Pedigree likelihood formulae based on founder and founder couple symmetry and validation of DNA testing software

Pedigree likelihood ratios are widely used in forensic genetics. Linkage of genetic markers affects the pedigree likelihood ratio. In this study, a series of novel formulae was established based on simplification due to founder and founder couple symmetry of the Lander-Green algorithm for dealing with linkage. These new formulae are based on the inheritance vectors and differ from existing formulae that are based on the number of alleles shared identical-by-descent. In contrast to previous formulae, the formulae of this study expand the calculation to more general relationships, which enables specifying the number of typed individuals in pedigrees, and the new formulae are no longer limited to calculation of pairs of linked markers. Alternatively, pedigree likelihood values incorporating multiple linked markers could be obtained by iterating the vector transition probability between pairs of linkage markers and the probability of genotypes of typed individuals given inheritance vectors; the vector transition probability formulae are provided in a table form. To demonstrate utilization of the proposed formulae system, a series of cases were designed based on the relationships to validate GeneVisa software (www.genevisa.net) with frequency data of three linked markers, SE33-D6S1043-D6S474, on chromosome 6. The calculation results were verified with the FamLink software. The results demonstrated that the proposed formulae can correctly obtain the pedigree likelihood ratio, demonstrating the application potential of these formulae to verify effectiveness of DNA testing software.