As discussed elsewhere on this website, the European R1a1 clade is 6,000 to 7,000 years old, and by 3,600 to 4,200 years ago, European R1a1 men had spread back through Anatolia and Iran to India and South Siberia. As a result, the general distribution of R1a1 men as a whole is of little use in determining the likely origins of the R1a1a Ashkenazi Levite progenitor, and it is necessary to focus upon those R1a1 men who are the closest genetic matches for R1a1a Ashkenazi Levites.
According to Family Tree DNA’s R1a1a and Subclades Y-DNA Project page, the Single Nucleotide Polymorphisms ("SNPs") defining the R1a1a Ashkenazi Levite cluster are currently identified as Z93+ Z94+ Z2124+ Z2122+ F1345+ Z2469/CTS6+, in that order.
In their 2013 paper, Rootsi & Behar et al. identified another SNP, M582 (also known as CTS2253 and Z2474), that defines the R1a1a Ashkenazi Levite cluster.
According to Rozhanskii and Klyosov, Z93+ is about 5,700 years old. The current chart on the FTDNA R1a1a and Subclades project page indicates that Z2122 branched off from Z2121/Z2124 in about 2500 B.C.E., and that F1345 branched off from Z2122 in about 1500 B.C.E.
Thus, the closest relatives of R1a1a Ashkenazi Levites who are not themselves R1a1a Ashkenazi Levites will be Z2122+ F1345+, while men who are somewhat more distant will be Z2122+ F1345-.
As of November 24, 2013, we were aware of five men who are not R1a1a Ashkenazi Levites (i.e., they are CTS6-) but who are Z2122+ F1345+: (1) Hilus (kit no. 158657), from Turkey; (2) Kussad (kit no. 116213), from Israel (Kussad's SNP test results, posted on the Full Genomes Corp. website, show that he is M582/CTS2253/Z2474-); (3) Łucki (kit no. 183799), from Poland; (4) McCulloch (kit no. 50283), from Scotland (there are two other members of the McCulloch clan who are close STR matches for McCulloch but who have not tested their SNPs; if tested, they, too, would be found to be F1345+); and (5) an unidentified man from somewhere in China. Both Hilus and Kussad have traced their direct male lines back to the steppes, north of the Black Sea (coincidentally or not, in the area of Khazaria).
A.J. Levin, Administrator of Family Tree DNA's Ashkenazi-Levite DNA Project (R1a1), has noted that the Z2122+ F1345+ CTS6- McCulloch clan, in Scotland, could be descended from a Sarmatian man who was among the 5,500 Sarmatians (recently conquered) whom the Roman Emperor Marcus Aurelius brought to Scotland to garrison Hadrian’s Wall in 175 C.E. Researchers have also hypothesized that Sarmatians may be the source of the R1b Y-DNA found in the Scottish border regions. (McCulloch is F2935+, while R1a1a Ashkenazi Levites are F2935-; F2935, like CTS6, is an SNP that is downstream from F1345.)
Levin has also noted that the presence of F1345+ in China and Turkey may reflect origins on the Turkic steppes.
In their 2013 paper, Rootsi & Behar et al. identify an Iberian man from the 1,000 Genomes database who shares six of the 19 SNPs that they found to be characteristic of R1a1a Ashkenazi Levites; one of the SNPs that he shares is M582. Rootsi & Behar note that this man "might represent the legacy of Jews or Moors in Iberia."
Advanced SNP testing that has recently become available, such as that used by Rootsi & Behar in their 2013 paper, will identify currently unknown SNPs that are shared by R1a1a Ashkenazi Levites and their closest matches who are not R1a1a Ashkenazi Levites, as well as SNPs that distinguish the two groups of men. The discovery of such SNPs will allow the construction of more precise trees showing the orders in which SNPs mutated.
Based upon the data from full Y-DNA sequencing, it should also be possible to calculate, with a far greater degree of certainty, how long ago R1a1a Ashkenazi Levites and their closest matches shared an ancestor. Michał Milewski's preliminary calculations, posted here, indicate that the MRCA shared by R1a1a Ashkenazi Levites and their Iberian match (i.e., at the level of the SNPs M582 and CTS6) likely lived about 3,000 years ago, and that the MRCA shared by R1a1a Ashkenazi Levites, their Iberian match, and Kussad (i.e., at the level of the SNP F1345) likely lived about 4,000 years ago.
SNP information, coupled with information concerning the geographic and ethnic origins of the matches, may also provide insight into the likely origins of the R1a1a Ashkenazi Levite progenitor.