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A computational analysis of locomotor anatomy and body mass
evolution in Allosauroidea (Dinosauria: Theropoda)
Karl T. Bates, Roger B. J. Benson, and Peter L. Falkingham
Abstract.—We investigate whether musculoskeletal anatomy and three-dimensional (3-D) body
proportions were modified during the evolution of large (.6000 kg) body size in Allosauroidea
(Dinosauria: Theropoda). Three adaptations for maintaining locomotor performance at large body size,
related to muscle leverage, mass, and body proportions, are tested and all are unsupported in this
analysis. Predictions from 3-D musculoskeletal models of medium-sized (Allosaurus) and large-bodied
(Acrocanthosaurus) allosauroids suggest that muscle leverage scaled close to isometry, well below the
positive allometry required to compensate for declining muscle cross-sectional area with increasing
body size. Regression analyses on a larger allosauroid data set finds slight positive allometry in the
moment arms of major hip extensors, but isometry is included within confidence limits. Contrary to
other recent studies of large-bodied theropod clades, we found no compelling evidence for significant
positive allometry in muscle mass between exemplar medium- and large-bodied allosauroids. Indeed,
despite the uncertainty in quantitative soft tissue reconstruction, we find strong evidence for negative
allometry in the caudofemoralis longus muscle, the single largest hip extensor in non-avian theropods.
Finally, we found significant inter-study variability in center-of-mass predictions for allosauroids, but
overall observe that consistently proportioned soft tissue reconstructions produced similar predictions
across the group, providing no support for a caudal shift in the center of mass in larger taxa that might
otherwise reduce demands on hip extensor muscles during stance. Our data set provides further
quantitative support to studies that argue for a significant decline in locomotor performance with
increasing body size in non-avian theropods. However, although key pelvic limb synapomorphies of
derived allosauroids (e.g., dorsomedially inclined femoral head) evolved at intermediate body sizes,
they may nonetheless have improved mass support.
Karl T. Bates. Department of Musculoskeletal Biology, Institute of Aging and Chronic Disease, University
of Liverpool, Sherrington Buildings, Ashton Street, Liverpool, L69 3GE, United Kingdom. E-mail:
k.t.bates@liverpool.ac.uk
Roger B. J. Benson. Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge,
CB2 3EQ, United Kingdom. E-mail: rbb27@cam.ac.uk
Peter L. Falkingham. School of Earth, Atmospheric and Environmental Science, University of Manchester,
Williamson Building, Oxford Road, Manchester, M13 9PL, United Kingdom. E-mail: peter.falkingham@
manchester.ac.uk
Accepted: 12 October 2011
Supplementary materials deposited at Dryad: doi: 10.5061/dryad.09kf4g02
Introduction
Theropoda is a monophyletic clade of
archosaurs that includes the largest obligate
bipeds that ever lived (Osmolska 1990; Sereno
1999). They have an abundant fossil record,
high taxonomic and morphological diversity,
and an enormous range of estimated body
masses (0.5–10,000 kg [Paul 1988; Hutchinson
et al. 2007]). Thus, they are an ideal study
group for addressing questions concerning
locomotor evolution, and particularly the
relationship between locomotor morphology,
dynamics, and body size in extinct tetrapods
(Hutchinson and Allen 2008).
Biomechanical assessments of locomotor
capabilities have delivered forceful evidence
for strong size effects on gait and perfor-
mance in non-avian theropods. Larger taxa
were restricted to more upright postures, and
had reduced running ability (Hutchinson
2004b; Hutchinson et al. 2007; Sellers and
Manning 2007; Gatesy et al. 2009). These
inferences are consistent with data from
living animals and with well-known scaling
principles (Biewener 1989, 1990); animals of
larger body mass have more restricted loco-
motor performance because muscle mass
scales isometrically, but muscle force and
power scale with negative allometry (mass
20.67
[Alexander 1977; Alexander and Jayes 1983]).
Combined with a decline in the relative speed
of muscular contraction (e.g., maximum con-
traction velocity mass
20.15
[Medler 2002; Marx
Paleobiology, 38(3), 2012, pp. 486–507
’2012 The Paleontological Society. All rights reserved. 0094-8373/12/3803–0009/$1.00
et al. 2006]), this yields negative allometry in
mass specific mechanical power output, lead-
ing to restrictions on maximal performance at
large size (Biewener 1989; 1990). These scaling
constraints also apply to skeletal strength (the
ability of the skeleton to resist locomotor
forces). Several different scaling models based
on extant tetrapods have been proposed
(McMahon 1975; Alexander and Jayes 1983;
Biewener 1990), and all predict that skeletal
strength increases less rapidly than locomotor
forces and moments as size is increased.
Musculoskeletal simulations have highlight-
ed the dramatic effect of unknown soft tissue
parameters on absolute predictions of locomo-
tor performance in fossil taxa. Studies attempt-
ing to quantify locomotor performance have
identified muscle mass and contractile prop-
erties (e.g., maximum isometric stress, maxi-
mum contraction velocity) as the major factors
limiting the precision of gait reconstructions in
extinct animals, including dinosaurs (Hutch-
inson 2004b; Sellers and Manning 2007; Bates
et al. 2010). Large error bars on absolute
performance predictions (e.g., maximum run-
ning speed 630% best estimate predictions
[Bates et al. 2010]) potentially hinder accurate
functional comparisons, particularly when
fossilized skeletal morphology is broadly
similar (see Hutchinson and Allen 2008).
How, then, might musculoskeletal adapta-
tions for large size be identified in extinct
lineages such as non-avian dinosaurs? Clearly
the most accessible lines of evidence are those
inferred directly from fossilized osteology, such
as limb bone size and shape, muscle attach-
ments (and their geometrical relationships to
joints), and overall body shape. Although they
do not provide direct measurements of loco-
motor energetics and performance, osteological
attributes arguably represent the best window
on musculoskeletal biomechanics in extinct
dinosaurs, given the inability to tightly con-
strain the soft tissue properties in these animals.
Studies that carefully and cautiously tie such
aspects of anatomical form to locomotor func-
tion may help to reveal the biological impor-
tance of character evolution and generate
hypotheses about how very large size influenc-
es locomotion in dinosaurs and other land
animals (Biewener 1989, 1990).
In this paper we attempt to test how, if at
all, musculoskeletal anatomy and three-di-
mensional (3-D) body proportions were mod-
ified during the evolution of large body size
in Allosauroidea, a monophyletic clade of
non-avian theropods that achieved near-glob-
al distribution during the Jurassic and Creta-
ceous (e.g., Benson et al. 2010). Most basal
allosauroids, such as the Jurassic genera
Allosaurus and Sinraptor, exceeded extant
bipeds in overall size by an order of magni-
tude, but were much smaller than most
Cretaceous carcharodontosaurids, which ri-
valed the largest tyrannosaurs in overall size
and body mass (Henderson and Snively 2003;
Therrien and Henderson 2007; Bates et al.
2009a,b). Conversely, Neovenatoridae, the
sister taxon of Carcharodontosauridae, also
includes relatively small bodied taxa such as
Australovenator and Fukuiraptor, with estimat-
ed body lengths of approximately 4–5 m
(Azuma and Currie 2000; Hocknull et al.
2009; Benson et al. 2010). Amid changes in
body size, pelvic and femoral osteology
underwent significant character evolution
(e.g., Brusatte and Sereno 2008; Brusatte et al.
2008; Benson et al. 2010), including modifica-
tions to the anterior and posterior iliac blades,
reorientation of the femoral head, and changes
in the relative size and shape of the femoral
condyles and pubic boot (Fig. 1). The func-
tional consequences of these osteological
changes is unexplored, although Brusatte
et al. (2008: p. 66) suggested ‘‘it is possible
that some of the other numerous hind limb
and pelvic synapomorphies of carcharodonto-
saurids [5carcharodontosaurians] were relat-
ed to a restructuring of the hind limb
musculature, which in turn may have affected
center of mass, stance, gait, and speed. This
hypothesis deserves further study.’’
In this study we use computational model-
ing approaches to test a series of specific
hypotheses about phylogenetic and size-
related trends in allosauroid locomotor evo-
lution. Specifically, we use phylogenetically
based reconstructions of hind limb myology
to reconstruct the 3-D geometry of musculo-
tendinous units in the pelvic limb of primi-
tive, smaller-bodied and larger, derived allo-
sauroids to quantitatively compare muscle
ALLOSAUROIDEA LOCOMOTOR EVOLUTION 487
FIGURE 1. A, Stratigraphically calibrated phylogeny of Allosauroidea by Benson et al. (2010). Filled circles indicate
Gondwanan taxa, and empty circles indicate Laurasian taxa. B, Left ilia of Allosaurus (left) and Mapusaurus (right) in
lateral view. C, Pubes of Allosaurus (left) and Aerosteon (right) in lateral view. D, Cranial view of the left femora of
Allosaurus (left), right femora (reversed) of Neovenator (center), and left proximal femora of Acrocanthosaurus (right). E,
Cranial view of the right distal tibia (reversed) of Chilantaisaurus (reversed, left) and left distal tibia of Aerosteon (right).
488 KARL T. BATES ET AL.
leverage. We also collate data from a series of
recent studies to examine body shape and
center of mass (CM) in allosauroids, and
examine predictions relative to body size and
character evolution.
