Technical Note: A Novel Geometric Morphometric
Approach to the Study of Long Bone Shape Variation
Me´ lanie A. Frelat,1,2
* Stanislav Katina,3,4,5
Gerhard W. Weber,6
and Fred L. Bookstein6,7
1
Dipartimento di Storie e Metodi per la Conservazione dei Beni Culturali, University of Bologna, 48121 Ravenna,
Italy
2
UMR 7268, University of Aix-Marseille – EFS - CNRS, 13334 Marseille, France
3
Department of Anthropology, Faculty of Science, Masaryk University, Kotla´rˇska´ 2, 611 37 Brno, Czech Republic
4
Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotla´rˇska´ 2, 611 37 Brno, Czech
Republic
5
School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW, UK
6
Department of Anthropology, University of Vienna, Althanstrasse 14, 1090 Vienna, Austria
7
Department of Statistics, University of Washington, Seattle, WA 98195-4322
KEY WORDS tibia; hominoids; semilandmarks; artiﬁcial afﬁne transformation; locomotion
ABSTRACT Procrustes-based geometric morphometrics
(GM) is most often applied to problems of craniofacial
shape variation. Here, we demonstrate a novel
application of GM to the analysis of whole postcranial
elements in a study of 77 hominoid tibiae. We focus on
two novel methodological improvements to standard GM
approaches: 1) landmark conﬁgurations of tibiae including
15 epiphyseal landmarks and 483 semilandmarks
along articular surfaces and muscle insertions along the
tibial shaft and 2) an artiﬁcial afﬁne transformation that
sets moments along the shaft equal to the sum of the
moments estimated in the other two anatomical directions.
Diagrams of the principal components of tibial
shapes support most differences between human and
non-human primates reported previously. The artiﬁcial
afﬁne transformation proposed here results in an
improved clustering of the great apes that may prove
useful in future discriminant or clustering studies. Since
the shape variations observed may be related to different
locomotor behaviors, posture, or activity patterns, we
suggest that this method be used in functional analyses
of tibiae or other long bones in modern populations or
fossil specimens. Am J Phys Anthropol 149:628–638,
2012. VVC 2012 Wiley Periodicals, Inc.
Geometric morphometrics (GM) allows researchers to
quantify the geometry of complex biological forms and to
compare them using statistics that consider the average
form as well as the variation around it. While GM has
been typically applied in this sense to cranial and mandibular
morphology (e.g., Bookstein et al., 1999; Vidarsdottir
et al., 2002; Harvati, 2003; Bastir and Rosas, 2006; Weber
et al., 2006; Coquerelle et al., 2011), applications to the
postcranial skeletal elements are uncommon (e.g.,
O’Higgins, 2000, Bouhallier et al., 2004; Taylor and Slice,
2005). Most of the analyses of the lower limb (e.g., Harmon,
2006, 2009a,b; Jungers et al., 2009; De Groote, 2011)
have been limited to certain anatomical areas such as epiphyseal
morphology, owing to the absence of appropriate
landmarks on long bone diaphyses. Apart from an automatic
feature detection algorithm developed to analyze sex
differences in femur size and shape (Mahfouz et al., 2007),
there seem to be no quantitative statements about the
geometry of entire long bones using landmark identiﬁcation.
Nevertheless, the method of sliding semilandmarks
(Bookstein, 1997; Gunz et al., 2005) allows the description
of curves such as crests or ridges along the bone shaft by
geometrically homologous points. The homology of those
semilandmarks comes from the structures from which
they are derived (e.g., attachments of muscles, articular
surfaces). Because semilandmarks slide on curves derived
from biologically homologous structures, their position on
the curve itself remains a geometrical homology.
