Because R1a1a Ashkenazi Levites belong to haplogroup R1a, generally believed to be of Slavic origins, and because R1a1a Ashkenazi Levites living today share a most recent common ancestor who lived about 1,000 to 1,300 years ago, many researchers have postulated that the R1a1a Ashkenazi Levite progenitor was an outsider to the Jewish population, perhaps a convert from Khazaria or Europe, who entered the Jewish population in about the year 1000.
More recent research and analysis supports the theory that would have been generally assumed prior to Y-DNA evidence - R1a1a Ashkenazi Levites are descended from a man who was part of the Jewish population in Biblical times, perhaps going back to the time, 4,000 years ago, when Judaism was founded.
In a January 2014 article, Thoughts About Jewish DNA Genealogy, originally posted in Russian and translated to English here, Anatole Klyosov concluded that the ancestors of R1a Jews appeared in the Middle East between 4,000 and 5,500 years ago. (Klyosov's methodology (1) determines the number of deviations in STR marker values between two haplotype clusters and (2) uses known mutation rates for STR markers to calculate the range of time in which the most recent common ancestor of men belonging to those two haplotype clusters lived.)
Klyosov determined that R1a Jews and R1a Arabs share a common ancestor who lived about 4,000 years ago. Klyosov also found that there are parallel branches between Jews and Arabs in haplogroups J1 and J2, with Jewish and Arab branches splitting off about 4,000 years ago. (Haplogroups J1 and J2 are two of the most prevalent Y-DNA haplogroups among Jews; a significant percentage of Cohanim belong to each of haplogroups J1 and J2.)
Thus, Klyosov concluded that three major Jewish Y-DNA haplogroups - R1a, J1, and J2 - are each descended from ancestors who lived about 4,000 years ago, the time when Abraham founded Judaism. He therefore postulated that the ancestors of R1a1a Ashkenazi Levites, like the ancestor of J1 and J2 Jews (who include many Cohanim), have been part of the Jewish population since the religion was founded.
Klyosov found that the progenitors of four other major Jewish Y-DNA haplogroups - E1b, G1, G2, and R1b - also lived in the Middle East before Judaism was founded. He identified other Jewish haplogroups - I1, I2, Q, R2, X, and T and subclades - that entered the Jewish population more recently, during the Diaspora. (Bennett Greenspan, president and CEO of Family Tree DNA, notes that: (1) about half of R1b Jews are descended have an ancient Middle Eastern variant of R1b while the remaining R1b Jews have a variant that is typical among Western European gentile men; and (2) haplogroup T is of Middle Eastern origins (it is found in its greatest frequencies in Lebanon).)
Klyosov explained that the fact that R1a1a Ashkenazi Levites are descended from a common ancestor who lived about 1,300 years ago is evidence that there was a bottleneck in the Jewish population at that time - i.e., most R1a Jewish lines died off at that time, but the R1a1a Ashkenazi Levite progenitor survived and had many male descendants. Klyosov noted that the R1a1a Ashkenazi Levite progenitor's origins in the Middle East are evidenced by the similarity of the STR marker values of present-day R1a1a Ashkenazi Levites with those of present R1a Arabs from the Arabian Peninsula.
Klyosov also provided insight into the deeper origins of the R1a1a Ashkenazi Levite progenitor. According to Klyosov, the R1a Jews and the R1a Arabs are descended from Aryans who swept out of the Russian plains about 4,900 years ago, traveling through the Caucasus to Mesopotamia (Abraham's birthplace) and to the Saudi peninsula. Klyosov notes that the Slavs are also descended from the Aryans. (Because of the racist connotations that the term "Aryan" has acquired as a result of the Nazis and white supremacists, today many scholars use the terms "Indo-Iranian" or "Indo-European" to refer to the historic Aryans; "Iran" means "land of the Aryans.")
As discussed in Klyosov's article, his methodology differs from that of population geneticists, who have reached different conclusions as to the ages of Y-DNA subclusters and the time at which the shared ancestors of such men lived. Klyosov's article criticized population geneticists for identifying known historical events and using their methodology to tie genetic evidence to those events; some population geneticists have leveled the same criticism at Klyosov.
As discussed here, Klyosov and his colleague Igor Rozhanskii have published two papers on the deep origins of the R1a haplogroup; the first article discusses the migrations of the R1a1 haplogroup during the period between 20,000 years ago and 3,500 years ago and postulates that bearers of R1a1 developed and transmitted the proto Indo-European language and migrated as the historic legendary Aryans; the second article discusses 38 branches of the R1a haplogroup that currently exist in, or migrated from, Europe over the past 9,000 years.
The December 2013 paper by Rootsi & Behar et al., discussed here, is consistent with Klyosov's conclusions in that it finds, based upon the geographic distribution of a Y-DNA SNP, M582, that is found in R1a1a Ashkenazi Levites and some other R1a1a men, that R1a1a Ashkenazi Levites originated in the Middle East.