Calculating Methods of Grandparent Index in the Presence of Mutation under Three Conditions

Kinship analysis of grandparents and grandchildren is an important content in the field of forensic identification, which includes three subtypes:double grandparents and biological mother test (DGBM), double grandparents and alleged mother test (DGAM), and double grandparents test (DG). Until now, no systematic formula has been reported in grandparent index (GI) calculation of grandparent identification in the presence of mutation, apart from few simple calculation methods of partial gene combination in DGBM. In this study, we first created a simplified representation model of grandfather and grandmother in 5 subtypes, in the form of a set of genotypes. The general probability formula of mutation of parent genotype into child genotype (P_(DG→Z)) was derived in 12 subtypes. Furthermore, the general formulas of GI under three conditions were derived: GI of double grandparents and biological mother (GI_DGBM), GI of double grandparents and alleged mother (GI_DGAM) and GI of double grandparents (GI_DG). The detailed formulas were further refined according to genotypes of double grandparents, mother and grandchild. In addition, the percentages of mutations of 5 genetic types in the group of unrelated individuals on 30 STR loci of the EX30 kit were calculated. Finally, models of simulated kinship groups and unrelated individual groups were established respectively. The geometric mean (Π) and 95% confidence interval (CI) of CGI, the percentages of cases where CGI<10000 in kinship groups, and the percentages of cases where CGI>0.0001 in unrelated individual groups were calculated in the same 30 STR loci. In this study, the novel formulas can be used to calculate all kinds of GI in the presence of mutation under three conditions. The genotype combinations in all mutation cases were reviewed. Among them, the occurrence rate of both paternal and maternal mutation groups was 13.31%, which could not be ignored. In EX30 kit, the formulas can achieve firm conclusions in DGAM cases for both the kinship group and unrelated individual group;in DGBM cases identifications, all cases in the kinship group and 99.89%cases in the unrelated individual group could be correctly identified;and more genetic markers should be added for DG cases. The geometric mean of CGI in kinship groups sorted by value were as following: Π_DGAM>Π_DGOM>Π_DG, and the rule in unrelated individual groups were as following: Π_DGAM<Π_DGOM<Π_DG. The results of this study show that the here-derived GI formulas could be applied to kinship analysis of grandparents and grandchildren in the presence of mutation under three conditions, which is of high application potential.