According to Davidski at the Eurogenes Blog, using new data points from an open access Estonian genome database, ancestry in the Ashkenazi Jewish (i.e. non-Spanish European Jewish) gene pool breaks down as genetically most similar to the following modern populations in the following proportions (rounded to the nearest percentage point):
* 50% to two populations (34% Samaritan and 16% Arab) from present day Israel
* 8% to Anatolians (i.e. populations from modern day Turkey)
* 30% to Tuscan Italians
* 12% to Polish
Two components with only trace admixture (less than 1%) are omitted.
These are listed in the likely order of admixture.
The Levantine component is presumably the source population, the Anatolian admixture probably arose en route to Europe, Tuscan admixture probably preceded a bottleneck event in the Ashkenazi Jewish population in the Middle Ages, and Polish admixture probably immediately followed that bottleneck.
Of course, the results of any such model depend upon the details of the methods used to assign ancestry and the source populations available to the model. But, the results generally conform to the leading historical accounts and to other efforts to identify the sources of the Ashkenazi Jewish gene pool. See, for example, a paper earlier this year on the subject, and a historical analysis released in 2013.