November 16, 2012

f3-statistics on craniometric data?

It occurred to me that the concept of f3-statistics, originally developed to detect admixture by exploiting allele frequency difference anti-correlations could very well be applied to craniometric data as well.

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?
As with "normal" f3-statistics, absence of a negative correlation does not reject admixture; this may be especially the case here, because phenotypes may be affected by strong natural selection during the post-admixture period.

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. 

13 comments:

hamarfox said...

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)

This is interesting. I'm not sure what period the Zalavar skull is from, but the medieval Norse would likely have had more recent genetic contact with Siberians (i.e. the ~2% non-ancient Siberian admix seen in modern Norwegians at k levels after the Amerindian component has effectively disappeared). The same may be true also of the Hungarian skulls.

What's the anti-correlation in regard to other, non-Buriat East Eurasians (especially Amerindians), Egyptians and the Norse & Zalavar skulls? And is a similar but smaller signal seen in the Berg skulls?

Dienekes said...

The most negative anti-correlation with Berg as an admixed population is:

EGYPT BURIAT BERG -0.250747185633129

So this appears to hold for all three European populations.

Dienekes said...

Currently running all 189 named populations in Howells' complete set (including "test" data). I am really curious to see how some very well-known prehistoric skulls will turn out to be!

hamarfox said...

Would you consider creating a spreadsheet of all the results? It'd be great to look over and make some comparisons.

I followed some links back to a 2004 article you wrote on Howell's data. Interestingly, there's reference to a 'Eurmerican' branch, which is especially interesting considering recent genetic revelations. But what was strange was that Buriats belonged to quite another branch, placed closest with Sinoids. It'd be interesting to see how categorically similar populations differ in their anti-correlation values in regard to a common third population, in order to get a better handle on what the numbers mean.

terryt said...

"Philippines as Buriat+Andaman; this makes sense if Philippines is the result of admixture between an 'East Asian' and a 'Negrito' population"

That is what I and many others have assumed for a very long time. The East Asian presence is a later intrusion on a 'Negrito' (or more probably Papuan) substrate.

"Hainan as Andaman+Anyang; south Chinese as Neolithic Chinese+'Negrito'-like old south Chinese?"

Again I and many others have assumed that for a very long time. But again the substrate is probably 'Papuan' or even 'Australoid'.

"Guam as Tolai+Buriat; admixture between 'Papuan'-like and East Asian-like people in Polynesia?"

The Polynesians themselves are a mixture of Papuan and east Asians. The mix was probably formed in Wallacea before the Austronesian-speaking people had reached the Admiralty Islands.

Lathdrinor said...

Given that south China is nigh entirely O in haplotype, is it necessary to theorize, in this case, that O was quite diverse anthropomorphically, as I had argued in the past? The argument here does not corroborate the idea that 'Mongoloid' morphology expanded with the O haplotype.

terryt said...

"is it necessary to theorize, in this case, that O was quite diverse anthropomorphically, as I had argued in the past?"

No, it is not necessary to assume that. Any particular haplogroup must first originate, and reach fixation, in a small population. We can surely assume that any such population would be fairly homogeneous phenotypically. Just because O occurs in phenotypically diverse populations today does not mean at all that it was phenotypically diverse originally. And actually O is not so phenotypically diverse in fact. Wherever it is present the population shows some degree of 'Mongoloid' phenotype, being most Mongoloid where it is present in the highest proportion.

Lathdrinor said...

"We can surely assume that any such population would be fairly homogeneous phenotypically."

Yes, of course. I needed to word it better. When I speak of O diversity, I speak of the diversity that it obtained *before* the expansion of 'Mongoloids,' but *after* the initial fixation of the haplotype. That is to say, I think that expansions of the haplotype happened before the expansion of 'Mongoloids,' and additionally did not initially correspond to the expansion of the set of traits that define 'Mongoloids.' I am not denying that later expansions of specific subtypes of O did carry 'Mongoloid' phenotypes, only that the initial expansions that deposited the older subclades of O were not so bountiful.

I reach this argument on the grounds that populations in the southern tip of China, Southeast Asia and Oceania, which have an overwhelming amount of O, yet look 'admixed' under the physiological microscope, while populations in northern Asia, which have LESS overall O - to the extent that the Mongolians, for example, have only ~20-25% - correspond better to the physiological stereotype. Provided that Mongoloid phenotypes expanded with haplotype O, how did it become less pronounced in populations with >80% O than populations with <25% O?

