The comparative modern mtDNA datasets with detailed information on geographic origin were used for the GDM. From these datasets, we performed genetic distance calculations in two ways. First, we used high resolution haplogroup frequency tables of 157 populations (n = 49,439 individuals), differentiating 211 sub-haplogroups. We calculated genetic distances of these modern populations from the three Carpathian Basin medieval populations (Supplementary Table S13). Second, we randomly chose maximum 140 sequences per population (n = 18,499 sequences altogether), in order to balance the differences in sample sizes, and calculated FST values between medieval Carpathian Basin and 141 present-day populations. The sequence length was uniform, ranging np 16068–16365 (Supplementary Table S14). The analysis was performed in Arlequin software, using Tamura & Nei substitution model47, with a gamma value of 0.177. For the haplotype definition, the original definition was used. FST values between conquerors, Avars, and the contact zone population and each modern population were combined with longitudes and latitudes according to population information in the literature. The FST values and coordinates were interpolated with the Kriging method implemented in Arcmap ArcGIS version 10.3.