Content uploaded by Alana C Sharp
Author content
All content in this area was uploaded by Alana C Sharp on Oct 06, 2016
Content may be subject to copyright.
Comparative Finite Element Analysis of the Cranial
Performance of Four Herbivorous Marsupials
Alana C. Sharp
1,2
*
1
School of Science and Technology, University of New England, Armidale, New South Wales, Australia
2
School of Earth, Atmosphere and Environment, Monash University, Clayton, Victoria, Australia
ABSTRACT Marsupial herbivores exhibit a wide vari-
ety of skull shapes and sizes to exploit different ecologi-
cal niches. Several studies on teeth, dentaries, and jaw
adductor muscles indicate that marsupial herbivores
exhibit different specializations for grazing and brows-
ing. No studies, however, have examined the skulls of
marsupial herbivores to determine the relationship
between stress and strain, and the evolution of skull
shape. The relationship between skull morphology, bio-
mechanical performance, and diet was tested by apply-
ing the finite element method to the skulls of four
marsupial herbivores: the common wombat (Vo m b a t u s
ursinus), koala (Phascolarctos cinereus), swamp wal-
laby (Wallabia bicolor), and red kangaroo (Macropus
rufus). It was hypothesized that grazers, requiring
stronger skulls to process tougher food, would have
higher biomechanical performance than browsers. This
was true when comparing the koala and wallaby
(browsers) to the wombat (a grazer). The cranial model
of the wombat resulted in low stress and high mechani-
cal efficiency in relation to a robust skull capable of
generating high bite forces. However, the kangaroo,
also a grazer, has evolved a very different strategy to
process tough food. The cranium is much more gracile
and has higher stress and lower mechanical efficiency,
but they adopt a different method of processing food by
having a curved tooth row to concentrate force in a
smaller area and molar progression to remove worn
teeth from the tooth row. Therefore, the position of the
bite is crucial for the structural performance of the
kangaroo skull, while it is not for the wombat which
process food along the entire tooth row. In accordance
with previous studies, the results from this study show
the mammalian skull is optimized to resist forces gen-
erated during feeding. However, other factors, includ-
ing the lifestyle of the animal and its environment, also
affect selection for skull morphology to meet multiple
functional demands. J. Morphol. 000:000–000, 2015.
V
C2015 Wiley Periodicals, Inc.
KEY WORDS: marsupial; functional morphology; finite
element analysis; feeding biomechanics; skull
INTRODUCTION
Among the Marsupialia, the Diprotodontia is
the most diverse group and includes many iconic
Australian species, such as kangaroos, koalas, and
wombats. Almost all of the living diprotodonts are
herbivorous, although some incorporate a more
insectivorous or omnivorous diet where available.
Diprotodonts also exhibits a variety of sizes and
morphologies from the tiny 10 g feather-tail glider
(Acrobates pygmaeus) to the largest kangaroo, the
red kangaroo (Macropus rufus) which can weigh
up to 90 kg (Dawson, 1995). This diversity allows
species to exploit many different ecological niches.
Within the Vombatiformes, wombats and koalas
display different morphology adapted for either
grazing (eating primarily the leaves of grasses) or
browsing (feeding primarily on the leaves and
stems of woody plants and herbs). Wombats are
unique among marsupials in having hypsodont
molars for processing a diet composed of tough
vegetation, including tussock grasses (Tyndale-Bis-
coe, 2005; Triggs, 2009). The jaw adductor muscu-
lature is large and well suited to generate a high
bite force. The zygomatic arch is set well away
from the midline and the temporalis muscle is con-
fined to the lateral surface of the cranium giving
the wombat’s skull a broad, flat appearance. The
laterally displaced zygomatic arch relative to the
ascending ramus of the mandible allows the mass-
eter muscles to exert a very strong lateral force to
the jaw, as well as the usual compressive force
(Murray, 1998; Tyndale-Biscoe, 2005). Mastication
is characterized by short powerful chewing strokes
using only the muscles of the working-side
(Crompton et al., 2008).
In contrast, koalas are browsers and almost
exclusively consume leaves from the genus Euca-
lyptus (Moore and Foley, 2000). As a consequence,
the skull and tooth morphology of koalas reflects a
diet of relatively soft vegetation. Koala molars are
characterized as having four tightly interlocking
cusps with curved blades well suited for shearing
Eucalyptus leaves (Lanyon and Sanson, 1986).
The close interlocking pattern is essential for the
*Correspondence to: Alana Sharp; School of Science and Technol-
ogy, University of New England, Armidale, NSW 2351, Australia.
E-mail: asharp6@une.edu.au
Received 28 January 2015; Revised 19 May 2015;
Accepted 26 May 2015.
Published online 00 Month 2015 in
Wiley Online Library (wileyonlinelibrary.com).
DOI 10.1002/jmor.20414
V
C2015 WILEY PERIODICALS, INC.
JOURNAL OF MORPHOLOGY 00:00–00 (2015)
efficient scissor-like action of the cutting edge.
Unlike in wombats and macropods, koalas do not
possess an inflected angle of the mandible and
hence, exhibit a masticatory motor pattern more
similar to an alpaca than a wombat (Crompton
et al., 2010). The incisors and premolars do not
restrict transverse jaw movement in the koala as
they do in macropods (Crompton, 2011).
The teeth of wallabies and kangaroos (Macropo-
didae) reflect a range of diets from facultative
insectivore and granivore through to strictly
browsers or grazers with intermediates between
the latter two (Sanson, 1989). Grazing macropods,
such as Macropus, have modified molars to crop
and break down tough grasses which compose 90%
of their diet (Sanson, 1980, 1989). They have
evolved high-crowned transverse lophs adapted to
shear food as the jaw moves vertically, and to
crush food between the lophs and the well-
developed links as the jaw moves transversely
(Sanson, 1980; Crompton, 2011). All grazing kan-
garoos also exhibit some degree of molar progres-
sion, a reduced premolar and a dorsally convex
curve of the lower tooth row so that the whole
tooth row is never in contact at one time. Molar
progression allows worn teeth to be removed from
the occlusal plane and gradually replaced by
unworn teeth that move anteriorly in the mandi-
ble and dorsally into the occlusal plane. As a tooth
becomes so worn that it is useless, it moves anteri-
orly and ventrally out of the occlusal plane. These
features correlate with a predominant diet of
tough grass (Bensley, 1903; Ride, 1959; Sanson,
1980, 1989).
In contrast, browsing wallabies, such as the
swamp wallaby (Wallabia bicolor), have more sim-
ple molars without strong links between the lophs,
a well-developed premolar, a flat tooth row, and no
molar progression (Sanson, 1980, 1989). These fea-
tures combined, the swamp wallaby has a cheek
tooth row crushing action for processing softer plant
material. Worn molars, therefore, retain some use-
ful function and are not replaced over the life of the
individual. The lower tooth row remains flat, so
that all teeth occlude simultaneously in the adults.
In the present study, the finite element (FE)
method is applied to examine the differences in
biomechanical performance between the skulls of
four herbivorous marsupials: the common wombat
(Vombatus ursinus), the koala (Phascolarctos cin-
ereus), the swamp wallaby (W. bicolor), and the
red kangaroo (M. rufus). These species have differ-
ent dietary preferences and show differences in
skull morphology (Fig. 1). The objective is to gain
a better understanding of how cranial morphology
reflects diet and feeding ecology of marsupial her-
bivores by comparing biomechanical metrics, such
as stress and strain.
