We have a new tool for studying human prehistory, studying the DNA of the animals we were in close contact with. We can infer much about migrations from looking at where the dogs came from. Because the Przewalski Horse is only 3% of the other modern horses, we know that it's ancestor the Botai horse was separate from the one the Yamnaya herded and rode, even though those tribes were close by. From that we know that they domesticated the horse independently. They may have gotten the idea from elsewhere, but they didn't pick up domesticated horse from the Botai.
The lineages of cattle and sheep tell us what peoples were in contact with each other.