they're still there, actually - in iran, in northern iraq, in syria, in turkey, in libya, in algeria.
the studies they've done suggest that the women are more caucasian, while the men are more turkish or more semitic. this is difficult to isolate, for obvious reasons, including the substantial amount of sex slaves that were transported from europe to the middle east during the height of the islamic period. the arabs liked white women, and would go out of their way to capture, enslave, rape and impregnate them, with modern day ukraine being the primary victim of that particular type of slave trade. but, it is nonetheless a measurable thing, and the thinking is that what happened was that successive waves of migrations from the east and the south killed all the white men, and raped all their women. the christofascist nature of the late roman empire in the region under homicidal, dictatorial rulers like justinian and heraclius (and the mirror image in the equally despotic late persian empire) didn't help - these people were sent to die as much as they were slaughtered. in the end, the arabs had an easy conquest because the romans and persians just killed each other off.
so, what happened was that the roman empire was overthrown in these areas by an arabic migration event, but it was rather incomplete. the footprints of persian, greek & roman dominance (following sumerian, hittite & assyrian dominance - and mixed up with periods of semitic rule) are still genotypically present, if not overwhelming, in pretty much the entire region. but, in egypt, particularly, there was a much higher level of population replacement, it does seem. and the best reason i've ever seen articulated for that is that it was the most wealthy region, even centuries after it lost an autonomous identity.
there's every reason to believe that population replacement in egypt will continue and that the egyptians of a thousand years from now will be impossible to compare to the egyptians of today.
but, you need to be careful with this - the earliest prehistory seems to be fully africoid, but the historical period was overwhelmingly light-skinned, until the byzantines permanently lost the area for rome in the 7th century, when a more tanned complexion become dominant, due to migration from the peninsula.