In the suggest period between 200,000 and 12,000 years ago, humans were living a nomadic lifestyle. The humans of this period were hunter-gatherers, and they were constantly moving from one place to another in accordance to the food supply and climate conditions. Because of this constant movement and constant search for better hunting grounds and places where there's much bigger and more constant supply of fruits, vegetables, root plants, they managed to disperse in very big space and little by little to colonize the planet. In this period the cultivation of plants was still not taking place, and also the humans still hadn't managed to domesticate any wild animals, apart from the wolf which gave rise to the dog, but it was used for hunting, not as a food source.
