Let's speculate about the linguistic affinities of the currently available ancient populations from the Caucasus and surrounds. I put together a series of outgroup f3-stats to help things along. They're available for download
here.
Maykop
Georgian 0.258224
Abkhasian 0.257899
Latvian 0.257376
Swedish 0.257301
Turkish_Trabzon 0.256996
Basque_Spanish 0.256589
Chechen 0.256514
Icelandic 0.256418
Norwegian 0.256325
Lezgin 0.256272
Irish 0.256227
Tabasaran 0.256092
Italian_Bergamo 0.25605
English_Cornwall 0.256032
Polish_East 0.255991
Scottish 0.255955
Adygei 0.255913
Steppe_Maykop
Latvian 0.261845
Russian_North 0.26145
Estonian 0.260355
Finnish 0.260211
Lithuanian 0.260072
Udmurd 0.259804
Ingrian 0.259663
Surui 0.259637
Vepsa 0.259608
Karelian 0.259532
Karitiana 0.259482
Russian_West 0.259397
Russian_Central 0.259274
Wichi 0.259106
Saami 0.258982
Komi 0.258945
Icelandic 0.258854
Swedish 0.258814
Mordovian 0.258604
Irish 0.25859
Eyeballing the stats might be enough to get a general impression about what they mean, but to understand them properly it's necessary to get technical with something like PAST3 (see
here). That's because f3-stats pick up shared genetic drift from all drift paths, and don't especially focus on more recently shared ancestry. This can often lead to confusing outcomes.
Below are a few examples of linear models based on my f3-stats. Note that many Indo-European speakers, especially from Northern Europe, are foremost attracted to ancient samples from the Pontic-Caspian steppe. On the other hand, non-Indo-European speakers, from such far flung locations as the Caucasus and Iberia, show relatively stronger affinity to ancient samples from Anatolia and the Caucasus. Moreover, Uralic speakers show elevated affinity to ancient hunter-gatherer samples from Eastern Europe and Siberia. Makes sense, right?









Based on these and other data, I'd say that Maykop and the culturally related Steppe Maykop were something of a multi-ethnic polity, with many near and far related languages spoken by its people, including perhaps Kartvelian, Northwest Caucasian, Yeniseian and Indo-European. But it seems to me that Proto-Indo-European was spoken by steppe foragers turned pastoralists just outside of the Maykop zone. And I'm quite sure that after the Maykop collapse various early Indo-European groups pushed across the Caucasus and deep into the Near East. Just take a look at the f3-stats and linear model for Hajji_Firuz_BA to see what I mean.
See also...
An exceptional burial indeed, but not that of an Indo-European
The Steppe Maykop enigma
Late PIE ground zero now obvious; location of PIE homeland still uncertain, but...