Adam and Eve

Sadly I don't have Iraqi people's genotypes to analyse with ADMIXTURE, still I expect a pretty boring "Mesopotamian Core" + a lot of "Nile Core" admixture. Sumerians and Akkadians? Certainly much more complex than that, still an attractive thought.
What follows is a highly speculative simplified narrative for the benefit of readers not familiar with some of these theories, which have been advanced before by others. Some could turn out correct, others wrong, but in general I think there is something in it. Something prevented the vast majority of Forager groups from developing this lifestyle, that once properly matured, allowed for demographic change in a scale (only recently completed with the settlement of Australia 200 years ago), such as Mankind may not have known ever since "Out-of-Africa some 50-100.000 years before.

Many people have advanced theories on the origins of agriculture. It's a very hard life, and it now seems it only pays back initially as a form of insurance, since grains can be stored, and planting planned, unlike meat, fish and gathered fruits.
It looks like before 10.000 years B.C Mesopotamia was much longer than today, extending to the very mouth of the Persian Gulf, almost all the way to India. It was likely an extremely rich environment for hunter-gatherers, with marches full of game, and several large grain grasses covering large areas, allowing for high densities of settled foragers, unlike most of the World. However the very unstable climatic situation at the end of the Ice Age must have meant that this rich environment was under constant change with maybe devastating floods and dry periods alternating: ideal circumstances for the birth of future planning, namely the planting of wild seeds in the empty soil after the calamities. Women largely gathered the plant-derived food, and men hunted and fished, just as in current forager groups. So Eve ate the fruits of Knowledge, of future planning and worrying, of continuous, high levels of cooperation between non directly related people, and doomed all of her children to a life of increasing control over destiny, but also slavery to the soil, rather than direct daily dependency on Nature's bounty.
After the Flood of this original Eden
Mesopotamians were put in even greater stress, and likely life as we know it began.

Something similar may have happened in the Green Sahara. A vastly rich environment full of game and rivers and large lakes, the Saharan desert probably allowed for high densities of hunter-gatherers in some areas, such as the Nile River. Then desertification started, beginning with the Eastern Desert, people cramming into an already full Nile valley. Similar pressures had similar results, and probably in mutual influence from an already expanding Mesopotamia, the Nile Core was born.

Turkey, a major centre in the maturation of the Mesopotamian Core, was in a previous post.
One Jordanian has obvious recent East African admixture, also to a lesser extent a Palestinian.
Areas with higher Nile Core occur in all countries, maybe in more fertile areas, maybe closer to the coast, further South, or all three combined. Some Mongol/Turkic influence can be seen in Syrians, even though far less than in Turks. "Coastal Migration" elements are either ancient Roma-like admixture or, less likely, a very old aboriginal signature.

Druze are an "Island-like" population with little outside influence. Their isolation (they live in mountainous areas) may have determined their smaller Nile Core element and their peculiar religion and culture, rather than the reverse.

Many Saudis, most Bedouins, and some Yemenis live or have until recently lived as pastoralist nomads. Unlike settled agricultural peoples, nomads receive a lot more admixture from elites and slaves. It's hard to draw consistent rent from pastoralist groups, and slaves are generally much better treated and have more social mobility in such societies. It's interesting to note the Mongol-like small element in these populations. The widespread but residual "Coastal Migration" element in Yemenis could very well be IMO aboriginal.

Differences in Mesopotamian Core and Masai-like ("Nilo-Saharan?") elements in Egyptians may betray a Southern versus Nile Delta origin. There is an obvious cline among Ethiopians, with larger "Mesopotamian Core" segments correlating with large "Nile Core" ones suggesting an Egyptian wave southwards after admixture with Mesopotamians. However larger percentual Nile Core versus Mesopotamian in Ethiopians versus Egyptians may imply a presence of the Nile Core there before this wave. This is also observable in North Africans, and may correspond to another earlier Egyptian wave, affecting only North Africa and East Africa, before large scale admixture with the Mesopotamian element in Egypt itself. Or maybe related Sahara desertification refugees?

Three Lybians have recent East African-like admixture. This may be happening in individuals with Nomadic ancestry, but may be typical of local desert groups such as the Tuareg. Tunisians are quite homogeneous as expected for an especially densely settled and fertile area in the region.
I'm not presenting graphs of the other North Africans as they're very similar, except for South Moroccans, who seem to have a very balanced "West African" pole-attracted element I think is native. Algerians have some similar unbalanced elements I think are about admixture with desert tribes.
North Moroccans are similar to Tunisians, without desert nomad elements, as the fertility of the region would predict.

Here is the spreadsheet:
Included is the Fst distance estimate by ADMIXTURE. Please note that even though some of these are accurate ("Nilo-Saharan?" vs "West African"), some like "Forager A" are not, since together with all Forager A fragments ADMIXTURE weights in all the more numerous San individuals inside the pole into the component. I actually now think Forager A is a more Siberian than a San like population, I'll present data soon. ADMIXTURE probably picked them up into "San" because it's clearly not Nganasan, further still from other Siberian poles, and the San pole was "childless", while the Nganasan pole had chunks of Chuvash, Russians and others to play with. More on that later.
spreadsheet