In David Anthony's paper, he links Anatolian, Tocharian, and Italo-Celtic to three migrations.
The first migration was in 4400 - 4200 BCE, and it was out from what's now Ukraine north of the Crimea on the Dneiper River. This migration followed the western shore of the Black Sea southward, with a branch going inland. Large numbers of settlements were abandoned and burned there, some very culturally different people started living there, as the Cernavoda culture. Numerous artifacts from there ended up in the steppe zone from the Dneiper to the lower Volga River, hinting at long-distance trade networks.
Continuing further along the Black Sea coast, they would have ended up in Anatolia, where we find the first recorded Indo-European language: Hittite, one of the Anatolian branch of the Indo-European family. Ancestors of Anatolian speakers were the first to split off from the main Indo-European group, and it is evident from archaisms in Hittite, and also from lacking Indo-European wheel-related vocabulary. Their split was before the invention of wheeled vehicles roughly around 3500 BCE.
The second migration was in 3300 - 3000 BCE, and it was far to the east, near the Altai Mountains, forming the Afanasievo culture. Some of them could easily have continued southward from there to the Tarim Basin in what is now Xinjiang in China. They would have then have become the ancestors of the Tocharian speakers, some millennia later.
The third migration was also about then, and it followed the route of the first one, though further inland. David Anthony identifies these migrants as bring the ancestors of the Italo-Celtic group, and possibly also Germanic. There were some additional outward migrations around then, like northwestward to make the Globular Amphora and Corded Ware cultures, and northeastward to make the Sintashta culure.
DA also describes four types of pastoralism (animal herding) that the steppe people had practiced.
1. Around 4500 - 4200 BCE in Khvalynsk, the main food item was fish, with land animals being eaten only on special occasions. It was mostly domesticated ones that were eaten, however.
2. Around 3300 BCE, wheeled vehicles enabled going much longer distances, making it possible to go much further into the steppes. Thus giving rise to the Yamnaya or Yamna culture.
3. Around 1900 BCE, at the beginning of the Late Bronze Age, many of these pastoralists settled down near marshes, likely from the climate becoming cold and arid. Their teeth had little decay, like those of hunter-gatherers, and unlike those of farmers.
4. Around 800 BCE, at the beginning of the Iron Age and continuing all the way into the Middle Ages, agriculture becomes very evident, with the herders also growing crop plants like grains.
Bantu expansion:
