X-chromosome markers in kinship testing: A generalisation of the IBD approach identifying situations where their contribution is crucial

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Abstract

The standard practice of forensic kinship evaluation uses unlinked autosomal markers. However, X-chromosome markers have recently gained recognition as a powerful tool to complement the information provided by autosomes, particularly in complex cases.

In this paper, the X-chromosome mode of transmission is addressed in the theoretical identity-by-descent framework. Formulas for the joint genotypic probabilities considering various pedigrees relating two inbred and/or non-inbred individuals are derived.

Finally, the importance of X-chromosome markers is highlighted by the fact that, in addition to complementing the autosomal information, X-chromosome transmission allows differential weighting of certain hypotheses regarding pedigrees belonging to the same autosomal class, i.e., pedigrees that are indistinguishable by the use of unlinked autosomal markers. Illustrative examples of common kinship testing are shown.

Introduction

A major share of the forensic genetics practical work is related with kinship evaluation. In fact, from identity to very complex genealogies, what is asked of the expert is to evaluate the posterior probability of genetic kinships between samples and/or individuals given a specific phenotype constellation (or the computation of likelihood ratios between the probabilities of alternative pedigrees). Indeed, in forensics the use of likelihood ratios has become globally accepted as the best way to evaluate genetic evidence, comparing the probability of the observations under the claimed kinship with the probability of the same observations under the alternative hypothesis of kinship (e.g., [1]). For this, the use of unlinked autosomal markers is currently standard practice in forensic laboratories (e.g., [1]). However, whatever the mode of transmission considered, there are pedigrees that are indistinguishable when the information available is limited to unlinked (or totally linked) markers [2]. Considering unlinked autosomal markers, the most common examples of indistinguishable pedigrees between two non-inbred individuals are avuncular, half-siblings and grandparent–grandchild [2]. Due to their relevance in the forensic field, it is also important to mention that the incestuous father–child relationships where the father is also father, brother or son of the child's mother (only the child is inbred) are also indistinguishable, when analyzing mother–child pair.

In this study the heterogametic transmission of X-chromosome specific markers was analyzed, since it has recently gained importance in kinship testing [3], [4] and could play an important role in the identification of related victim remains in mass disasters, for example, where solely genetic information is available. The use of X-linked genetic information has been already addressed and freely available software has also been released [5]. However, it has not gained wide use in forensic context and, as the authors recognise, it has not been validated, explicit formulas were not published and the software may be difficult to implement for most potential users.

In this paper, a theoretical framework for this mode of transmission is presented and formulas for different pedigrees involving two individuals will be deduced. Moreover, some cases in which X-markers can solve kinship situations that are indistinguishable if autosomal unlinked markers alone are used, will be highlighted.

The study of kinship requires the analysis of identical-by-descent (or IBD) alleles, since given two individuals their joint genotypic probabilities only depend on the IBD partitions and on the frequencies of the involved alleles [6], and therefore all the results will be based on the complete set of IBD measures for X-chromosome markers.

Section snippets

Definitions

Two alleles are said to be IBD if they have descended from the same ancestral allele [6]. Note that, without mutation, IBD equates identity-by-state (IBS), but the reciprocal is not the case (see Box S1 in Supplementary Material, for an example). Furthermore, IBS is an observable trait while IBD is not [6]. Two individuals are said to be related if their coancestry coefficient is non-null; that is equivalent to say, if an allele of one can be IBD to an allele of the other [7].

A measure of

Identity-by-descent partitions for X-chromosome markers considering two individuals

We present a set of identity-by-descent partitions for X-chromosome specific markers between two individuals: male (M) or female (F), representing each coefficient by a capital lambda Λ, where the subscript is the order of the partition and the superscript the sex combination of the individuals. All the possible sex combinations for two individuals will be considered: female–female (Case 1), female–male (Case 2) and male–male (Case 3).

It must be noted that for pedigrees where the only non-zero

Distinguishing pedigrees belonging to the same autosomal kinship class

We will conclude by analyzing the X-chromosome markers’ contributions to distinguishing pedigrees belonging to the same autosomal kinship class. In Table 4, Table 5 we present a collection of such cases displaying, respectively, the most frequently encountered in routine forensic practice involving two non-inbred individuals: half-sibs, grandparent–grandchild and avuncular, and the incestuous situations: parent plus grandparent–child, parent plus half-sib–child and parent plus uncle/aunt–child,

Acknowledgements

The authors are indebted to Pedro Silva, Thore Egeland and one anonymous reviewer for their fruitful comments and suggestions on this manuscript.

This work was partially supported by Fundação para a Ciência e a Tecnologia through POCI 2010 (Programa Operacional Ciência e Inovação 2010) and PhD grant SFRH/BD/37261/2007.

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