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.