Most Ashkenazi Jews have some non-Jewish convert to Judaism ancestors

A large percentage of the maternal ancestors of modern Ashkenazi Jews were European woman, especially Italians, who converted to Judaism during Roman Empire times, according to a report in Science Daily Oct. 8, 2013, of a research project using the new science of archaeogenetics to settle a long-standing controversy about the origin of Europe’s Ashkenazi Jews.

Are Ashkenazi Jews (Jews of eastern and central European origin who historically spoke Yiddish, a Judeo-German language) principally descended from forbears who came from the Land of Israel in the first to third century?

Or were most of Ashkenazi Jews’ ancestors Europeans who converted to Judaism in the centuries before the Church convinced Christian governments to make conversion to Judaism a crime?

An article in the journal Nature Communications by Professor Martin Richards, entitled “A substantial prehistoric European ancestry amongst Ashkenazi maternal lineages.” claims to have settled the question.

Analysis of a very large number of mitochondrial DNA samples (that trace maternal lines only) has shown that on the female line, Ashkenazim are descended not from the Near East or from Khazaria in the North Caucasus; but from southern and western European females who married into the Jewish community.

Ashkenazi Jewish lineages were among the large quantity of publicly available mitochondrial genomes of people from Europe, the Caucasus and the Middle East that entered the analysis. In a large majority of cases, Ashkenazi lineages are most closely related to those of southern and western Europe from many centuries ago.
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This suggests that, many Jewish men who migrated into Europe from Palestine around 2,000 years ago, married European women who became Jewish. This seems to have happened first along the Mediterranean coast, especially in Italy, and later — but probably to a lesser extent — in western and central Europe and North Africa.

Thus, on the female line of descent, a large percentage of Ashkenazi Jews can trace part or most of their ancestry to local female converts to Judaism from southern and western Europe.