Do stature and BMI contain information on living standards or adaptation to climate?

We have previously argued that the cross-section of stature and BMI contain information on the polarization of living standards between nations. We have also documented the dramatic revolution in Western living standards during 1860-1960 as revealed by secular gains in stature. The picture that emerges from these analyses suggests that living standards were considerably less polarized as late as the late-nineteenth century; that the hockey stick was not hit in earnest until after 1920; and that the morphological transition to modernity was largely complete by 1960-1980. The interpretation of time-variation is much less problematic than the interpretation of cross-sectional variation. There is a virtual consensus among physiologists and scholars of public health that gains in stature and BMI track gains in net nutritional status (nutrition and disease burdens considered jointly). No such consensus exists on the interpretation of population differences in stature and BMI.

Do population differences in stature and BMI reflect morphological adaptation to the macroclimate or do they reflect differences in living standards?

Two tribes of scholars are deeply interested in this question. On the one hand you have economic historians who are interested in the economic information contained in anthropometric data. On the other you have paleoanthropologists (more generally, physical anthropologists) who are interested in the information on population history and climatic adaptation contained in anthropometric data. For the latter tribe, anthropometry is the bread and butter of their discipline. Each side insists that their component dominates. The first insist that biological information gets averaged away when we take population means; the latter argue that, to the contrary, and just like all other species, humans have faithfully displayed morphological climatic adaptations throughout the entire human career. Who is right?

Paleoanthropologists argue that bigger bodies in colder climates (from the Neanderthals on) reflect Bergmann’s Rule: within a morphologically variable species spanning a wide geographic range, larger-bodied variants will be found in the colder parts of the range, and smaller-bodied variants in warmer parts. In a seminal paper, Ruff (1994) argued that Bergmann’s Rule is a particular instance of a more general, thermoregulatory “surface law”:

Simply stated, because surface area increases as the square of linear dimensions, and volume increases as the cube, the ratio of surface area to volume decreases as an object (or body) becomes larger. In terms of thermoregulation, because heat production is proportional to body mass (or volume, since body density varies only relatively slightly) and heat dissipation is proportional to exposed body surface area, a larger body will have a higher ratio of heat production to heat dissipation than a smaller body (of the same shape), which is the physiological basis for the clinal variation incorporated in Bergmann’s “Rule.”

In order to get to the bottom of this conundrum I taught myself some physical anthropology. (I also had some fun with debunking racial craniology on the way.) In the past few days I got my hands on substantial anthropometric datasets. And now I think I have solved the problem.

I will argue in a forthcoming paper bridging the two literatures that it can be demonstrated econometrically—using very large datasets for the entire Holocene as well as data on a large number of living indigenous groups—that both groups are right. More importantly, and happily for us, economic and climatic information are largely contained in different measures of the human body. Specifically, in the Holocene, stature does not contain significant climatic information; it contains economic information. Conversely, BMI contains information on climatic adaptation and population history which confounds the economic interpretation of the cross-sectional variation in this variable. The bottomline is that cross-sectional variation in BMI should not be used by economists as a measure of relative living standards and differences in stature should not be used by physical anthropologists to investigate climatic adaptation. It is shape not size of human bodies that reflects climatic adaptation.

In what follows I will document the main results. We begin with some established relationships in anthropometry. The basics of long bone estimation are straightforward. Stature (ST) is a linear function of femur length (FL). (Femur is the thigh bone.) We use the estimates from Ruff et al. (2005),

Male:     ST=2.72*FL + 42.85,
Female: ST=2.69*FL + 43.56,

where both stature and femur length are measured in centimeters. Similarly, body mass (BM) is bilinear in stature and pelvic bone width (BW). Also from Ruff et al. (2005),

Male:     BM=0.422*ST + 3.126*BW – 92.9,
Female: BM=0.504*ST + 1.804*BW – 72.6,

where body mass is measured in kilograms, and both stature and pelvic bone width are measured in centimeters. From body mass and stature, we immediately obtain BMI via the well-known formula, BMI equals weight in kg divided by squared height in meters.

We estimate these three variables from the Goldman Osteometrics Dataset that contains detailed information on 1,538 skeletons spanning the globe across the Holocene. Our first result is that BMI turns out to be a linear function of pelvic bone width. This is not an artifact of circularity in the formulas (BMI as computed above is a highly nonlinear function of femur length and pelvic bone width). Rather, it is an empirical regularity with important consequences. Namely, even if there exists an optimal BMI (which is highly unlikely) or an optimal range (which is much more reasonable), it is not independent of your body type. Rather, Figure 1 suggests that it is a function of your pelvic bone width. This information should be included in estimating “optimal BMI” and optimal range for BMI from mortality and morbidity data.


Figure 1. Pelvic bone width and BMI. Source: Goldman Osteometrics Dataset; author’s computations.

Our second result (in no sense original) is that BMI is independent of stature. This fact will be very important for our main results. It holds both at the individual level and for grouped means. (The data can be grouped by geographic location; a fact that will come in handy in what follows.) See Table 1. Estimates in bold are significant, and those in italics are insignificant, at the 5 percent level.

