Neanderthals and the weak version of the Out of Africa theory of human origins

Modern humans are largely descended from a series of population expansions that began around 80,000 years ago somewhere in eastern Africa and culminated about 60,000 years ago in a major population event that would create 96-99% of the gene pool outside Africa. The remaining 1-4% came from Neanderthals in Europe and West Asia, and other human ancestors elsewhere. This admixture seems to have occurred in two stages: an early one in the Middle East, when modern humans began spreading out of Africa, and a later one, when modern humans began to spread from Asia to Oceania. Curiously, the admixture looks Neanderthal in both cases.