Answers to Quora Questions by Yair Davidiy (6 February, 21 Shevet, 5778)
If DNA findings as published in the popular press are correct then the answer is , Yes.
DNA studies concerning ethnic origins usually concentrate on either YDNA which is male transmitted, from father to son indefinitely, or on mtDNA which goes through the female from mother to daughter.
[Personally I think that ENVIRONMENT determines DNA at historically distinct moments BUT we are here dealing with what conventional opinion says. We are not discussing my own views or lack of them.]
Regarding Ashkenazi Jews present thinking goes like this in very general terms:
In northwest Italy there is a region named Tuscany. In Ancient Times this area was settled by Etruscans. The Etruscans originally came (at least in part) from Lydia which was in what is now Western Turkey. DNA tests on Italians from Tuscany indicate some connection to people from some areas of Western Turkey. Ashkenazi mtDNA is close (at ca. 60%) to Italian mtDNA in general and especially to that of Tuscany. It has been suggested that peculiarities of the Ashkenazi Tuscany type mtDNA relate back more to Lydia than to Tuscany. Nothing has been proven on this matter but it may be worth noting.
Incidentally the Lydians descended from Lud a son of Shem.
22 The sons of Shem were Elam and Asshur and Arpachshad and Lud and Aram.
The Israelites were descended from Arpachshad through Abraham but they took many of their women from Aram.
At all events it is now assumed that Ashkenazi Jews came from the Middle East to Europe via Italy. In Italy many women had converted to Judaism and the Ashkenazis lacked women. They married the Italian converts. A genetic bottleneck occurred in which the population diminishes and then expands like water being poured into a bottle from a jug. The result of such a bottleneck is that what emerges may be drastically different, in its relative composition, from what went in to it. Descendants of Jews who had married Italian women became dominant and then migrated to the rest of Europe where they continued to dominate. [Alternately, the bottleneck did not have to take place specifically in Italy. It could have occurred in France or Germany with Jews who had originally came from Italy emerging as the most numerous survivors.] Most Ashkenazis are somehow or other related to each other. If some have Italian ancestry (through their mothers) to a large degree then the chances are that they all have some of it.
There are numerous article on the Web discussing these issues giving more technical details and references.
There are students of Jewish History who may find the above description difficult to accept. It is not exactly consistent with most models of Jewish History. Nevertheless this is what the DNA boys claim so if you have your doubts take it up with them.