Surely, admixture with archaic Negrito / Australoid populations are not sufficient explanations by themselves, given that Mongolians with <25% O are 'less admixed' under this model, physiologically, than far southern Chinese with >80%. It is necessary, then, to posit that Mongoloid traits did not expand with O, but instead expanded with populations that contained *subtypes* of O; alternatively, it was not O populations, but an unknown population in northern East Asia who developed these traits under environmental duress, and who subsequently admixed with O populations, who then carried the admixed traits to other O populations. Although, because of the presence of O in every 'Mongoloid' population, I favor the former scenario, simply by lack of evidence for that 'other population' who developed 'Mongoloid' traits.

In both of these scenarios, the a priori given has to be that O was, at the time of the 'Mongoloid' expansion, physiologically diverse, such that one distribution of the population was 'Mongoloid,' while the other was, well, not. Without theorizing on the specific traits of the unadmixed initial O population, I am nonetheless able to argue that the 'Australoid / Negrito' traits you see in southern O populations were already present in them by the time bona fide 'Mongoloid' traits began to expand in their midst. Thus, we have a scenario of physiological diversity within O from the Paleolithic / early Neolithic.

To argue otherwise requires you to explain why a >80% O population is less 'Mongoloid' than a <25% O population. The only answers that I find viable are those involving 'Mongoloid' traits being primarily the result of maternal genetics and an obscenely sex biased admixture in southern East Asia and Oceania. Further, this requires O to be maternally homogeneous before the expansion of 'Mongoloid' traits. Yet, judging by the varied distribution of different subclades of O in different areas of the world, its expansion was not recent.

Thus, I am forced to argue that, because O's expansion preceded the expansion of 'Mongoloid' traits, and because populations with very high distributions of O are less 'Mongoloid' than populations with moderate distributions of O, that O was physiologically diverse and that 'Mongoloid' traits did not initially expand with O, but was the result of later expansions by subtypes of O, who came upon it rather late in the Paleolithic / early Neolithic.

terryt said...

"I am nonetheless able to argue that the 'Australoid / Negrito' traits you see in southern O populations were already present in them by the time bona fide 'Mongoloid' traits began to expand in their midst".

Absolutely not necessary at all to take such a position. Neither the Australian Aborigines nor the New Guinea Islanders have anything like a Mongoloid look and basically have no O. On the other hand they do share several haplogroups closely related to some found in SE Asia. It is most likely that the 'original' SE Asians looked much like modern Melanesians or Australian Aborigines until the arrival of Y-DNA O and the Mongoloid phenotype.

"I reach this argument on the grounds that populations in the southern tip of China, Southeast Asia and Oceania, which have an overwhelming amount of O, yet look 'admixed' under the physiological microscope"

Those SE Asian and Oceanic admixed populations contain substantial proportions of non-O haplogroups such as C2, F (mainly F2) and K. It is probably these haplogroups that represent the non-Mongoloid element. In fact where O makes up a greater proportion of the Y-DNA we find the more Mongoloid-looking populations.

"alternatively, it was not O populations, but an unknown population in northern East Asia who developed these traits under environmental duress, and who subsequently admixed with O populations, who then carried the admixed traits to other O populations".

I basically agree with much of that. The 'unknown population in northern East Asia who developed these traits under environmental duress' I would take to be C3, but when O began its expansion it had largely accumulated the Mongoloid phenotype and so was not particularly 'admixed'. It became so as it entered regions to the south already inhabited by 'Papuan' populations (or 'Negrito' populations if you prefer).

terryt said...

"Yes, of course. I needed to word it better. When I speak of O diversity, I speak of the diversity that it obtained *before* the expansion of 'Mongoloids,' but *after* the initial fixation of the haplotype. That is to say, I think that expansions of the haplotype happened before the expansion of 'Mongoloids,'".

I see no need to postulate any phenotypic diversity for Y-DNA O before the Mongoloid expansion. I am reasonably sure that it was haplogroup O, especially O3, that spread the Mongoloid phenotype, towards the south at any rate. O's 'brother' N was probably responsible for the expansion north, along with C3. Although I am also reasonably sure that the phenotype originated somewhere near where C3 originated.

"while populations in northern Asia, which have LESS overall O - to the extent that the Mongolians, for example, have only ~20-25% - correspond better to the physiological stereotype".