Hypotheses
Muscle leverage and body mass distribution
are crucial determinants of locomotor mechan-
ics in bipedal animals (Biewener 1989, 1990;
Hutchinson 2004a; Bates et al. 2010). In extant
bipeds, muscles support the limb by produc-
ing net extensor (anti-gravity) moments about
the hip, knee, and ankle at mid-stance during
running (Supplementary Figure 1) (Roberts
2001; Gu
¨nther and Blickhan 2002; Rubenson et
al. 2003; Main and Biewener 2007). Maintain-
ing a net extensor moment at the knee at mid-
stance requires the knee joint to be positioned
anterior to the whole-body CM, which should
lie approximately above the center of pressure
(see Gatesy et al. 2009). Given these con-
straints, and a sub-horizontal trunk posture
(Hutchinson 2004b), the cranio-caudal position
of the CM should largely dictate the hip joint
angle at mid-stance (Supplementary Figure 1).
This, in turn, constrains the moment arm of the
ground reaction force (GRF) with respect to
limb joints, and the force-generating capacity
of muscles because of the sensitivity of their
moment arms to joint angle (e.g., Biewener
1989, 1990; Hutchinson et al. 2005, 2008). For
example, a more craniad CM requires greater
hip flexion at mid-stance and a posture in
which the maximum force output of extensor
muscle is reduced (Supplementary Figure 1B),
while the moment arm of the vertical GRF
about limb joints increases as the two become
less aligned (Supplementary Figure 1C). The
maximum GRF that can be supported by the
limb, and by inference running ability, is
therefore reduced (Biewener 1989, 1990;
Hutchinson 2004a,b; Gatesy et al. 2009).
Reliable estimates of muscle leverage and
mass distribution are therefore a prerequisite
for many studies seeking to describe the
underlying mechanics of animal motion. This
is especially true for studies of the locomotor
capabilities of extinct animals, which must
largely rely on first principles such as the basic
mechanical relationships described above. We
propose and test the following hypotheses: (1)
allosauroids will exhibit positive allometric
scaling of their hip muscle moment arms,
particularly in major hip extensor muscles; (2)
allosauroids will exhibit positive allometric
scaling in hip extensor muscle mass; (3)
allosauroids will exhibit a caudal shift in CM
position as body size increases. Predictions 1
and 3 are consistent with size-related trends in
extant animals, such as the positive allometry
in extensor muscle moment arms demonstrat-
ed for some mammals (e.g., Alexander et al.
1981; Biewener 1989, 1990) and the caudal shift
in the CM position in large birds (Abourachid
and Renous 2000). Positive allometry in hip
extensor muscle mass (Hypothesis 2) is crucial
to maintaining locomotor performance as
body size increases (Biewener 1989; Roberts
et al. 1998; Hutchinson 2004a,b), and was
proposed by Persons and Currie (2011; see
also Paul 2008) as a mechanism for maintain-
ing some degree of ‘‘athleticism’’ in large
tyrannosauroids such as Tyrannosaurus rex
(but see Hutchinson et al. 2011a,b). Addressing
these questions using primary anatomical data
for allosauroids will also allow us to test
hypothesized functional consequences of pel-
vic and femoral character state evolution in
allosauroids (Brusatte et al. 2008).
Materials and Methods
Musculoskeletal Modeling
Musculoskeletal computer models of Allo-
saurus (MOR 693) and Acrocanthosaurus (NCSM
14345) were constructed to quantitatively test
hypotheses about size and phylogenetic chang-
es in muscle leverage in allosauroids (Brusatte
et al. 2008, and above). These models consist of
r
Abbreviations: ab, anterior blade; abm, anterior blade margin; asp, ascending process; ip, iliac ischial peduncle; fh,
femoral head; lc, lateral condyle; ilp, iliac peduncle; isp, pubic ischial peduncle; meb, medial buttress; pan,
preacetabular notch; pb, pubic boot; pob, posterior blade; pup, pubic peduncle; sac, supracetabular crest. Scale bars,
200 mm.
ALLOSAUROIDEA LOCOMOTOR EVOLUTION 489
digitized pelvic, femoral, and shank bones and
estimated joint center positions, muscle-tendon
origins, insertions, and 3-D paths. Mimicking
previous analyses of Tyrannosaurus rex (Hutch-
inson et al. 2005) and Velociraptor mongoliensis
(Hutchinson et al. 2008), these models were
constructed to estimate the major muscle
moment arms about the hip joint in Allosaurus
and Acrocanthosaurus across a spectrum of limb
postures.
A Polhemus FastSCAN cobra laser scanner
(www. polhemus.com) was used to acquire
high-resolution scans of bone surface geome-
try of the femur, tibia, and fibula of both
specimens. These scans were combined with
LiDAR (Light Detection And Range) scans of
pelvic bones from previous studies (Bates et al.
2009a,b). More details on the scanning and
model-building procedure can be found in the
supplementary data and studies by Bates et al.
(2009a).
The computer-aided design (CAD) package
Maya was used to digitally rearticulate hind
limb bones and rig 3-D muscle-tendon units
and joint center positions in a standard neutral
posture (e.g., Hutchinson et al. 2005, 2008).
Following Hutchinson et al. (2005, 2008), the
femur and shank bones were articulated to give
a knee joint spacing equivalent to approximate-
ly 7.5% femoral length. The rigid pelvic
segments (combined ilium, ischium, and pubis)
remained in the articulations of the skeletal
mounts, but were rotated together so that the
pelvis was pitched horizontally. The hip joint
was treated as 3-D ball-and-socket joint, with
rotational axes defined as orthogonal and the
flexion-extension axis perpendicular to the
craniocaudal axis of the body (the x-axis in
the global coordinate system of the model). This
serves as a simplified, but standardized, ap-
proach to defining joint axes in both models to
maintain consistency and comparative value
in the absence of joint tissues and articulations
in fossils (e.g., Hutchinson et al. 2005; Bonnan
et al. 2010).
Pelvic and femoral musculature was recon-
structed on the basis of osteological correlates
of homologous muscle-tendon origins and
insertions in extant archosaurs (Hutchinson
2001a,b; Carrano and Hutchinson 2002). The
anatomical basis for choice of centroids for
muscle origins and insertions in allosauroids
is consistent with work on tyrannosauroids
(Carrano and Hutchinson 2002) and other
non-avian theropods (Hutchinson 2001a,b). A
total of 24 muscles were placed in each limb
of the two models and the abbreviations for
each of these are shown in Supplementary
Table 1. Analysis of the models was carried
out in GaitSym (www.animalsimulation.org),
a forward dynamic modeling program based
on the Open Dynamics Engine (ODE) physics
library (www.opende.sourceforge.net). Muscle
lines of action run either directly from origin to
insertion, or through an additional number of
intermediate points (‘‘via points’’) that guide
the muscle’s path (Fig. 2). For example, in the
case of the knee extensors, intermediate points
are used to model their passage through the
groove between femoral condyles and over the
cnemial crest of the tibia. The positions of these
points are recalculated at each step in the
simulation (output across a wide spectrum of
hip flexion-extension angles) to allow them to
move, and the total length and its rate of change
are stored. At any particular joint angle, the
moment arm of the muscle is given by the
differential of muscle-tendon displacement
over joint angle in the plane of motion being
studied (An et al. 1984).
In their analysis of Tyrannosaurus rex,
Hutchinson et al. (2005) demonstrated that
uncertainties regarding the exact centroids of
muscle origins and insertions, as well as the
precise 3-D paths, have a significant effect on
the magnitude of moment arms. While
acknowledging that this uncertainty applies
equally here, we did not carry out an
exhaustive sensitivity analysis. However,
necessary assumptions were applied equally
to both Allosaurus and Acrocanthosaurus and
should not alter the nature of the comparison
between these two taxa, which is the sole
purpose of this analysis.
Hip Extensor Muscle Mass Predictions
We use the approach of Hutchinson et al.
(2011b; see also Bates et al. 2009a) to estimate
the volume of hip extensor musculature in
Allosaurus and Acrocanthosaurus using our
musculoskeletal models (Figs. 2, 3). The vol-
umes of the major limb bones (femur, tibia,
490 KARL T. BATES ET AL.
FIGURE 2. Reconstruction of pelvic and femoral muscle origins and insertions in Allosaurus (A) and Acrocanthosaurus
(B) on the basis of archosaurian muscle homologies and the extant phylogenetic bracket (EPB) of extant crocodilians
and birds. 3-D musculoskeletal models (not to scale) of Allosaurus MOR 693 (C) and Acrocanthosaurus NCSM 14345 (D)
used to estimate major hip muscle moment arms. Muscle origins, insertions, and 3-D paths for 24 pelvic and femoral
muscles shown in A and B have been reconstructed around digitized pelvic, femoral, and shank (tibia, fibula) bones.
See Supplementary Table 1 for muscle abbreviations.
ALLOSAUROIDEA LOCOMOTOR EVOLUTION 491
fibula, metatarsals, and pedal digits) were
calculated from the water-tight 3-D bone
models (using FormZ), and then these bone
volumes were subtracted from the individual
segment (thigh, shank, metatarsus, and pes)
volumes for each animal reconstructed by
Bates et al. (2009a,b) (Fig. 3A–D). This left a
smaller volume that would have consisted of
limb muscles, skin, and other minor constitu-
ents (e.g., nerves, blood vessels, cartilage).
