Above : Young women in the IDF. Around half of Jews living in Israel are Ashkenazi Jews.
5 years ago, a full genome wide study estimated Ashkenazi Jews to have very substantial European ancestry. European ancestry they absorbed through assimilation after they were dispersed from the Levant in the ancient world. The article's authors stated.
"To quantify the level of admixture within the AJ genome given the model of a Middle Eastern origin and European admixture, we applied a likelihood method to differentiate the relative ancestry of each locus across the genome. We used the combined Palestinian and Druze populations to represent the Middle Eastern ancestor and tested three different European groups as the European ancestral population. Using these proxy ancestral populations, we calculated the amount of European admixture in the AJ population to be 35 to 55%."
SOURCE : Bray, S. M., J. G. Mulle, A. F. Dodd, A. E. Pulver, S. Wooding, and S. T. Warren. 2010. Signatures of founder effects, admixture, and selection in the Ashkenazi Jewish population. Proceedings of the National Academy of Sciences 107:16222–16227.
Now finally, because of a further and more detailed analysis, we know where in Europe this ancestry comes from. The truth is the Ashkenazi's European ancestry stems from several major areas, really. However, the most recent comprehensive analysis reveals what others who had been able to connect the dots of previous genetic data had long speculated, most of this historical European ancestry in Ashkenazi Jews comes from Southern Europe. In particular Southeastern Europe [not Iberia or France].
So basically Ashkenazi Jews could be modeled as being 50% Middle Eastern and 50% European. The Middle Eastern ancestry was pretty much all Levantine, which is not surprising. Meanwhile 3/4s of the European ancestry looked to be South European, for 37.5% total South European admixture. The remaining admixture in the Ashkenazi was mostly East European.
The only problem is that modern populations are not identical to ancient or even medieval populations. Similar yes, but not identical. The Levant for instance has seen geneflow from Africa and the Arabian peninsula. I would think the Levantine Christian populations would be more suitable for a more accurate assumption of what the ancient Levantines including the Hebrews were genetically like, as they've seen far less geneflow from The Arabian peninsula and Africa than the Islamic groups. The good thing is that they were included in the data set, but unfortunately not exclusively. I feel because of this it's possible the "European" ancestry estimate for Ashkenazi Jews could be a bit inflated. Europe too has probably gone through more minimal genetic changes in it's various regions over the past 2 and a half millennia (Although there is certainly no evidence of any substantial Sub-saharan, Arabian, or Turkic admixture in the sampled European groups).
But anyway, despite the small drawbacks of using admixture models based around modern populations, this article is very informative in the broader scope of things. Ashkenazi Jews have major European ancestry, and most of this is Southern European. Knowing this only lends further credence to accurately labeling them an 'East Mediterranean people' as I pointed out in an earlier article, as most of Southeastern Europe, like the Levant, borders the Eastern part of Mediterranean sea. As we can see by PCA below, the Jews form their own genetic cluster and are closests to those populations. Unfortunately their two clostest populations in the Near Eastern direction [Levantine Christians] and European direction [Southern Italians and Southern Greeks] weren't featured in this PCA, but you still get the point.
SOURCE : Ames Xue, Itsik Pe’er, and Shai Carmi, The time and place of European geneflow into Ashkenazi Jews, Biology of Genomes 2015 poster presentation.