Personally, I regard the glacial refugee area in the Danubian bassin as the most probable kernel for the IE expansion. As time frame I´d like to suggest the Atlanticum climate optimum around 6.500 BC.
Just some thoughts of mine:
Lexical components of IE indicate a moderate climate (e.g. there existed words for beech and oak, but not for camel or cypress).
The Danubian centre historically shows the greatest linguistic diversity with ties to all four major IE meta-families:
Balkan-IE (Albanian, Armenian, Phrygian, Thracian, Illyrian, maybe Messapian),
NW-IE/Old European (Germanic, Celtic, Italic, Veneto-Liburnian, Balto-Slavic),
East-IE (Indo-Aryan) and even with the Hethito-Luvic group - which some archaeologists tend to link with Starcevo-Körös-Cris.
Modern archaeology is emphasizing a mesolithic-neolithic continuity in most parts of Europe.
The TBK and Bandkeramik culture, respectively their successors and mixture forms like SK and laterly Adlerberg-Mondsee or Aunjetitz culture show a commmon hydronymic base, the so-called "old-European" which one could try to identify with the north-west group and which proofs ethnic continuity since the neolithics in central Europe.
Commenting on the most important opponent theories:
C14 data confirm that SK expanded from west to east, so there is no indication of a Kurgan invasion into central or SE Europe.
Concerning the Anatolia thesis I only want to underline one point among many others: If Asia minor really has been the original homeland then the neolithic culture of Greece and Bulgaria, namely Sesklo-Dimini is a perfect candidate for a missing link between Anatolia and the Balkans.
The problem with that is that the inhabitants of the southern Balkan peninsula before the first Hellenic wave most probably have been non-IE as the strong non-IE substrate in Greece much place names indicate.
Place names even indicate that the unknown pre-IE "Pelasgian" language also existed in southern Italy, western Anatolia and the valleys of the Pindos mountains.
Genetically Europe has been developed out of its own UP gene pool. The minor "neolithic" contribution attributed to farming came to Europe via two ways: from Turkey to SE Europe and from Northern Africa to the Mediterranian coast of Italy, France and Spain. Only the first one is relevant in this context despite both are clumbed together to found the Renfrew thesis.
Because of a lower sea level during the ice age, there was a land bridge between Anatolia and Europe. And remember that the Gravettian culture was introduced into Europe via Anatolia and the Middle East in the Würm II-III-interstadial.
So I claim: Much of the "neolithic" genes are in fact UP or mesolithic and spread to Europe in a many milennia lasting diffusion process.
Also note that the dissemination gradient of "neolithic genes" towards north is decreasing fast which is more in-line with a diffusion model than a invasion scenario.
So why not assume that the IE tribes originated where the bulk of them historically appear?
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