However, this volume excludes the likely
sizable contribution of major tail-based hip
extensors such as the caudofemoralis longus
(CFL). The CFL volume was estimated in Maya
software by drawing a smooth curve between
the lateral tip of the transverse processes and
the ventral tip of the chevron for each vertebra
between the sacrum proximally and the
transition point of the tail (Gatesy 1990)
distally, and then continuing this curve along
the ventral and lateral borders of the trans-
verse processes, centra, and chevron to form a
series of complete loops (Hutchinson et al.
2011b). These loops were then lofted to form
a solid volume, which was then deformed
to connect to the fourth trochanter via a
small, thin extension representing the tendon
(Fig. 3E,F). The final output of our limb muscle
mass analysis is a total ‘‘locomotor’’ muscle
mass estimate.
Center-of-Mass Predictions
We tabulated data from published studies to
evaluate hypotheses related to center-of-mass
FIGURE 3. 3-D volumetric reconstructions of Allosaurus MOR 693 (left) and Acrocanthosaurus NCSM 14345 (right) from
the studies of Bates et al. (2009a,b). These studies produced a range of volumetric models but shown here are the initial
‘‘best estimate’’ reconstructions (A, B) and models with highly disproportionate trunk to hind limb volumes (C, D).
This includes a comparison of Allosaurus MOR 693 with a relatively slender hind limb but large trunk against
Acrocanthosaurus 14345 with a relatively muscular hind limb and emaciated trunk (C), and Allosaurus MOR 693 with a
relatively muscular hind limb and emaciated trunk against Acrocanthosaurus NCSM 14345 with a relatively slender
hind limb but large trunk (D). E, F, Reconstructed caudofemoralis longus musculature in Allosaurus MOR693 (E) and
Acrocanthosaurus NCSM 14345 (F) in right lateral view.
492 KARL T. BATES ET AL.
evolution among allosauroids (see Brusatte
et al. 2008, and above). All published CM
predictions are derived from 3-D computer
generated volumetric reconstructions, although
the specific methods of model construction
vary in each case. Henderson and Snively
(2003) and Therrien and Henderson (2007)
produced 3-D body volumes for Allosaurus,
Sinraptor dongi,Sinraptor hepingensis (formerly
Yangchuanosaurus), Fukuiraptor and Acrocantho-
saurus from reconstructed sagittal and frontal
drawings, with mass computations made by
summing the mass properties of independent
transverse slices through the volume (Hender-
son and Snively 2003). Subsequently, laser
scanning and CAD applications have been
used to derive a range of further estimates for
Allosaurus and Acrocanthosaurus (Bates et al.
2009a,b). To evaluate the significance of any
variation in predicted CM position within
Allosauroidea, we also extracted available
data on other non-avian theropods from
Hutchinson et al. (2007; Tyrannosaurus) and
Bates et al. (2009a; Tyrannosaurus,Struthiomi-
mus). The trunk skeleton and body volume of
Struthiomimus from the latter study were
reposed in a straight sub-horizontal posture
(i.e., removing extreme dorsoflexion of the
neck and tail) to provide meaningful com-
parison with the other models (see Supple-
mentary Figure 2). For comparative purposes
the CM of the combined Head-Arms-Torso
(HAT) or trunk segment was normalized as a
fraction of femoral length anterior to the hip
joint. Femur length represents the most
appropriate normalizing factor given not
only our postural hypotheses but also the
particular characteristics of our material,
because a femur is well preserved for all
specimens whereas other metrics, such as
gleno-acetabular distance or body length
(Allen et al. 2009; Bates et al. 2009a), will be
more influenced by skeletal preservation and
mounting biases (Hutchinson et al. 2011b).
Scaling Metrics
Producing detailed musculoskeletal models
is relatively costly and time consuming, and
relies on access to fairly complete skeletal
remains. Thus, our analysis of muscle mo-
ment arms and CM positions is restricted to a
small subsample of allosauroid taxa. To
widen this sample we collected data neces-
sary to produce a variety of scaling metrics
that would provide a broader (though less
definitive) picture of major hip muscle mo-
ments and body shape across Allosauroidea.
Muscle Moment Arms.—Where preservation
was sufficient, the distance between the
fourth trochanter and the proximal end of
the femur (F4T) was measured in a range
of allosauroid taxa. The fourth trochanter and
adjacent femoral surface are associated
with the insertion of several important limb
retractors in archosaurs (Gatesy 1990, 1995;
Hutchinson 2001b). The relative distance
between the fourth trochanter and the prox-
imal end of the femur was again calculated
as a percentage of femoral length following
Carrano (1998). Low values of this metric
indicate a more proximally placed fourth
trochanter (F4T) and thus shorter muscle
length and lower moment arm. We used
regression analysis to explore the relationship
between size and this femoral measurement in
Allosauroidea. To avoid problems with highly
skewed data, all linear data were log-
transformed and proportional indices were
arcsin-transformed (Carrano 2001), with cor-
relations subsequently analyzed using re-
duced major axis (RMA) regression. F4T was
regressed against femoral length, which serves
as a proxy for body size in the absence of
reliable body mass estimates for most speci-
mens. All data transformations and statistical
analyses were conducted in PAST (Hammer et
al. 2001), apart from arcsin transformations of
proportional data and calculation of 95%
confidence intervals on regression slopes,
which were performed in a custom-written
MatLab (www.mathworks.co.uk) script. Raw
data and information on the specimens
included can be found in Supplementary
Table 2.
CM.—In an attempt to detect any signifi-
cant change in skeletal body proportions that
might influence CM position, we measured
the ratio of pre- to post-sacral body length
from scaled reconstructions of allosauroid
taxa illustrated in the literature (Currie and
Zhao 1993; Coria and Salgado 1995; Azuma
and Currie 2000; Brusatte et al. 2008) and
ALLOSAUROIDEA LOCOMOTOR EVOLUTION 493
combined these with measurements taken from
our 3-D models (Bates et al. 2009a,b). Propor-
tionally larger pre-sacral body lengths may
indicate a more cranially positioned CM,
whereas relatively longer post-sacral lengths
would suggest a more caudally positioned CM.
Results
Musculoskeletal Modeling
Normalized values for hip flexor and exten-
sor muscle moment arms in Allosaurus and
Acrocanthosaurus are shown in Figures 4 and 5.
Additional information (e.g., hip abduction-
adduction, femoral long-axis rotation, knee
joint muscle moment arms) can be obtained
from the corresponding author. In general,
muscle moment patterns for flexion/extension
(and also abduction/adduction and long-axis
rotation, not shown here) in Allosaurus and
Acrocanthosaurus were very closely matched in
their overall patterns (i.e., joint angle depen-
dency) and magnitudes when normalized by
femoral length (Figs. 4, 5). Many hip flexor and
extensor muscles had moment arms that
varied substantially with joint angle, but did
so nearly identically in both Allosaurus and
Acrocanthosaurus (Fig. 4). This is reflected in
the summed extensor moments across the
range of joint angles studied (Fig. 5), which
also demonstrates the tendency for extensor
muscle moment arms to decrease with increas-
ing joint flexion, peaking with the hip flexed at
216.3uin Allosaurus and 219uin Acrocantho-
saurus (Fig. 5A). Several muscles (e.g., ADD 1
and 2, AMB, IFE) switched from hip extensors
to flexors and did so at similar joint angles in
both taxa (Fig. 4).
Hip Extensor Muscle Mass
The volumes of hind limb segments of
Allosaurus MOR693 and Acrocanthosaurus
NCSM 14345 from previous studies (Bates
et al. 2009a,b), and new estimates of bone
volume and CFL mass are tabulated in
Tables 1 and 2. Bates et al. (2009a,b) produced
a suite of differently sized and proportioned
reconstructions in an attempt to constrain
a plausible range of mass set values for
Allosaurus and Acrocanthosaurus based on
fossilized skeletal evidence (e.g., Fig. 3A–D).
For simplicity we focus on our locomotor
muscle predictions relative to three of these
models: the original ‘‘best estimate’’ models,
and the minimum (i.e., near skeleton-hugging)
and maximal (plus 15% of best estimate)
models (Fig. 3A–D) (see Bates et al. 2009a,b
for more details and images).
CFL volumes were estimated at 0.056 m
23
for Allosaurus MOR693 and 0.123 m
23
for
Acrocanthosaurus NCSM 14345 (Tables 1 and
2). Total hind limb bone volumes were
estimated at 0.016 m
23
in Allosaurus MOR693
and 0.057 m
23
in Acrocanthosaurus NCSM
14345, corresponding to 6–8% and 5–7.5% of
the limb segment volumes in the two models
(Tables 1, 2). Removing bone volume from
total limb segment volumes and adding CFL
volumes (and multiplying by a density
1056 kg m
23
for skeletal muscle [Sellers and
Manning 2007]) produced ‘‘locomotor’’ mus-
cle mass predictions ranging from 222 to
319 kg in Allosaurus MOR693 and from 880 to
1130 kg in Acrocanthosaurus NCSM 14345.
These values equate to 16.1–17% of total body
mass in the Allosaurus reconstructions and
14.5–15.8% of body mass in the Acrocantho-
saurus models (Tables 1, 2).
Scaling exponents of predicted CFL mass,
hind limb soft tissue mass (i.e., non-bony limb
segment mass), and overall locomotor muscle
mass relative to a range of body mass
estimates for Allosaurus MOR693 and Acro-
canthosaurus NSCM 14345 from Bates et al.
