Through out history we see the human population exploiting it's environment to the maximum possible with the technology current for the time. We filled all possible ecological niches available, expanding the population to the limits imposed by technology, not environment. For example, ancient Egypt, in the largest desert in the world, was the 'bread basket' for thousands of years. Mesopotamia in considered the cradle of civilization, again in the middle of a desert. Faced with 'impossible' situations, human kind has repeatedly risen to the challenge, and triumphed. If we can do it in desserts, why not in rain forests? In other words, the question isn't did it happen, but rather, what technology enabled a large and diverse population. After all, why would humans in the Americas been inherently different than humans elsewhere?