From Doctor Science at Obsidian Wings:
While the out-of-Africa population grew from just hundreds to 200 million in 100,000 years, and rose to just over 300 million by AD 1500, the African population increased from 1 million to no more than 20 million in 100,000 years, and rose to only 47 million by AD 1500. And the disparity persists to the present day, though both groups were descended from the same evolutionary stock. Both groups inherited the talents and physiological attributes that evolution had bestowed during the preceding 4 million years in Africa.
Why did the migrant population grow so much faster? Or, to approach the disparity from another direction, what prevented the African population from achieving similar levels of growth? Since the ancestral genetic stock was identical, the divergent history of the two groups implies that Africa itself was in some way responsible.
My answer to Reader's question should be obvious. Once you think of Homo sapiens as an invasive species -- like stink bugs, or kudzu, or cane toads -- the answer is blindingly obvious.
The only part of the world to which human beings are truly native is sub-Saharan Africa. Ecologically, there are no "native peoples" anywhere else in the world, because outside of Africa Homo sapiens is always an invasive alien species. You'd think that the fact that we're adapted to Africa in a way we aren't adapted to anywhere else would be an advantage, but it turns out not to work that way. The overwhelming factor, for H. sapiens as well as stink bugs, is that our native range is adapted to us -- humans or bugs become dangerously invasive when we can escape not just the limited space of our native range, but the constraints on our population that come from other co-native species: predators or parasites (including diseases).