(2009a,b) are shown in Table 3. Regardless of
which combination of body mass values are
used, predicted CFL masses scale with strong
negative allometry (body mass
0.44–0.75
). Scaling
of hind limb soft tissue mass and overall
locomotor muscle mass is much more depen-
dent on the combination of body mass values
used for Allosaurus and Acrocanthosaurus. If
relatively consistent body dimensions are
assumed (e.g., best estimate, minimal, or
maximal masses used for both taxa) then hind
limb soft tissue mass scales with isometry
(body mass
0.98–1.04
) and total locomotor muscle
mass shows slight negative allometry (body
mass
0.93–0.95
). Only under the assumption of
larger body masses for Allosaurus and lighter
masses for Acrocanthosaurus (Fig. 3) do hind
limb soft tissue mass and overall locomotor
494 KARL T. BATES ET AL.
muscle mass exhibit strong positive allometry
(Table 3).
CM Predictions
Normalizing CM predictions by femoral
length for Allosaurus (MOR 693) and Acro-
canthosaurus (NCSM 14345) reveals an almost
identical plausible range in CM positions for
these taxa (Fig. 6), based on data from Bates
et al. (2009a,b). Best estimate volumetric
reconstructions predict a trunk CM position
24.83% of femoral length in front of the
acetabulum for Allosaurus, compared to
25.25% for Acrocanthosaurus (Fig. 6). The
FIGURE 4. Normalized hip flexor-extensor moment arms for pelvic and femoral muscles in Allosaurus and
Acrocanthosaurus across a range of hip joint angles. Positive hip joint angles and moment arms represent hip extension,
and negative values flexion, and for size-independent comparison raw values have been normalized by femoral length. A
hip joint value of 0urepresents vertical femur. Muscle name abbreviations can be found in Supplementary Table 1.
ALLOSAUROIDEA LOCOMOTOR EVOLUTION 495
plausible CM range for these allosauroids is
more clearly distinguishable from those cal-
culated for the more derived coelurosaurian
theropods (Tyrannosaurus and Struthiomimus)
in the same studies (Bates et al. 2009a,b),
whose best estimated and overall predicted
ranges are noticeably more craniad (e.g.,
44.56% and 37.11% of femoral length anterior
to the acetabulum for Tyrannosaurus BHI 3033
and Struthiomimus BHI 1266). However, best
estimate predictions from other independent
studies place the CM 45–57.7% of femoral
length anterior to the hip in Allosaurus,
Sinraptor,Fukuiraptor and Yangchuanosaurus
(Henderson and Snively 2003; Therrien and
Henderson 2007), and approximately 70%
of femoral length anterior to the hip in
Acrocanthosaurus (Henderson and Snively 2003).
FIGURE 5. The relationship between hip joint angle and the summed muscle moment arms for hip extension (A) and
flexion (B) normalized by femoral length for Allosaurus and Acrocanthosaurus. Negative hip joint angles represent hip
flexion and positive angle extension along a sagittal plane corresponding to a hip abduction angle of 10u. Error bars
of 625% shown for Acrocanthosaurus data, corresponding to the approximate expected error prediction of Hutchinson
et al. (2005).
TABLE 1. Body mass (kg), bone, CFL, and limb segment volume (kg m
23
) data for Allosaurus MOR693.
Best guess Minimum Maximum
Segment volume
Thigh 0.146 0.127 0.193
Shank 0.041 0.036 0.051
Metatarsus 0.009 0.001 0.012
Pes 0.006 0.006 0.006
Total limb segment volume 0.202 0.170 0.262
Bone volume
Femur 0.005 0.005 0.005
Shank 0.007 0.007 0.007
Metatarsals 0.002 0.002 0.002
Pes 0.002 0.002 0.002
Total bone volume 0.016 0.016 0.016
CFL volume 0.056 0.056 0.056
CFL % thigh muscle volume 28.426 31.461 22.951
Locomotor muscle mass data
Total limb segment volume
minus bone volume
0.186 0.154 0.246
Bone % limb segment volume 7.849 9.338 6.052
Locomotor muscle volume 0.242 0.210 0.302
Locomotor muscle mass 255.705 221.691 319.065
Total body mass 1500.910 1307.690 1976.850
Locomotor muscle mass as
%body mass
17.037 16.953 16.140
496 KARL T. BATES ET AL.
Scaling Metrics
Muscle Moment Arms.—Regression analy-
sis shows that F4T scales with positive
allometry with respect to FL in Allosauroi-
dea, but that isometry is included within the
95% confidence limits (Fig. 7, Supplementa-
ry Table 3). Carcharodontosaurians scale
with greater positive allometry than non-
carcharodontosaurians, but the sample size
is low in each case. Both subgroups have
genera that plot above and below the
regression for Allosauroidea, suggesting that
phylogenetic influence on the relative posi-
tion of the fourth trochanters is negligible
and that both contain taxa in which this
muscle insertion is either more proximal or
more distal than would be predicted by
simple scaling.
TABLE 2. Body mass (kg), bone, CFL, and limb segment volume (kg m
23
) data for Acrocanthosaurus NCSM 14345.
Best guess Minimum Maximum
Segment volume
Thigh 0.664 0.611 0.770
Shank 0.142 0.123 0.185
Metatarsus 0.033 0.028 0.041
Pes 0.007 0.007 0.007
Total limb segment volume 0.846 0.769 1.003
Bone volume
Femur 0.021 0.021 0.021
Shank 0.026 0.026 0.026
Metatarsals 0.008 0.008 0.008
Pes 0.002 0.002 0.002
Total bone volume 0.057 0.057 0.057
CFL volume 0.123 0.123 0.123
CFL % thigh muscle volume 16.057 17.251 14.106
Locomotor muscle mass data
Total limb segment volume minus bonevolume 0.789 0.712 0.946
Bone % limb segment volume 6.704 7.376 5.655
Locomotor muscle volume 0.912 0.835 1.069
Locomotor muscle mass 963.369 882.057 1129.161
Total body mass 6177.040 5569.560 7750.610
Locomotor muscle mass as %body mass 15.596 15.837 14.569
TABLE 3. Scaling of predicted CFL mass, limb segment soft tissue and overall ‘‘locomotor’’ muscle mass relative to a
range of body mass estimates for Allosaurus MOR 693 and Acrocanthosaurus NCSM 14345 by Bates et al. (2009a,b). Body
masses and muscle masses used to calculate the scaling exponents for the various models are listed in Table 2.
Comparison
Body mass model used
ScalingAllosaurus MOR693
Acrocanthosaurus
NCSM 14345
CFL mass Best estimate Best estimate BM‘0.56
Minimum Minimum BM‘0.54
Maximum Maximum BM‘0.57
Maximum Minimum BM‘0.75
Minimum Maximum BM‘0.44
Limb segment soft tissue
mass
Best estimate Best estimate BM‘1.01
Minimum Minimum BM‘1.04
Maximum Maximum BM‘0.98
Maximum Minimum BM‘1.71
Minimum Maximum BM‘0.61
Overall locomotor muscle
mass
Best estimate Best estimate BM‘0.94
Minimum Minimum BM‘0.95
Maximum Maximum BM‘0.93
Maximum Minimum BM‘1.57
Minimum Maximum BM‘0.57
ALLOSAUROIDEA LOCOMOTOR EVOLUTION 497
CM.—Measurement of the ratio of pre- to
post-acetabular body length from scaled recon-
structions and 3-D models (Currie and Zhao
1993; Coria and Salgado 1995; Azuma and Currie
2000; Brusatte et al. 2008; Bates et al. 2009a,b) can
be found in Table 4. The data show very little
difference between allosauroid taxa, suggesting
little change in body length proportions.
FIGURE 6. Trunk center-of-mass (CM) predictions for allosauroids and selected coelurosaurs from computer generated
volumetric models. The plausible range of trunk CM positions predicted for Allosaurus MOR 693 (A) and
Acrocanthosaurus NCSM 14345 (B) are nearly identical and are closely clustered together in front and below the hip
joint. C, Normalizing data using femoral length demonstrates that predictions for additional allosauroid taxa from
other studies plot within the ranges for Allosaurus and Acrocanthosaurus, with the exception of Henderson and Snively’s
(2003) reconstruction of Acrocanthosaurus (see text for discussion). Overall this suggests the magnitude of soft tissue
uncertainties means it is difficult to test the hypothesis of a CM shift within Allosauroidea. However, the cranial shift in
CM predictions in coelosaurs (Tyrannosaurus,Struthiomimus) suggests it is possible to identify differences and trends
across larger clades within Theropoda, despite this ambiguity in the size and geometry of soft tissues.
498 KARL T. BATES ET AL.
Discussion
Musculoskeletal Modeling:
Hip Muscle Leverage
The 3-D models provide little quantitative
support for our muscle leverage scaling
hypothesis (Hypothesis 1: that allosauroid
hind limb muscle moment arms will scale
with positive allometry). Indeed, despite its
considerably smaller body size, Allosaurus
MOR 693 has larger relative moment arms
than the larger Acrocanthosaurus for a number
of important hip extensors when normalized
by femoral length (Fig. 4B; CFL, CFB, ISTR).
This difference appears significant, as these
muscles have well-constrained attachment
sites and 3-D paths and hence their predicted
moment arms are among the most reliable in
extinct theropods (Hutchinson et al. 2005).
