There is a breakdown on John Hawks' blog of a recent paper in Science about the Indo-European expansion. Using a method derived from epidemiology, the authors reached the conclusion that Proto-Indo-European was spoken in Anatolia. This is the Anatolian hypothesis, that Indo-European languages spread after agriculture was introduced to what is now Turkey, with the expansion dating to some point in the last 10,000 years, perhaps around 6000 BCE. The method used in the paper is based on a statistical analysis of cognate terms in Indo-European languages, which is not a usual method in historical linguistics. Linguists have experimented with statistical methods in the past, and they have rejected most of them in favour of rigorous analysis of languages. Unless the sample is chosen judiciously, statistical methods are useless. And it's important to remember that historical linguists and archaeologists have other methods, methods with a proven utility.
Among those methods is the Wörter
und Sachen method, which involves examining the objects found in archaeological investigations and then seeing how they fit together with a reconstructed language. If you find evidence of wheeled vehicles at a site, and your proto-language has a reconstructed term for wheels, axles, or carts, then there is the possibility that the speakers of the language were also the people who lived at the site. The more reconstructed terms there are for things at a site, the better the case is that the speakers were also the inhabitants.
Proto-Indo-European has terms for all aspects of wool production. It has words for a variety of domesticated animals as used by pastoralists, and its terms of 'wealth' are related to pastoralism. It has words indicating a tribal social structure based around clans with patrilineally-descended heads. All of these things correlate best with a pastoral society inhabiting the steppe, and not with an agricultural economy as the Anatolian hypothesis would predict. The wool terminology in particular makes no sense if the Anatolian hypothesis is assumed; it is a necessary feature of the Anatolian hypothesis that the expansion, into Europe at least, took place about 8,000 years or so ago, but wool sheep are only found archaeologically from about 4000-3500 BCE. Why would Indo-European languages share words for wool and woollen technologies if the speakers of the proto-language knew nothing about wool because wool sheep literally did not exist at that point?
This is a slightly weak argument, because the reconstructed term, *HwlHn-, could possibly have referred to the short undercoat of sheep. That seems unlikely, but it's technically possible, and so the wool evidence is just one part of the case for a steppe origin.
Proto-Indo-European has a lot of reconstructed words for wheeled vehicles. The earliest wheeled vehicles are found in the Caucasus and on the Pontic-Caspian steppe, not Anatolia, and this vocabulary is most lacking in Hittite, one of the few Indo-European languages actually found in Anatolia. The Hittites were a literate civilization of the mid-to-late second millennium BCE (c. 1400 BCE), and a major power in the Near East. They were, alongside the Luwians, some of the only Indo-European speakers in the area, which was dominated by non-Indo-European speakers (perhaps an indication that Indo-European speakers came from elsewhere), including the Hattians - the people who gave the Hittites their popular name. The Hittites were famous for using chariots, and they used them to dominate their neighbours, even defeating Egypt under Riʻmīsisu II (Ramesses) at the battle of Kadesh in the 13th century BCE.
But there's something interesting about the Hittite use of chariots: it was clearly introduced from elsewhere, and the people who introduced it spoke Indo-European languages. A chariot manual by a man named Kikkuli, in the Mitanni empire - a Hurrian-speaking empire in what is now Syria - was written almost entirely in Hittite, except for the words for the chariot terminology itself. This terminology, incredibly, was in a language whose closest relation was actually Sanskrit. That makes this manual, and other Mitanni texts, the earliest written attestation of an Indic language anywhere in the world, and it comes from Syria. Quite amazing.
So where did these Indic speakers, who introduced chariots into the Near East, come from? Archaeological evidence shows the earliest use of chariots to be on the Eurasian steppe around the second millennium BCE. The remains are clearly related to those found further west on the steppe as well, and the archaeological cultures related to the emergence of charioteering were steppe pastoralists and metallurgists. These remains, found for instance at a site called Sintashta in modern Russia, are believed to be associated with speakers of Indo-Iranian, the proto-language from which the languages of Persia and India descend. This identification is particularly secure for a number of reasons. One is that sites like Sintashta show evidence of activities, including ritual and warfare, that correlate perfectly with Indic texts like the Rig Veda. The Rig Veda is a set of over a thousand hymns in Vedic Sanskrit, an archaic form of the language. The hymns describe rituals of all kinds, including especially funerary rituals, and these expositions in the Vedas correlate perfectly with the evidence found at Sintashta and other similar sites.