Tibial morphology includes information about phylogenetic
history, mode of locomotion, and substrate
preference because the tibia is the element transmitting
body weight from the condyles of the femur to the foot
(Lewis, 1989; Ruff, 2002). Differences between human
and ape tibiae are often described qualitatively (Fig. 1a)
or with simple measurements (e.g., Stern and Susman,
1983; Tardieu, 1981; Senut and Tardieu, 1985; Jungers,
1987; Stern, 2000; Marchi, 2007). Those differences are
mainly attributed to different locomotor modes: bipedalism,
arboreal or terrestrial quadrupedalism, and suspensory
behavior. Most of those morphological features are
often used for the assessment of fossil specimens as well
(e.g., Trinkaus, 1975; Tardieu, 1988; Latimer et al.,
1987; Berger and Tobias, 1995; Stringer et al., 1998;
Lovejoy et al., 2009; Zipfel et al., 2011).
Grant sponsor: EU PF6 Marie Curie Actions grant (EVAN,
Human Resource and Mobility Activity); Grant number: MRTN-CT-
2005-019564.
*Correspondence to: Me´lanie A. Frelat, Dipartimento di Storie e
Metodi per la Conservazione dei Beni Culturali, Universita` di Bologna,
Via degli Ariani, 1, 48121 Ravenna (RA), Italy.
E-mail: melanieagnes.frelat@unibo.it
Received 1 February 2012; accepted 19 September 2012
DOI 10.1002/ajpa.22177
Published online 2 November 2012 in Wiley Online Library
(wileyonlinelibrary.com).
VVC 2012 WILEY PERIODICALS, INC.
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 149:628–638 (2012)
Fig. 1. (a) A human tibia labeled with the name of the anatomical regions used in the text, in anterior (upper left), posterior
(upper right), and superior (lower left) views. The superior view of the tibial plateau in apes is also shown (lower right) to underline
the difference in ligament attachments of the knee joint (after Senut and Tardieu, 1985). (b) A human tibia with our 498 landmarks
and semilandmarks, in superior (upper right), inferior (middle right), anterior, medial, posterior, and lateral (lower, from left to
right) view. In black are anatomical landmarks (15) and in gray are semilandmarks on curves (483). Names of the landmarks and
curves are as listed in Tables 1 and 2, respectively.
629GM ANALYSIS OF TIBIAL SHAPE VARIATIONS
American Journal of Physical Anthropology
Apart from our preliminary reports (Frelat et al.,
2008, 2009, 2010), we have found no other quantitative
anthropometric analyses of the overall tibial surface.
Rather, the typical investigation involves only a limited
set of landmarks or focuses on a speciﬁc joint surface
(Organ and Ward, 2006; Harcourt-Smith et al., 2008;
Turley et al., 2011). To evaluate how features on the epiphyses
and characteristics of the diaphysis covary, we
introduce a method that captures and analyses in one
single rigid structure the entire tibial external morphology
using hundreds of measuring points. We can thus
describe the relationships among size, shape and orientation
of the articulations, positions of muscles, and
shape of the shaft. After standard Procrustes analysis in
shape and form space, we suggest reducing the dominating
effect of variation in shaft length by computing
afﬁne-adjusted Procrustes shape coordinates in a novel
way. Our purpose is to improve the visualization of
effects of species and sex upon the form of the bones.
This article aims thus to provide a GM technique
enriched by a novel and alternative version of that nonafﬁne
projection, one that better matches the symmetries
of the descriptions we apply to the form of the tibia
(length versus cross-sections). The result of this nonstandard
correction should be thought of as the intentional
ampliﬁcation of a certain residual signal in order to
circumvent the effects of a known cause (species) on the
unadjusted conﬁguration [the original form of the bone,
including the dominance of the length of the shaft in the
standard formula for centroid size (CS)].
MATERIALS
We collected data from 77 tibiae of four extant hominoids:
Homo sapiens (n 5 28, 13 females, 11 males, and
4 indeterminate), Gorilla gorilla (n 5 20, 7 females and
13 males), Pan troglodytes (n 5 19, 12 females and 7
males), and Pongo pygmaeus (n 5 10, 6 females and 4
males). Human tibiae are from the Po¨ch collection of
Bushman remains (n 5 20) of the Department of Anthropology,
University of Vienna, Austria, and the Gars Thunau
archeological collection (n 5 8) of the Department of
Anthropology, Natural History Museum of Vienna. Most
of the Great Apes tibiae are from the Schultz Collection
at the Institute and Museum of Anthropology, University
of Zurich, Switzerland, while a few are housed in the
Department of Zoology, Natural History Museum of
Vienna. Only adult tibiae free of pathologies were
included in this study.