Therefore, despite inherent uncertainties it is
probably safe to conclude that these muscles
had relatively larger moment arms in Allo-
saurus MOR 693 than in Acrocanthosaurus
NCSM 14345 with respect to limb segment
(femoral) length. These muscles likely made
up a substantial proportion of hind limb
extensor muscle mass (Tables 1, 2), as they
do in extant tailed saurians (Hutchinson
2004a,b; Allen et al. 2009; Persons and Currie
2011; Hutchinson et al. 2011b), and hence
would have provided a substantial propor-
tion of hip extensor muscle force and power
during locomotion. Negative allometry in the
moment arms of these muscles would there-
fore have had a significant negative effect on
locomotor performance without compensato-
ry changes in muscle mass, architecture or
physiology.
Assessing the scaling of muscle leverage
relative to body mass is difficult for extinct
animals; uncertainties underpinning the pre-
diction of absolute moment arm magnitudes
are further confounded by poorly constrained
body mass estimates (Tables 2, 3) (Hutchinson
et al. 2007; Bates et al. 2009a,b). Using identical
procedures for both animals, Bates et al.
(2009a,b) predicted total body masses of
approximately 6200 kg for Acrocanthosaurus
NCSM 14345 and 1500 kg for Allosaurus MOR
693 (Fig. 3A,B). Summed hip extensor moment
arms (Fig. 5A) at moderately flexed joint
angles scale with slight positive allometry
when these body masses are used (i.e., body
mass
0.34–37
with the hip flexed between 20u
and 240u). However, given the uncertainties
inevitable in the estimation of both moment
TABLE 4. Ratio of pre- to post-acetabular body length (m) in reconstructions of allosauroids (data from Bates et al.
2009a,b; Brusatte et al. 2008; Currie and Zhao 1994; Azuma and Currie 2000; Coria and Salgado 1995) shows very little
difference between allosauroid taxa, further suggesting that a significant change in CM within the group cannot
currently be substantiated.
Total length Hip to tail % Hip to tail Head to hip % Head to hip
Allosaurus 7.57 4.70 62.09 2.87 37.91
Fukuiraptor 4.20 2.28 54.17 1.93 45.83
Sinraptor dongi 7.20 4.00 55.56 3.19 44.27
Sinraptor
hepingensis
8.00 4.55 56.88 3.45 43.13
Neovenator 7.60 4.60 60.53 3 39.47
Acrocanthosaurus 11.21 6.58 58.67 4.63 41.33
Giganotosaurus 12.50 7.01 56.11 5.58 44.66
FIGURE 7. RMA log-log regression plots for FL against
F4T. Regression lines are shown for the whole data set
(i.e., Allosauroidea) and for the two taxonomic subgroups
(non-carcharodontosaurians and carcharodontosaurians).
The RMA regression line for Allosauroidea shows
positive allometry, but 95% confidence intervals of the
slope include isometry (slope 1.2773 60.297, Supple-
mentary Table 3).
ALLOSAUROIDEA LOCOMOTOR EVOLUTION 499
arm magnitudes and body mass, this cannot be
considered strong support for positive allom-
etry in hip extensor moment arms. For
example, if the mass of 6200 kg for Acrocantho-
saurus represents a 5% underestimate, and the
mass of Allosaurus a 5% overestimate, then
slight negative allometry and isometry are
predicted in hip extensor muscle leverage (i.e.,
body mass
0.32–34
with the hip flexed between
20uand 240udegrees).
The caudofemoralis musculature inserts
around the fourth trochanter on the caudal
surface of the proximal femur (Gatesy 1990,
1995) (Fig. 3E,F), and the relative distance of
the fourth trochanter from the proximal end
of the femur (F4T) provides a reasonable
approximation of the extensor moment arm of
this muscle group (Carrano 1998; Bonnan
2004). The regression plot of F4T against FL
suggests that the extensor moment of the
caudofemoralis musculature (CFL and CFB)
exhibits positive allometry in Allosauroidea,
and that this allometry is slightly more
pronounced in carcharodontosaurians than
non-carcharodontosaurians (Fig. 7, Supple-
mentary Table 3). This apparently contradicts
the findings of the 3-D models. However, the
plot (Fig. 7) reveals why the individuals
modeled here show the opposite relationship.
Allosaurus MOR 693 plots fractionally above
the regression lines for Allosauroidea and for
non-carcharodontosaurians, suggesting it has
marginally greater extensor moment arms for
the caudofemoralis muscles than would be
predicted from its size and phylogenetic
position. Conversely, Acrocanthosaurus NCSM
14345 plots comfortably below regression
lines for Allosauroidea and carcharodonto-
saurians, suggesting it has a smaller extensor
moment arms for the caudofemoralis muscles
than would be predicted from its size and
phylogenetic position. This finding highlights
the significant scatter present about the RMA
regression for Allosauroidea and this (com-
bined with the relatively low sample size)
yields broad 95% confidence limits, which
include isometry.
The regression analysis provides tenuous
support for the hypothesis of positive allo-
metric scaling in hip extensor moment arms,
but suggests variation in magnitudes at both
small and large body size. Perhaps more
importantly, these results demonstrate the
importance of employing multiple indepen-
dent assessments of functional morphology.
In other words, studies of a limited number of
‘‘exemplar taxa’’ (e.g., Allosaurus and Acro-
canthosaurus) may not reveal the complete
macroevolutionary picture. Slight positive
allometric scaling of the moment arm of
major hip extensors may have evolved in
allosauroids as an adaption to help counter
the negative allometry of muscle force and
power output as body size increased. One
effect of increasing the mechanical advantage
(Biewener 1989) of the major hip extensors
(CFL and CFB) may have been that any given
contraction would have imparted greater
force but less rotation and lower angular
velocity, resulting in a slower but more
forceful movement (Christiansen 2002). How-
ever, we find little evidence that the magni-
tude (or statistical significance) of this trend
was sufficient (e.g., .body mass
0.4
) to main-
tain absolute or relative locomotor perfor-
mance in the largest allosauroids.
Hip Extensor Muscle Mass
Our predictions of total locomotor muscle
mass in the models of Allosaurus and Acro-
canthosaurus have two components: hind limb
soft tissue mass and CFL mass. CFL mass
unambiguously scales with strong negative
allometry, regardless of the combination of
body mass values assumed (Tables 1–3,
Fig. 3A–D). When relatively consistent body
dimensions are assumed (e.g., best estimate,
minimal, or maximal masses used for both
taxa; Fig. 3A,B) then hind limb soft tissue
mass scales with isometry, indicating that the
slight negative allometry in total locomotor
muscle mass is a consequence of the strong
negative allometry in CFL mass in the two
models.
Our predicted CFL mass of 130 kg for
Acrocanthosaurus is broadly consistent with
estimates for slightly larger specimens of
Tyrannosaurus, derived using a similar mod-
eling approach. Hutchinson et al. (2011b)
estimated CFL mass at 162–192 kg for four
adult specimens of Tyrannosaurus rex, lower
than the value of 261 kg that Persons and
500 KARL T. BATES ET AL.
Currie (2011) obtained in modeling one of the
same adults. Qualitatively consistent with our
model predictions, the models of Hutchinson
et al. (2011b) suggest either no change or a
decrease (i.e., negative allometry) in percent-
age of body mass made up by the CFL during
ontogeny in Tyrannosaurus rex (e.g., data in
their Tables 6, 7). However, Persons and
Currie (2011) argued for an increase in CFL
mass as a proportion of body mass in large
tyrannosaurids, implying positive allometric
scaling of this important limb retractor. As
pointed out by Hutchinson and colleagues
(Hutchinson et al. 2011a,b), the apparent
relative increase in CFL mass found by Persons
and Currie (2011) was largely the product an
extremely low total body mass value for their
adult Tyrannosaurus rex specimen, rendering
their scaling conclusions questionable at best.
Our results strongly support negatively allo-
metric scaling in CFL across a large range of
plausible body masses for Allosaurus and
Acrocanthosaurus (Tables 1–3, Fig. 3) and there-
fore provide no support for our original
scaling hypothesis (Hypothesis 2).
Scaling results for hind limb soft tissue and
total locomotor muscle mass are less equivo-
cal, and depend on subjective reconstruction
of theropod body size and shape. If body size
and shape are reconstructed comparably in
Allosaurus and Acrocanthosaurus then hind
limb soft tissue mass scales approximately
proportional to body mass, whereas total
locomotor muscle mass experiences a small
relative decrease. However, reconstruction of
these two taxa with vastly disproportionate
extra-skeletal soft tissue dimensions (hence
body mass; Fig. 3C,D) does potentially allow
for strong positive or negative allometry in
muscle mass (Table 3). Although this may
seem ‘‘anti-scientific’’ as an approach, it is an
inevitable caveat of soft tissue reconstruction
in extinct taxa and emphasizes that a level of
uncertainty in predictions must be accepted
(Hutchinson and Allen 2008). We therefore
are currently able to reject elements of our
muscle mass scaling hypothesis, specifically
that the CFL muscle (the largest single hip
extensor muscle [Hutchinson et al. 2011b;
Persons and Currie 2011]) became relatively
larger as size increased in allosauroids.
However, scaling of overall muscle mass is
more difficult to test; if body proportions
are restored proportionally in our models
(Fig. 3A,B) then our scaling hypothesis can be
rejected in favor of isometric or even slight
negative allometry in muscle mass (Tables 1–
3). However, uncertainties in the reconstruction
of absolute body size and shape (Hutchinson
et al. 2007; Bates et al. 2009a,b) clearly allow for
relatively smaller or larger muscle masses as
body size increased within lineages of non-avian
theropods.
