Theory and statistics of mutation rates: A mathematical framework reformulation for forensic applications

Mutation is a fundamental topic in forensic genetics since the calculation of kinship likelihoods depends on estimates of germinal mutation rates. Germinal mutation rates have been computed by simply proportioning the number of true parent(s)-child genotypic configurations inconsistent with Mendelian segregation. For STRs, current technology is based on PCR fragment size determination and germinal mutations are detected when parent-child do not share alleles' length. For technical reasons, it is uncommon to obtain the sequence composition of STR alleles, and the identification of the allele that mutated is based on assumptions. It has been assumed that one-step are much more common than multi-step mutations. Whenever a genotypic parent-child configuration is compatible with Mendelian rules by a single-step mutation, this is the one assumed, despite other possible mutational events. Multi-step events are therefore evoked exclusively when a single-step cannot reconcile the observation with the true kinship, leading to an overestimation of single step mutation rates. For any mode of transmission other than purely haploid it is theoretically impossible to identify both the allele at “origin” (in parents) and at “destination” (in offspring). Therefore, a more sophisticated statistical framework than the simple proportioning is then required to properly evaluate mutation rates. Moreover, the possibility of the occurrence of silent alleles should be simultaneously modeled since it has to be considered whenever an apparently homozygous individual is involved.