This article presents a formal and mathematically well-supported framework where a general counting rule is given, allowing a secure and expeditious decision on the usefulness of typing (unlinked) X-chromosomal markers on pairwise kinship testing involving two non-inbred individuals. Moreover the counting rule now presented allows the derivation of algebraic expressions for the joint genotypic probabilities associated with any pedigree.
In studies involving pedigree reconstruction and kinship estimation, it is acknowledged that some pedigrees have the same algebraic expressions for the joint genotypic probabilities and are, therefore, indistinguishable when considering only genetic information, no matter what the mode of transmission considered. Indeed, although standard forensic practice considers solely unlinked autosomal markers, the existence of pedigrees with the referred theoretical property (that are then said to belong to the same kinship class) is possible when considering any kind of genetic transmission. The research on genetic relatedness has always been linked to the root concept of identity-by-descent (IBD). However, although the basic theoretical core for autosomal transmission has been long formalized, a general method allowing the decision if two pedigrees linking two non-inbred individuals are distinguishable using unlinked autosomal markers along with the respective IBD partitions (and consequently the algebraic expressions for the joint genotypic probabilities) was only recently published. In this work X-chromosomal transmission will be at stake, considering that the analytical framework for X-chromosomal markers has been recently established and the importance of X-chromosome markers for these questions has been steadily growing, particularly in forensics, as a tool both to complement the information given by autosomes in complex kinship testing cases and to differentiate pedigrees belonging to the same autosomal kinship class. Therefore, here it will be presented a formal and mathematically well supported framework where a general counting rule is given, allowing a secure and expeditious decision on the usefulness of typing (unlinked) X-chromosomal markers on pairwise kinship testing involving two non-inbred individuals. Moreover the counting rule now presented allows the derivation of algebraic expressions for the joint genotypic probabilities associated with any pedigree. (Published Abstract)