CM Predictions
When scaled relative to femoral length,
existing data on CM positions fail to demon-
strate a significant difference between small
and large allosauroids, or indeed between
primitive allosauroids like Allosaurus and
Sinraptor and more derived members of the
Carcharodontosauria (Fig. 6). Simple mea-
surement of the ratio of pre- to post-sacral
body length from scaled reconstructions
(Table 4) shows very little difference between
allosauroid taxa. Therefore our results do not
support the hypothesis of a caudal shift in
CM as body size increased (Hypothesis 3), or
indeed any phylogenetic shift in the Carchar-
odontosauria as postulated by Brusatte et al.
(2008).
Best estimate predictions from various
independent volumetric reconstructions place
the CM at 37–46% of femoral length anterior
to the hip in Allosaurus (Henderson and
Snively 2003; Bates et al. 2009b) and 45–
57.7% in Sinraptor dongi and Sinraptor hepin-
gensis (Henderson and Snively 2003; Therrien
and Henderson 2007). For carcharodontosaur-
ians the existing data set contains a single
reconstruction of Fukuiraptor and two inde-
pendent reconstructions of the same specimen
of Acrocanthosaurus (NCSM 14535; Henderson
and Snively 2003; Bates et al. 2009a). Best
estimate reconstructions of Acrocanthosaurus
NCSM 14345 from these two studies also differ
significantly in trunk CM predictions; the
model of Henderson and Snively (2003)
predicts the CM of Acrocanthosaurus NCSM
14345 to be approximately 70% of femoral
length anterior to the hip versus 37% in the
best estimate model of Bates et al. (2009a). The
ALLOSAUROIDEA LOCOMOTOR EVOLUTION 501
difference of 33% of femoral length means that
Henderson and Snively’s (2003) prediction lies
approximately 0.42 m craniad of that of Bates
et al. (2009a), quite a sizable difference.
The disparity between the two models of
Acrocanthosaurus is emphasized when the
data are viewed in the context of CM
predictions for other theropod groups, par-
ticularly data from those studies employing
sensitivity analyses (Hutchinson et al. 2007;
Bates et al. 2009a,b). Studies by Bates et al.
(2009a,b) produce near identical best estimate
and maximum plausible range CM predic-
tions for Allosaurus and Acrocanthosaurus.
However, these studies do suggest a subtle
difference in best estimate and plausible CM
ranges between allosauroids and more de-
rived theropod clades (tyrannosaurs and
ornithomimosaurs; Fig. 6C). The CM position
predicted by Henderson and Snively (2003)
for Acrocanthosaurus NCSM 14345 lies signif-
icantly anterior to the maximum plausible
craniad position suggested by Bates et al.
(2009a), and plots towards the craniad ex-
treme of the range for Tyrannosaurus suggest-
ed by the two independent sensitivity analy-
ses (Hutchinson et al. 2007; Bates et al. 2009a).
The reason for this large disparity is clear
when the relative proportions of reconstruct-
ed body segments are compared. The initial
model of Bates et al. (2009a) has a significant-
ly larger tail volume (1.149 m
3
versus
,0.679 m
3
) but smaller forelimb volume
(0.012 m
3
versus 0.036 m
3
) than the model of
Henderson and Snively (2003). The smallest
tail volume in the sensitivity analysis of Bates
et al. (2009a) measured 0.975 m
3
, still consid-
erably higher than that of Henderson and
Snively’s (2003) model. Bates et al. (2009a)
suggested that their smallest volume ap-
peared highly ‘‘emaciated’’ and probably
unreasonably small given that the proximal
tail housed major hind limb retractor muscu-
lature in non-avian theropods (Gatesy 1990,
1995; Allen et al. 2009; Persons and Currie
2011). For their reconstructions of non-avian
tail size, Allen et al. (2009) used extant saurian
proportions and thus produced generally
larger tails than Bates et al. (2009a,b) and
Hutchinson et al. (2007). Consequently they
positioned CM more caudally by around 10%.
All in all, these considerations cast doubt on
the extreme cranial CM predicted by Hen-
derson and Snively (2003) for Acrocantho-
saurus, and emphasize the need to base such
reconstructions on primary 3-D data collected
directly from skeletons rather than on illus-
trations sourced from the literature.
Comparison of CM predictions of allosaur-
oids and basal coelurosaurs suggests that
relative differences between morphologically
and phylogenetically disparate theropod
clades may be identifiable. Although some
overlap exists in the respective plausible
ranges, the suggested trend toward a more
craniad CM in coelurosaurs matches predic-
tions based on the gradual reduction of
relative tail length and general modification
of the theropod body form in the lineage
leading to crown-group birds (Gatesy 1990,
1995). These results suggest that through
further volumetric modeling it will be possi-
ble to identify and constrain the tempo and
mode CM evolution along the lineage to
crown-group birds, and specifically to deter-
mine whether body shape evolution was
correlated with a gradual cranial migration
in CM position in the bird line (Gatesy 1990,
1995) or alternatively by conservatism until a
sudden cranial shift occurred in association
with the origin of flight (Christiansen and
Bonde 2002).
Scaling Patterns in Allosauroids:
Implications for Locomotion
Muscle moment arms, masses, and CM
position are by themselves not directly pre-
dictive of locomotor energetics and perfor-
mance. For example, moment arms provide a
quantitative definition of function in terms of
joint rotation direction and relative magni-
tude (thus enabling quantitative comparisons
between taxa), but extrapolation of joint
control and whole-limb behavior from mo-
ment arms is unlikely to provide more than a
general picture of locomotor style. Thus, the
strong decline in hip extensor moment arm
magnitudes in Allosaurus and Acrocanthosaurus
presented here adds further support to more
upright (though not completely columnar)
stance for large non-avian theropods, as
suggested by Hutchinson et al. (2005) for
502 KARL T. BATES ET AL.
Tyrannosaurus, rather than flexed birdlike
postures supposed by others (e.g., Bakker
1986; Paul 1988, 2008). More specific predic-
tions of optimum joint angles require biome-
chanical models or simulations in which
additional suppositions are made regarding
muscle properties.
Both static (Hutchinson 2004b; Gatesy et al.
2009) and dynamic (Sellers and Manning
2007; Bates et al. 2010) biomechanical models
have recently been used in an attempt to
quantitatively constrain stance and gait in
non-avian theropods. By refining the values
of input parameters into these biomechanical
models our results will likely alter the
quantitative predictions of these studies, but
are unlikely to change their conclusions
qualitatively. Although some ambiguity inev-
itably exists, we find no strong quantitative
support in allosauroids for any of the hy-
pothesized adaptations for maintaining loco-
motor performance across a fourfold (or
,3500 kg) increase in body mass (Supple-
mentary Table 4). A key observation is that
highly disproportionate reconstructions of
body proportions (e.g., Fig. 3C,D) are re-
quired to achieve any kind of significant
positive allometry in locomotor muscle mass.
Back to the Bones: Locomotor Evolution
in Allosauroidea
The anatomical and biomechanical data
generated here do suggest that at least aspects
of the broad hypothesis concerning locomotor
evolution in allosauroids proposed by Bru-
satte et al. (2008) can be refuted. A ‘‘restruc-
turing of hind limb musculature’’ implies
significant repositioning of muscle origins
and/or insertions. This can be achieved either
by a muscle shifting its attachment from one
bone or area of bone to another, or by a
change in bone shape or proportion that
serves to shift the position of that muscle
with respect to the joint(s) over which it acts
(i.e., a significant change in moment arm). We
find little support for a significant restructur-
ing of musculature in our moment arm
analysis, suggesting that effects of any shape
or proportional change in pelvic limb osteol-
ogy were subtle and beyond the resolution of
palaeontological analysis. The similarity in
muscle geometry inferred here for all allo-
sauroids (and indeed most basal tetanurans;
Carrano and Hutchinson 2002) (Figs. 2, 4, 5)
indicates that these animals shared the
same basic mechanism for 3-D limb control
(Hutchinson and Gatesy 2000).
What, then, do these analyses tell us about
the functional consequences of the evolu-
tionary modification in pelvic limb osteology
in Allosauroidea? Osteological synapomor-
phies are of central interest to understanding
the evolution of locomotion, but are rarely
considered in functional studies such as this
one. Allosauroid osteology has been exten-
sively documented and several well-estab-
lished synapomorphies exist for the subclade
Carcharodontosauria (Fig. 1) (Brusatte and
Sereno 2008; Brusatte et al. 2008; Benson et al.
2010). These changes highlight that evolution
of skeletal morphology within Allosauroidea
is clearly more complex than purely size-
driven adaptations and responses. The com-
paratively small body sizes of basal carchar-
odontosaurians such as Neovenator and Eo-
carcharia indicate that carcharodontosaurian
pelvic and hind limb synapomorphies
evolved independently of significant chang-
es in body size (Fig. 1). Moreover, the
retention of these features in relatively small
bodied megaraptorans such as Australovena-
tor and Fukuiraptor suggests that they were
not functionally dependent on large body
size.
