invalid. Here we present an implementation of an efficient model for calculating likelihood ratios (LRs) with markers on the X-chromosome which are linked and in LD. Furthermore, the model was applied on several cases based on data from the eight X-chromosomal loci included in the Mentype(®) Argus X-8 (Biotype). Using a simulation approach we showed that the use of X-chromosome data can offer valuable information for choosing between the alternatives in each of the cases we studied, and that the LR can be high in several cases. We demonstrated that when linkage and LD were disregarded, as opposed to taken into account, the difference in calculated LRs could be considerable. When these differences were large, the estimated haplotype frequencies often had a strong impact and we present a method to estimate haplotype frequencies. Our conclusion is that linkage and LD should be accounted for when using the tested set of markers, and the used model is an efficient way of doing so., (Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.)

Pedigree inference, for example determining whether two persons are second cousins or unrelated, can be done by comparing their genotypes at a selection of genetic markers. When the data for one or more of the persons is from low-coverage next generation sequencing (lcNGS), currently available computational methods either ignore genetic linkage or do not take advantage of the probabilistic nature of lcNGS data, relying instead on first estimating the genotype. We provide a method and software (see familias.name/lcNGS) bridging the above gap. Simulations indicate how our results are considerably more accurate compared to some previously available alternatives. Our method, utilizing a version of the Lander-Green algorithm, uses a group of symmetries to speed up calculations. This group may be of further interest in other calculations involving linked loci. [ABSTRACT FROM AUTHOR]

Advances in massively parallel sequencing technology have enabled the combination of a much-expanded number of DNA markers (notably STRs and SNPs in one or combined multiplexes), with the aim of increasing the weight of evidence in forensic casework. However, when data from multiple loci on the same chromosome are used, genetic linkage can affect the final likelihood calculation. In order to study the effect of linkage for different sets of markers we developed the biostatistical tool ILIR, (Impact of Linkage on forensic markers for Identity and Relationship tests). The ILIR tool can be used to study the overall impact of genetic linkage for an arbitrary set of markers used in forensic testing. Application of ILIR can be useful during marker selection and design of new marker panels, as well as being highly relevant for existing marker sets as a way to properly evaluate the effects of linkage on a case-by-case basis. ILIR, implemented via the open source platform R, includes variation and genomic position reference data for over 40 STRs and 140 SNPs, combined with the ability to include additional forensic markers of interest. The use of the software is demonstrated with examples from several different established marker sets (such as the expanded CODIS core loci) including a review of the interpretation of linked genetic data. [ABSTRACT FROM AUTHOR]

Within forensic genetics, there is still a need for supplementary DNA marker typing in order to increase the power to solve cases for both identity testing and complex kinship issues. One major disadvantage with current capillary electrophoresis (CE) methods is the limitation in DNA marker multiplex capability. By utilizing massive parallel sequencing (MPS) technology, this capability can, however, be increased. We have designed a customized GeneRead DNASeq SNP panel (Qiagen) of 140 previously published autosomal forensically relevant identity SNPs for analysis using MPS. One single amplification step was followed by library preparation using the GeneRead Library Prep workflow (Qiagen). The sequencing was performed on a MiSeq System (Illumina), and the bioinformatic analyses were done using the software Biomedical Genomics Workbench (CLC Bio, Qiagen). Forty-nine individuals from a Swedish population were genotyped in order to establish genotype frequencies and to evaluate the performance of the assay. The analyses showed to have a balanced coverage among the included loci, and the heterozygous balance showed to have less than 0.5 % outliers. Analyses of dilution series of the 2800M Control DNA gave reproducible results down to 0.2 ng DNA input. In addition, typing of FTA samples and bone samples was performed with promising results. Further studies and optimizations are, however, required for a more detailed evaluation of the performance of degraded and PCR-inhibited forensic samples. In summary, the assay offers a straightforward sample-to-genotype workflow and could be useful to gain information in forensic casework, for both identity testing and in order to solve complex kinship issues. [ABSTRACT FROM AUTHOR]

Several applications necessitate an unbiased determination of relatedness, be it in linkage or association studies or in a forensic setting. An appropriate model to compute the joint probability of some genetic data for a set of persons given some hypothesis about the pedigree structure is then required. The increasing number of markers available through high-density SNP microarray typing and NGS technologies intensifies the demand, where using a large number of markers may lead to biased results due to strong dependencies between closely located loci, both within pedigrees (linkage) and in the population (allelic association or linkage disequilibrium (LD)). We present a new general model, based on a Markov chain for inheritance patterns and another Markov chain for founder allele patterns, the latter allowing us to account for LD. We also demonstrate a specific implementation for X chromosomal markers that allows for computation of likelihoods based on hypotheses of alleged relationships and genetic marker data. The algorithm can simultaneously account for linkage, LD, and mutations. We demonstrate its feasibility using simulated examples. The algorithm is implemented in the software FamLinkX, providing a user-friendly GUI for Windows systems (FamLinkX, as well as further usage instructions, is freely available at ). Our software provides the necessary means to solve cases where no previous implementation exists. In addition, the software has the possibility to perform simulations in order to further study the impact of linkage and LD on computed likelihoods for an arbitrary set of markers. [ABSTRACT FROM AUTHOR]

