A mathematical framework for genetic relatedness analysis involving X chromosome aneuploidies

The unique features of the X chromosome can be crucial to complement autosomal profiling or to disentangle complex kinship problems, providing in some cases a similar or even greater power than autosomes in paternity/maternity investigations. While theoretical and informatics approaches for pairwise X-linked kinship analyses are well established for euploid individuals, these are still lacking for individuals with an X chromosome aneuploidy. To trigger the fulfilment of this gap, this research presents a mathematical framework that enables the quantification of DNA evidence in pairwise kinship analyses, involving two non-inbred individuals, one of whom with a non-mosaic X chromosome aneuploidy: Trisomy X (47, XXX), Klinefelter (47, XXY) or Turner (45, X0) syndrome. As previously developed for a regular number of chromosomes, this approach relies on the probability of related individuals sharing identical-by-descent (IBD) alleles at one specific locus and it can be applied to any set of independently transmitted markers, with no gametic association in the population. The kinship hypotheses mostly considered in forensic casework are specifically addressed in this work, but the reasoning and procedure can be applied to virtually any pairwise kinship problem under the referred assumptions. Algebraic formulae for joint genotypic probabilities cover all the possible genotypic configurations and pedigrees. Compared with the analyses assuming individuals with a regular number of chromosomes, complicating factors rely on the different possibilities for both the parental origin of the error (either maternal or paternal), and the type of error occurred (either meiotic or post-zygotic mitotic). These imply that a non-inbred female with Triple X or a male with Klinefelter syndrome may carry two IBD alleles at the same locus. Thus, and contrarily to what occurs for the standard case, IBD partitions depend not only on the kinship hypothesis under analysis but also on the genotypic configuration of the analyzed individuals. For some cases, parameters of interest can be inferred, while for others recommended values based on the available literature are provided. This work is the starting point to analyze X-chromosomal data under the scope of kinship problems, involving individuals with aneuploidies, as it will enhance the quantification of the DNA evidence not only in forensics but also in the medical genetics field. We hope it will trigger the development of approaches including other complicating factors, as a greater number of individuals, possibility of the occurrence of mutations and/or silent alleles, as well as the analysis of linked markers.