mumimor: "I was really surprised at how much peasants and generally poor people moved around."
If your family tree doesn't branch... you might be European.
That might be quite a large assumption given the tendency of the ruling class to breed with each other and the relative immobility of the peasants.
Many people object to this, arguing that modern-day isolated populations must be an exception. But it doesn’t take very much migration: just one “outsider” who bore a child into an isolated group sometime in the last few thousand years would suffice. Another example from Rohde, Olsen, and Chang’s paper: their simulation assumes 10 migrants across the Bering strait every generation; but decreasing this to one migrant every 10 generations (300 years!) only increases their estimate by a few hundred years.
1 in 200 men are direct descendants of Genghis Khan
As has been said on one of the other threads, statistical likelihood assuming social and physical mobility is highly flawed. Even the data on the FAQ says that people on the Italian and Iberian peninsulas are less related than other branches.
If all Europeans share the same set of common ancestors 1000 years ago (and likely many shared ancestors more recently), how can there be variation in the number of shared ancestors?
You can be related to the same ancestor multiple times. For instance, someone could be your great, great, great, great, great grandfather on your mother’s side and also on your father’s side. Because of this, you and I can share the same ancestral individual as a common ancestor many times over. People who share more common ancestors have more overlap this degree of relatedness. We can measure this difference through degree of shared genome, since even when everyone is a common genealogical ancestor, not everyone is a common genetic ancestor.
Things like this are why I wonder whether the descent-from-Charlemagne thing necessarily works for Ashkenazi Jews. It's not logically certain that all Europeans are descended from Charlemagne, and when you consider the high rate of endogamous marriage among some groups you have to wonder whether it's even mathematically certain.
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