Finite element analysis (FEA) is an engineering
technique that reconstructs stress, strain, and
deformation in response to applied loads, taking
into account the material properties and geometry
of the structure (Richmond et al., 2005; Rayfield,
2007; Bright, 2014). The FE method centers on
representing complex geometry by a finite number
of elements with simple geometries, readily ana-
lyzed using mathematics. This allows the mechani-
cal function of complex structures, such as the
skull and the masticatory apparatus, to be studied
in a non-invasive way. The FE method has been
used to investigate cranial morphology and feeding
biomechanics in many taxa, including mammals,
reptilian sauropsids, birds, and dinosaurs (e.g.,
Rayfield, 2004, 2005; Dumont et al., 2005;
McHenry et al., 2006; Jasinoski et al., 2009; Tseng
and Wang, 2010; Attard et al., 2011; Dumont
et al., 2011; Cox et al., 2012; Oldfield et al., 2012;
Soons et al., 2012; Young et al., 2012; Piras et al.,
2013; Figueirido et al., 2014; Gill et al., 2014;).
It is hypothesized that the differences in skull
shape have arisen to better accommodate the
stresses produced by the given processing require-
ments of the animals dietary preference. Different
skull morphologies will display different patterns
of stress and strain during biting and these differ-
ences may relate to the diets, bite location, and
bite force between the four species. Therefore, the
skull morphology of each species will be adapted
for their diet and mode of feeding. Specifically, it
is hypothesized that grazers will be more special-
ized for processing tough vegetation, and this will
correlate with higher performance in one or more
performance metrics—lower stress and higher bite
forces. In contrast, browsers have a greater var-
iance in dietary habits and hence will be well
adapted to multiple feeding modes, but may expe-
rience higher stress under similar biting condi-
tions to grazers.
MATERIAL AND METHODS
Data Acquisition
The crania and mandibles of a swamp wallaby [W. bicolor
(Desmarest (1804)); NMV C10226] and a red kangaroo [M. rufus
(Desmarest (1822)); NMV C23045] were scanned by computed
tomography (CT) using a Siemens Sensation 64 scanner (Sie-
mens Medical Solutions) at St. Vincent’s Public Hospital in Mel-
bourne, Australia (Table 1). CT-scans and magnetic resonance
imaging (MRI) of wet specimens of a common wombat [V. ursi-
nus (Shaw, (1800))] and koala [P. cinereus (Goldfuss, (1817))]
were generated by the University of Melbourne Veterinary Hos-
pital in Werribee (Table 1). These specimens were also used for
dissection, along with two additional wombats, two koalas, and
one eastern gray kangaroo [Macropus giganteus (Shaw, (1790))].
Wet specimens were collected under the Victorian Department
of Sustainability and Environment permit to receive and retain
specimens of wildlife found dead from natural or accidental
causes (Flora and Fauna Permit number 10005574); no animals
were euthanized for this study. CT-scans of a dry skull of a
koala (P. cinereus) were also generated at the University of
Texas (Austin) CT-facility and obtained from the Digital Mor-
phology Library (http://www.digimorph.com) with permission
from Dr. Timothy Rowe, Project Director of Digimorph (http://
www.digimorph.org/specimens/Phascolarctos_cinereus/) .
2 A.C. SHARP
Journal of Morphology
Model Construction
The CT-data were imported into the image visualization and
processing software program Avizo (Visage Imaging), in which
a combination of automated thresholding, the process of select-
ing and isolating areas of interest based on their gray values,
or density, and manual editing were used to separate the cra-
nium from the mandible and generate three-dimensional (3D)-
surface models. The 3D-surface models were constructed from a
mesh of triangular elements, which were smoothed and edited
to improve the quality of the mesh, including testing the aspect
ratio and the dihedral angles of the surface triangles. The
aspect ratios of the triangles were adjusted to below 10 and the
dihedral angles were set at above 10 degrees to ensure a good
quality mesh. The surface meshes were then converted to solid
3D FE-meshes composed of 4-node tetrahedral elements (tet4)
(Table 2). The element size was chosen so that thin bones in
the skull were composed of at least two elements thick to simu-
late bending in the models. The element type and mesh density
where considered sufficient for this type of comparative analy-
sis (Bright and Rayfield, 2011a; Tseng and Flynn, 2015).
Finally, each model was exported as an Abaqus input file
(*.inp) for easy importation to the FEA software package Aba-
qus CAE v6.12 (Simulia). The cranium and mandible were
imported separately for each species, so that the mandible
could be used for muscle force alignment.
Material Properties
Due to a lack of data on the material properties for the bone
in marsupial herbivores, all models were assigned as homoge-
neous and isotropic. Average values of Young’s modulus (E520
GPa) and Poisson’s ratio (m50.3) for mammalian bone were
assigned to all models in Abaqus CAE (Erickson et al., 2002;
Dumont et al., 2005; Tseng and Wang, 2010; Tseng et al., 2011;
Figueirido et al., 2014). This methodology is suitable for the
Fig. 1. Three-dimensional FE models of the skull of V. ursinus (row 1), P. cinereus (row 2), M.
rufus (row 3), and W. bicolor (row 4) all scaled to the same skull length. Skulls are shown in lat-
eral (A), dorsal (B), and anterior (C) views. Scale bars represent 5 cm.
TABLE 1. Details of the CT and MRI(*) scan data for each spec-
imen used in this study. All measurements in mm
Species
Slice
thickness
Interslice
spacing
Voxel
size
Red kangaroo (M. rufus) 0.6 0.3 0.209
Swamp wallaby (W. bicolor) 0.6 0.4 0.199
Koala (P. cinereus) 0.238 0.238 0.105
Common wombat (V. ursinus) 0.5 0.5 0.129
*Common wombat (V. ursinus) 2.5 2.5 0.55
*Koala (P. cinereus) 1.0 1.0 0.379
3CRANIAL PERFORMANCE IN MARSUPIAL HERBIVORES
Journal of Morphology
present study, which compares relative stress and strain val-
ues, and is not concerned with absolute values. It has also been
demonstrated that varying material properties within the
model has less of an impact on large-scale patterns of stress
and strain than variation in model shape (Strait et al., 2005;
Tanner et al., 2008; Walmsley et al., 2013). Therefore, by apply-
ing the same material properties to each model, and modeling
the bone as homogenous and isotropic, it will enable direct com-
parison between models and is not likely to affect confidence in
the results obtained.
Constraints
To prevent rigid body motion, each model was constrained by
a single node at both temporomandibular joints (TMJ). The left
TMJ was fully constrained against displacement in the x- (lat-
eral), y- (vertical), and z-direction (anterior–posterior), and the
node on the right TMJ was constrained in the y- and z-axis to
allow lateral displacement of the skull. A single node was also
constrained at the bite point(s) in the axis perpendicular to the
occlusal plane.
A number of biting scenarios were modeled to simulate bilat-
eral and unilateral molar biting and incisor biting. It has been
observed that wombats, koalas, and macropods all display dif-
ferent modes of feeding (Sanson, 1989; Lentle et al., 2003;
Crompton et al., 2008, 2010; Crompton, 2011), so all possible
molar biting scenarios were modeled for each species: unilateral
biting on each molar, bilateral biting on each pair of molars,
and on the entire tooth row for both unilateral and bilateral
biting. When the incisors were constrained, the models were
loaded bilaterally.
Modeling Muscle Forces
The jaw adductor musculature was modeled as three main
components; the temporalis, masseter, and pterygoid muscles.
Each muscle group was modeled with two to four subdivisions
based on other published studies (Davison and Young, 1990;
Murray, 1998; Tomo et al., 2007; Crompton et al., 2008; War-
burton, 2009) and dissections carried out for this study follow-
ing the methods outlined in Sharp and Trusler (2015). The
muscles included are masseter superficialis, masseter profun-
dus, zygomaticomandibularis,temporalis superficialis, tempora-
lis posterior, temporalis profundus, pterygoideus medialis, and
pterygoideus lateralis.