METHODS
All morphometric and statistical analyses were performed
in R (R Development Core Team, 2011) based on
programs written by SK and MAF. Surface representations
were produced in Amira 5.3.0 by MAF.
GM analysis
Each tibial surface was scanned with a triTOS surface
scanner (Breuckmann Gmbh). We analyzed mostly right
tibia; any left tibiae were mirrored ﬁrst. All of them were
aligned with the coordinate axes so that the main axis of
the shaft corresponded to the z-axis and the maximum
mediolateral length of the tibial plateau corresponded to
the x-axis. The yz-plane corresponded then to the sagittal
plane of the bone. For each 3D model of the whole tibia, a
set of 15 landmarks (Table 1) and 483 semilandmarks on
curves (Table 2) was digitized in the Rapidform 2006 software
package by one of the authors (MAF). The 15 ‘‘real’’
landmarks lie on epiphyses (Fig. 1b). As there are no
Type I landmarks (juxtaposition of tissues or equivalent;
TABLE 1. List of landmarks shown in Figure 1
Landmarks Type
Label in
Figure 1
Centroid of the anterior insertion of the
medial meniscus
III 1
Most anterior point on the (anterior)
attachmenta
of the lateral meniscus
II 2
Centroid of the insertion of the anterior
cruciate ligament
III 3
Tip of the medial intercondylar eminence II 4
Tip of the lateral intercondylar eminence II 5
Centroid of the posterior insertion of the
medial meniscus
III 6
Most posterior point on the (posterior)
attachmenta
of the lateral meniscus
II 7
Centroid of the insertion of the posterior
cruciate ligament
III 8
Most proximal point of the medial border on
the metaphyseal line, beneath the groove
on the medial condyle
II 9
Most proximal point on the soleal line, often
faintly marked tubercle just inferior to the
ﬁbular facet
II 10
Most anterolateral point on the distal
articular surface
II 11
Most anteromedial point on the distal
articular surface
II 12
Most posteromedial point on the distal
articular surface
II 13
Most posterolateral point on the distal
articular surface
II 14
Tip of the malleolus II 15
a
The lateral meniscus has a unique attachment in apes while
humans have an anterior and a posterior attachment. In this
case, the most anterior point is taken on the anterior insertion
and the most posterior point on the posterior one.
TABLE 2. List of curves and number of semilandmarks shown
in Figure 1
Semilandmarks on curve Type
Label in
Figure 1 N
Lateral articular facet Observed LAF 49
Medial articular facet Observed MAF 49
Proximal ﬁbular articular facet Observed FAF 20
Tuberosity groove Ridge TG 20
Anterior proximal metaphyseal line
of the shaft
Observed APML 24
Posterior proximal metaphyseal line
of the shaft
Observed PPML 24
Anterior border of the shaft Ridge AB 99
Interosseous border of the shaft Ridge IB 49
Medial border of the shaft Ridge MB 48
Soleal line Ridge SL 29
Vertical line Ridge VL 20
Anterior border of the distal articular
facet
Observed ADAF 13
Lateral border of the distal articular
facet
Observed LDAF 8
Posterior border of the distal articular
facet
Observed PDAF 13
Medial border of the distal articular
facet
Observed MDAF 18
Total No. semilandmarks 483
630 M.A. FRELAT ET AL.
American Journal of Physical Anthropology
Bookstein, 1991) on the tibia, our landmarks are variously
of Type II (extremes of curvature characterizing single
structures) or Type III (constructed points) such as
centroids of ligament attachment areas. The latter were
computed automatically in Rapidform from the border of
the areas and projected onto the surface (see Table 1). To
capture diaphyseal shape, semilandmarks were equidistantly
digitized on observed curves such as the borders of
epiphyseal articular surfaces and crest-lines created by
muscular attachments on the diaphysis (Table 2 and Fig.
