Discrimination of half-siblings when maternal genotypes are known

Pairwise relatedness testing in the context of inbreeding: expectation and variance of the likelihood ratio

In this paper we investigate various effects of inbreeding on the likelihood ratio (LR) in forensic kinship testing. The basic setup of such testing involves formulating two competing hypotheses, in the form of pedigrees, describing the relationship between the individuals. The likelihood of each hypothesis is computed given the available genetic data, and a conclusion is reached if the ratio of these exceeds some pre-determined threshold. An important aspect of this approach is that the hypotheses are usually not exhaustive: The true relationship may differ from both of the stated pedigrees. It is well known that this may introduce bias in the test results. Previous work has established formulas for the expected value and variance of the LR, given the two competing hypotheses and the true relationship. However, the proposed method only handles cases without inbreeding. In this paper we extend these results to all possible pairwise relationships. The key ingredient is formulating the hypotheses in terms of Jacquard coefficients instead of the more restricted Cotterman coefficients. While the latter describe the relatedness between outbred individuals, the more general Jacquard coefficients allow any level of inbreeding. Our approach also enables scrutiny of another frequently overlooked source of LR bias, namely background inbreeding. This ubiquitous phenomenon is usually ignored in forensic kinship computations, due to lack of adequate methods and software. By leveraging recent work on pedigrees with inbred founders, we show how background inbreeding can be modeled as a continuous variable, providing easy-to-interpret results in specific cases. For example, we show that if true siblings are subjected to a test for parent-offspring, moderate levels of background inbreeding are expected to inflate the LR by more than 50%.

Key individuals for discerning pedigrees belonging to the same autosomal kinship class

The existence of pedigrees belonging to the same kinship class (i.e. indistinguishable through independent markers) is well known in the forensic community, and theoretical frameworks for autosomal and X-chromosomal markers were already developed for a pair of individuals. Nevertheless, studies for the cases where a greater number of individuals is available for testing are still lacking. With this work, we intend to pave the way for a theoretical and general framework, identifying the individuals/relatives that should be chosen to distinguish autosomal analyses between such pedigrees. In this work we identify the individuals/relatives that are non-informative for calculations (the pedigrees under discussion remaining indistinguishable independently of their genetic profile), as well as those that will likely be very informative, influencing the statistical outcome. For example, given the respective genotypes, to compare the likelihoods of the father of the individual B to be: (a.) the father, or (b.) a full-brother, of the individual A, the hypotheses H₁: "The individual A is paternal half-sibling of the individual B", and H₀: "The individual A is paternal uncle/aunt of the individual B" are considered. It is proved that considering just individuals A and B the hypotheses are equally likely. In this work we show that the same is also true for the case where the mother of B is available for testing, notwithstanding the hypotheses being differently weighted if the mother of A is considered. Similar considerations are done for other kinship hypotheses and/or individuals/relatives. Irrelevance of the genetic profile of some specific relatives are mathematically demonstrated, and data obtained from 20,000 simulated families are presented for the other cases.

On the use of dense SNP marker data for the identification of distant relative pairs

There has been recent interest in the exploitation of readily available dense genome scan marker data for the identification of relatives. However, there are conflicting findings on how informative these data are in practical situations and, in particular, sets of thinned markers are often used with no concrete justification for the chosen spacing. We explore the potential usefulness of dense single nucleotide polymorphism (SNP) arrays for this application with a focus on inferring distant relative pairs. We distinguish between relationship estimation, as defined by a pedigree connecting the two individuals of interest, and estimation of general relatedness as would be provided by a kinship coefficient or a coefficient of relatedness. Since our primary interest is in the former case, we adopt a pedigree likelihood approach. We consider the effect of additional SNPs and data on an additional typed relative, together with choice of that relative, on relationship inference. We also consider the effect of linkage disequilibrium. When overall relatedness, rather than the specific relationship, would suffice, we propose an approximate approach that is easy to implement and appears to compete well with a popular moment-based estimator and a recent maximum likelihood approach based on chromosomal sharing. We conclude that denser marker data are more informative for distant relatives. However, linkage disequilibrium cannot be ignored and will be the main limiting factor for applications to real data.

Inspecting close maternal relatedness: Towards better mtDNA population samples in forensic databases

Reliable data are crucial for all research fields applying mitochondrial DNA (mtDNA) as a genetic marker. Quality control measures have been introduced to ensure the highest standards in sequence data generation, validation and a posteriori inspection. A phylogenetic alignment strategy has been widely accepted as a prerequisite for data comparability and database searches, for forensic applications, for reconstructions of human migrations and for correct interpretation of mtDNA mutations in medical genetics.

There is continuing effort to enhance the number of worldwide population samples in order to contribute to a better understanding of human mtDNA variation. This has often lead to the analysis of convenience samples collected for other purposes, which might not meet the quality requirement of random sampling for mtDNA data sets. Here, we introduce an additional quality control means that deals with one aspect of this limitation: by combining autosomal short tandem repeat (STR) marker with mtDNA information, it helps to avoid the bias introduced by related individuals included in the same (small) sample. By STR analysis of individuals sharing their mitochondrial haplotype, pedigree construction and subsequent software-assisted calculation of likelihood ratios based on the allele frequencies found in the population, closely maternally related individuals can be identified and excluded. We also discuss scenarios that allow related individuals in the same set.