Most carcharodontosaurian hind limb sy-
napomorphies represent modifications to the
skeleton at joint surfaces, perhaps indicating a
subtle change in joint axes of rotation and
habitual limb orientation during stance. Dor-
sal inclination of the femoral head occurs
synchronously with expansion of the lateral
femoral condyle in carcharodontosaurians
(Fig. 1D) (Brusatte and Sereno 2008; Brusatte
et al. 2008). Maintaining a parallel insertion of
the femoral head into the acetabulum (i.e.,
femoral head at 90uto vertical) with a dorsally
inclined morphology would serve to angle the
femur outward from the body (i.e., abduct)
relative to the primitive condition. This
would effectively increase the joint spacing
at the knee between the lateral condyle and
the shank. In this scenario, expansion of the
ALLOSAUROIDEA LOCOMOTOR EVOLUTION 503
lateral condyle into this space would serve
as a mechanism to maintain the size and
geometry of the knee joint capsule.
However, two significant caveats must be
acknowledged when inferring function from
fossil bones alone. First, it is not known how
well the extremities of fossil theropod long
bones represent the geometry of the actual
joint shape in life. In extant archosaurs the
morphology of the articular cartilage is often
quite dissimilar to the bone surface morphol-
ogy (Bonnan et al. 2010), and the same
appears to be true where ‘‘soft tissue’’ is
preserved at joint surfaces in dinosaur fossils.
Experimental taphonomic studies on extant
archosaurs have shown that removal of the
epiphyseal articular cartilage has a varied
effect on long bone geometry, both within and
between species (Bonnan et al. 2010). Second,
although joint articulations are an important
component of functional studies, they ulti-
mately tell us little about how an extinct
animal habitually moved its limbs (e.g.,
Gatesy et al. 2009). Limb joints function to
facilitate 3-D rotation and translation of their
bounding skeletal segments; hence a spec-
trum of segment articulations inevitably
exists. Total joint range of motion estimated
from the articular geometry of fossil bones is
always likely to far exceed the levels of joint
excursions used in steady-state locomotion
like walking and running (see Gatesy et al.
2009 for discussion).
Nonetheless, it seems highly plausible that
reorientation of the femoral head may have
significant consequences for bone loading and
stress concentrations. Beam mechanics theory
suggests that increasing the dorsal inclination
places the femoral head in a progressively
more compressive loading regime, reducing
bending and hence peak stress at the junction
between the head and shaft and perhaps also
along the lateral side of the femoral shaft as
stress becomes more uniformly distributed.
This effect is demonstrated qualitatively with
simple 2-D finite element beam models in the
supplementary information (Supplementary
Figure 2).
We therefore have a promising functional
hypothesis, but one that requires significant-
ly more complex and anatomically realistic
biomechanical models before it can be sup-
ported qualitatively or quantitatively. Con-
ceptualization of the femoral loading in a
beam model of course grossly simplifies
external and internal femoral geometry, but
it does illustrate the principle behind femoral
head inclination as a mechanism for stress
reduction. Further investigation of this hy-
pothesis in allosauroids would be particu-
larly interesting because it may represent
evidence for the evolution of increased
weight-bearing capacity independent of any
change in body size.
Conclusion
This study tested three principal hypothe-
ses related to the evolution of large body size
in Allosauroidea. The first is that allosaur-
oids exhibited strong positive allometry in
hip muscle moment arms (.body mass
0.4
) as
a measure for maintaining high-level loco-
motor performance as size increases (Alex-
ander et al. 1981; Biewener 1989, 1990).
Predictions from 3-D musculoskeletal models
and simple scaling metrics provide little if
any quantitative support for this hypothesis,
and instead indicate that muscle leverage
generally scaled close to isometry (,body
mass
0.33
; femoral length
1.00
), but with some
variation at both small and large body sizes.
A second hypothesis suggested that larger
allosauroids would show a significant rela-
tive increase in locomotor muscle mass as
compensation for the negative allometry in
muscle cross-sectional area (hence muscle
force and power) as size increases. Contrary
to other recent quantitative (Persons and
Currie 2011) and qualitative (Paul 2008)
studies of large-bodied theropod clades, we
found no compelling evidence for significant
positive allometry in muscle mass. Consis-
tently proportioned reconstructions of differ-
ent-sized allosauroids suggested isometric
scaling of muscle mass, but strong negative
allometry in the caudofemoralis musculature
(Tables 1–3). Our final hypothesis posited
that larger allosauroids would have modified
body proportions to shift the CM caudally
as body size increased to lessen demands
on anti-gravity hip muscles (Hutchinson
2004a,b; Gatesy et al. 2009). Again consistently
504 KARL T. BATES ET AL.
proportioned soft tissue reconstructions
produced similar CM predictions for allosaur-
oids, and given the large error bars in CM
predictions for extinct taxa (Fig. 6) little quan-
titative support was found for this hypothesis,
although more upright postures are generally
more plausible given the strong angular
dependency of hip extensor muscle moment
arms (Figs. 4, 5) (Hutchinson et al. 2005).
Overall, our data set supports studies that
argue for a significant decline in locomotor
performance with increasing body size in non-
avian theropods (Hutchinson 2004b; Hutch-
inson et al. 2005, 2007; Sellers and Manning
2007; Gatesy et al. 2009).
Our analyses also allow us to reject
previous hypotheses concerning the func-
tional consequences of pelvic and hind limb
synapomorphies of the carcharodontosaur-
ians, specifically the suggestion that these
osteological characters are associated with a
restructuring of hind limb musculature or
significant shift in CM position (Brusatte et al.
2008). We recommend that future work
consider carcharodontosaurian pelvic limb
synapomorphies as load-bearing adapta-
tions, specifically as adaptations for stress
reduction. Qualitative interpretation of mor-
phology using beam mechanics and stress
concentration theory indicates that dorsal
inclination of the femoral head may have
functioned to reduce bending and perhaps
torsional stress in both the femoral head and
shaft (Supplementary Figure 2). The moder-
ate body sizes of basal carcharodontosaurids
and neovenatorids (Brusatte and Sereno
2008; Benson et al. 2009) makes this hypoth-
esis particularly novel and interesting be-
cause they suggest the phylogenetic origin of
an adaptation for improved weight support
independent of any change in body size
(Fig. 1).
Acknowledgments
This research was partly funded by grants
from the Jurassic Foundation and the Palae-
ontological Association Sylvester-Bradley
Award. We thank D. Henderson and J.
Hutchinson for kindly providing a break-
down of their theropod center-of-mass data,
and P. Larson (BHI), B. Breithaupt (formerly
University of Wyoming Geological Muse-
um), V. Sneider (North Carolina Museum of
Natural Sciences), C. Mehling (American
Museum of Natural History), P. Barrett
(Natural History Museum, London), and P.
Roath (Museum of the Rockies) for generous
access to specimens. A. Chamberlain is
thanked for loan of the Polhemus scanner.
K.T.B. thanks E. Schachner for participation
in alligator dissections. This work benefited
from discussion and comments from W.
Sellers, J. Farlow, V. Allen, J. Hutchinson, E.
Schachner, J. Foster, P. Larson, J. Codd, and
S. Maidment.
Literature Cited
Abourachid, A., and S. Renous. 2000. Bipedal locomotion in
ratites (Paleognatiform) [sic]: examples of cursorial birds. Ibis
142:538–549.
Alexander, R. M. 1977. Mechanics and scaling of terrestrial
locomotion. Pp. 93–110 in T. J. Pedley, ed. Scale effects in
animal locomotion. Academic Press, New York.
Alexander, R. M., and A. S. Jayes. 1983. A dynamic similarity
hypothesis for the gaits of quadrupedal mammals. Journal of
Zoology 201:135–152.
Alexander, R. M., A. S. Jayes, G. M. O. Maloiy, and E. M. Wathuta.
1981. Allometry of the leg muscles of mammals. Journal of
Zoology 194:539–552.
Allen, V., H. Paxton, and J. R. Hutchinson. 2009. Variation in
cente r of mass estimates fo r extant sauropsids and its
importance for reconstructing inertial properties of extinct
archosaurs. Anatomical Record 292:1442–1461.
An, K. N., K. Takahashi, T. P. Harrigan, and E. Y. Chao. 1984.
Determination of muscle orientations and moment arms.
Journal of Biomechanical Engineering 106:280–283.
Azuma, Y. and P. J. Currie. 2000. A new carnosaur (Dinosauria:
Theropoda) from the Lower Cretaceous of Japan. Canadian
Journal of Earth Sciences 37:1735–1753.
Bakker, R. T. 1986. Dinosaur heresies. William Morrow, New
York.
Bates, K. T., P. L. Manning, D. Hodgetts, and W. I . Sellers.
2009a. Estimating mass properties of dinosaurs using l aser
imaging and computer modelling. PLoS ONE 4(2):e4532
doi:10.1371.
Bates, K. T., P. L. Falkingham, B. H. Breithaupt, D. Hodgetts, W. I.
Sellers, and P. L. Manning. 2009b. How big was ‘Big Al’?
Quantifying the effect of soft tissue and osteological unknowns
on mass predictions for Allosaurus (Dinosauria: Theropoda).
Palaeontological Electronica 12(3):14A. http://palaeo-electronica.
org/2009_3/186/index.html.
Bates, K. T., P. L. Manning, L. Margetts, and W. I. Sellers. 2010.
Sensitivity analysis in evolutionary robotic simulations of
bipedal dinosaur running. Journal of Vertebrate Paleontology
30:458–466.
Benson, R. G. J, M. T. Carrano, and S. L Brusatte. 2010. A new
clade of archaic large-bodied predatory dinosaurs (Theropoda:
Allosauroidea) that survived to the latest Mesozoic. Naturwis-
senschaften 97:71–78.
