What route did humans take out of Africa to migrate into the Middle East?

I understand that the first wave of human migration out of Africa is believed to be cross the Red Sea, into Yemen, and down a coastal route to Australia. But what about Middle Easteners? I've heard conflicting theories: One states that Middle Easteners came from the group of humans which migrated into Yemen--that they then migrated north from Yemen on the Arabian Peninsula to the Middle East. However, I've also heard that Middle Easteners were the product of a totally separate second migration out of Africa up the Nile corridor and across the Sinai Peninsula into the Middle East. Does anyone know what route Middle Easteners took to arrive in the Middle East and when?