I am sending you my article from Mol Ecol (which is behind a paywall). That contains some real examples of Fst close to zero even though the demes consisted entirely of private alleles. But for readers here, I also just explained above that this apparently impossible situation will always happen when within-group variation (heterozygosity) is high. That math proof trumps even the real examples.

Fst is consistently misintepreted in the literature and mis-taught in most standard texts. The nice thing about this (unlike most controversies) is that anyone can prove it to themselves by doing numerical examples with high-diversity demes.

I’ll have a look at Barbujani and Colonna when I can. This is a busy week in the world of politics so I’m having a hard time getting other stuff done!

You questioned my statement that Fst could be close to zero even if the groups shared no alleles at all (including cases when the groups belonged to different species. I hope I answered your question and showed why Fst or Gst have no relevance to the question of genetic divergence between groups.

My original comment was not aimed at anything you said but at the invalid reasoning in the Barbujani and Colonna article that Jason Antrosio (#1) cited favorably.

Conversely, lets suppose we have lots of groups, and all but one group are fixed for the same allele (so virtually all groups are genetically identical at that locus). The odd group is fixed for a different allele. So Hs=0 and Ht=some number. Then (Ht-Hs)/Ht =1.00, supposedly indicating maximum differentiation between groups, even though almost all groups are genetically identical. So Fst or Gst are not good ways to describe differentiation, though they do have legitimate uses for other tasks.

You do not give an example in that link.

Meanwhile I noticed another misconception in the Barbujani and Colonna article: “If Ne*m, the product of
effective population size (Ne) and migration rate (m), is
large, the effects of migration prevail and populations tend
to converge genetically; if Ne*m is small, genetic drift plays the predominant evolutionary role, so that populations tend to diverge.” This is widely (maybe almost universally) believed, but it is false, as anyone can check by running simulations of the finite island model. The actual factor controlling cohesion or divergence of subpopulations is P/u where P is the relative migration rate between pairs of subpopulations, and u is the mutation rate at the locus of interest. Since it is the relative migration rate that matters, not the absolute number of migrants, differentiation can arise even across somewhat leaky barriers. See my comments and simulations under Nolan Kane’s post at:
http://www.molecularecologist.com/2011/03/should-i-use-fst-gst-or-d-2/
For the reasons why Fst or Gst do not measure differentiation of allele frequencies between groups, see Jost, L. (2008) Gst and its relatives do not measure differentiation, Molecular Ecology 17: 4015-4026. For more on the mathematics of diversity and differentiation, and the myths surrrounding it, stick [Jost diversity] into Google Scholar.

It amuses me now much different the populations look, now that I know they are different species.

That simply isn’t true. Dividing species into nominal races when faced with variation is considered doing it wrong in evolutionary biology. The distinction you are making in your comment between “anthropologists” and “evolutionary biologists” is not correct at all.

They could have obtained low Fst values even if the groups belonged to different species entirely and shared no alleles,

Let’s have an example of that. (Not that Fst is conclusive here, but I’d love to see what the heck you are talking about here.)

As a population geneticist, I have been more disturbed by the misuse of genetic arguments in this debate. I really don’t know enough about the data to have a strong opinion about what to conclude, but I do see that many of the quantitative arguments mentioned in these posts are invalid. The Barbujani and Colonna article you linked to is a case in point. It bases part of its argument on the fact that a measure of population structure, Fst, is very low between human subpopulations. Fst is a highly nonlinear measure that is not a measure of differentiation between groups. They could have obtained low Fst values even if the groups belonged to different species entirely and shared no alleles, so the lowness of Fst is not a very good argument against the idea of race. Their description of Fst in the accompanying glossary also makes multiple mistakes: “Fst ranges from 0, when all subpopulations are identical, to 1, when different alleles are fixed in different subpopulations.” No, Fst can approach zero even if all subpopulations are completely distinct (no shared alleles). See the work of Hedrick or myself. And when there are many subpopulations, Fst can equal unity even if nearly all of them are fixed for the same allele. See the work of Gregorius. The kinds of arguments used by Barbujani and Colonna are common in the literature, and they are misleading.

I explain this in my comment here:

http://kenanmalik.wordpress.com/2012/03/04/why-both-sides-are-wrong-in-the-race-debate/#comment-1825

I do not criticize Barbujani and Colonna’s conclusions (I don’t know the data at all), only the invalid reasoning.