The maximum force produced by a muscle is proportional to
the total cross-sectional area of all muscle fibers perpendicular
to their longitudinal axes, or the physiological cross-sectional
area (PCSA). Muscle force magnitudes are then calculated by
multiplying muscle cross-sectional area by a constant value of
muscle stress, 0.3 N mm
22
(Weijs and Hillen, 1985; van Spron-
sen et al., 1989; Thomason, 1991; Strait et al., 2005; Wroe
et al., 2005; McHenry et al., 2007; Rayfield, 2007; Cox et al.,
2012). Morphological cross-sectional area (MCSA), the cross-
sectional area perpendicular to the longitudinal axis at the
thickest part for each muscle, can be substituted for PCSA in
muscles where the fibers run parallel to the longitudinal axis.
All muscles for all species were modeled with parallel fibers as
was observed in dissections of fresh wombat, koala, and kanga-
roo specimens.
All muscle forces applied to the models were calculated from
the MSCA of 3D-digitally reconstructed muscles for each spe-
cies. Each muscle was reconstructed by manually segmenting
the muscles in Avizo from CT- and MRI-data. Each muscle was
selected first in the frontal plane and then edited in the sagittal
and horizontal planes for biological accuracy. Muscle attach-
ment sites and orientation were also identified for each muscle
from gross dissections, and this information was used to vali-
date the digital reconstructions. The MCSA for each muscle
was then measured from the 3D-muscle reconstructions in Rhi-
noceros 5.0 (“Rhino”) following a similar method to Quayle
(2011). In summary, a line representing the fiber direction of
each muscle was drawn along the surface of the reconstructed
muscle in the 3D-model from the midpoint of the origin to the
midpoint of the insertion. This line was then used to produce
perpendicular cross-sections through the muscle, and the area
at the thickest point was calculated (Fig. 2). The estimated
muscle force for each muscle for each species is presented in
Table 3.
Muscle forces were applied to the skulls by distributing the
load for each muscle over the entire surface of the muscle ori-
gin. Muscle orientations were determined by creating a vector
between the origin and the corresponding insertion on the man-
dible. In order to simulate unilateral biting and differential
activation of the working- and balancing-side muscles, a per-
centage of maximum activation (muscle force) was applied to
the opposite site to the bite point (balancing-side), while maxi-
mum force was applied to the working-side. Activation of bal-
ancing- and working-side muscles differ for each species, so a
range of values were applied to each model based on data
derived from muscle activation patterns in marsupials (Cromp-
ton et al., 2008, 2010; Crompton, 2011). Seven different simula-
tions were run for each species: one with all balancing-side
muscles at 0%, one with all balancing-side muscles at 10%, and
so on up to 60% of the maximum muscle force applied to the
working-side.
Analyzing Model Performance
The type of stress reported in this study is von Mises (VM)
stress, which is a good predictor of stress in ductile materials.
TABLE 2. Four-node tetrahedral element properties for each FE model
Kangaroo Wallaby Wombat Koala
Element number 4,960,971 2,309,180 1,997,767 1,045,853
Mean element edge length 0.472 0.489 0.755 0.839
Fig. 2. Muscle force was estimated by calculating the maxi-
mum cross-sectional area of each muscle from 3D-reconstructed
muscles of each species. This process is shown on the internal
superficial masseter of the common wombat (V. ursinus)wherea
line representing the vector of muscle force was drawn through
the centre of the muscle and the maximum cross-sectional area
perpendicular to this line was determined. The maximum cross-
sectional area was then multiplied by an estimate of muscle ten-
sion (0.3 N mm
22
) to give muscle force. This process was
repeated for each muscle for all species.
4 A.C. SHARP
Journal of Morphology
The failure of ductile materials, such as bone and many other
biological materials, most often occurs due to deformation. Duc-
tile failure is predicted when the VM-stress reaches the yield
strength of the material, so VM-stress is a good indicator of the
strength of a structure. When comparing the maximum VM-
stress between models, the structure with the lower value is
less likely to fail under a given load. Median VM-stress was
also compared for each model. This removes the influence of
modeling artifacts and outliers due to constraints on single
nodes, and gives an idea of the spread of stress over the entire
model. Stress distributions plotted as contour maps were
extracted from Abaqus. The distribution of stress was also ana-
lyzed by sampling stress values in different areas of the cra-
nium. For analysis of variation over the dorsal cranium, 10
equidistant landmarks were sampled along the mid-sagittal
axis from the tip of the nasals to the occipital crest. The maxi-
mum stress was also calculated for the working-side and
balancing-side zygomatic arch for each species.
Strain energy (U) is a performance metric that quantifies
energy efficiency, or work efficiency. Analyses of stresses or
deformations alone provide limited insight into the trade-offs
between stiffness and internal load distributions. Strain energy
is the energy stored in the structure due to the work done by
the externally applied loads. The strain energy of a structure
equals the area under the stress-strain curve and relates to the
stiffness of a structure. A stiff structure will more easily trans-
fer energy from the muscle force to the bite, whereas a flexible,
compliant structure will store more energy and work will be
expended to deform the structure (Dumont et al., 2009). Assum-
ing that the function of the jaw system is to transmit forces
more efficiently, without causing failure, this implies that the
system should minimize deformation. Thus, stiffer models will
be more efficient than compliant models.
Finally, the mechanical efficiency of each model during biting
was compared by calculating the ratio of the bite reaction force
to the applied muscle force (Dumont et al., 2009). This measure
provides a scale independent estimate of the efficiency of the
jaw lever system that is defined by the fulcrum (TMJ), the
effort (muscle force), and the resistance (bite point) as a third-
class lever. It tells us the efficiency at which the muscle force is
translated to bite force.
Scaling
When comparing performance metrics such as stress and
strain, the size of the structure must be taken into account.
Results such as strain energy and maximum VM-stress will
depend on the size of the structure. For example, a smaller
structure will be stiffer than a larger one, whereas a larger
structure will be stronger. To remove the effects of size and
compare the performance of the models based on their shape
alone, the models were scaled to the same surface area or vol-
ume. All surface area and volume data was calculated from the
models in Avizo.
To compare the strength (VM-stress) between models, the mod-
elswerescaledtothesameratioofmuscleforcetosurfacearea.
We can compare the stress results of model Aand Bby scaling
the results for model Bto match the force (F):surface area (SA)
ratio of model Afollowing Eq. (1) (Dumont et al., 2009):
ðstressÞB0¼SAB
SAA
FA
FB
stressðÞ
B(1)
When comparing strain energy, which is the amount of
energy stored per unit volume, the models were scaled to the
same force:volume ratio. Therefore, to compare strain energy
(U) of models of different volume (V), the results from model B
can be scaled to the same force:volume ratio to model Aaccord-
ing to Eq. (2) (Dumont et al., 2009; Strait et al., 2010):
UB0¼VB
VA
1=3FA
FB
2
UB(2)
Validation
The only way to validate FE models is to compare the results
to in vivo or in vitro data of bone strain (Rayfield, 2007; Bright,
2014). Studies of in vivo forces and strains generated during
biting are often logistically challenging to accomplish, as they
require specialty equipment. To date, there are no data on bone
strain in the crania of the marsupial herbivores modeled in this
study. However, the general approaches applied here have been
validated against experimental data from other taxa (Metzger
et al., 2005; Kupczik et al., 2007; Bright and Gr€
oning, 2011;
Bright and Rayfield, 2011b; Porro et al., 2013).
In the absence of validated data for material properties and
forces, a sensitivity analysis was carried out to determine the
effects of modeling different bite positions and muscle activa-
tion patterns. Previous sensitivity studies have shown that var-
iations in muscle force and bite position has the greatest effect
on FEA results. In these studies, the number of muscles, and
total force generated by muscles, is more important than mus-
cle activation patterns, or using multiple material properties
TABLE 3. Muscle forces (N) applied for each model and the percentage that each muscle contributes to the total muscle force.