The use of genetic markers located on the X chromosome has seen a significant increase in the last years and their utility has been well studied. This paper describes the software FamLinkX, freely available at http://www.famlink.se , implementing a new algorithm for likelihood computations accounting for linkage, linkage disequilibrium and mutations. It is obvious that such software is sought for among forensic users as more and more X-chromosomal markers become available. We provide some simulated examples demonstrating the utility of the implementation as well as its application in forensic casework. Though algebraic derivations are generally unfeasible, the paper outlines some theoretical considerations and provides a discussion on the validation of the software. The focus of this paper is to compare the software to existing methods in a forensic setting, perform a validation study as well as to provide an idea of the discriminatory power for X-chromosomal markers. [ABSTRACT FROM AUTHOR]

The vast majority of human familial identifications based on DNA end up with a well founded conclusion, normally using a standard set of genetic short tandem repeat (STR) loci. There are, however, a proportion of cases that show ambiguous results. For such occasions a number of different supplementary markers could be typed in order to gain further information. There are numerous markers available for such supplementary DNA typing, including STRs, deletion and insertion polymorphisms (DIPs), and single nucleotide polymorphisms (SNPs). The purpose of this work was to describe a precise method for decision making, aiming to aid the comparison of different sets of markers for different case scenarios in order to find the most efficient set for routine casework. Comparisons are based on a particular function relating the expected additional value of information from new data to the amount of information already obtained from initial data. The function can be computed approximately by approximating likelihood-based error rates using simulation. In this paper we focused on paternity investigations, more specifically the use of supplementary markers in cases where a smaller number of genetic inconsistencies make the matter inconclusive. We applied the method to a comparison of three different kits: Investigator HDplex (STRs), Investigator DIPplex (DIPs), and the SNPforID-plex (SNPs) to study their efficiencies in gaining information in different case scenarios involving various alternative relationships between the tested man and the tested child. We show that the Investigator HDplex was the most efficient set of supplementary markers for the standard paternity case. However, for paternity cases with a close relative being the alternative father, the Investigator HDplex and the SNPforID-plex showed similar patterns in their ability to deliver a well-founded conclusion. The Investigator DIPplex was the least efficient set. [ABSTRACT FROM AUTHOR]

In relationship testing the aim is to determine the most probable pedigree structure given genetic marker data for a set of persons. Disaster Victim Identification (DVI) based on DNA data from presumed relatives of the missing persons can be considered to be a collection of relationship problems. Forensic calculations in investigative mode address questions like “How many markers and reference persons are needed?” Such questions can be answered by simulations . Mutations, deviations from Hardy–Weinberg Equilibrium (or more generally, accounting for population substructure) and silent alleles cannot be ignored when evaluating forensic evidence in case work. With the advent of new markers, so called microvariants have become more common. Previous mutation models are no longer appropriate and a new model is proposed. This paper describes methods designed to deal with DVI problems and a new simulation model to study distribution of likelihoods. There are softwares available, addressing similar problems. However, for some problems including DVI, we are not aware of freely available validated software. The Familias software has long been widely used by forensic laboratories worldwide to compute likelihoods in relationship scenarios, though previous versions have lacked desired functionality, such as the above mentioned. The extensions as well as some other novel features have been implemented in the new version, freely available at www.familias.no . The implementation and validation are briefly mentioned leaving complete details to Supplementary sections. [ABSTRACT FROM AUTHOR]

Abstract: Ideally for use in forensic analyses, genetic markers on the same chromosome should be more than 50 Mb in physical distance to ensure full recombination and thus independent inheritance. The forensic community has given attention to two STR markers, D12S391 and vWA, that are 6.3 megabases (Mb) apart on chromosome 12. Recent studies have shown no significant linkage disequilibrium between vWA and D12S391 in U.S. and worldwide populations, although genetic linkage has been identified. It is important to evaluate the impact of linkage effects on kinship analysis. In this study, we aimed to determine a more precise measurement of the recombination frequency between vWA and D12S391 based on a larger number of informative meiosis than has been studied previously. We estimated the recombination frequency (θ) to 0.089 (95% CI 0.044–0.158). Using pedigrees simulated under specific kinship scenarios where recombination was expected to affect the likelihood ratio (LR), we evaluated the impact on LR values of including or ignoring linkage between vWA and D12S391. For all pedigree scenarios considered, on average, LR values ignoring linkage were slightly underestimated than when linkage was considered. However, in the incest scenario considered, LR values could be overestimated up to 25–30 times when linkage was ignored. We demonstrate that the effect of ignoring linkage in the likelihood ratio calculation can be considerable. These results suggest that linkage should be considered during kinship analysis when vWA and D12S391 are tested for pedigrees where a recombination could impact the LR value. [Copyright &y& Elsevier]