1a,b). We located enough semilandmarks to reproduce
most of the individual measurements that others have
used to characterize variations in this bone and to capture
and sample the relatively large expanse of otherwise
uncharted shaft surface. The complete set of semilandmarks
was slid along curves to minimize the bending
energy of the thin-plate spline (TPS) function (Bookstein,
1991). For further statistical analyses, those 483 relaxed
semilandmarks (Fig. 1b) are treated as geometrically homologous
points across all the specimens of the sample
(Bookstein, 1997; Gunz et al., 2005).
In order to place an upper limit to the effect of intraobserver
error in landmark digitization upon the ultimate
analyses, we selected ﬁve tibiae for redigitizing the
15 landmarks three times at intervals of at least a week
by one of us (MAF). We calculated mean-squared Procrustes
distance of each replicated form from its mean
(replication mean square error) and mean-squared Procrustes
distance between all 77 cases, taken once each,
and the grand mean (total mean square error). Then the
intraobserver error is given by the ratio of replication
mean square error to total mean square error. The mean
of all ﬁve ratios was 0.00996. We were expecting this
rather high value because none of our landmarks correspond
to the Type I deﬁned by Bookstein (1991).
The 77 conﬁgurations were transformed into shape
coordinates by generalized Procrustes analysis (Rohlf
and Slice, 1990). This procedure involves translating,
rescaling, and rotating conﬁgurations relative to each
other so as to minimize the overall sum of squared distances
between corresponding (semi)landmarks. Rescaling
usually adjusts landmark coordinates so that each
conﬁguration has a unit CS [square root of the summed
squared Euclidean distances from all (semi)landmarks to
their center of gravity; Bookstein 1991]. Procrustes
shape coordinates were then subjected to principal component
analysis (PCA) in both shape space and form
space (Mitteroecker et al., 2004).
The artiﬁcial nonafﬁne component
To this point, our procedure has followed the standard
Procrustes protocol. All landmarks are treated in precisely
the same way and likewise all semilandmarks that
have been slid on their curves. However, another symmetry
of the Procrustes toolkit causes difﬁculties since
Procrustes procedures treat all spatial directions of a
geometry in the same way. Variations along the long axis
of the tibia have been considered as of equal importance
to variations within the planes of the articulations at the
proximal and distal epiphyses. In the resulting superpositions,
the variation of the shaft length dominates any
other variation that may occur (Fig. 2b). This dominating
effect is not due to the relative density of points along
the shaft to points on the epiphyses—that will not affect
any of the estimates of these axes—but rather to the
structure and the length of the tibia itself. In this case,
dividing by CS is almost exactly the same as dividing by
maximal length of the tibia. We, therefore, scaled each
tibia separately so that all three of the spatial axes (x, y,
z) contribute in a ﬁxed ratio of weights (Fig. 2c).
Variation of bone length with respect to its width, its
depth, or their root mean square can be construed as one
version of the afﬁne component of shape variation (Rohlf
and Bookstein, 2003), so what we have done can be interpreted
as a novel, and thus artiﬁcial, alteration of this
component. Any change in a conﬁguration of landmarks
or semilandmarks can be thought of as the sum of an
afﬁne component (Fig. 2a, upper right and lower left) and
a nonafﬁne component (Fig. 2a, lower right). The afﬁne
component of a deformation is the portion of observed
shape change that globally transforms the standard Cartesian
coordinate system into a new grid where all
stretching and compression are the same everywhere in
space and in every direction. There are several ways of
estimating the uniform part of any transformation (Bookstein,
1991), all of them sharing the usual symmetries of
Procrustes distance as weighting all Euclidean directions
equally. Our artiﬁcial afﬁne transformation breaks that
symmetry of the Procrustes distance formula and results
in all three of the spatial axes (x, y, z) contributing with
commensurate weights. For each form, z coordinates (longitudinal
axis of the tibia) are scaled by the square root of
the within-case z-coordinate variance and the x and y
coordinates (AP and ML directions) by the square root of
the sum of the within-case x- and y-coordinate variances.