Each muscle force was estimated based on the cross-sectional area of the reconstructed muscles
Muscle Kangaroo Wallaby Wombat Koala
m.Tpr 70 10% 31 8% 160 13% 144 14%
m.Tpo 88 12% 72 19% 83 7% 160 16%
m.Tl 40 6% 20 5% 68 6% 46 5%
Temporalis total 198 28% 123 33% 311 26% 350 35%
m.ZMM 122 17% 51 14% 136 11% 103 10%
m.Mp 97 14% 55 15% 166 14% 115 11%
m.Mi 70 10% 27 7% 173 14% 153 15%
m.Ms 32 5% 20 5% 115 10% 112 11%
Masseter total 321 45% 153 41% 590 49% 484 48%
m.PTm 172 24% 80 21% 242 20% 142 14%
m.PTl 20 3% 21 6% 58 5% 28 3%
Pterygoid total 192 27% 101 27% 300 25% 170 17%
Total 711 100% 377 100% 1,201 100% 1,003 100%
Abbreviations: m.Tpr, deep temporalis; m.Tpo, posterior temporalis; m.Tl, lateral temporalis; m.ZMM, zygomaticomandibularis;
m.Mp, deep masseter; m.Mi, intermediate masseter; m.Ms, superficial masseter; m.PTm, medial pterygoid; m.PTl, lateral
pterygoid.
5CRANIAL PERFORMANCE IN MARSUPIAL HERBIVORES
Journal of Morphology
when comparing broad patterns of deformation and stress
(Metzger et al., 2005; Ross et al., 2005; Strait et al., 2005; Fit-
ton et al., 2012; Walmsley et al., 2013). Hence, muscle forces
were modeled as accurately as possible by including multiple
muscle groups and 3D-muscle vectors directed from the origin
to the insertion for each muscle. For the present study, a com-
parative approach has been applied, which compares relative
stress and strain values, and is not intended to predict absolute
values (Dumont et al., 2005; McHenry et al., 2006; Rayfield,
2007; Wroe, 2008; Attard et al., 2011). Therefore, modeling com-
plex material properties of trabecular bone, cortical bone, and
tooth enamel, cranial sutures, or the periodontal ligament was
not considered necessary for the current study, and would likely
introduce more complexity and assumptions that cannot be
validated with in vivo or ex vivo data at this time.
RESULTS
Bilateral Biting
The predicted distribution of VM-stress is differ-
ent for all species for each biting location (Fig. 3).
In all models, the rostrum is most highly stressed
during incisor biting, and the zygomatic arch is
the most highly stressed region in molar biting.
However, in the common wombat and koala, which
have shorter rostrums compared with macropods,
the rostrum is also slightly stressed during biting
at the premolar. For all bite locations, the koala
also has four clear hot spots of stress on the zygo-
matic arch: on the dorsal and ventral surface mid-
way along its length; on the masseteric process at
the attachment for the superficial masseter; and,
at the zygomatic root of the squamosal, superior to
the TMJ. In contrast, the red kangaroo, swamp
wallaby, and common wombat models only experi-
ence two hot spots: kangaroo and wallaby both at
the zygomatic suture and the masseteric process;
and, wombat at the anterosuperior site of the
zygomatic suture and the excavated maxillojugal
region located under the orbit. The koala, wallaby,
and kangaroo models also experience higher stress
at the anterior ventral boarder of the orbit, which
is not present in the wombat.
Fig. 3. Predicted distribution of VM stresses across the cranial models of the common wombat (V. ursinus), koala (P. cinereus), red
kangaroo (M. rufus), and swamp wallaby (W. bicolor) during bilateral biting. Arrows indicate the bite location for each row and the
bottom row shows bilateral biting on all molars simultaneously. Warm colors indicate areas of high VM stress and cool colors indicate
low stress. Gray areas indicate VM stress that exceeds the specified maximum of 10 MPa.
6 A.C. SHARP
Journal of Morphology
Figure 4 presents quantitative performance met-
rics that complement the stress contour plots for
bilateral biting at different bite points. The kanga-
roo model registered the highest maximum VM-
stress for all cheek tooth locations, indicating that
the cranial structure is more susceptible to frac-
ture under high forces. The wallaby model only
exceeded the kangaroo for maximum VM-stress
when biting at the incisors. The kangaroo also reg-
istered a distinct increase in maximum stress
when biting at the fourth molar; which biting at
M1 maximum stress was lowest and biting at M4
was considerably higher. This increase is slightly
less distinct in the wallaby and is not evident in
the wombat or koala models that maintain a rela-
tively flat distribution of stress along the entire
tooth row. The koala model experiences the lowest
stress at the incisors, premolar and first molar,
indicating that for these bite locations the koala
model is more resistant to fracture. The wombat
model also experiences relatively low maximum
VM-stress, especially at the second, third, and
fourth molars.
When comparing median VM-stress, which elim-
inates the outliers created by single node con-
strains and offers an estimate of the distribution
of stress over the entire skull, the wombat model
performs better than all other models; it is least
stressed and, therefore, more resistant to fracture
overall (Fig. 4). Low median VM-stress may also
indicate that the distribution of stress over the
skull is more even in the wombat model. The high-
est median VM-stress was recorded in the kanga-
roo model, and intermediate stress was recorded
for the wallaby and koala models.
The red kangaroo also performed poorly in
terms of the mechanical efficiency with which
muscle force was transmitted to bite force, or the
efficiency of the jaw as a third-class lever (Fig. 4).
For all models, the mechanical efficiency increased
along the tooth row as the bite point (the resist-
ance) approached the TMJ (the fulcrum). The
wombat model is the most mechanically efficient
when biting at the molars (except M4 where the
wallaby is most efficient) and the koala is the
most mechanically efficient when biting at the
incisors. The kangaroo model is the least mechani-
cally efficient for all bite locations.
When comparing the energy efficiency of the
models, the koala model has the lowest internal
strain energy and is, therefore, stiffer, spending
less energy on deformation (Fig. 4). The common
wombat has higher strain energy for all bite
Fig. 4. Biting performance during bilateral biting at each tooth in the red kangaroo (M. rufus),
swamp wallaby (W. bicolor), common wombat (V. ursinus), and koala (P. cinereus) cranial models.
Abbreviations: I, incisor; PM, premolar; M1, first molar; M2, second molar; M3, third molar; M4,
fourth molar.
7CRANIAL PERFORMANCE IN MARSUPIAL HERBIVORES
Journal of Morphology
locations except M4, indicating it is less stiff and
the least energy efficient.
Unilateral Biting
Figure 5 displays dorsal view plots of stress dis-
tribution for each model while biting at the left
second molar and the balancing-side muscle force
is half that of the working-side. The pattern of
stress when viewed in lateral view on the
working-side is similar to that for bilateral biting
in Figure 3. The balancing-side zygomatic arch,
however, experiences less stress during unilateral
biting for all models (Table 4). The quantitative
results for stress distribution along the dorsal sur-
face are also presented in Figure 5. The stress dis-
tribution changes considerably for each species but
is generally highest in the middle of the cranium
where it is narrowest. Overall, the kangaroo model
experiences higher stress at most locations along
the dorsal surface of the skull.
Table 4 presents quantitative performance met-
rics for unilateral biting at the left second molar
when the balancing-side muscle force is 50% of the
Fig. 5. Predicted distribution of VM stresses across the cranial models of the (A) common wombat (V. ursinus), (B)koala(P. ciner-
eus), (C) red kangaroo (M. rufus), and (D)swampwallaby(W. bicolor) in dorsal view during unilateral biting at the second molar,
balancing-side at 50% activation. Warm colors indicate areas of high VM-stress and cool colors indicate low stress. Gray areas indi-
cate VM-stress that exceeds the specified maximum of 10 MPa. The graph (E)showsVM-stress along the mid-sagittal plane for each
species. The positions of the landmarks are shown on the wombat skull on the right.
8 A.C. SHARP
Journal of Morphology
working side. For this biting scenario, the wombat
performed best in terms of mechanical efficiency
and has the lowest VM stress between the models.
