Previous estimates of correlations of anthropometric variables and latitude appearing on these pages and in the draft paper (“Ruff’s surface law holds for Holocene population but Bergmann’s size law does not”) were incorrect as a result of a bug in the code. The estimates that appear below supercede all previous estimates.
I sent my results to Christopher Ruff. His comments were extremely helpful and led me to discover a devastating flaw in my estimates. My earlier computations were compromised by an unforeseen bug in Matlab. Specifically, I did not know that the function grpstats permutes the groups in a different manner from the function categories so that all the correlation estimates were attenuated. In order to make sure that my estimates were kosher, this time I computed the unweighted coefficients independently twice; the first time in Matlab and the second time in Excel. Their congruence gives us good confidence that the numbers are kosher.
A second issue was my growing appreciation that morphological adaptation of the human body to the macroclimate could very well be gendered. I therefore decided to finally take my father’s suggestion and work exclusively in a sex-specific setting so to not rely on OLS or WLS corrections for the sex ratio.
A third issue was that some of our variables (stature and BMI) were measured with more noise than others (femur length, pelvic bone width, femur head diameter) since the former are estimates while the latter are direct measurements of the skeletons. We can therefore expect coefficient estimates of the former to be attenuated relative to the latter. We must therefore rely more on the latter than the former.
A final issue, pointed out by Ruff, was that New World populations can be expected to be adapted to the macroclimate of Siberia (from whence they migrated to the New World at the end of the Pleistocene) and not their New World locations. Since the skeleton samples for them are attached to the wrong latitude, this would tend to attenuate our coefficient estimates due to additional noise. We should therefore rely more on the Old World sample than the full sample.
Our preferred test statistic is weighted Spearman’s rho for the Old World sample where the weights are given by the number of fossils at the location. In light of the manifest heteroskedasticity due to the tremendous variation in sample size at each location, weighted rho is a more powerful test statistic than the unweighted version.
The results that emerge are very strong. Essentially, all the main anthropometric variables are strong correlates of latitude in the Holocene sample. This means that the economic interpretation of the cross-section of not only BMI but stature as well is confounded. The evidence is consistent with a thermoregulatory theory, or more generally, a Heliocentric theory of morphological adaptation of geographically-situated populations to the macroclimate during the Late Pleistocene (ie, since the dispersal of Homo sapiens out of Africa 130-50 Ka).
All the information contained in anthropometric variables can be extracted from the seat of the pants. Specifically, femur (thigh bone) length controls stature and pelvic bone width and the diameter of the femur head (the knob at the top of the thigh bone) controls BMI. The main results can therefore be read off Table 1.
Table 1. Sex-specific Spearman’s correlation coefficients with latitude. | ||||||
Full sample | Old World | |||||
N | 42 | 39 | 25 | 24 | ||
Male | Female | Male | Female | Tail | ||
Femur length | rho | 0.369 | 0.201 | 0.545 | 0.301 | |
pVal | 0.009 | 0.110 | 0.000 | 0.076 | Right | |
weighted rho | 0.264 | 0.132 | 0.477 | 0.349 | ||
pVal | 0.045 | 0.212 | 0.000 | 0.015 | Right | |
Femur head diameter | rho | 0.657 | 0.607 | 0.703 | 0.610 | |
pVal | 0.000 | 0.000 | 0.000 | 0.001 | Right | |
weighted rho | 0.720 | 0.757 | 0.867 | 0.739 | ||
pVal | 0.000 | 0.000 | 0.000 | 0.000 | Right | |
Pelvic bone width | rho | 0.460 | 0.662 | 0.539 | 0.684 | |
pVal | 0.001 | 0.000 | 0.002 | 0.000 | Right | |
weighted rho | 0.719 | 0.792 | 0.741 | 0.780 | ||
pVal | 0.000 | 0.000 | 0.000 | 0.000 | Right | |
Source: Goldman Osteometrics Dataset, author’s computations. |
The evidence is astonishingly unambiguous. By our preferred test statistic, the correlation coefficient of latitude and femur length for is around 0.55 (p<0.001) for men and 0.33 (p=0.020); for femur head diameter, around 0.80 (p<0.001); and for pelvic bone width, about 0.87 (p<0.001) for men and 0.72 (p<0.001) for women. Note that all the estimates are attenuated in the full sample relative to the Old World sample. This suggests that the “wrong latitude” problem for the New World is very serious; implying that the adaptation is encoded precisely in Late Pleistocene population history. But there is very little wriggle room in the evidence. What we have under the null hypothesis is the statistical equivalent of a straight flush in poker. The probability of observing these rank correlations in these measured postcranial variables by chance is negligible.
As expected, the correlations of the controlling variables in the seat of the pants translate into very high correlations for estimated height and BMI. See Table 2. Note that the estimates for stature are identical to that for femur length, as it indeed ought to be since the former is computed as a linear function of the latter. The full sample estimates are pairwise smaller than the Old World estimates, reemphasizing the “wrong latitude” problem in the dataset. By our preferred test statistic, the correlation of latitude with stature is around 0.60 (p<0.001) and for BMI is about 0.80 (p<0.001).