For instance, Vedic funerals were accompanied by funerary games including chariot races. In these races the chariots would turn left. Not only are chariots found in southern Russia from the right time period (including the earliest known in the world), but the evidence also shows a curious feature: bits for horses that are asymmetrical. The right side of the bit is larger than the left, indicating a consistent preference for turning left!
There's much more evidence than that - especially the fact that most Iranian languages were found in western Central Asia and southern Russia before the Turkic and Slavic expansions, and the fact that the Aryan migrations into India appear on the basis of archaeological evidence to have come from the northwest, and the fact that Iranian migrations into what is now Iran (and was once Elam and Babylon) began in the east. Had the Iranic peoples come from Anatolia, they would surely have attacked the neo-Babylonian empire from the west, instead of taking it under Kurush in the sixth century BCE from a base in modern Fars province, Iran.
In the Science article, there's a map (you can see it on John Hawks' blog) of the distribution of the Indo-European languages, showing the centre of distribution to be in Anatolia, but this is quite wrong; extinct Iranian languages are missed off the map, and they are known to have been spoken in what is now Russia (the Pontic-Caspian steppe) into historical times. Alan (which became the modern language of Ossetian spoken in the Caucasus), Scytho-Sarmatian - these were Iranic languages spoken on the steppe by pastoralists in historical times. Bactrian was an Iranic language spoken in Central Asia, in what is now Turkic-speaking territory. They are left off the map and the analysis because they are poorly known, but they were certainly spoken on the steppe and they were certainly Iranic. This is an impossible distribution if you take the Anatolian hypothesis to be true, and they'd also mess up the map if they were placed on it - in fact, they'd distort it completely. If you look at the map provided, it shows a neat distribution of Indo-Iranian east of Anatolia in a neat bubble, implying that Indo-Iranian simply moved east. But that is not the present, and certainly not the past, distribution of Indo-Iranian languages, and it equally certainly fails to represent the actual propagation of those languages in Eurasia.
The homeland of Iranic and Indic languages was in the steppe north of the Caspian sea; that makes most sense of the archaeological and linguistic evidence from all fronts. The archaeological cultures of the Indo-Iranians show clear continuity with archaeological cultures to their west on the Pontic-Caspian steppe, indicating that they came from further west, and they clearly displaced other groups who had previously resided there. These Pontic-Caspian archaeological cultures show a perfect correlation with the terminology of reconstructed Proto-Indo-European as well. Looking at it as if Indo-European languages came from Anatolia doesn't make sense of these facts. So instead we should ask, how did Indo-European languages end up in Anatolia? How did Hittite come to be spoken there?
Hittite is an archaic Indo-European language that preserved several features lacking in all other Indo-European sub-families, and at first sight this gives some reason for believing in the Anatolian hypothesis. But actually it doesn't, and the much more plausible view is that the Hittites and Luwians entered Anatolian from west of the Black Sea earlier than the formulation of 'classical' Proto-Indo-European. The ancestors of the Hittites spoke what is called 'pre-Proto-Indo-European'; the language that became Hittite in Anatolia, after isolation from other Indo-European speakers and contact with non-Indo-Europeans, and Proto-Indo-European on the steppe after linguistic and technological innovations. The reason Hittite preserves archaic features is because it doesn't descend from Proto-Indo-European at all, but rather from the language that became Proto-Indo-European.
This also correlates with the archaeological evidence, which shows a quick migration from the steppes through the country west of the Black Sea and south towards Greece and Asia Minor at the expected time of the propagation of pre-Proto-Indo-European.
Another piece of very good evidence for a steppe homeland for Indo-European comes from the unrelated Uralic languages. Finnish, Hungarian, and Saami are modern Uralic languages found in Europe, and others are to be found further east, including Mordvin and Mari, spoken in Russia. Here is a map showing the present distribution of Uralic languages; they are all to the north of the Black and Caspian Seas, and the geographic centre of distribution is in the Ural mountains, likely on the European side. That is where the Uralic homeland seems to have been.