This would indicate that the cranial structure is
very efficient at transmitting muscle force to bite
force and is more resistant to failure under high
loads. In terms of energy efficiency, however, the
wombat has the highest strain energy and, there-
fore, spends more energy in deformation. The red
kangaroo model has the lowest mechanical effi-
ciency and experiences the highest stresses over
the skull, meaning it is more likely to fail under
high loads. However, it has low internal strain
energy so it is maximizing energy efficiency by
being stiffer. The koala model has the lowest
strain energy, indicating it is the stiffest model,
and has intermediate values for the other perform-
ance metrics.
As a part of the sensitivity study, the balancing-
side muscle activation was varied during unilat-
eral biting to identify how this affects the mechan-
ical response in each model. Since each species
studied here exhibits different muscle activation
while chewing (Crompton, 2011), the balancing-
side muscle force was adjusted to test a range of
scenarios (from 0 to 60% activation) to allow com-
parisons between species. The level of muscle acti-
vation on the balancing-side did not have a great
effect on the overall trends seen in stress, strain,
or mechanical efficiency (Fig. 6). When the
balancing-side muscle activation was increased
from 0 to 60%, median VM-stress, maximum VM-
stress, and strain energy increased in each model.
The only exception was the wombat model, in
which maximum VM-stress decreased until an
activation of 40% and then increased. Mechanical
efficiency remained relatively constant for each
model. In most cases, this means that varying the
activation of the balancing-side muscles does not
change the trends or conclusions drawn from this
comparative study. The only exception is maxi-
mum VM-stress in which the wombat model
decreased, while the other models increased. At
lower values of balancing-side muscle activation,
the wombat model has slightly higher VM-stress
compared with the koala model. If we were inter-
ested in absolute values for validation with in vivo
data, the activation would need to be considered to
provide specific conditions for each species. As
each species displays different masticatory motor
patterns while chewing, it might be important to
simulate the activation of each species to obtain
absolute values that match those seen in reality.
DISCUSSION
The results indicate that all four models behave
differently under biomechanical loads, reflecting
variation in skull morphology which is potentially
correlated with diet. When simulating unilateral
biting, the common wombat (V. ursinus) model
experienced relatively low maximum and median
VM stress compared with the other species mod-
eled (Table 4). The wombat model also had the
highest mechanical efficiency meaning the cra-
nium is not only strong, but also very efficient at
transmitting muscle force to bite force. This indi-
cates that the wombat skull is optimized to resist
failure from high bite forces, and, efficiently trans-
mits the force from its large masticatory muscles
to the teeth. A wombat’s diet is composed of tough
vegetation, including tussock grasses, and many
adaptations have evolved to process such abrasive
food. The broad flat skull, short rostrum, and large
masseter muscles all provide a powerful compres-
sive bite along the cheek tooth row. Hypsodont
molars are a unique case in marsupials and
require constant abrasion to maintain a functional
tooth and cutting edge, and hence, this requires a
powerful grinding system. Together, these morpho-
logical features provide strong, robust skulls able
to resist the high biomechanical demands imposed
by feeding on tough vegetation.
Red kangaroos (M. rufus) also eat tough, abra-
sive vegetation but have evolved a very different
method of processing this food. In contrast to
wombats, grazing kangaroos have long rostra, nar-
row skulls, and have a curved tooth row with
molar progression where new molars erupt from
the back of the tooth row and move forward to
replace worn teeth at the front. These morphologi-
cal differences also manifest as biomechanical
TABLE 4. Performance metrics for unilateral biting at the left second molar with the balancing-side muscle force at 50% of the
working side
Kangaroo Wombat Koala Wallaby
Mechanical efficiency 0.281 0.364 0.351 0.356
Max VM stress 986 296 359 475
Adjusted max VM stress 3.6 2.21 2.75 2.61
Median VM stress 0.747 0.315 0.515 0.458
Max stress at zygomatic arch (left/right) 17.7/7.06 14.14/6.20 32.49/12.96 16.44/8.82
Strain energy (lJ) 14.4 18.3 13.6 16.6
“Adjusted Max VM Stress” is the maximum stress with the top 5% of values removed to account of modeling artefacts from single
node constraints. Values in bold indicate higher performance. All stress values in megapascals; VM, von Mises; lJ, microjouls.
9CRANIAL PERFORMANCE IN MARSUPIAL HERBIVORES
Journal of Morphology
differences: high stress and low mechanical effi-
ciency in the kangaroo compared with the wombat.
During unilateral biting, the kangaroo model expe-
rienced the highest maximum and median VM-
stress and the lowest mechanical efficiency, indi-
cating that the cranium is relatively weak and
inefficient at transmitting muscle force to bite
force. A curved tooth row and molar progression
have evolved to enhance the ability of kangaroos
to effectively process the tough, abrasive vegeta-
tion without over stressing the skull. The curved
tooth row allows pressure, or force, to be concen-
trated between the first and second molar to grind
vegetation (Sanson, 1980, 1989), and worn teeth
are removed from the tooth row when they are no
longer functional. The position of the bite is cru-
cial for the structural performance of the skull:
maximum stress, and hence the likelihood of fail-
ure is lowest when biting at M1.
Different tooth row morphologies observed
between the wombat and kangaroo (flat vs. curved,
respectively) also result in different patterns of
stress with changes in bite position. The maximum
VM-stress recorded for the wombat remains rela-
tively consistent as the bite point moves from the
premolar to the fourth molar; the lowest stress
being recorded at M2 and M3. In contrast, the max-
imum stress for the kangaroo peaks at the premo-
lar and fourth molar and is lowest at the incisors
and first molar. Premolar and fourth molar contact
is not a major or consistent part of chewing in
adult kangaroos, and therefore, greater stresses are
experienced when forces act at these points. When
biting at M1, as they do in reality, the kangaroo
skull experiences less stress and is, therefore, less
likely to fail. This is likely connected to the condi-
tion in which they chew, and as such the skull is
optimized for chewing at this position. Conversely,
all molars have a significant role for wombats
which process food along the entire tooth row,
exerting an effect on skull performance and shape
by applying forces at these points.
The difference between the wombat and kanga-
roo reflects their independent lines of evolution
and multiple factors that drive selection of skull
morphology. Many studies have used stress as a
predictor of diet in extinct and extant animals,
concluding that low stress indicates an adaptation
for stronger skulls, given that lower stress means
it is less likely to fail, and therefore, a diet high in
Fig. 6. VM stress, strain energy, and mechanical efficiency during unilateral biting at the sec-
ond molar with varying levels of activation (0–60%) of the balancing-side muscles for each species
studied.
10 A.C. SHARP
Journal of Morphology
hard foods is likely (Dumont et al., 2005; Tanner
et al., 2008; Wroe, 2008; Attard et al., 2011; Young
et al., 2012; Attard et al., 2014). It is assumed that
selection for high structural strength is optimal
and a driver for evolution within species that con-
sume hard foods. Similarly, increasing mechanical
efficiency is viewed as optimal to transmit muscle
force to bite force. However, the kangaroo model
had both higher stress and lower mechanical effi-
ciency, despite the high biomechanical demands of
consuming tough food. In accordance with previous
studies, these results show the mammalian skull
may not be optimized solely to resist forces gener-
ated during feeding ( Hylander and Johnson, 1997;
Dumont et al., 2005, 2011). Non-biomechanical fac-
tors or ecological factors, including the lifestyle of
the animal and its environment (e.g., latitude) have
a role in selection for skull morphology to meet
multiple functional demands (Milne and O’Higgins,
2002; Hadley et al., 2009). Phylogenetic, ecological,
locomotor, and sensory constraints on the evolution
of the kangaroo skull may restrict its size and mor-
phology. Analyzing the lower jaws may have a
stronger link to diet as they are not as affected by
other constraints or functional influences such as
housing neural and sensory organs.
