Open thread: How did steppe ancestry spread into the Biblical-era Levant?

It’s likely that two of the Philistines from Feldman et al. 2019 harbor relatively recent steppe ancestry. They’re labeled ASH067 and ASH068 in the paper. The former individual is a male who belongs to Y-chromosome haplogroup R1, which appears to be R1b-M269 judging by the data from the relevant BAM file.
This is just the second instance of Y-haplogroup R1 from the pre-Crusades Levant, and, of course, neither R1 nor R1b-M269 appear in the Near Eastern ancient DNA record prior to the expansions of the Yamnaya and other closely related pastoralist groups from the steppes and forest steppes of Eastern Europe.
So how did the Yamnaya-related ancestry spread into the Biblical-era Levant? Did it come via Anatolia, the Caucasus and/or the Mediterranean?
To try and answer this question I analyzed separately the genome-wide data for ASH067 and ASH068 with qpAdm, relying on outgroup and reference populations that weren’t featured in the qpAdm runs in the Feldman et al. paper. I also limited the analyses to what were in my view the most proximate two- and three-way solutions in terms of chronology and geography.
The models with the best statistical fits, each labeled with their «tail probs», are available in a zip file here. From my experience with qpAdm, I’d say that the most useful models generally show comparably high tail probs but low chisq values and standard errors. Please note also that I discarded all of the models with at least one standard error higher than 0.2 and/or based on less than 100K SNPs.
As far as I can see, these two are among the very best outcomes. Bell_Beaker_FRA are nine samples associated with the Bell Beaker culture (BBC) from what is now France. Interestingly, the BBC population was rich in Y-haplogroup R1b-M269.

Levant_ISR_Ashkelon_IA1_ASH067
Bell_Beaker_FRA 0.116±0.059
GRC_Minoan 0.507±0.111
Levant_ISR_Ashkelon_LBA 0.377±0.117
tail prob 0.530432
chisq 9.018
Levant_ISR_Ashkelon_IA1_ASH068
Bell_Beaker_FRA 0.237±0.044
GRC_Minoan 0.763±0.044
tail prob 0.943265
chisq 4.736

In my opinion, these models basically confirm that both ASH067 and ASH068 harbor Yamnaya-related ancestry. It’s heavily diluted and minor, but it’s there. Admittedly, even after looking over the qpAdm output several times, I’m still not quite sure how their ancestors acquired this ancestry. But for the time being, Mediterranean Europe appears to be the most plausible proximate source one way or another. Any thoughts about that? Feel free to share them in the comments below.
See also…
Evidence of European ancestry in the Philistines
R1b-M269 in the Bronze Age Levant
Late PIE ground zero now obvious; location of PIE homeland still uncertain, but…
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