The top f3 statistics can be seen below:
Kshatriya_M Sardinian Bulgarians_Y -0.003813 0.000295 -12.918 237507
Velamas_M Sardinian Bulgarians_Y -0.003783 0.000285 -13.287 238276
Piramalai_Kallars_M Sardinian Bulgarians_Y -0.003693 0.000306 -12.061 238106
Kanjars_M Sardinian Bulgarians_Y -0.003643 0.000298 -12.227 237838
GIH30 Sardinian Bulgarians_Y -0.003638 0.000259 -14.028 240548
North_Kannadi Sardinian Bulgarians_Y -0.00355 0.000317 -11.187 237882
Muslim_M Sardinian Bulgarians_Y -0.003542 0.000333 -10.632 236964
Chamar_M Sardinian Bulgarians_Y -0.003505 0.000303 -11.585 238882
INS30 Sardinian Bulgarians_Y -0.003467 0.000264 -13.153 240279
Dharkars_M Sardinian Bulgarians_Y -0.003452 0.000309 -11.155 238211
Brahmins_from_Uttar_Pradesh_M Sardinian Bulgarians_Y -0.003448 0.000278 -12.42 238041
Indian_D Sardinian Bulgarians_Y -0.003411 0.000256 -13.308 241225
Iyer_D Sardinian Bulgarians_Y -0.003364 0.000291 -11.568 237509
Jatt_D Sardinian Bulgarians_Y -0.003327 0.000289 -11.513 236735
Pathan Sardinian Bulgarians_Y -0.003212 0.000239 -13.444 240969
Iyengar_D Sardinian Bulgarians_Y -0.003209 0.000308 -10.416 236840
Dusadh_M Sardinian Bulgarians_Y -0.003181 0.000313 -10.172 237512
Sindhi Sardinian Bulgarians_Y -0.003094 0.000239 -12.919 241268
Balochi Sardinian Bulgarians_Y -0.002804 0.00024 -11.686 240924
To maximize the number of SNPs and number of individuals, I used the Sardinian+Pathan pair as reference populations. 509,395 SNPs were used for this experiment. The exponential fit can be seen below:
There was a technical issue with the jackknife which I am currently investigating, but the mean time of the admixture was estimated at 126.83004 generations, or 3,680 years. This is similar to the value of 3,850 years I obtained on the Greek sample.
If this date is accepted, then the interesting issue is why an individual from Bulgaria was Sardinian-like during the Iron Age. Possibly, either this individual was Sardinian-like in the broad sense, despite having minority West Asian admixture, or a few centuries after the admixture event, there was still an uneven distribution of the constituent elements, with most individuals still predominantly Sardinian-like. Given that the indigenous element was probably most numerous, so only part of it would have the opportunity to admix with the intrusive West Asian-like population, and this influence would spread to the population-at-large over time.
In any case, this evidence, such as it is, appears consistent with my idea about a Bronze Age invasion of Europe from Asia.
Naturally, only a broad sampling of ancient DNA variation from the Balkans, perhaps targeting different sites, cultures, times, social status, and physical types will be sufficient to track the early appearance of an intrusive population.
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