Biewener, A. A. 1989. Scaling body support in mammals: limb
design and muscle mechanics. Science 245:45–48.
———. 1990. Biomechanics of mammalian terrestrial locomotion.
Science 250:1097–1103.
ALLOSAUROIDEA LOCOMOTOR EVOLUTION 505
Bonnan, M. F. 2004. Morphometric analysis of humerus and
femur shape in Morrison sauropods: implications for functional
morphology and paleobiology. Paleobiology 30:444–470.
Bonnan, M. F., J. L. Sandrik, T. Nishiwaki, D. R. Wilhite, R. M.
Elsey, and C. Vittore. 2010. Calcified cartilage shape in
archosaur long bones reflects overlying joint shape in stress-
bearing elements: Implications for nonavian dinosaur locomo-
tion. Anatomical Record 293:2044–2055.
Brusatte, S. L., and P. C. Sereno. 2008. Phylogeny of Allosauroidea
(Dinosauria: Theropoda): comparative analysis and resolution.
Journal of Systematic Palaeontology 6:155–182.
Brusatte, S. L., R. B. J. Benson, and S. Hutt. 2008. The osteology of
Neovenator salerii (Dinosauria: Theropoda) from the Wealden
Group (Barremian) of the Isle of Wight. Monograph of the
Palaeontological Society 162(631):1–166.
Carrano, M. T. 1998. Locomotion in non-avian dinosaurs:
integrating data from hind limb kinematics, in vivo strains,
and bone morphology. Paleobiology 24:450–469.
———. 2001. Implications of limb bone scaling, curvature and
eccentricity in mammals and non-avian dinosaurs. Journal of
Zoology, London 254:41–55.
Carrano, M. T., and J. R. Hutchinson. 2002. Pelvic and hind limb
musculature of Tyrannosaurus rex (Dinosauria: Theropoda).
Journal of Morphology 253:207–228.
Christiansen, P. 2002. Locomotion in terrestrial mammals: the
influence of body mass, limb length and bone proportions on
speed. Zoological Journal of the Linnean Society 136:685–714.
Christiansen, P., and N. Bonde. 2002. Limb proportions and avian
terrestrial locomotion. Journal fu
¨r Ornithologie 143:356–371.
Coria, R. A., and L. Salgado. 1995. A new giant carnivorous
dinosaur from the Cretaceous of Patagonia. Nature 377:
224–226.
Currie, P. J., and X. J. Zhao. 1993. A new carnosaur (Dinosauria:
Theropoda) form the Jurassic of Xinjiang, People’s Republic of
China. Canadian Journal of Earth Sciences 30:2037–2081.
Gatesy, S. M. 1990. C audofemoralis mus culature and the
evolution of theropod locomotion. Paleobiology 16:170–186.
———. 1995. Functional evolution of the hind limb and tail from
basal theropods to birds. Pp. 219–234 in J. J. Thomason, ed.
Functional morphology in vertebrate palaeontology. Cam-
bridge University Press, Cambridge.
Gatesy, S. M., M. Baeker, and J. R. Hutchinson. 2009. Constraint-
based exclusion of limb poses for reconstructing theropod
dinosaur locomotion. Journal of Vertebrate Paleontology
29:535–544.
Gu
¨nther, M., and R. Blickhan. 2002. Joint stiffness of the ankle and
the knee in running. Journal of Biomechanics 35:1459–1474.
Hammer, Ø., D. A. T. Harper, and P. D. Ryan. 2001. PAST:
paleontological statistics software package for education and
data analysis. Palaeontolog ia Electronica 4. http://palaeo-
electronica.org/2001_1/past/issue1_01.htm.
Henderson, D., and E. Snively. 2003. Tyrannosaurus en pointe:
allometry minimized rotational inertia of large carnivorous
dinosaurs. Proceedings of the Royal Society of London B
271(Biology Letters Suppl. 3):S57–S60.
Hocknull, S. A., M. A. White, T. R. Tischler, A. G. Cook, N. D.
Calleja, T. Sloan, and D. A. Elliott. 2009. New mid-Cretaceous
(latest Albian) dinosaurs from Winton, Queensland, Australia.
PLoS ONE 4(7):1–51.
Hutchinson, J. R. 2001a. The evolution of pelvic osteology and soft
tissues on the line to extant birds (Neornithes). Zoological
Journal of the Linnean Society 131:123–168.
———. 2001b. The evolution of femoral osteology and soft tissues
on the line to extant birds (Neornithes). Zoological Journal of
the Linnean Society 131:169–197.
———. 2004a. Biomechanical modeling and sensitivity analysis of
bipedal running. I. Extant taxa. Journal of Morphology 262:421–
440.
———. 2004b. Biomechanical modeling and sensitivity analysis of
bipedal running ability. II. Extinct taxa. Journal of Morphology
262:441–461.
Hutc hinson , J. R., and V. Allen . 2008. Th e evolutionary
continuum of limb function from early theropods to birds.
Naturwissenschaften 96:423–448.
Hutchinson, J. R., and S. M. Gatesy. 2000. Adductors, abductors,
and the evolution of archosaur locomotion. Paleobiology
26:734–751.
Hutchinson, J. R., F. C. Anderson, S. S. Blemker, and S. L. Delp.
2005 . Analysis of h ind lim b muscle mome nt arms i n
Tyrannosaurus rex using a three-dimensional musculoskeletal
computer model: implications for stance, gait, and speed.
Paleobiology 31:676–701.
Hutchinson, J. R., V. Ng-Thow-Hing, and F. C. Anderson. 2007. A
3D interactive method for estimating body segmental param-
eters in animals: application to the turning and running
performance of Tyrannosaurus rex. Journal of Theoretical
Biology 246:660–680.
Hutchinson, J. R., C. E. Miller, G. Fritsch, and T. Hildebrandt.
2008. The anatomical foundation for multidisciplinary studies
of animal limb function: examples from dinosaur and elephant
limb imaging studies. Pp. 23–38 in R. Frey and H. Endo, eds.
Anatomical imaging techniques: towards a new morphology.
Springer, Berlin.
Hutc hinson, J. R., K. T . Bates, and V. A. Al len. 20 11a.
Tyrannosaurus rex redux: Tyrannosaurus tail portrayals. Ana-
tomical Record 294:756–758.
Hutchinson, J. R., K. T. Bates, J. Molnar, V. Allen, and P. J.
Makovicky. 2011b. A computational and comparative analysis
of limb and body proportions in Tyrannosaurus rex with
implications for locomotion, physiology and growth. PLoS
ONE 6(10): e26037. doi:10.1371/journal.pone.0026037.
Main, R. P., and A. A. Biewener. 2007. Skeletal strain patterns and
growth in the emu hindlimb during ontogeny. Journal of
Experimental Biology 210:2676–2690.
Marx, J. O., C. M. Olsson, and L. Larsson. 2006. Scaling of skeletal
muscle shortening velocity in mammals representing a 100,000-
fold difference in body size. European Journal of Physiology
452:222–230.
McMahon, T. A. 1975. Allometry and biomechanics: limb bones in
adult ungulates. American Naturalist 109:547–563.
Medler,S. 2002. Comparativetrends in shorteningvelocity and force
production in skeletal muscle. American Journal of Regulatory
and Integrative Comparative Physiology 283:R368–R378.
Osmolska, H. 1990. Theropoda. Pp. 148–319 in D. B. Weishampel,
P. Dodson, and H. Osmo
´lska, eds. The Dinosauria. University
of California Press, Berkeley.
Paul, G. S. 1988. Predatory dinosaurs of the world. Simon and
Schuster, New York.
———. 2008. The extreme lifestyles and habits of the gigantic
tyrannosaurid superpredators of the Late Cretaceous of North
America and Asia. Pp. 307–354 in P. Larson and K. Carpenter,
eds. Tyrannosaurus rex: the tyrant king. Indiana University
Press, Bloomington.
Persons, W. S., and P. J. Currie. 2011. The tail of Tyrannosaurus:
reassessing the size and locomotive importance of the M.
caudofemoralis in non-avian theropods. Anatomical Record
294:119–131.
Roberts, T. J. 2001. Muscle force and stress during running in
dogs and wild turkeys. Bulletin of the Museum of Comparative
Zoology 156:283–295.
Roberts, T. J., M. S. Chen, and C. R. Taylor. 1998. Energetics of
bipedal running. II. Limb design and running mechanics.
Journal of Experimental Biology 201:2753–2762.
Rubenson, J., D. B. Heliams, D. G. Lloyd, and P. A. Fournier. 2003.
Gait selection in t he ostrich : mechanical and metabolic
characteristics of walking and running with and without an
506 KARL T. BATES ET AL.
aerial phase. Proceedings of the Royal Society of London B
271:1091–1099.
Sellers, W. I., and P. L. Manning. 2007. Estimating dinosaur
maximum running speeds using evolutionary robotics. Pro-
ceedings of the Royal Society of London B 274:2711–2716.
Sereno, P. C. 1999. The evolution of the dinosaurs. Science
284:2137–2147.
Therrien, F., and D. M. Henderson. 2007. My theropod is bigger
than yours…or not: estimating body size from skull length in
theropods. Journal of Vertebrate Paleontology 27:108–115.
ALLOSAUROIDEA LOCOMOTOR EVOLUTION 507
