The Caucasus range and whereabouts is another region where the "Forager A" (picked up by the San pole) element is concentrated. After a few more interesting populations at the individual level, I will present some runs trying to find out more about this, but for now I can say already that it's probably even less related to actual San than ancient Mesopotamians were related to the Chukchi. Foragers groups very likely existed in a genetic continuum worldwide, with few exceptions.
In populations North of the highest peaks of the Caucasus, like the Adygei, which were likely spared the full force of the Nile wave by geography, these components are more frequent. This area is where Coastal Migration foragers begin to disappear and "Siberian"-like elements become more frequent. It may have been the route for earlier dispersal of the "Siberian" belt of forager peoples around the World.
Just as in the West Caucasus, you can see some Siberian/Central Asian Nomadic influence as Turkic and Mongol and other pastoralists made their way into the Middle East.
Kurds and Iranians now have "Coastal Migration" (attracted to the Papuan+Melanesian pole) as their aboriginal element. In India this component then increases to levels I don't think would exist without an indigenous incipient Neolithic.
You can also see how the "Nile Core" element starts decreasing in Iran. Just as in the West, the high drag of a wave travelling over already Neolithic lands can be observed here.