In those populations we find C3, definitely associated with a Mongoloid phenotype, and O's 'brother' N, also definitely associated with a Mongoloid phenotype.

"Provided that Mongoloid phenotypes expanded with haplotype O, how did it become less pronounced in populations with >80% O than populations with <25% O?"

Does it in fact obey that formula? What populations with more than 80% O do not look 'Mongoloid'? I agree that some populations with less than 25% O look Mongoloid, but these have huge proportions of C3 and N.

"In both of these scenarios, the a priori given has to be that O was, at the time of the 'Mongoloid' expansion, physiologically diverse'

I disagree completely that such a position is necessarily so. The O population became admixed as it moved south, not before.

"judging by the varied distribution of different subclades of O in different areas of the world, its expansion was not recent".

On the contrary, the fact that many downstream O haplogroups are widely distributed yet little diversified indicates a comparatively recent expansion of the whole O clade. Presumably we have at least three main expansions though: O1, O2 and O3. O3 alone though obviously involving more than just one expansion of its own.

"Thus, I am forced to argue that, because O's expansion preceded the expansion of 'Mongoloid' traits, and because populations with very high distributions of O are less 'Mongoloid' than populations with moderate distributions of O, that O was physiologically diverse and that 'Mongoloid' traits did not initially expand with O"

I hope I have shown why I disagree completely with your first two claims, so your whole argument immediately falls apart.

Lathdrinor said...

Terryt: Karafet et. al argued in 'Major East–West Division Underlies Y Chromosome Stratification across Indonesia' (2010) that the expansion of O subclades to Oceania occurred in three main waves, with the first occurring between 30-15 kya and involving the subclades P203, M95, M122, and M119. I am not aware of a stereotypical Mongoloid 'O' population existing at the time, and especially not in Southeast Asia, which is where the expansion to Oceania is thought to have started. My first proposition is therefore well supported.

As for the second proposition, I am aware of the presence of C3 and N in 'Mongoloid' populations, but this is not contradictory to my argument. As for populations with >80% O being 'less Mongoloid,' isn't this what the f3 results show? I concur that there exist populations in Oceania that are not Mongoloid and which have no 'O,' but to say that Filipinos and Indonesians, for example, are very Mongoloid requires better support than simply asserting it. Yes, O primary populations possess Mongoloid traits, which reached them via a later expansion of O - my thinking being the Austronesian expansion. But that does not preclude earlier expansions of O that did not possess stereotypical Mongoloid traits. Otherwise, the populations in question, with their >80% O, ought to be Mongoloid to a far greater extent than they are today, even when we control for greater paternal contribution. That is my argument.

terryt said...

"Karafet et. al argued in 'Major East–West Division Underlies Y Chromosome Stratification across Indonesia' (2010) that the expansion of O subclades to Oceania occurred in three main waves, with the first occurring between 30-15 kya and involving the subclades P203, M95, M122, and M119".

Yes, I know they did. But their paper is full of holes as I pointed out on this blog and at Leherensuge at the time. For a start they pointed out that the O clades are very minor in Oceania. And they make up a proportion only of the last wave across Wallace's Line. Earlier waves did not involve O haplogroups.

"Yes, O primary populations possess Mongoloid traits, which reached them via a later expansion of O - my thinking being the Austronesian expansion".

That doesn't make any sort of sense. What later expansion? The Austronesians are certainly not particularly 'Mongoloid' as they are quite admixed with non-Mongoloid populations through much of their range, especially out in the wider Pacific.

"But that does not preclude earlier expansions of O that did not possess stereotypical Mongoloid traits".

It's difficult to imagine any sort of O expansion that did not involve Mongoloid traits.

terryt said...

Here is the discussion we had regarding the paper some time back:

http://dienekes.blogspot.co.nz/2010/03/major-east-west-divide-in-indonesian-y.html

In his introduction Dienekes wrote:

"But, isn't it strange that the authors claim a Paleolithic gene pool, while, at the same time, discovering a sharp divide? Common sense dictates that genetic distinctions across a long time span would be blurred, and there would be no sharp divide. Sharp divides are created by recent population movements and are maintained by insurmountable geographical barriers (e.g., the Sahara or the Pacific) that persist for a long-time".

In spite of several comments expressing doubts I agree 100% with this comment. Wallace's Line would hardly have been any sort of obstacle for a population that had been in the region since the Paleolithic.