Significance of the Bottleneck / Founder Effect in the R1a1a Ashkenazi Levite Population

Considered in isolation (and without reference to the 2013 paper by Rootsi & Behar et al.), the fact that all R1a1a Ashkenazi Levites are descended from a man who lived about 1,000 to 1,500 years ago may seem to be strong support for the hypothesis that the R1a1a Ashkenazi Levite progenitor was a non-Jew who entered the Jewish population at about that time. 

Interestingly, however, researchers into two other significant Jewish Y-DNA clusters have found a bottleneck/founder effect at about the same time, which approximately coincides with the time when Jews moved to Ashkenaz (the Rhineland), the cradle of the Ashkenazi population. (A bottleneck refers to a contraction in the population of a Y-DNA cluster, while a founder effect refers to the entrance into a population of a man with a previously unrepresented Y-DNA haplotype; either a bottleneck or a founder effect will be evidenced by a cluster of men sharing a Most Recent Common Ancestor ("MRCA"), with a clear delineation in a time to MRCA from other Y-DNA clusters.) 

Vitaly Goldberg has calculated the time to an MRCA as 1,050 years plus or minus 80 years for J-L816, another major Ashkenazi haplogroup. J-L816, like R1a1a, is rarely found among Sephardic Jews. Haplogroup J is commonly found in the Middle East, so there is no obvious reason to assume a non-Jewish origin for the J-L816 progenitor. 

Daniel Ventura has calculated the time to an MRCA for G2c (G-M377) in Europe, another major Ashkenazi cluster, as 955 years plus or minus 107 years. G2 is very rare among Sephardim, but it has been found in a handful of Lebanese Christians and a few other Middle Easterners. Ventura hypothesizes, based in part on a G2c sample from Sicily with an MRCA with G2c Ashkenazi Jews going back 2,000 years, that G2c Jews may have been among the Jews taken by Titus to Rome after the destruction of the Second Temple. 
A population bottleneck/founder effect may result either from either or both a contraction in the population (analogized to a bottleneck) – resulting from, e.g., disease, famine, or pogroms – or migration from one place to another (i.e., a founder effect). These events need not occur contemporaneously. The law of averages dictates that many men who lived 1,000 to 1,500 years ago will not have descendants on their direct male lines; if there was a single generation in which any of those men had no direct male descendants who lived to father male children, the Y-DNA line would break. Thus, as a statistical matter, bottlenecks/ founder effects like those found in R1a1a Ashkenazi Levites must not have been particularly unusual.

Because some direct male lines have been remarkably successful – the R1a1a Ashkenazi Levite progenitor living 1,000 to 1,500 years ago appears to be the direct male ancestor of as much as 13% of the Ashkenazi population (about 1.3 million people) – it follows that relatively few direct male lines from that period have survived. 

One would expect that there would have been a possibility of similar bottlenecks/founder effects any time that a small group of Jews migrated a considerable distance. For example, in the 7th and 8th centuries, there may have been a bottleneck/founder effect when some Jews moved to North Africa and the Iberian Peninsula along with the Moors.  

For a discussion of evidence of bottlenecks/founder effects in the Ashkenazi population that might have resulted from migrations as evidenced by mtDNA, see
D. Behar, et al., mtDNA Evidence for a Genetic Bottleneck in the Early History of the Ashkenazi Jewish Population (2004)

Thus, while the evidence of a bottleneck/founder effect in the Jewish population about 1,000 to 1,500 years ago is consistent with non-Jewish origins (including Khazarian origins) for the R1a1a Ashkenazi Levite progenitor, it is also consistent with Jewish origins of a progenitor who was one of the early founders of the Ashkenazi population, a theory supported by the 2013 paper by Rootsi & Behar et al.
Finally, the 2013 paper by Rootsi & Behar et al. shows that there are a significant number of M582/Z2474+ men who are not R1a1a Ashkenazi Levites.  Few if any of those men have STR markers reported on Family Tree DNA project pages. Those men's STR results should provide insight into the timing of other bottlenecks/founder effects in the R1a1a Ashkenazi Levite lineage, which, in turn, may shed light upon the historic events that may be linked to such bottlenecks/founder effects. 
From Augustin Calmet's great Bible Dictionary: Het algemeen
groot historisch, oordeelkundig, chronologisch, geografisch,
en letterlyk naam - en woord-boek van den gantschen H. Bybel . . . 
(Leiden: Samuel Luchtmans, 1725-27) (here 1725)
The white robe of the High Priest for the solemn Day of Atonement
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