So there are some things here that i find irksome.

Lets begin with a very useful heuristic.

"Pots are not people, genes are not languages"

This means that when i learnt english my original genetic materoal did not change. Similarly if a population adopts parts of a material culture that would be interpreted as such archeologically this does not mean they had the same language or that they were genetically related. Everyone can build a sky scraper.

This is one of the reasons we cant know what happened before historical records. We can make educated guesses based on how we think certain demografic and linguistic phenomena work based on observations of hostoracal societies.

From these we can conclude that advection, great migrations moving enough people to affect genetics, only happens in very rate ocasions. In the americas, australia, and mybe the roman peopling of the western mediterranean and russian siberia. If you are an advectionist you have to explain why pre historic societies behaved in this way. But i have not seen anyone do that. Advection is often just assumed.

The main mover of demografic change in humans historically has been difussion. That is merchants and individual people moving around foliwing some sort of gradient.

As such you should expect genetic markers to be areanged in large gradients, defined by geografical features. The article finds this. And this is correct.

Everything else is either wrong or likley wrong. The mixing events are an artifice of statistical models asuming advection. They also make a number of other dubious asumptions regarding mutation rates and reconvination.

The timline for the development of slavs and indoeuropen is also wrong. The earliest ie language in the historical record is hittite. This is newer that 4000 ybp. Then there is tocharian wich should have diverged about the same time, indo aryan apearsa few hundreth years latter. We can asume diferent rates of linguistuc change, but bsed on the historical record and asuming creolization to speed language change as beckwith does its likley proto indoeuropean began to diverge arounf 4000ybp so claiming protobaltoslavic diverged from the rest of indoeuropean languages 7 to 3.5 kybp is equivalent to claiming slavic languages are as distinct as tocharian. Utter nonsense.

Finally we know from the historical record iranians(language wise) came from the east around 3kybp likley after they produced a horse big enough to carra a human on its back. We dont know were in the east they came from could be the altai, could be hazarajat, could be elswhere. But we know that when they got to ukraine there were already proto slavs there the bodi who happened to be agriculturalusts ocuping areas near bodies of watter hence bodi. So their model of origin for protoslavs can be easily disproven by the historical record. Specially the model with so many advection events.

Finally asuming advection is a calvinist doctrine that implies your birth (genetics) determines rour position, that race is a rwal thing and the main mover of history instead of just an artifice of circumstance. And that genocide was common. But the truth is genocide is ver hard, it requiers either a certain level of state capacity we have only arrived at in the last 150 years or vast technologica demografic or epidemiological gradients. All these asumptions and implications are wrong and the sort of people tgat beleve them are irksome.