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It's quite puzzling they're not finding any significant genetic overlap with Finno-Ugric populations. How can then the conqueror and the modern Hungarians speak a Finno-Ugric language? Something just doesn't add up. Unless the Avars were Finno-Ugric speaking and their language persisted into modern Hungarian? There's no evidence of that plus it's generally hypothesized that they were also some type of Turkic speakers.

And how come out of 102 samples from 8 different cemeteries only 4 Y hgs were sequenced?
At the end of the ninth century a new development took place in the Carpathian Basin: the people that later became known as the Magyars arrived. Vámbéry estimates the numbers of the new arrivals as being “a few thousand” [néhány ezer], and he has no doubt that these Turkish-Tatar warriors melted into the mass of local peoples. In doing so, Vámbéry explains, they exchanged their “pure Turkish language” for the “mixed language” of their Pannonian “relatives.” Though the new arrivals were few, their “militaristic spirit”, characteristic of their not yet adulterated nomadic lifestyle, inspired the Carpathian Basin’s post-Avar population to rise to remarkable deeds again as exemplified by their military expeditions far and wide in Europe. Furthermore, according to Vámbéry, the union of these two peoples had long-term benefits for the newly arrived conquerors as well.