An ideal population sample would be representative for its population: this new approach represents another contribution towards this goal.

The mating system of polar bears: a genetic approach

Parentage analysis data for 583 individuals genotyped at 27 microsatellite loci were used to study the mating system of polar bears ( Ursus maritimus Phipps, 1774) in the Barents Sea area. We discriminated statistically between full and half-siblings identified through only one common parent. We document for the first time multiple paternity in polar bears. We demonstrated for both sexes low fidelity to mating partners over time. We did not detect any significant difference between the age distribution of adult males at capture and the age distribution of males siring cubs. This might indicate that the male’s age and size are less indicative of the reproductive success than previously thought. This is further supported by a rather long mean litter interval of 3.9 years for males siring several litters. The mating system of polar bears in the Barents Sea appears to be promiscuous, usually with a single successful father siring full siblings within a year, but with consecutive litters of a mother being fathered by different males. We discuss how population density, landscape characteristics, and adult sex ratio might influence the mating system of polar bears. This is of particular importance for management decisions such as, e.g., implementing sex ratios in hunting quotas.

Identification of distant family relationships

MOTIVATION

Family relationships can be estimated from DNA marker data. Applications arise in a large number of areas including evolution and conservation research, genealogical research in human, plant and animal populations, forensic problems and genetic mapping via linkage and association analyses. Traditionally, likelihood-based approaches to relationship estimation have used unlinked genetic markers. Due to the fact that some relationships cannot be distinguished from data at unlinked markers, and given the limited number of such markers available, there are considerable constraints on the type of identification problem that can be satisfactorily addressed with such approaches. The aim of this article is to explore the potential of linked autosomal single nucleotide polymorphism markers in this context. Throughout, we will view the problem of relationship estimation as one of pedigree identification rather than identity-by-descent, and thus focus on applications where determination of the exact relationship is important.

RESULTS

We show that the increase in information obtained by exploiting large sets of linked markers substantially increases the number of problems that can be solved. Results are presented based on simulations as well as on real data.

AVAILABILITY

The R library FEST is freely available from http://folk.uio.no/thoree/FEST.

Considerations for the interpretation of STR results in cases of questioned half-sibship

Likelihood ratios (LRs) were calculated for a cohort of 60 pairs of true half-sibs and compared with LR values calculated for unrelated, paired children. STR results for the half-sib group were obtained from 60 archived cases involving a true mother, two children, and an alleged father subjected to typing with a multiplex STR kit (Identifiler multiplex, Applied Biosystems) and in which the alleged father was excluded as the father of only one of the two children (half-sib pairs). The distribution of LR values among true half-sibs was compared to those produced from paired, unrelated children selected in two ways: One method for producing unrelated pairs was to randomly select Identifiler profiles from children in 120 distinct paternity cases and group them into 60 ethnically matched pairs (random pairs). In a second approach, the children in the true half-sib group were shuffled and ultimately paired with someone from a different case. A total of 49 ethnically matched, unrelated pairs were created (shuffled pairs). In the shuffled pairs group, comparisons were thus based on a constant set of phenotypes. LRs comparing the probability of half-sibship versus being unrelated were produced for all groups with standard methods. Among pairs of known half-sibs, LRs ranged from a low of 0.1 to a maximum of 3763. Among random and shuffled pairs, LRs ranged from a low of 0.0001 to 12 for shuffled pairs or 42 for random pairs. LRs of greater than 2 were produced in 8 instances among random pairs and in 4 instances among the shuffled pairs. Overall, results suggest that half-sib indices of 30 or greater are fairly characteristic of individuals who are related as half-sibs. In contrast, half-sib indices of 0.1 or less are fairly characteristic of unrelated individuals who claim to be half-sibs. LRs falling between 0.1 and 10.0 are uninformative, as this region represents the overlap in the LR distributions produced from the true and false half-sib groups when the Identifiler multiplex kit is used for testing.

Structured Incorporation of Prior Information in Relationship Identification Problems

The objective of this paper is to show how various sources of information can be modelled and integrated to address relationship identification problems. Applications come from areas as diverse as evolution and conservation research, genealogical research in human, plant and animal populations, and forensic problems including paternity cases, identification following disasters, family reunions and immigration issues. We propose assigning a prior probability distribution to the sample space of pedigrees, calculating the likelihood based on DNA data using available software and posterior probabilities using Bayes' Theorem. Our emphasis here is on the modelling of this prior information in a formal and consistent manner. We introduce the distinction between local and global prior information, whereby local information usually applies to particular components of the pedigree and global prior information refers to more general features. When it is difficult to decide on a prior distribution, robustness to various choices should be studied. When suitable prior information is not available, a flat prior can be used which will then correspond to a strict likelihood approach. In practice, prior information is often considered for these problems, but in a generally ad hoc manner. This paper offers a consistent alternative. We emphasise that many practical problems can be addressed using freely available software.