There are a lot of genes that affect skin color, and as a result it’s something that can potentially change *very* fast.
Imagine that one dark-skinned African has a gene that says “build lots of pigment-producing cells” and another gene that says “don’t turn the pigment-producing cells on too frequently”. Meanwhile, a second dark-skinned African has “don’t build too many pigment-producing cells” but “run the pigment-producing cells almost constantly”. Their child could potentially inherit the combination of “don’t build too many pigment-producing cells” and “don’t turn the pigment-producing cells on too frequently”, and so be substantially lighter-skinned than either parent.
If there turns out to be a major survival advantage to being light-skinned (e.g., protection from vitamin D deficiency at high latitudes, or elite social status within the Proto-Indo-European caste system), such that light-skinned children live and dark-skinned children die, the family could end up completely light-skinned in just a generation or two.
That is, in fact, basically what happened. To the best of my knowledge, every individual gene that lightens skin color is found even in the darkest-skinned African tribes. The only thing Europeans did was combine those genes with one another. So there was no need to wait for new mutations to arise, which is the step that takes so long in normal evolution.
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