Are Adult Physiques Geometrically Similar?
The Dangers of Allometric Scaling Using Body Mass
Power Laws
Alan M. Nevill,
1
Arthur D. Stewart,
2
* Tim Olds,
3
and Roger Holder
4
1
School of Sport, Performing Arts and Leisure, University of Wolverhampton, Walsall, WS1 3BD UK
2
Department of Biomedical Sciences, University of Aberdeen, Aberdeen, Scotland, AB25 22D UK
3
School of Physical Education, Exercise and Sports Studies, University of South Australia, Underdale, South
Australia, 5032 Australia
4
School of Mathematics and Statistics, University of Birmingham, Birmingham, B15 2TT UK
KEY WORDS corrected girth; anthropometry; allometric scaling; athlete
ABSTRACT Human physique classification by soma-
totype assumes that adult humans are geometric similar
to each other. However, this assumption has yet to be
adequately tested in athletic and nonexercising human
populations. In this study, we assessed this assumption by
comparing the mass exponents associated with girth mea-
surements taken at 13 different sites throughout the body
in 478 subjects (279 athletic subjects, and 199 nonexercis-
ing controls). Corrected girths which account for subcuta-
neous adipose tissue at the upper arm, thigh, and calf
sites, and which simulate muscle circumference, were also
calculated. If subjects are geometrically similar to each
other, girth exponents should be approximately propor-
tional to M
1/3
, where M is the subjects’ body mass. This
study confirms that human adult physiques are not geo-
metrically similar to each other. In both athletic subjects
and nonexercising controls, body circumferences/limb
girths develop at a greater rate than that anticipated by
geometric similarity in fleshy sites containing both muscle
and fat (upper arms and legs), and less than anticipated in
bony sites (head, wrists, and ankles). Interestingly, head
girths appear to remain almost constant, irrespective of
subjects’ body size/mass. The results also suggest that
thigh muscle girths of athletes and controls increase at a
greater rate than that predicted by geometric similarity,
proportional to body mass (M
0.439
and M
0.377
, respectively).
These systematic deviations from geometric similarity
have serious implications for the allometric scaling of vari-
ables such as energy expenditure, oxygen uptake, anaer-
obic power, and thermodynamic or anthropometric studies
involving individuals of differing size. Am J Phys An-
thropol 124:177–182, 2004. © 2004 Wiley-Liss, Inc.
In 1921, the first systematic anthropometric as-
sessment of humans was proposed as a rationale for
testing human efficiency by quantifying body tissues
in a sample of barbers, butchers, blacksmiths, and
gymnastics instructors (Matiegka, 1921). The au-
thor recognized that “above average stature is not
always an indication of physical superiority.” In the
decades which followed, other physique descriptions
referred to as “somatotyping” were proposed (Shel-
don et al., 1940; Parnell, 1954), and these were later
revised by Heath and Carter (1967). The latter com-
prised the primary physique assessment tool still in
use today, based on 10 anthropometric measure-
ments. These generate the coordinates for a tripolar
schema involving fatness, musculoskeletal robust-
ness, and mass in relation to stature. The authors
stated that the resulting somatotype “is a measure
of shape, not size,” with the inherent assumption
that adults of differing size are geometrically simi-
lar. Subsequent decades were witness to a rapid
increase in the prevalence and severity of obesity,
and to unprecedented muscle gains due to more
sophisticated training or pharmacological interven-
tion. As such, humanity exhibits an “expanding uni-
verse” of possible physiques, in which the bound-
aries are being continually pushed back. This has
enabled an increased variance in physique which,
with sufficient data, can test the hypothesis of
whether geometric similarity is observed in humans.
A useful insight into the issue is provided by com-
parison of different animal species. Larger mam-
mals expend more energy than smaller mammals
due to their larger energy cost of metabolism and
locomotion. However, if energy expenditure is ex-
pressed as a simple ratio standard, per unit body
mass, smaller mammals consume more energy per
unit body mass than larger mammals. A theoretical
*Correspondence to: Arthur D. Stewart, Ph.D., Department of Bio-
medical Sciences, University of Aberdeen, Aberdeen, AB25 22D UK.
E-mail: a.d.stewart@abdn.ac.uk
Received 21 February 2003; accepted 22 April 2003.
DOI 10.1002/ajpa.10351
Published online 19 September 2003 in Wiley InterScience (www.
interscience.wiley.com).
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 124:177–182 (2004)
© 2004 WILEY-LISS, INC.