After this artiﬁcial afﬁne scaling, variability along the longitudinal
axis of the bone and variability perpendicular to
this direction will contribute equally to the ﬁnal shape distances.
Compared to the original coordinates (Fig. 2b),
inﬂuence of shaft length is no longer disproportionate but
now is weighted equally with the net variability of the two
other directions (Fig. 2c). Subsequently, all specimens are
ﬁtted again by means of a generalized Procrustes analysis,
the resulting forms bringing the PCA out from under
the strong dominance of the length of the bone.
Visualizations
To describe shape variations among hominoids, for
each species, we constructed mean shapes of tibial surfaces
both in the original space and in the afﬁne-rescaled
space. The tibial surface representations (target, T) corresponding
to the deformation of the mean shape (consensus,
C) along the PC axes were computed using the
triangulated surface mean shapes and the TPS as an
interpolation function (Bookstein, 1991). To ease visualization
of shape deformations, TPS warps were extrapolated
by factors ki, where in shape space
Ti ¼ C Æ ki3eigenvector½shapei
and in form space
Ti ¼ ðC Æ ki3eigenvectors½shapeiÞ
3 expðki3eigenvector½sizeiÞ;
where
ki ¼ 23sqrtðeigenvalueiÞ
to express two standard deviations, in order to scale
standard deviations in the direction of the ith PC.
(Eigenvectors are presumed to be unit vectors.)
631GM ANALYSIS OF TIBIAL SHAPE VARIATIONS
American Journal of Physical Anthropology
RESULTS AND DISCUSSION
Shape space PCA (before afﬁne adjustment)
The ﬁrst PC explains approximately 40% of total
shape variation and the second PC almost 16% (Fig. 3).
The main deformations on PC1, as illustrated by the
ﬁrst row of tibial surface representations (Fig. 3), generally
correspond to the locomotor-related differences
between apes and humans known from the literature
(e.g., Martin and Saller, 1959; Trinkaus, 1975; Lewis,
1981; Stern and Susman, 1983; Tardieu, 1981, 1988;
Senut and Tardieu, 1985; Susman et al., 1984; Latimer
et al., 1987; Aiello and Dean, 2002), such as size of the
medial condyle, shape of the tuberosity, pattern of muscle
attachments on the shaft, curvature of the shaft, or
position of the insertions of the menisci and of the cruciate
ligaments (Fig. 1a). Thus, variation on PC1 clearly
separates bipeds from nonbipeds. African apes are not
separated from Asian apes, but the two human groups
seem to spread out differently, the Austrian group clustering
in the higher range of the human variation.
On PC2, Gorilla and Pan form distinct clusters with
minor overlap, and the medieval Austrian specimens
clearly separate from the Bushmen. Pongo overlap with
both African species: male Pongo cluster with Gorilla
and female Pongo with Pan. Variation on PC2 is less
complicated (Fig. 3, second row of tibial surface representations)
and generally relates to overall tibial robusticity
(diaphyseal thickness in relation to bone length;
Martin and Saller, 1959)—especially in the ML dimensions,
the posterior projection of the tibial plateau, the
degree of torsion of the distal epiphysis relative to the
tibial plateau, and the size and orientation of the distal
epiphysis. Compared to Pan and female Pongo on one
side and the Bushmen on the other, Gorilla and male
Pongo and the Austrian group have a thicker shaft and
relatively bigger epiphyses, respectively. Their shaft also
shows less torsion, condyle articular facets are more balanced,
and their tibiotalar plane shows a slight angulation
relative to the horizontal. Those morphological features
are coupled with a shortened and laterally displaced
vertical line and an elongated soleal line,
implying a greater posterior area for the ﬂexor digitorum
longus (plantarﬂexion of the ankle and foot) on the posterior
face, a displacement of the tibialis posterior (plantarﬂexion,
inversion) on the lateral face at the expense
of the tibialis anterior (dorsiﬂexion, inversion). Those
variations are consistent with differences in locomotor
behavior among apes, both Pan and Gorilla being
knuckle-walkers with different degree of arboreal activity,
but at very different body sizes (Reynolds, 1987; Larson
et al., 2001; Polk et al., 2009). However, this analysis
Fig. 2. (a) Transformations of a square grid (upper left): afﬁne transformations (shear, upper right, and scaling in x-axis direction,
lower left), involving simple stretching/compression in orthogonal directions that are the same everywhere in the space; and
nonafﬁne transformation (lower right), carrying local ‘‘bending’’ involving twisting, stretching, and shifting of small regions (from
Slice, 2005). Comparison of the grand mean shape in the original geometry of the surface scans (b) with the artiﬁcial nonafﬁne version
of it (c).
