There's a book by Jared Diamond that describes the migration habits and domestication of plant and animal species by early humans very well. The rough hypothesis is that Asia and the Middle East, being largely "horizontal" to the Earth, presented a very ready migration route through a steady climate. North America, South America, Europe, and Africa presented a "vertical" route that would have posed climate changes due to changes in latitude. It took comparitavely little time for our human ancestors to migrate through most of Asia and down to Australia while taking comparitevely long to get to the European north-lands and the Americas.

The same author also posits that, contrary to the theory of "man the great hunter", early man was not so dependent on meat as was previously thought. His tools and the sites that have been found do not suggest a heavily meat-based diet. Animal bones aren't really found in large quantities until you get to the point of late Homo Erectus and Homo Sapiens. It's possible that they did follow herds of easier to catch and kill animals though....