Even as a recently as the Arabic empires a thousand years ago, big parts of what is now the Sahara was then arable land, and pretty decent too, I mean it's there, right next to Italy and Spain. I don't know about the Arabian peninsula but argiculture does shit to an mf'er, and the people who lived there way before were sparse nomads, just like in Sibiria etc. (not that nomads were perfectly sustainable or anything). And your ancient homelands being conquered by barbarians might make returning to the non-shitty lands hard. Also your DNA comment is pretty cringe