Very obviously the timing of all of this movement into and out of Africa is related to what the ice ages were doing at the time. There are about half a dozen of them that definitely affected Europe and Asia over that period, but there are a full 21 cycles (according to the Antarctic ice cores), and they influenced our development as well.
It is also related to the existence of the Gibraltar land bridge, allowing migration from Africa to Europe without the Middle East digression, IMHO.