632 M.A. FRELAT ET AL.
American Journal of Physical Anthropology
fails to highlight clear shape differences between Pongo
and the African apes. On the contrary, Pongo overlap
with both species, males clustering with Gorilla and
females with Pan. Yet within-species allometry is not
detected, eliminating the effect of body size as a plausible
explanation. Better hypotheses for those differences
may lie in their different behaviors, which are probably
the consequence of substrate-use constraints imposed on
large-bodied gorillas and male orangutans (Cant, 1992;
Hunt, 1992; Remis, 1995; Doran, 1996; Gebo, 1996; Carlson,
2005; Thorpe and Crompton, 2006). These results
are consistent with other studies that focused on femoral
articular morphology and/or femoral shaft strength
(Tardieu, 1983; Ruff, 2002; Harmon, 2007) but show
some slight differences with what has been described by
a recent GM study using a limited number of landmarks
(see below, Turley et al., 2011). However, more human
specimens, with known main activities, are needed to be
able to interpret human shape variation.
Form space PCA (before afﬁne adjustment)
When CS is reintroduced into the data set (form space,
Fig. 4), PC1 (84.8% of the total Procrustes form variance)
expresses overall size increase and static withinspecies
allometry while PC2 explains only about 4% of
the variation. As CS is highly inﬂuenced by overall tibial
length, variation along PC1 depicts a signiﬁcant elongation
of the tibial shaft coupled with an increase in the
dimensions of the epiphyses. Those size changes are
associated with the typical morphological differences
between the species as already described in shape space
PC1 (see above and Fig. 3, ﬁrst row). Shape deformations
along form space PC2 are not shown here as they
are predominantly the same as those visualized in shape
space (Fig. 3, second row) and generally involve increase
of overall tibial robusticity.
Fig. 3. PC scores of the Procrustes shape coordinates in
shape space. The four groups of tibial surface representations,
visualized in anterior, lateral, superior, and inferior view, are
extreme deformations of the average shape along PC1 and PC2.
To ease visualization of shape differences, deformations are
extrapolated.
Fig. 4. PC scores of the Procrustes shape coordinates in
form space. The four groups of tibial surface representations,
visualized in anterior, lateral, superior, and inferior view, are
extreme deformations of the average shape along PC1.
633GM ANALYSIS OF TIBIAL SHAPE VARIATIONS
American Journal of Physical Anthropology
Human and ape allometric trajectories are clearly distinct,
even parallel, suggesting that CS or tibial length
inﬂuences human and ape tibiae similarly. While apes
and modern human have different mean shapes, the trajectories
describe similar shape transformations. Shorter
tibiae of both human and non-human sample exhibit a
more curved shaft and relatively broad epiphyses while
longer tibiae are straight and have relatively narrow epiphyses
(see discussion below). Our results regarding
human and non-human static allometry are consistent
with previous investigations of diverse anatomical
regions using either GM or more traditional methods
(e.g., Jungers, 1982; Jungers and Stern, 1983; Ackerman
and Krovitz, 2002; Kidd and Oxnard, 2002; Penin et al.,
2002; Mitteroecker et al., 2004). They support earlier
descriptions referring to morphological relationship
between Gorilla and Pan as evidence of a ‘‘peramorphic’’
pattern of morphology produced by hypermorphosis (the
extension of common growth patterns to larger sizes:
Gould, 1975; Shea, 1983).
