From the article:
"All of the Ashkenazi Jews alive today can trace their roots to a group of about 330 people who lived 600 to 800 years ago..."
I've been following this story for some time. I've seen other genetic anthropologists disagree with parts of this article--for example, that the estimates of generation length are too short, and perhaps some other estimates of genetic drift or with the choice of comparison population. Different but seemingly reasonable interpretations of the same data also give us 440 people about 1,000 or 1,200 years ago, which gets us into the correct ballpark for the actually documented historical migration of Jewish people from Italy to the Ashkenazi heartland.
This was about the same time the Germans moved into a lot of these areas, too, btw. Germans settled western Germany was settled long before eastern Germany. I don't have the exact dates at hand, but many German cities were founded surprisingly (to me, at least, except for the part where it exactly confirmed a theory I'd developed based on regional temperaments,) late. To be clear, the Jews had lived in many areas for just as long as everyone else, and if they arrived later, it was often by invitation of the local elites, who believed the Ashkenazim would improve their economies.
If the later date estimates are correct, they imply a tremendous tragedy.
Ashkenazi Y-DNA (that is, ancestral men,) appears largely Middle Eastern. The MtDNA (from the mother's side,) appears largely Italian. That is, initial Jewish migrants from the Middle East to Italy were mostly men. They married Italian women, and their descendants--perhaps 330 to 440 of them--later moved to the area later known as Germany.
This rather destroys the whole "Khazar" theory of Ashkenazi origins.
I think it is a mistake to conclude that the Askenazi did not marry Germans based on this data, though. I suspect that the children of German-Jewish unions tended to chose due to social oppression to embrace the opportunities afforded by their Gentile-side and entered the general German population. Likewise, people who self-identify as Basque show little of the ancestry that is probably common to the original Indo-European speakers, while Spaniards do have that ancestry. You might conclude that Basques and Spaniards haven't mixed, but Spaniards show some Basque ancestry--people who were half-Basque/half-Spaniard have probably tended to identify as Spaniard instead of Basque.
Today, of course, the Jewish demographic situation is changing rapidly, but that's a subject for another day.