Proofs? Ancient and modern Egyptians and Romans have been proven to be more or less the same people living there now, with only slight shifts. In Europe populations have stabillized at the Bronze Age despite later migrations. I doubt things changed much with Babylonians, the populations were too big to suffer new founder effects and Arabs were relatively small if that's what you're implying. Compare the case of Hungarians, who are local Pannonian inhabitants that adopted an Asiatic language and have almost no no genetic influx from the Asians.