Here's how this links to Indo-European studies: Proto-Uralic shows the presence of loanwords from Proto-Indo-European. This has been known for some time. The loans are documented in The Encyclopedia of Indo-European Culture (Mallory and Adams 1997), as well as David Anthony's brilliant book, The Horse, The Wheel, and Language, which is more recent. They aren't loans from living Indo-European languages into living Uralic languages, but loans from Proto-Indo-European into Proto-Uralic, at a very early period. There is also considerable evidence that a later form of Uralic was in contact with speakers of Indo-Aryan languages, as several Indo-Aryan loanwords have been discovered.
What this means is that Proto-Indo-European and Proto-Uralic were spoken in adjacent areas, and that their speakers were in contact with one another for a sustained period. Proto-Uralic was not spoken in Anatolia, but on the European side of the Ural mountains, adjacent to the Pontic-Caspian steppe, again indicating that Proto-Indo-European was spoken there as well.
I'm not going to go into the rest of the evidence, but needless to say, there's a lot of it. But here's a
final point. If the Anatolian hypothesis were actually correct, and
Indo-European languages came from Anatolia and not the steppe, then who
were those people on the steppe whose archaeological cultures correlate
so closely with Indo-European material? Where did they go? Why do we
not have evidence of another major language family spreading from the western Pontic-Caspian steppe around 3000 BCE?
In the paper, it is suggested that the steppe hypothesis is possible - after the Anatolian migration had done its work. That is really a little mad. What it claims is that Indo-European expanded into Europe as a result of the introduction of agriculture into Anatolia from the Near East 8,000 years or so ago. Agriculture allowed the Indo-Europeans to migrate, grow large populations, and dominate Europe. That's the Anatolian hypothesis so far. But then it is necessary to believe that these ardent agriculturalists, people for whom agriculture must have been incredibly important, abandoned agriculture entirely, entered the steppe (without leaving archaeological remains of having done so), became pastoralists, relied on wild foods like Chenopodium for their carbohydrate intake, took to wagons, herded cattle, and then spread across the Eurasian steppe. And, somehow, the peoples of Europe shared their cultural, religious, and linguistic innovations, including the importance of cattle, horses, oaths, sky deities, and youthful tribal warfare. That isn't parsimonious, and it relies solely on the statistical study showing that the Anatolian branch retained the largest number of common cognates - which is already consistent with the idea that Hittite descends from the pre-Proto-Indo-European that came off the steppe before Proto-Indo-European as we know it had formed.
So here is the picture presented by archaeology and linguistics: speakers of pre-Proto-Indo-European originated on the Pontic-Caspian steppe, north of the Black Sea, around the fifth millennium BCE. Some of these speakers migrated west, passing through and attacking the towns of the Cucuteni-Tripolye archaeological culture. They passed to the south and turned east, eventually ending up in Anatolia, where the pre-Proto-Indo-European language diverged into Hittite and Luwian. These people were in contact with speakers of lots of other language families, and they were also in contact with other groups in the Near East. The Hittites were migrants into Anatolia, which partially explains why their lives were completely different to those of other Indo-European groups, and why they absorbed and adopted the traits of non-Indo-European native Anatolian groups, like the Hurrians.
The rest of the speakers of pre-Proto-Indo-European stayed just where they were, developing a strongly pastoral economy based on large herds of cattle herded with the aid of wagons and domesticated horses. They were in contact with speakers of Proto-Uralic and probably Kartvelian, and the pre-Proto-Indo-European language became what we know as Proto-Indo-European. The speakers of this language, associated with the Yamnaya archaeological culture, spread in several directions: to the east went wagon-riding pastoralists whose remains show continuity with the Tocharian (Indo-European-speaking) peoples of western China. Also in that direction went people with similar cultural traits whose languages became Indo-Iranian. They centred north of the Caspian sea before some of them migrated south, east of the Caspian, through the cities of Central Asia and the Indus. To the west of the Pontic steppe went speakers of Proto-Indo-European whose languages diverged to form Balto-Slavic (dominant throughout the area north of the Black Sea and up to the Baltic in early historic and prehistoric times), Italo-Celtic, Germanic, and other subgroups of Indo-European.
That is the model that makes most sense of the data. The Anatolian hypothesis makes sense of very little of it, and I don't think any single study of any sub-group of Indo-European languages will ever override the combined evidence of archaeology and linguistics. The phylogeographic model may work well for modelling language families, but it also has to take account of other evidence, and also of extinct languages. The studies in Science do not do this, and the Anatolian hypothesis is simply not correct.