The Out of Africa model is a theory of human evolution claiming that "modern" humans emerged in Africa and Africa alone, spreading to the rest of the world later.
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There are fossil anomalies that does not fit into the theory. These fossil anomalies include Dali in China (big brain combined with primitive erectus-like skull features as well as distinctly East Asian cheek bones), Solo Man in Indonesia (mostly erectus-like skulls but bigger brains, the skeletons are more gracile than typical erectus, tool sophistication usually associated with early sapiens), and some early Cro-Magnons in Europe (robust bones, occetipal buns, and neanderthal-like shoulder joints).
It is often claimed that genetic studies support the theory (human populations across the world show a low degree of genetic sequence variation, but somewhat higher in Africa than elsewhere), but that conclusion is based on the assumption that mutations are random, which is not true, see self-organization and inheritance of acquired characteristics. Unlike random mutation Out of Africa theory, directed mutation convergence can explain the discrepancy between similarity of genetic sequence and the diversity in the number of copies of genes seen across human populations. Random mutation theory cannot explain anything close to such a bias favoring copy count mutations over sequence mutations, see self-organization.
East Acheulian tool limit
There is also the fact that Acheulian tools are found only west of a certain geographical line. It can be argued that those east of the line used bamboo instead of stone in their tools, but migration of whole tribes tend to bring their habits with them. So it is possible that single individuals crossed the Acheul limit and were quickly assimilated by tribes on the other side, but the line was never crossed by whole tribes. This means that the introduction of sapiens traits in Asia was under the control of preexisting Asian erectus tribal cultures.
Late Neanderthal symbolic art
There is archaeological evidence in Europe that symbolic art started appearing a few thousand years before the first anatomically modern humans in Europe. That means that the last Neanderthals started making symbolic art. There is also evidence that Neanderthals had been specialized big game hunters for most of their history but started adopting more varied food sources towards the end of their existence. All of this happened when forests shrank and grasslands expanded in Europe. This change of late Neanderthal lifestyle implies that they changed rather than simply dying out. When they no longer needed a keen olfactory system to track their prey through forests, their shrinking nasal cavities may have morphed their skulls into a sapiens shape.
Chronological contradiction within Africa
Although the oldest anatomically modern human fossils and the oldest symbolic art are both from Africa, they are not from the same parts of Africa. The oldest symbolic art is from near-coastal caves near Cape in South Africa (only there have symbolic art older than 100,000 years been found) while the oldest anatomically modern human fossils are from Omo valley, Ethiopia (195,000 years old). There is quite a geographical distance between South Africa and Ethiopia. In fact, Ethiopia is much closer to Saudi Arabia than to South Africa, and Saudi Arabia is not even in Africa! So clearly anatomical modernity did not cause the origin of symbolic art. And if anatomical modernity had evolved because it promoted symbolic behavior, then the rise of symbolic art should have begun during the early stages of anatomical modernization and the amount of symbolic art should have stabilized when anatomical modernity had been reached, but that is empirically falsified by archaeology. The archaeological record shows that symbolic art started emerging when anatomical modernization was virtually complete at best (and well after it in some parts of Africa), and the amount of symbolic art continued to increase well after that. That is not what should be expected if anatomical modernity was a side effect of the evolution of symbolic behavior!
Paleoclimatology shows that desertification struck Africa 190,000 to 130,000 years ago. Prior to that, a wet period meant that most of Africa was covered in jungles. The Omo fossils, being 195,000 years old, shows that the first anatomically modern humans emerged in a jungle environment. Their lack of symbolic art clearly shows that their anatomical modernity was not a result of a more complex language than their earlier ancestors had. But in deep jungles, reptiles tend to be the dominant predators, not mammals, and reptiles lack the smell glands that mammals have. This means that Omo Man had no use for a keen caveman olfactory system, allowing their nasal cavities to shrink and morph their skulls into a sapiens shape. Their cautiousness against dangerous reptiles may have been what limited their time to think, preventing their language from becoming complex. Anatomically modern but with a primitive language, living deep in a jungle, very cautious against dangerous reptiles? That makes them an analogy to the Piraha, although of course Omo Man did not look Native American.