Richard Lewontin argued that since most (> 85%) genetic variation in humans is within-group, rather than between groups, human populations can’t be very different. Of course, if this argument is valid, it should apply to any genetically determined trait. Thus the variation in skin color within a population should be larger than the skin color differences between populations – except that it’s not. The difference in skin color between Europeans and Pygmies is large, so large that there is no overlap at all. No European is as dark as the lightest Pygmy (discounting rare cases of albinism).
As it happens, we now know quite a lot about the genetic architecture of skin color. It is somewhat unusual, in that a handful of alleles shaped by recent selection account for light skin in Europeans and Asia (different alleles in Asia than in Europe). So, is skin color an exception? Maybe Lewontin’s argument works on highly polygenic traits like height, that are influenced by many alleles of small effect. But no! Pygmies are notoriously short, while Bantus are about the same height as Europeans. We know that in a mixed population (part-Pygmy and part-Bantu) height goes up with the percentage of Bantu ancestry. So, there is a big, non-environmental difference in height (several standard deviations), even though height (itself highly heritable) is influenced by many genes of small effect.
So Lewontin’s argument does not work. You can’t predict group differences in trait values from the distribution of genetic variation – except in the limiting case where all of the variation is within-group, which means that the two populations are genetically identical. You know you can’t apply it to other traits, whether they are influenced by a few genes or by many. It’s not essential to know _why_ it doesn’t work – the mere fact that its predictions don’t come true is reason enough to discard it.
We do know why, though. Selection generates correlated genetic differences. Selection for increased height causes changes in the frequency of many alleles, in principle at all loci that influence height, although that is still a small subset of the genome. What matter is the difference in that subset: the overall distribution of genetic variation tells you nothing. Moreover, imagine that in the ancestral population, there were two alleles for each of those loci – a short allele with a frequency of 0.7 and a tall allele with a frequency of 0.3. Suppose that after selection for height, the frequency of each short allele was 0.3 and the frequency of the tall allele was 0.7. This could significantly increase height. In that subset of the genome, about 85% of the variation between those two population is within-group while 15% is between-group.