Abstract: The present number of STR loci adopted in relationship testing is chiefly limited to unlinked markers, in most cases residing on different chromosomes. In order to solve more complex cases of relatedness, e.g. deficient paternities and disputed sibships, the number of core loci can be extended. The inclusion of multiple loci on the same chromosome will, however, increase the risk of possible linkage between markers. We present a new software, FamLink, freely available from http://www.FamLink.se, that can perform statistical calculations based on pedigree structures and account for linkage between pairs of markers. In addition, FamLink can simulate genotype data in order to study the effect of accounting for linkage or not. We demonstrate the importance of taking linkage properly into account using examples and real cases. [Copyright &y& Elsevier]

Abstract: In the past decades, microarray technology has definitely put an edge to the field of genetic research. Our aim was to determine whether single nucleotide polymorphism (SNP) microarrays could be used as a tool in establishing genetic relationships where current molecular genetic methods are not sufficient. We used the Genechip, Affymetrix GenomeWide SNP Array 6.0, which detects more than 900,000 SNP markers dispersed throughout the human genome. The intention was to find a good selection of SNP markers that could be used for statistical evaluation of relatedness in a forensic setting. We conducted pairwise comparisons in the R-package FEST as well as pedigree comparisons in Merlin. Our methods were applied on two separate families, where relationships as distant as 3rd cousins were known. In addition, a question about a possible common ancestry between the two families was tested. Relationships as distant as 2nd cousins could be readily distinguished both from unrelated and other, genetically, closer relationships. This was achieved with a selection of 5774 markers, where each pair of markers was separated by a genetic distance of at least 0.5cM (centiMorgan). When considering 3rd cousins, and more distant relationships, the number of markers needs to be extended, consequently decreasing the genetic distance between the markers. However, inclusion of a too large number of markers presents new challenges and our results imply that the use of too dense sets of markers always yields the highest probability for the genetically closest relationship hypothesis. Simulations confirm that this is most probably caused by the fact that the computational model assumes linkage equilibrium between markers, a problem that will be further evaluated. Our results do however suggest that SNP-data derived from microarrays are well suited for kinship determination provided linkage disequilibrium is properly accounted for. [Copyright &y& Elsevier]

Abstract: X-chromosomal short tandem repeats (X-STR) have proven to be informative and useful in complex relationship testing. The main feature of X-STR markers, compared to autosomal forensic markers, is that all loci are located on the same chromosome. Thus, linkage and linkage disequilibrium may occur. The aim of this work was to study population genetic parameters of eight X-STR markers, located in four linkage groups. We present haplotype frequencies, based on 718 Swedish males, for the four linkage groups included in the Argus X-8 kit. Forensic efficiency parameters have been calculated as well as the allelic association between the tested markers for detection of linkage disequilibrium. To study the occurrences of recombination between the loci, both Swedish and Somali families were typed. A mathematical model for the estimation of recombination frequencies is presented and applied on the family samples. Our study showed that the tested markers all have highly informative forensic values and that there is a significant degree of linkage disequilibrium between the STR markers within the four linkage groups. Furthermore, based on the tested families, we also demonstrated that two of the linkage groups are partially linked. A consequence of these findings is that both linkage and linkage disequilibrium should be accounted for when producing likelihood ratios in relationship testing with X-STR markers. [Copyright &y& Elsevier]

Abstract: To meet the demands to solve more complex cases, we are in need of more markers than the short tandem repeats (STR-markers) at present available in the forensic community. As a complement, the single nucleotide polymorphisms (SNP''s) may play an important role. A basis for genetic calculations is a solid frequency database. The aim of this work has been to build a database with Swedish frequencies appropriate for 49 of the 52 SNP-multiplex developed by the SNPforID consortium. A set of 78 samples from unrelated individuals with Swedish names was amplified with SNP-primers and run in a capillary instrument as described by the consortium. All data were checked for Hardy–Weinberg equilibrium and linkage disequilibrium. Significant p-values could not be found. An additional aim was to get an idea of the mutation frequency of the SNP''s. 236 meiosis were tested, which correspond to 11,564 possible mutation spots. Mutations were not found in the material. [Copyright &y& Elsevier]

Use of X-STR markers extends and gives additional possibilities to a forensic DNA expert for kinship analysis. FamLinkX is software for the calculation of likelihood ratios (LRs) for kinship cases based on X-STR DNA profiles that takes linkage and linkage disequilibrium as well as mutations of X-STR markers into account. Belarusian haplotype frequencies database of 360 unrelated Belarusian males has been uploaded to FamLinkX. LR values for 6 deficient paternity cases and 2 forensic cases involving two putative full siblings, females, were calculated with different values of lambda ( λ = 1, 10, 100) in order to account for uncertainties in the haplotype frequency estimation. To demonstrate the ethnic sensitivity of X-STR markers and importance of the choice of the appropriate X-STR population database for LR calculation we calculated LR values for the same kinship cases using Belarusian and Swedish X-STR databases. LR values for the same kinship case differed from each other up to 6000 times depending on the chosen database. X-STRs genotyping lets us to determine relatedness successfully in all cases whereas the results of autosomal STR profiling and mitochondrial sequencing (for the cases where only the samples of putative full-siblings were available) were not sufficient to resolve family relationships issues. LR values were considered to be high enough in all cases. [ABSTRACT FROM AUTHOR]