Another factor that may influence skull shape in
marsupials is digestive tract morphology; wombats
and koalas have hindgut fermentation, while mac-
ropods have foregut fermentation (Hume, 1984;
Stevens and Hume, 1998). In ungulates, Fletcher
et al. (2010) observed that hindgut feeders have
jaws that show significantly lower levels of stress
than foregut feeders (e.g., they are more “robust”)
and this may be due to their relatively greater lev-
els of food ingestion and mastication. The hindgut
digestive system in wombats enables them to uti-
lize a diet high in fiber while having small home
ranges, low food intake, and longer retention times
(Barboza and Hume, 1992; Barboza, 1993). How-
ever, the breakdown of food by the teeth is particu-
larly important to release cell contents and
maximize the energy available because once the
food has passed into the digestive tract, it cannot
return for further mechanical processing by the
teeth. Therefore, wombats need to chew their food
considerably more before it is swallowed. This may
explain why the skull of wombats exhibits less
stress (e.g., higher performance) than grazing kan-
garoos. Grazing kangaroos like the red kangaroo
can also utilize a diet high in fiber due to their
complex stomach morphology and foregut fermen-
tation. As a consequence of this foregut fermenta-
tion system, kangaroos, like ruminants, can
regurgitate and chew their food multiple times
with the food becoming softer with each cycle,
allowing kangaroos to process tough vegetation
without high bite forces.
In contrast to wombats and kangaroos, the
swamp wallaby (W. bicolor) and koala (P. cinereus)
are both browsers consuming softer vegetation.
The wallaby has a varied diet including leaves
from shrubs and bushes, fungi and some grass
(Edwards and Ealey, 1975; Sanson, 1980). This
broad diet has manifested morphologically as sim-
ple bilophodont molars, a flat tooth row, and no
molar progression. During unilateral biting, the
stress and mechanical efficiency of the wallaby
model are intermediate to the wombat and kanga-
roo models. With a generalist diet, they have
maintained generalist skull morphology, because
high biomechanical performance, high bite force,
and strong skulls are not required for processing
softer food.
The higher performance of the wallaby skull
compared with the kangaroo (e.g., lower stress
and higher mechanical efficiency) could be
explained by the length of the rostrum. In a recent
study using geometric morphometric of cranial
shape, it was shown that macropods follow the
“rule” that among closely related species, larger
mammals tend to have a longer face and a propor-
tionally smaller braincase (Cardini et al., 2015).
Rostrum length and shape has also been linked to
latitude in various species of macropods (Milne
and O’Higgins, 2002; Hadley et al., 2009). The rel-
atively longer rostrum in the red kangaroo
explains both the higher stress and lower mechan-
ical efficiency compared with the swamp wallaby.
In addition, the swamp wallaby can handle stress
at different bite positions, whereas the red kanga-
roo, being a more specialized species with a nar-
rower diet is adapted to function best at specific
bite positions.
Koalas almost exclusively consume leaves from
the genus Eucalyptus (Moore and Foley, 2000), a
poor-quality food source high in toxins. Numerous
adaptations allow the koala to cope with such a
diet, including low energy requirements, a com-
plex hindgut, and the ability to regurgitate and
remasticate preingested leaf material (Moore and
Foley, 2000; Logan, 2003). Being a browser also
means they do not consume abrasive silicates or
grit. The koala model experiences intermediate
median VM-stress during bilateral and unilateral
biting, indicating that the skull is relatively weak
compared with the wombat model, and strong
compared with the kangaroo model. During bilat-
eral biting, maximum VM-stress was lowest at the
incisors, premolars, and first molar. This may indi-
cate that koalas have a relatively strong skull
when biting at these teeth and these teeth may be
the proffered location for chewing in reality.
The koala model has the lowest strain energy,
indicating that the skull is relatively stiff com-
pared with the other skull models examined here.
This increases work efficiency during mastication
by spending less energy on deformation. Since the
models have been scaled to remove the effect of
size, deformation is due to skull shape alone. The
11CRANIAL PERFORMANCE IN MARSUPIAL HERBIVORES
Journal of Morphology
skull shape of the koala is very high compared
with macropods and narrow compared with the
wombat and this may explain the lower strain
energy. It was expected that the wombat model
would have the lowest strain energy to increase
functional efficiency. Surprisingly, the wombat
model had the highest strain energy for almost all
biting scenarios, indicating the skull is more com-
pliant than the other skull models. Despite under-
going more deformation, the skull is the strongest
(low-VM stress) and is, therefore, least likely to
fail under high bite forces. Therefore, the energy
spent on deformation may be inconsequential. The
temporalis fascia and postorbital ligament were
not modeling in this study and may prevent some
deformation of the zygomatic arch as it is pulled
down by the muscle. Therefore, in future studies it
might be interesting to model the effect of these
ligamentous structures.
There are some limitations to be addressed in
this study. This study provides useful, quantitative
comparisons between four species of herbivorous
marsupial during simulated biting, but the models
used here, like any model, are constrained by the
simplifications, assumptions and data used to con-
struct them. Perhaps most critically, the approach
used here does not incorporate realistic material
properties for bone, enamel, sutures or fascia, and
ligaments that can affect deformation. This simpli-
fication, however, was considered necessary
because of the lack of material properties data for
marsupials. The assumption was made that this
would not affect the conclusions, as the goal of the
study was to make broad comparisons of cranial
biomechanics, and it was not considered necessary
to model the material properties in more detail. It
has also been shown in previous work that using
homogeneous or inhomogeneous material proper-
ties has little effect on stress patterns (Strait
et al., 2005; Walmsley et al., 2013; Gil et al.,
2015).
Future work might improve on this study by
increasing the sample size of species, in particular
including more species of macropods to compare a
broader range of diets and ecological niches. Simi-
larly, the other surviving genera of wombat, Lasio-
rhinus, could be included to examine the role of
habitat type and morphology between wombat spe-
cies. It is also a limitation of this study that the
jaw was not modeled, as this structure may corre-
spond more closely to diet as it is not limited by
other constraints or functional influences such as
housing neural and sensory organs. However, the
main aim of this study was to examine the
respond of the cranium to biomechanical demands
to elucidate the connection between forces during
feeding and other factors that might influence
skull morphology. In agreement with previous
studies, the results of this study show the mam-
malian skull is optimized to resist forces generated
during feeding, but other factors, including phylog-
eny and ecology, have a role in selection for skull
morphology to meet multiple functional demands.
In summary, the results derived from this study
suggest that the biomechanical performance of
marsupial herbivore skulls is reflective of their
morphology and has links to masticatory demands,
including bite location and diet. The results high-
light the relative importance of biomechanical and
non-biomechanical factors in constraining skull
morphology to meet multiple functional demands.
Despite the fact that common wombats and red
kangaroos have a similar diet of tough, abrasive
grasses, their skull morphology is considerably dif-
ferent due to different biomechanical, phyloge-
netic, and ecological factors that drive selection.
Tooth and jaw morphology in the kangaroo has
adapted to concentrate force in a smaller area,
and remove worn molars from the tooth row,
instead of having strong skulls with large muscles
and high bite forces as seen in wombats. This vari-
ation in skull morphology to meet the demands of
the same diet suggests a complex interplay of mul-
tiple selective pressures in controlling skull shape.
ACKNOWLEDGMENTS
I would like to thank P. Vickers-Rich and T.
Rich for supervision during this project; E.
Dumont, I. Grosse, and D. Pulaski for assistance
during the Finite Element Modeling in Biology
workshop at the University of Massachusetts,
Amherst; R. Close for providing instruction and
advise with Avizo and Abaqus; E. Rayfield and P.
Cox for comments on an earlier adaptation of this
manuscript; P. Trusler, A. Evans, and L. Murphy
for helping with dissections and many discussions
on teeth and skulls; S. O’Hara from St. Vincent’s
Hospital for providing the CT-scan data; K. Rob-
erts for access to the Museum Victoria collections;
and two anonymous reviewers for their helpful
feedback which improved this manuscript.