Table 1a. Spearman’s rank correlations for individuals.
Males N=924 Weight BMI
Stature 0.756 0.063
Weight 0.664
0.000 0.054
Females N=516 Weight BMI
Stature 0.810 0.008
Weight 0.554
0.000 0.851
Table 1b. Spearman’s rank correlations for group means.
Males N=41 Weight BMI
Stature 0.736 0.229
Weight 0.769
0.000 0.149
Females N=39 Weight BMI
Stature 0.814 0.184
Weight 0.687
0.000 0.263
Source: Goldman Osteometric Dataset, author’s computations.

Since BMI and stature are statistically orthogonal, they could plausibly contain different information. Is that the case? More precisely, is it the case that pelvic bone width (and hence BMI) reflects climatic adaptation while femur length (and hence statute) reflects net nutritional status as promised? In order to test this hypothesis we interrogate both the Goldman Osteometric Dataset and the data in Ruff (1994). We can reject our hypothesis if there is a significant gradient of latitude or thermal burdens in the cross-section of femur lengths/stature, or an insignificant gradient for pelvic bone width/BMI. On the other hand, if latitude is priced in the cross-section of pelvic bone width/BMI but not femur length/stature for ancient and indigenous skeletons, that would be consistent with our hypothesis. For then it would imply that the polarization of human stature in modern data is a consequence of the differential health transition across the globe. We begin with the Ruff (1994) data.

Table 2. Gradients of latitude.
Dependent variable: Stature Pelvic bone width Weight BMI
Estimated gradient 0.092 0.065 0.255 0.076
Robust standard error 0.084 0.009 0.043 0.017
t-Statistic 1.097 7.429 6.009 4.553
p-Value 0.139 0.000 0.000 0.000
Intercept Yes Yes Yes Yes
N 56 56 56 56
Source: Ruff (1994), author’s computations.

Table 1 reports our estimates. We compute heteroskedasticity-robust standard errors as is appropriate for comparing geographically-grouped population means. We see that latitude is not priced into stature but is priced into pelvic bone width, weight and BMI. We cannot therefore reject our hypothesis.

Betti et al. (2009) furnish data for minimum and maximum temperatures (as well as distance from Africa along postulated Out-of-Africa migration routes which we include here to avoid the bias resulting from omission of null results) that we matched with the Goldman data by hand. Table 3 presents our estimates for sex-combined population means.


Table 3. Sex-combined Spearman’s rank correlations for group means.
N=45 Femur length Pelvic bone width
Min Temp -0.089 -0.430
p-Value 0.584 0.006
N=45 Femur length Pelvic bone width
Max Temp -0.046 -0.261
p-Value 0.777 0.104
N=45 Femur length Pelvic bone width
Distance from Africa 0.032 0.065
p-Value 0.845 0.689
Source: Goldman Osteometric Dataset, Betti et al. (2009).

We see that, consistent with our hypothesis, minimum temperature is significantly correlated with pelvic bone width but not stature. We find no statistically significant correlation between maximum temperature or distance from Africa and either of our anthropometric measures. This is consistent with our work with modern data where we found that winter lows were especially significant. Table 4 repeats this analysis with stature and BMI separately for the sexes.

Table 4a. Spearman’s rank correlations for group means (female).
N=39 Stature Weight BMI
Min Temp -0.090 -0.301 -0.399
p-Value 0.606 0.079 0.018
N=39 Stature Weight BMI
Max Temp 0.044 -0.160 -0.424
p-Value 0.802 0.358 0.011
N=39 Stature Weight BMI
DFA -0.001 0.054 0.129
p-Value 0.996 0.758 0.461
Table 4b. Spearman’s rank correlations for group means (male).
N=42 Stature Weight BMI
Min Temp -0.124 -0.243 -0.337
p-Value 0.452 0.142 0.039
N=42 Stature Weight BMI
Max Temp -0.079 -0.165 -0.178
p-Value 0.633 0.324 0.285
N=42 Stature Weight BMI
DFA -0.069 0.054 0.183
p-Value 0.677 0.748 0.271
Source: Goldman Osteometric Dataset, Betti et al. (2009).

Table 4 is consistent with Table 3 with a single exception. For females, max temperature is also priced into BMI. This is entirely congruent with our hypothesis.

The evidence marshaled above is uniformly consistent with our hypothesis that cross-sectional variation in stature contains information on net nutritional status or living standards whereas the cross-sectional variation in BMI is potentially confounded by climatic adaptation. Specifically, BMI is a function of pelvic bone width (and not just under or over-nutrition) which correlates with the macroclimate throughout the Holocene in accordance with Ruff’s “surface law.” This is not true of stature, which was not polarized along latitude until the differential exit from the Malthusian world during 1860-1960. It is shape not size of human bodies that reflects climatic adaptation.


Figure 3. Gradients of latitude and cattle per capita in the cross-section of human stature, 1880-1960.


Figure 4. Western stature, 1710-1990.



Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s