Fig. 5. PC scores of the scaled (nonafﬁne component) Procrustes shape coordinates in shape space. The four groups of tibial surface
representations, visualized in anterior, lateral, superior, and inferior view, are extreme deformations of the average shape along
PC1 and PC2.
634 M.A. FRELAT ET AL.
American Journal of Physical Anthropology
PCA of our ‘‘artiﬁcial nonafﬁne component’’
After we altered the afﬁne component of the data as
described above, the eigenvalues of PC1 and PC2 show
only little change (variation on PC1 is now 42%, and
12% on PC2) but our species cluster rather more neatly
(Fig. 5). Again, variation on PC1 depicts the typical morphological
differences between the species observed in
shape and form space (Fig. 5, ﬁrst row).
On PC2, however, the artiﬁcial afﬁne transformation
results in a rather different grouping of the non-human
species than the unscaled analysis did (Fig. 3). Pan cluster
well away from Gorilla and Pongo, which clearly
overlap one another. Deformations along PC2 are mainly
due to the anteroposteriorly more curved diaphysis, associated
with a wider attachment area for the tibialis
posterior and a longer one for the ﬂexor digitorum tibialis,
both of which provide stability to the ankle joint.
Pan tibiae are more anteroposteriorly curved and, also,
show more axial torsion than those of Gorilla and Pongo
(Fig. 6). These features are associated with the posterior
displacement of the distal epiphysis. Pan also has more
balanced condyle areas, a proximal facet for the ﬁbula
that expands anteriorly and medially, and a squarer distal
trochlear surface. It seems that the same trend exists
in humans, where a large fraction of Bushmen (huntergatherers)
has an anteriorly curved tibia while Austrian
individuals (agriculturalists) have straighter tibiae and
cluster near the bottom of the Bushman range. But, here
again more human specimens are needed to be able to
interpret human shape variation. The biomechanical
role and the adaptive meaning of limb bone curvature,
the main feature responsible for the variation on PC2, is
not quite straightforward (Bertram and Biewener, 1988;
Shackleford and Trinkaus, 2002; Yamanaka et al., 2005;
De Groote et al., 2010). As summarized by De Groote
et al. (2010), ‘‘curvature in combination with muscle and
joint reaction forces may 1) lower bending stress by translating
bending stress to axial compression, 2) facilitate
muscle expansion and packing, 3) be a compromise
between bone strength and predictability of bending
strains and material feature, or 4) bring the muscle mass
closer to the overall longitudinal axis of the diaphysis.’’
Since the areas of insertions of two of the muscles providing
stability of the ankle are largest in Pan, their higher
curvature could be related to the relative size or position
of those muscles. It could also be related to differences in
mechanical loading, i.e., bending, due to substrate preferences
or various components of locomotor behavior. Those
results are consistent with the fact that Turley et al.
(2011) did not ﬁnd the presumed similarities between Gorilla
and Pan, especially regarding tibial articular morphology.
Our analysis thus seems to accord with their hypothesis
that those two species differ in their mode of
locomotion, although this might not be related to size
since we did not ﬁnd any correlation with CS.
Finally, on PC3, Gorilla and Pongo separate (5% of the
scaled shape variation) with minor overlap (ﬁgure not
shown here). This variation is mainly due to axial torsion
and anteroposterior curvature of the shaft and relative
size of the epiphyses (Fig. 6). Pongo have greater
axial rotation and curvature of the shaft and broader
articular surfaces, consistent with arboreal activity and
terrestrial ﬁst-walking (Fig. 6). On the other side, Gorilla
exhibits a more trapezoidal tibiotalar surface associated
with an anterior displacement of the medial malleolus
(Fig. 6), consistent with what the increase in mass
entails for stabilizing up terrestrial activity or vertical
climbing (DeSilva, 2009). Those results are consistent
with the ﬁndings by Turley et al. (2011) and previous
observations among extant hominoids (Latimer et al.,
1987; Turley et al., 2008).