LITERATURE CITED
Attard MRG, Chamoli U, Ferrara TL, Rogers TL, Wroe S. 2011.
Skull mechanics and implications for feeding behaviour in a
large marsupial carnivore guild: The thylacine, Tasmanian
devil and spotted-tailed quoll. J Zool 285:292–300.
Attard MRG, Parr WCH, Wilson LAB, Archer M, Hand SJ,
Rogers TL, Wroe S. 2014. Virtual reconstruction and prey
size preference in the Mid Cenozoic thylacinid, Nimbacinus
dicksoni (Thylacinidae, Marsupialia). PLoS One 9:e93088.
Barboza PS. 1993. Digestive strategies of the wombats—feed-
intake, fiber digestion, and digesta passage in 2 grazing mar-
supials with hindgut fermentation. Physiol Zool 66:983–999.
Barboza PS, Hume ID. 1992. Hindgut fermentation in the wom-
bats: Two marsupial grazers. J Comp Physiol B 162:561–566.
Bensley BA. 1903. On the evolution of the Australian Marsu-
pialia; with remarks on the relationships of the marsupials in
general. Trans Linn Soc Lond 2nd Ser: Zool 9:83–217.
Bright JA. 2014. A review of paleontological finite element mod-
els and their validity. J Paleontol 88:760–769.
12 A.C. SHARP
Journal of Morphology
Bright JA, Gr€
oning F. 2011. Strain accommodation in the zygo-
matic arch of the pig: A validation study using digital speckle
pattern interferometry and finite element analysis. J Morphol
272:1388–1398.
Bright JA, Rayfield EJ. 2011a. The response of cranial biome-
chanical finite element models to variations in mesh density.
Anat Rec 294:610–620.
Bright JA, Rayfield EJ. 2011b. Sensitivity and ex vivo valida-
tion of finite element models of the domestic pig cranium.
J Anat 219:456–471.
Cardini A, Polly D, Dawson R, Milne N. 2015. Why the long
face? Kangaroos and Wallabies follow the same ‘Rule’ of cra-
nial evolutionary allometry (CREA) as placentals. Evol Biol
42:169–176.
Cox PG, Rayfield EJ, Fagan MJ, Herrel A, Pataky TC, Jeffery
N. 2012. Functional evolution of the feeding system in
rodents. Plos One 7:e36299.
Crompton AW. 2011. Masticatory motor programs in Australian
herbivorous mammals: Diprotodontia. Integr Comp Biol 51:
271–281.
Crompton AW, Lieberman DE, Owerkowicz T, Baudinette RV,
Skinner J. 2008. Moter control of masticatory movements in
the southern hairy-nosed wombat (Lasiorhinus latifrons). In:
Vinyard CJ, Ravosa MJ, Wall CE, editors. Primate craniofa-
cial function and biology. New York: Springer.
Crompton AW, Owerkowicz T, Skinner J. 2010. Masticatory
motor pattern in the koala (Phascolarctos cinereus): A com-
parison of jaw movements in marsupial and placental herbi-
vores. J Exp Zool 313A:564–578.
Davison CV, Young WG. 1990. The muscles of mastication of
Phascolarctos cinereus (Phascolarctidae: Marsupialia). Aust J
Zool 38:227–240.
Dawson T. 1995. Kangaroos: Biology of the Largest Marsupials.
Ithaca: Comstock Publishing Associates. 62 p.
Dumont ER, Piccirillo J, Grosse LR. 2005. Finite-element anal-
ysis of biting behavior and bone stress in the facial skeletons
of bats. Anat Rec A Discov Mol Cell Evol Biol 283a:319–330.
Dumont ER, Grosse IR, Slater GJ. 2009. Requirements for com-
paring the performance of finite element models of biological
structures. J Theor Biol 256:96–103.
Dumont ER, Davis JL, Grosse IR, Burrows AM. 2011. Finite
element analysis of performance in the skulls of marmosets
and tamarins. J Anat 218:151–162.
Edwards GP, Ealey EHM. 1975. Aspects of the ecology of the
swamp wallaby Wallabia bicolor, (Marsupialia: Macropodi-
dae). Aust Mammal 1:307–318.
Erickson GM, Catanese J, Keaveny TM. 2002. Evolution of the
biomechanical material properties of the femur. Anat Rec
268:115–124.
Figueirido B, Tseng ZJ, Serrano-Alarc
on FJ, Mart
ın-Serra A,
Pastor JF. 2014. Three-dimensional computer simulations of
feeding behaviour in red and giant pandas relate skull biome-
chanics with dietary niche partitioning. Biol Lett 10:20140196.
Fitton LC, Shi JF, Fagan MJ, O’Higgins P. 2012. Masticatory
loadings and cranial deformation in Macaca fascicularis:A
finite element analysis sensitivity study. J Anat 221:55–68.
Fletcher TM, Janis CM, Rayfield EJ. 2010. Finite element anal-
ysis of ungulate jaws: Can mode of digestive physiology be
determined? Palaeontol Electron 13:21A.
Gil L, Marc
e-Nogu
eJ,S
anchez M. 2015. Insights into the con-
troversy over materials data for the comparison of biome-
chanical performance in vertebrates. Palaeontol Electron
18.1.10A:1–24.
Gill PG, Purnell MA, Crumpton N, Brown KR, Gostling NJ,
Stampanoni M, Rayfield EJ. 2014. Dietary specializations
and diversity in feeding ecology of the earliest stem mam-
mals. Nature 512:303–305.
Hadley C, Milne N, Schmitt LH. 2009. A three-dimensional geo-
metric morphometric analysis of variation in cranial size and
shape in tammar wallaby (Macropus eugenii) populations.
Aust J Zool 57:337–345.
Hume I. 1984. Principal features of digestion in kangaroos.
Proc Nutr Soc Aust 984:77.
Hylander WL, Johnson KR. 1997. In vivo bone strain patterns
in the zygomatic arch of macaques and the significance of
these patterns for functional interpretations of craniofacial
form. Am J Phys Anthropol 102:203–232.
Jasinoski SC, Rayfield EJ, Chinsamy A. 2009. Comparative
feeding biomechanics of Lystrosaurus and the generalized
dicynodont Oudenodon. Anat Rec 292:862–874.
Kupczik K, Dobson CA, Fagan MJ, Crompton RH, Oxnard CE,
O’Higgins P. 2007. Assessing mechanical function of the zygo-
matic region in macaques: Validation and sensitivity testing
of finite element models. J Anat 210:41–53.
Lanyon JM, Sanson GD. 1986. Koala (Phascolarctos cinereus)
dentition and nutrition. I. Morphology and occlusion of cheek
teeth. J Zool 209:155–168.
Lentle RG, Hume ID, Stafford KJ, Kennedy M, Haslett S,
Springett BP. 2003. Comparison of tooth morphology and
wear patterns in four species of wallabies. Aust J Zool 51:61–
79.
Logan M. 2003. Effect of tooth wear on the rumination-like
behavior, or merycism, of free-ranging koalas (Phascolarctos
cinereus). J Mammal 84:897–902.
McHenry CR, Clausen PD, Daniel WJ, Meers MB, Pendharkar
A. 2006. Biomechanics of the rostrum in crocodilians: A com-
parative analysis using finite-element modeling. Anat Rec A
Discov Mol Cell Evol Biol 288:827–849.
McHenry CR, Wroe S, Clausen PD, Moreno K, Cunningham E.
2007. Supermodeled sabercat, predatory behavior in Smilo-
don fatalis revealed by high-resolution 3D computer simula-
tion. Proc Natl Acad Sci USA 104:16010–16015.
Metzger KA, Daniel WJT, Ross CF. 2005. Comparison of beam
theory and finite element analysis with in vivo bone strain
data from the alligator cranium. Anat Rec A Discov Mol Cell
Evol Biol 283A:331–348.
