Probably Roman by historical connection.

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Ashkenazi Jews descend from a very specific ethnic genetic lineage. I realize I could convert and no longer be Jewish, or someone with no genetic relatives who are Jews could convert into Judaism. I realize your belief doesn’t change your genes and vice versa.

But Jews who come from other Jews who were born Jews tend to come from a specific genetic family tree, one that came to Europe with the Romans as soldiers, slaves, merchants, and sometimes even royalty, where many took European spouses and had babies that were roughly half European and half Levantine. Which is why Ashkenazi and Sephardic Jews have European genetic features. The key though is that due to prejudice, at certain pivotal moments and places in history, the European admixture was severely limited and Jews were murdered in medieval quantities that approach genocide. This resulted in genetic bottlenecks described in the article.

The challenge then is the mystery of which European community or communities created the bulk of the Ashkenazi European genetic family tree. There are a lot of theories involving everything from Carolingian France (tolerant of Jews) to Germanic pagans along the Rhein to Italians and other mid-late Roman Empire peoples. The truth is probably a little of all of this, since many Catholic and Lutheran Europeans also have Jews in their family trees dating back to medieval times.

But generic bottlenecks create major challenges in identifying admixture populations because the genes themselves don’t have racial or religious traits, they can only be used to compare to other generic populations to source a common ancestor. The problem is that when prejudice and genocide severely limit a genetic community to a small population of founders, your genes resemble that community far more than any other community, creating a distinctive genetic pattern that is hard to match with others. So while we know that Ashkenazi and Sephardic Jews have European admixture, it’s currently impossible to identify with certainty who those people were.