Fig. 6. Differences between the tibial mean shape of the four species of hominoids visualized in the scaled space, after the artiﬁcial
afﬁne transformation (from left to right: P. troglodytes, G. gorilla, P. pygmaeus, and H. sapiens). Top row: lateral view; second
row: posterior view; third row: superior view; bottom row: inferior view.
635GM ANALYSIS OF TIBIAL SHAPE VARIATIONS
American Journal of Physical Anthropology
CONCLUSIONS
The present study demonstrates that GM is an effective
tool for investigating tibial shape in 3D and introduces
a new method, an artiﬁcial afﬁne transformation, to
eliminate the dominating effect of the long shaft when
comparing humans and non-humans. Among the advantages
of our method, we note that most features hitherto
described in the literature that distinguish modern
humans from apes can be captured and visualized as
well by an approach based on landmarks and semilandmarks
(Fig. 1b). But, beyond that, it allows investigators
to visualize the covariation of the three functionally distinct
parts of the tibia that are the two epiphyses and
the diaphysis (Figs. 3–5) and to separate size from shape
in the analysis (compare Figs. 3 and 4). For example,
compared to the above-mentioned GM studies of long
bones, our method is able to highlight the relationship
between shaft curvature, muscle position, relative size
and shape of the condyles, and shape and orientation of
the tibiotalar articular surface (Figs. 3–6). Altogether,
our study of the tibia demonstrates that a comprehensive
GM approach can be applied to hominoid long bone
elements. It can be used to study shape or form separately,
and it can scale the inﬂuence of the dominating
shaft.
Compared with traditional osteometry, another
advantage of the introduction of the artiﬁcial afﬁne component
is that it not only conﬁrms the differentiation
between bipeds and nonbipeds (Figs. 3–5) but also distinguishes
tibial shapes both among non-human hominoids
(Figs. 5 and 6) and among humans (Figs. 3 and 5). Those
shape variations may be related to different locomotor
and positional behavior, to substrate preferences among
nonbipedal Great Apes (e.g., Reynolds, 1987; Cant, 1992;
Hunt, 1992; Remis, 1995; Doran, 1996; Larson et al.,
2001; Carlson, 2005; Thorpe and Crompton, 2006; Polk
et al., 2009), or to distinct activity patterns in human
populations (Ruff et al., 1984; Ruff, 1987; Bridges, 1995;
Carlson et al., 2007; Stock and Shaw, 2007; Shaw and
Stock, 2009, 2011; Shaw and Ryan, 2011). Further investigation
may reveal how the morphological variation
quantiﬁed in this study is related to locomotion/activity
patterns, phylogeny, and development, a topic beyond
the scope of this article.
Of course, the new method has some drawbacks as
well. Scaling the tibia ﬂattens its geometry at the epiphysis,
putting all 3D variation in this region into what
would appear to be a single plane. Shape changes on the
epiphyses are no longer correctly rendered. Those features
must be examined in the original shape space
instead (Figs. 3 and 4).
While locomotor information may be inferred from our
results to some extent, only a combination of GM with
biomechanical approaches will permit a thorough understanding
of how external shape and form are associated
to bone structural strength.
ACKNOWLEDGMENTS
We thank Christine Tardieu, Bence Viola, Philipp Mitteroecker,
Kristian Carlson, Michael Coquerelle, Colin
Shaw, and Caroline Simonis for helpful discussions and
support in the course of this study. We are also grateful
to Maria Teschler-Nicola, Barbara Herzig, Christopher
Zollikofer, and their staff for allowing access to the
specimens in their care. Special thanks go to Alexandre
Bourdeu for his assistance with the Breuckmann Scanner
in the Department of Anthropology of the University
of Vienna. The authors are grateful for the comments of
the Associate Editor and two anonymous reviewers on
an earlier draft.
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