Milne N, O’Higgins P. 2002. Inter-specific variation in Macro-
pus crania: Form, function and phylogeny. J Zool 256(GEO-
BASE):523–535.
Moore BD, Foley WJ. 2000. A review of feeding and diet selec-
tion in koalas (Phascolarctos Cinereus). Aust J Zool 48:317–
333.
Murray P 1998. Palaeontology and palaeobiology of wombats.
In: Wells RT, Pridmore PA, editors. Wombats. Chipping Nor-
ton, Sydney: Survey Beatty. pp 1–9.
Oldfield CC, McHenry CR, Clausen PD, Chamoli U, Parr WCH,
Stynder DD, Wroe S. 2012. Finite element analysis of ursid
cranial mechanics and the prediction of feeding behaviour in
the extinct giant Agriotherium africanum. J Zool 286:163–170.
Piras P, Maiorino L, Teresi L, Meloro C, Lucci F, Kotsakis T,
Raia P. 2013. Bite of the cats: Relationships between func-
tional integration and mechanical performance as revealed by
mandible geometry. Syst Biol 62:878–900.
Porro LB, Metzger KA, Iriarte-Diaz J, Ross CF. 2013. In vivo
bone strain and finite element modeling of the mandible of
Alligator mississippiensis. J Anat 223:195–227.
Quayle MR. 2011. A morphological study of the kingfisher skull
[Honours Thesis]. University of Newcastle: Newcastle,
Australia, 1–106 p.
Rayfield EJ. 2004. Cranial mechanics and feeding in Tyranno-
saurus rex. Proc R Soc Lond B Biol Sci 271:1451–1459.
Rayfield EJ. 2005. Aspects of comparative cranial mechanics in
the theropod dinosaurs Coelophysis,Allosaurus and Tyranno-
saurus. Zool J Linn Soc 144:309–316.
Rayfield EJ. 2007. Finite element analysis and understanding
the biomechanics and evolution of living and fossil organisms.
Ann Rev Earth Planet Sci 35:541–576.
Richmond BG, Wright BW, Grosse I, Dechow PC, Ross CF,
Spencer MA, Strait DS. 2005. Finite element analysis in func-
tional morphology. Anat Rec A Discov Mol Cell Evol Biol
283A:259–274.
Ride WDL. 1959. Mastication and taxonomy in the macropodine
skull. In: Cain AJ, editor. Function and Taxonomic Importance.
Systematics Association Publication No. 3, London, pp 33–59.
Ross CF, Patel BA, Slice DE, Strait DS, Dechow PC, Richmond
BG, Spencer MA. 2005. Modeling masticatory muscle force in
13CRANIAL PERFORMANCE IN MARSUPIAL HERBIVORES
Journal of Morphology
finite element analysis: Sensitivity analysis using principal
coordinates analysis. Anat Rec A Discov Mol Cell Evol Biol
283A:288–299.
Sanson G. 1980. The morphology and occlusion of the molari-
form cheek teeth in some Macropodinae (Marsupialia: Macro-
podidae). Aust J Zool 28:341–365.
Sanson G. 1989. Morphological adaptations of teeth to diets
and feeding in the Macropodoidea. In: Grigg G, Jarman P,
Hume I, editors. Kangaroos, Wallabies and Rat Kangaroos.
Sydney: Surrey Beatty & Sons. pp 151–168.
Sharp AC, Trusler PW. 2015. Morphology of the jaw-closing
musculature in the common wombat (Vombatus ursinus)
using digital dissection and magnetic resonance imaging.
PLoS One 10:e0117730.
Soons J, Herrel A, Genbrugge A, Adriaens D, Aerts P, Dirckx J.
2012. Multi-layered bird beaks: A finite-element approach
towards the role of keratin in stress dissipation. J R Soc
Interface 9:1787–1796.
Stevens CE, Hume ID. 1998. Contributions of microbes in ver-
tebrate gastrointestinal tract to production and conservation
of nutrients. Physiol Rev 78:393–427.
Strait DS, Wang Q, Dechow PC, Ross CF, Richmond BG,
Spencer MA, Patel BA. 2005. Modeling elastic properties in
finite element analysis: How much precision is needed to pro-
duce an accurate model? Anat Rec A Discov Mol Cell Evol
Biol 283A:275–287.
Strait DS, Grosse IR, Dechow PC, Smith AL, Wang Q, Weber
GW, Neubauer S, Slice DE, Chalk J, Richmond BG. 2010.
The structural rigidity of the cranium of Australopithecus
africanus: Implications for diet, dietary adaptations, and the
allometry of feeding biomechanics. Anat Rec 293:583–593.
Tanner JB, Dumont ER, Sakai ST, Lundrigan BL, Holekamp
KE. 2008. Of arcs and vaults: The biomechanics of bone-
cracking in spotted hyenas (Crocuta crocuta). Biol J Linn Soc
95:246–255.
Thomason JJ. 1991. Cranial strength in relation to estimated
biting forces in some mammals. Can J Zool 69:2326–2333.
Tomo S, Tomo I, Townsend GC, Hirata K. 2007. Masticatory
muscles of the great-grey kangaroo (Macropus giganteus).
Anat Rec 290:382–388.
Triggs B. 2009. Wombats. Australia: CSIRO Publishing.
Tseng ZJ, Flynn JJ. 2015. Convergence analysis of a finite ele-
ment skull model of Herpestes javanicus (Carnivora, Mamma-
lia): Implications for robust comparative inferences of
biomechanical function. J Theor Biol 365:112–148.
Tseng ZJ, Wang X. 2010. Cranial functional morphology of
fossil dogs and adaptation for durophagy in Borophagus
and Epicyon (Carnivora, Mammalia). J Morphol 271:1386–
1398.
Tseng ZJ, McNitt-Gray JL, Flashner H, Wang X, Enciso R.
2011. Model sensitivity and use of the comparative finite ele-
ment method in mammalian jaw mechanics: Mandible per-
formance in the gray wolf. Plos One 6:e19171.
Tyndale-Biscoe H. 2005. Wombats: Vegetarians of the under-
world. Life of Marsupials. Collingwood, Victoria: CSIRO. pp
267–286.
van Spronsen PH, Weijs WA, Valk J, Prahl-Andersen B, van
Ginkel FC. 1989. Comparison of jaw-muscle bite-force cross-
sections obtained by means of magnetic resonance imaging
and high resolution CT scanning. J Dent Res 68:1765–1770.
Walmsley CW, McCurry MR, Clausen PD, McHenry CR. 2013.
Beware the black box: Investigating the sensitivity of FEA
simulations to modelling factors in comparative biomechanics.
PeerJ 1:e204.
Warburton NM. 2009. Comparative jaw muscle anatomy in
kangaroos, wallabies, and rat-kangaroos (Marsupialia: Macro-
podoidea). Anat Rec 292:875–884.
Weijs WA, Hillen B. 1985. Cross-sectional areas and estimated
intrinsic-strength of the human jaw muscles. Acta Morphol
Neerl Scand 23:267–274.
Wroe S. 2008. Cranial mechanics compared in extinct marsu-
pial and extant African lions using a finite-element approach.
J Zool 274:332–339.
Wroe S, McHenry C, Thomason J. 2005. Bite club: Comparative
bite force in big biting mammals and the prediction of preda-
tory behaviour in fossil taxa. Proc R Soc B Biol Sci 272:619–
625.
Young MT, Rayfield EJ, Holliday CM, Witmer LM, Button DJ,
Upchurch P, Barrett PM. 2012. Cranial biomechanics of Dip-
lodocus (Dinosauria, Sauropoda): Testing hypotheses of feed-
ing behaviour in an extinct megaherbivore. Die
Naturwissenschaften 99:637–643.
14 A.C. SHARP
Journal of Morphology
