Any book that mentions that garbage theory of "Out of Africa" goes straight to my waste basket.
I do not think everybody evolved directly out from Africa.
I also do not believe that Neanderthals went completely extinct.
Scientists like to be politically correct and state that neanderthals and homo erectus did not interbred with homo sapiens from Africa.
That is totally wrong. there was a study, I cannot find the link, that stated that every racial group, with the exception of a lot of black/Africans, has some trace of Neanderthal DNA in them.
There is a little more Neanderthal DNA in East Asians compared to Caucasian people. I think we evolved separately in various regions of the world, but somehow, these bi-peds from different species met somewhere and interbred with each other which probably formed the different racial groups we have on this planet.