In a class by itself is the mitochondrial DNA of Ashkenazi women. It does not correlate closely with the DNA of non-Jewish women in Western, Central, or Eastern Europe and it has a large Middle Eastern component. Yet in their maternal lineage, Ashkenazim, too, exhibit a strong “founder effect.” Over forty percent of them, a 2005 study showed, descend from just four “founding mothers” having Middle-Eastern-profile mitochondrial DNA. Since Ashkenazi Y-chromosome DNA does not exhibit so dramatic a founder’s effect, one can assume that Ashkenazi Jewry, too, began with the migration of a preponderantly male group of Jews to new territories. Because these territories, however, were more contiguous with the old ones than were far-flung regions like Bukhara or Yemen, the men were more able to import wives from existing Jewish communities and less dependent on marrying local Gentiles.
But where did Ashkenazi Jewry, male and female alike, derive from if not from the Rhineland? One possibility that is more consistent with the linguistic data is that it entered southern Germany from northern Italy and pushed further north from there into the Slavic-speaking areas of Europe. Another is that Jews migrated to Slavic lands from the Byzantine Empire. These hypotheses, which are not mutually exclusive, can now claim a measure of scientific support, since the Y chromosomes of Ashkenazi Jews have more in common with those of Italians and Greeks than with those of West Europeans.
[. . .]
As far as much of the rest of the world is concerned, biological Jewishness has always been an embarrassing anachronism—at least ever since the time of the Roman Empire and early Christianity. For the most part, Jews have nevertheless managed to go their own unembarrassed way. The genetic record shows that they have on the whole succeeded.
[Hillel Halkin, "Jews and Their DNA", September 2008]