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Lewontin's famous 1972 book chapter
Few people actually read this, which is a shame because the science is interesting for historical purposes, and the fulltext of his famous fallacy is rarely read. I believe this is a pity because it is really obvious when you actually read it.
Lewontin, R. C. (1972). "The Apportionment of Human Diversity". Evolutionary Biology. pp. 381–398.
The conclusion section reads as follows:
The results are quite remarkable. The mean" proportion of the total species diversity that is contained within populations is 85.4%, with a maximum of 99.7% for the Xm gene, and a minimum of 63.6% for Duffy. Less than 15% of all human genetic diversity is accounted for by differences between human groups! Moreover, the difference between populations within a race accounts for an additional 8.3%, so that only 6.3% is accounted for by racial classification. This allocation of 85% of human genetic diversity to individual variation within populations is sensitive to the sample of populations considered. As we have several times pointed out, our sample is heavily weighted with "primitive" peoples with small populations, so that their Ho values count much too heavily compared with their proportion in the total human population. Scanning Table 3 we see that, more often than not, the Hpop values are lower for South Asian aborigines, Australian aborigines, Oceanians, and Amerinds than for the three large racial groups. Moreover, the total human diversity, Hspecies, is inflated because of the overweighting of these small groups, which tend to have gene frequencies that deviate from the large races. Thus the fraction of diversity within populations is doubly underestimated since the numerator of that fraction is underestimated and the denominator overestimated. When we consider the remaining diversity, not explained by within-population effects, the allocation to within-race and between-race effects is sensitive to our racial representations. On the one hand the over-representation of aborigines and Oceanians tends to give too much weight to diversity between races. On the other hand, the racial component is underestimated by certain arbitrary lumpings of divergent populations in one race. For example, if the Hindi and Urdu speaking peoples were separated out as a race, and if the Melanesian peoples of the South Asian seas were not lumped with the Oceanians, then the racial component of diversity would be increased. Of course, by assigning each population to separate races we would carry this procedure to the reductio ad absurdum. A post facto assignment, based on gene frequencies, would also increase the racial component, but if this were carried out objectively it would lump certain Africans with Lapps! Clearly, if we are to assess the meaning of racial classifications in genetic terms, we must concern ourselves with the usual racial divisions. All things considered, then, the 6.3% of human diversity assignable to race is about right, or a slight overestimate considering that Hpop is overestimated. It is clear that our perception of relatively large differences between human races and subgroups, as compared to the variation within these groups, is indeed a biased perception and that, based on randomly chosen genetic differences, human races and populations are remarkably similar to each other, with the largest part by far of human variation being accounted for by the differences between individuals. Human racial classification is of no social value and is positively destructive of social and human relations. Since such racial classification is now seen to be of virtually no genetic or taxonomic significance either, no justification can be offered for its continuance.
That's it. Notice the absence of any premise connecting the conclusion
"Human racial classification is of no social value and is positively destructive of social and human relations"
to the intended premise
"The mean proportion of the total species diversity that is contained within populations is 85.4% [...]. Less than 15% of all human genetic diversity is accounted for by differences between human groups! Moreover, the difference between populations within a race accounts for an additional 8.3%, so that only 6.3% is accounted for by racial classification.".
What's the intended premise supposed to be? What if we found the values were a 50-30-20 split? Even a cursory comparison to other species with subspecies no one denies would reveal these human values are quite typical (Woodley 2010, Fuerst 2015, Stoeckle & Thaler 2018).