The basic idea is quite simple: suppose that for a metric trait, two populations A and B have mean value a and b and that a third population C is formed by mixture between A and B. Unlike allele frequencies where the admixed population's frequency will be between a and b immediately post-admixture, anthropometric traits may respond in unexpected ways to admixture (e.g., heterosis might cause first-generation offspring to exceed both their parents in height, rather than exhibit an intermediate value). I will leave the justification of the hypothesis that "mixed-origin offspring will possess intermediate metric traits" to the physical anthropologists, who may have gathered data on such things, and, for the present, I will take it for granted.
So, assuming that c, the mean trait in the mixed population, is between a and b, we can easily see that (c-a)(c-b) will be negative, and hence so will be the correlation coefficient (over many traits) between C-A and C-B, where by C-A I denote the k-long vector difference of mean trait values between populations C and A.
Going back to my analysis of Howells' dataset, I calculated population means for 57 traits over the NORMALIZED_DATA array of modern populations (in which sexual dimorphism has been removed and traits of different scale have been normalized in standard deviation units), and calculated 30*choose(29,2) correlations for each of 30 populations, expressed as a mixture of any pair of the remaining 29.
I list below, the top 20 anti-correlations, and highlight a few in bold (third population as mixture of first two):
BURIAT ANDAMAN PHILLIPI -0.54005191575771
EGYPT BURIAT NORSE -0.490018084440697
ANDAMAN ANYANG HAINAN -0.48323680182295
BURIAT ANDAMAN HAINAN -0.480939028739347
EGYPT BURIAT ZALAVAR -0.476445836100052
ANDAMAN ANYANG PHILLIPI -0.457902384166767
DOGON BURIAT PHILLIPI -0.416551851781419
BERG EASTER_I ZALAVAR -0.378996437433417
AUSTRALI BURIAT ARIKARA -0.375898166338775
BURIAT EASTER_I MOKAPU -0.37169703838378
ESKIMO ANDAMAN S_JAPAN -0.366611599944932
ESKIMO PERU N_JAPAN -0.354535077363928
TOLAI BURIAT ARIKARA -0.348110323746154
BERG EGYPT ZALAVAR -0.344843098962355
DOGON ESKIMO GUAM -0.344577928128792
TOLAI BURIAT GUAM -0.338804214799388
ESKIMO PHILLIPI GUAM -0.336537918547276
DOGON BURIAT HAINAN -0.332635954428392
TASMANIA BURIAT ARIKARA -0.331301837598433
ESKIMO PERU S_JAPAN -0.330302035072489
Some interesting ones:
- Philippines as Buriat+Andaman; this makes sense if Philippines is the result of admixture between an "East Asian" and a "Negrito" population
- Norse as Egypt+Buriat; the Howells "Egypt" sample is "Mediterranean" in the classical sense. Perhaps this involves the same "East Eurasian"-like signal of admixture detected by genetic methods? Similar signal also occurs for Zalavar (from Hungary)
- Hainan as Andaman+Anyang; south Chinese as Neolithic Chinese+"Negrito"-like old south Chinese?
- Arikara as Buriat+Australian; admixture between "Australoid" Paleo-Indians and "Mongoloid" ones? or between 1st wave Indians and later ones (sensu Reich et al. 2012)?
- Guam as Tolai+Buriat; admixture between "Papuan"-like and East Asian-like people in Polynesia?
And, there are some difficult-to-interpret cases (e.g., Philippines as Buriat+Dogon) which may point to limitations of the method; for example, the Dogon may act as a stand-in for the "equatorial"-like physique of the true "Andaman"-like mixing element. Presumably such limitations can be overcome by limiting the analysis to "selectively neutral" traits, rather than the whole suite of 57 Howells variables used here.
I certainly think that the idea ought to be investigated further: it might be redundant when genetic data are available, but may prove useful in the analysis of admixture when such data do not exist, e.g., in anthropological data of prehistoric specimens from hot climates where archaeogenetic evidence may never materialize.