Table 2. Sex-specific Spearman’s correlation coefficients with latitude. | ||||||
Full sample | Old World | |||||
N | 42 | 39 | 25 | 24 | ||
Male | Female | Male | Female | Tail | ||
Estimated stature | rho | 0.369 | 0.201 | 0.477 | 0.301 | |
pVal | 0.009 | 0.110 | 0.007 | 0.076 | Right | |
weighted rho | 0.264 | 0.132 | 0.545 | 0.349 | ||
pVal | 0.045 | 0.212 | 0.000 | 0.015 | Right | |
Estimated BMI | rho | 0.425 | 0.640 | 0.351 | 0.638 | |
pVal | 0.004 | 0.000 | 0.043 | 0.001 | Right | |
weighted rho | 0.659 | 0.757 | 0.525 | 0.698 | ||
pVal | 0.000 | 0.000 | 0.000 | 0.000 | Right | |
Source: Goldman Osteometrics Dataset, author’s computations. |
Thus, BMI and stature are both confounded by morphological adaptation to the macroclimate. We cross-check our work by presenting our independent Excel-based estimates for unweighted Spearman’s rho together with Pearson’s r (although we know that Pearson’s r has a potentially severe liberal bias due to the nonnormality of latitude in the sample—but this does not seem to be a problem). Table 3 displays the results for Holocene men, and Table 4 that for Holocene women.
Table 3. Correlation coefficients with latitude for Holocene Men. | ||||
Pearson | Spearman | |||
Men | Full sample | Old World | Full sample | Old World |
Femur length | 0.395 | 0.459 | 0.371 | 0.571 |
Femur head diameter | 0.589 | 0.640 | 0.655 | 0.674 |
Pelvic bone width | 0.448 | 0.497 | 0.461 | 0.583 |
Stature | 0.395 | 0.459 | 0.371 | 0.571 |
BMI | 0.474 | 0.592 | 0.423 | 0.619 |
Source: Goldman Osteometrics Dataset, author’s computations in Excel. Estimates in bold are significant at the 5 percent level. |
Table 4. Correlation coefficients with latitude for Holocene Women. | ||||
Pearson’s r | Spearman’s rho | |||
Women | Full sample | Old World | Full sample | Old World |
Femur length | 0.110 | 0.330 | 0.201 | 0.509 |
Femur head diameter | 0.590 | 0.590 | 0.607 | 0.699 |
Pelvic bone width | 0.630 | 0.660 | 0.662 | 0.729 |
Stature | 0.110 | 0.330 | 0.201 | 0.509 |
BMI | 0.630 | 0.660 | 0.640 | 0.760 |
Source: Goldman Osteometrics Dataset, author’s computations in Excel. Estimates in bold are significant at the 5 percent level. |
The fate of the surface law is very interesting. (Chris asked me not to refer to it as “Ruff’s surface law” since it had been proposed by others before him; notably Mayr.) Turns out, once we look at sex-specific data, body surface and body weight are linear functions of each other. They both scale together at the individual level so it is not clear how to interpret correlation estimates for the ratio of surface area to body weight (although they are significant in a signed one-tailed test). See Figure 1.
In sum, the evidence is consistent with manifest adaptation of the basic parameters of the human skeleton to the macroclimate specifically during the Late Pleistocene. This means that the economic interpretation of the cross-sectional variation in both stature and BMI is confounded by our population geohistories. We must therefore rely exclusively on the time-variation of the variables to extract economic information, for instance, by looking at the cross-section of percentage changes in stature and BMI across nations.
There is massive variation in human morphology. ANOVA reveals that, depending on the particular anthropometric variable, roughly three-fifths of the variation is between individuals within populations; and two-fifths is systematic variation between populations at different geographic locations. Race is a poor way to understand the latter. What we have instead are geographic clines. Indeed, there is continuous geographic variation in human morphology as attested by a very significant gradient for latitude. We have suggested that the most parsimonious interpretation of this pattern is in terms of the imperatives of thermoregulation, as Ruff has argued.
The overall pattern suggest a Heliocentric theory. While it is tempting to try to connect this to our Heliocentric theory of the spread of the secondary industrial revolution and therefore of contemporary global polarization, that temptation must be resisted. The latter is a very specific theory that ties the rate of intensity of work performed on the same machine at different temperatures to explain the geographic distribution of global production.
Ruff’s thermoregulatory theory is also a Heliocentric theory in that it ties the heat of the sun directly to human morphology. The empirical evidence is consistent with the idea that Holocene bodies reflect a population history of differential survival not of discrete types, but of highly-varied and continuously-distributed morphological “parameters” of the human skeleton during the Late Pleistocene in a manner that was systematically differentiated by latitude in accordance with the generalized Bergmann’s rule. Although the pace of change may have accelerated in the recent past, our skeletons have the wrath of Ra written all over them.
Many thanks to Christopher Ruff for his guidance.