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Your evidence is backed by some data, but alternative sources claim opposing views:
http://www.ftdna.com/pdf/43026_Doron.pdf is the source for the below:
A 2006 study by Behar et al.,[55] based on high-resolution analysis of Haplogroup K(mtDNA), suggested that about 40% of the current Ashkenazi population is descended matrilineally from just four women, or "founder lineages", that were "likely from a Hebrew/Levantine mtDNA pool" originating in the Middle East in the 1st and 2nd centuries CE. Moreover, a maternal line "sister" was found among the Jews of Portugal, North Africa, France, and Italy. They wrote:
Both the extent and location of the maternal ancestral deme from which the Ashkenazi Jewry arose remain obscure. Here, using complete sequences of the maternally inherited mitochondrial DNA (mtDNA), we show that close to one-half of Ashkenazi Jews, estimated at 8,000,000 people, can be traced back to only four women carrying distinct mtDNAs that are virtually absent in other populations, with the important exception of low frequencies among non-Ashkenazi Jews. We conclude that four founding mtDNAs, likely of Near Eastern ancestry, underwent major expansion(s) in Europe within the past millennium...[13][55]
http://www.nature.com/ejhg/journal/v15/n4/full/5201764a.html is for the below:
A 2007 study by J. Feder et al.[56] confirms the hypothesis of the founding of non-local origin among the maternal lines. Their study did not address the geographical origin of Ashkenazim and therefore does not explicitly confirm the origin "Levantine" of these founders. This study revealed a significant divergence in total haplogroup distribution between the Ashkenazi Jewish populations and their European host populations, namely Russians, Poles and Germans. They concluded that, regarding mtDNAs, the differences between Jews and non-Jews are far larger than those observed among the Jewish communities. The study also found that "the differences between the Jewish communities can be overlooked when non-Jews are included in the comparisons." It supported previous interpretations that, in the direct maternal line, there was "little or no gene flow from the local non-Jewish communities in Poland and Russia to the Jewish communities in these countries."[57]
See also, from http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1004401 :
A 2014 study by Fernandez et al have found that Ashkenazi Jews display a frequency of haplogroup K which suggests an ancient Near Eastern origin, stating that this observation clearly contradicts the results of the study led by Richards which suggested a predominantly European origin for the Ashkenazi communities.[62]
The text/sources above were drawn from the wikipedia article on this subject, with direct links to the source material.
What are we to draw from these contradictory conclusions?
A few potential things:
1. Ashkenazi interbred with European (potentially Italian) women about 2000 years ago, and have since kept to themselves.
2. The European identity of these haplogroups is misconstrued, as the same haplogroups are found also in the ME.
3. The Jews have widely interbred with European peoples in the period between 100-2000 AD.
I think the third is ruled out by history, and 1 and 2 are reasonable hypotheses.
Conversely, the paternal ancestry is definitive: These Jews are Jews. They are semitic, Middle Eastern in origin, and often carry the same y-chromosome across important priestly distinctions.
So, are Jews a "race"? No, though they are likely to be considered a sub-race of the family/sub-race of the Caucasoid race that are the Semitic peoples.
I would say 'population,' as 'sub-race' is largely meaningless. Race is basically a popular term synonymous with a human population that is phenotypically quite distinct from a visual perspective alone (white, black), and Jews are certainly not that.
As for the maternal genetic basis of Ashkenazim, Wiki gives a good summary of the issues. IMO, the 2013 study by the Richards team is remarkably compelling, and is of a far higher quality and scope than the older, smaller, and more partisan studies done by others ... it would seem many other scientists feel the same.
http://en.wikipedia.org/wiki/Genetic_studies_of_Jewish_origins#Mt-DNA_of_Ashkenazi_Jews
Key supporting point, quoted from the Wiki article, which ties into my other post, and which I will address separately:
"In addition, this data was consistent with historians who have suggested that "many women converted to Judaism across Mediterranean Europe during the so-called Hellenistic period between about 300 B.C.E. and 30 B.C.E."[60] Diaspora communities were established in Rome and the Italian peninsula centuries before the fall of the Second Temple in 70 CE."