We tested the continuity of populations as described by Brandt et al.24 with an absolute frequency of 22–37 mtDNA haplogroups. We performed tests assuming three effective population sizes (Ne = 500; 5,000; 500,000), and compared Avars with all conquest-period Hungarians, and with the southeast group of the latter (n = 45), who lived on the territory of the preceding Avar group. We also compared 10th–12th century and modern-day Hungarians and the culturally isolated minority populations, Szeklers and Csangos, who live in Romania (Supplementary Table S7).