The Genetic Origin of the Indo-Europeans

[Jaska]

now I see their hypothesis. Pay attention everybody. Basically what they are saying is that WHG/EHG on the Dneper Don and even full fledged EHG on the Volga were not PIE. For them PIE starts when the CHG/TTK kicks in to form the northern caucasus-lower Volga cline. So the cluster that makes PIE is the CHG/TKK
so what the  paper is all about is a revisited "southern arc hypothesis" For them PIE is born north of the caucasus but thanks to a southern caucasian influence.

They do not explicate where the language came from: they only talk about Proto-Indo-Anatolian after the admixture. But it is true that the more western river valleys can be excluded at this point. So the potential candidates for bringing in the Indo-European language are the Lower Volga EHG ancestry, the Central Asian ancestry, and the Caucasus HG ancestry (perhaps even the Levantine ancestry, concerning their hypothesis B).

The carrying capacity of a territory limits the manpower that can be mustered by the inhabitants to defend themselves from invasion or to invade foreign territories. - - However, if you asked me to consider the likelihood that any population of present-day Europe might expand their territory and spread their language over the entire (sub)continent in the future, the Kalmyks would not be the first people to come to mind.

My point is that it is not predictable: there are many factors for language expansion, one of them always being the luck. Manpower is not always so crucial: not all languages spread via hostile takeovers. We know now that there was a population bottleneck even in the Yamnaya population, when the effective population size was very low.