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It's true inasmuch as we literally talk about "genetic diversity" in the context of anthropological research, but implications that people try to smuggle in with these words are false. I'll just quote Cochran again.
On African genetic variation:
And the venomously sarcastic Economists and biology:
TL;DR: Africans do have greater genetic diversity, but "genetic variation is mostly in neutral loci", i.e., greater genetic diversity does not imply greater phenotypic diversity, and even if there is greater variation in one phenotypic trait (e.g. height), this does not imply that there is greater variation in all traits. Correct?
Pretty much. Actually it's four points.
Most of the asserted "genetic diversity" of Africa as a whole is due to peoples from ancient population clusters, which make up less than 1% of African population and are not associated with colloquial "black people". They are anthropological marvels, but frankly they're not the guys anyone is talking about. Related Razib Khan post.
"Genetic diversity" for a given population is overwhelmingly a measure of ancestral population size and diversity of interchangeable variants that have spread by genetic drift. Out-of-Africa populations have passed through a series of severe bottlenecks, so they've shed some genetic markers we can find in African Bantus. Doesn't have much to do with anything consequential. It's like a JPG that's gone through lossy compression: there are color bands now, and less diversity of color patches or raw pixel values, but it doesn't mean the semantics of the image is altered, or that the range of any color channel is diminished, in fact the opposite can be true.
Local adaptation can very quickly act on non-neutral loci, a few thousand years are more than enough to change a typical polygenic trait by 1 SD. We have no grounds to presume that ancestral (>50KYA) diversity explains modern diversity for groups that have evolved in different environments.
By the same logic, yes, traits are independent products of selection. Just like all Sub-Saharan Africans are pretty dark relative to other races, they can be pretty ... fast runners, putting aside their internal ranking and their variation in toxin resistance or deep-diving talents or cricket skills.
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