Biomechanical Consequences of Rapid Evolution in the
Polar Bear Lineage
Graham J. Slater1*, Borja Figueirido2, Leeann Louis3, Paul Yang1, Blaire Van Valkenburgh1
1Department of Ecology and Evolutionary Biology, University of California Los Angeles, Los Angeles, California, United States of America, 2Departamento de Ecologı ´a y
Geologı ´a, A´rea de Paleontologı ´a, Facultad de Ciencias, Universidad de Ma ´laga, Campus Universitario de Teatinos, Ma ´laga, Spain, 3Cornell University Museum of
Vertebrates, Ithaca, New York, United States of America
The polar bear is the only living ursid with a fully carnivorous diet. Despite a number of well-documented craniodental
adaptations for a diet of seal flesh and blubber, molecular and paleontological data indicate that this morphologically
distinct species evolved less than a million years ago from the omnivorous brown bear. To better understand the evolution
of this dietary specialization, we used phylogenetic tests to estimate the rate of morphological specialization in polar bears.
We then used finite element analysis (FEA) to compare the limits of feeding performance in the polar bear skull to that of
the phylogenetically and geographically close brown bear. Results indicate that extremely rapid evolution of semi-aquatic
adaptations and dietary specialization in the polar bear lineage produced a cranial morphology that is weaker than that of
brown bears and less suited to processing tough omnivorous or herbivorous diets. Our results suggest that continuation of
current climate trends could affect polar bears by not only eliminating their primary food source, but also through
competition with northward advancing, generalized brown populations for resources that they are ill-equipped to utilize.
Citation: Slater GJ, Figueirido B, Louis L, Yang P, Van Valkenburgh B (2010) Biomechanical Consequences of Rapid Evolution in the Polar Bear Lineage. PLoS
ONE 5(11): e13870. doi:10.1371/journal.pone.0013870
Editor: Andrew Allen Farke, Raymond M. Alf Museum of Paleontology, United States of America
Received July 2, 2010; Accepted October 18, 2010; Published November 5, 2010
Copyright: ? 2010 Slater et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: The work was funded by the National Science Foundation (http://www.nsf.gov/) NSF 0709792, 0517748; Ministerio de Cinencia E Innovacion (http://
www.micinn.es/portal/site/MICINN/). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: firstname.lastname@example.org
The polar bear Ursus maritimus is unique among living ursids as
the only member of the family with an exclusively carnivorous
diet. As a result of this specialized diet, the the polar bear has
evolved a series of craniodental adaptations that allow it to
efficiently process a diet of seal flesh and blubber. For example,
polar bears exhibit reduced surface area of the grinding molar
teeth, a feature normally pronounced in more omnivorous ursids,
and a low, slender skull , . Despite possessing such distinctive
phenotypic features, molecular and paleontological data unequiv-
ocally indicate that the carnivorous polar bear evolved relatively
recently, approximately 150–700ka (Fig. 1), from coastal popula-
tions of the more generalized and omnivorous brown bear Ursus
arctos [3–6]. In this study, we take a combined evolutionary and
biomechanical approach to examine the evolution of adaptations
to carnivory in the polar bear cranium. We first use multivariate
evolutionary contrasts  to test whether the unique cranial
morphology of the polar bear resulted from increased rates of
cranial shape evolution in the polar bear lineage, relative to other
branches of ursid phylogeny. We expect this to be the case if
adaptation to the harsh arctic environment and a hypercarnivor-
ous diet posed novel evolutionary challenges for a large ursid. We
then use 3D finite element analysis (FEA) to examine the impact of
craniodental adaptations to hypercarnivory on various aspects of
cranial performance, such as bite force and skull strength, during
feeding. FEA is an engineering method used to examine patterns
of stress and strain in man-made objects when placed under load
and, in recent years, has been adapted to study the evolution of
biological form and function [8–14]. In FEA, the structure of
interest, here the skull, is represented as a finite number of
elements, joined at their vertices by nodes. The elements are
assigned material properties that specify how they respond when
placed under load. Recent developments in FE modeling of
biological structures have resulted in methods for more realistic
modeling of jaw muscles  and appropriate protocols for
assessing comparative performance across species . Here, we
use FEA to compare feeding performance in the carnivorous polar
bear to that of its phylogenetically and geographically closest
relative, the omnivorous brown bear.
Multivariate rates of evolution for cranial shape are given in
Table 1, where node numbers refer to nodes in Figure 1. The rate
of skull shape evolution in the polar bear lineage was about double
the mean rate observed for other parts of ursid phylogeny (mean
ursid rate=0.024, +/20.007, polar bear rate=0.059). This
difference was significant based on a one-tailed T-test (t6=4.92,
Surface area to volume ratios for the finite element models of
polar and brown bear skulls were similar, indicating that similar
amounts of bone are used in the skulls of both species (SA/V: polar
bear=0.61, brown bear=0.59). This finding suggests that
differences in stress magnitudes between the polar bear and scaled
brown bear skull models can be interpreted in light of differences
in external shapes of the skulls. Bite forces measured from the two
scaled finite element models were also comparable for all
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simulated bites, although the polar bear’s bite was slightly stronger
in each case (Table 2, Fig. 2a). These results suggest that the
potential leverage of the jaw muscle systems is also similar for the
Stress distributions and magnitudes differed between the two
models for all bites. For each biting scenario, the polar bear skull
exhibited more widely varying stresses (Fig. 3) and higher peak
stresses (Table 3) than for the brown bear. Differences between the
two species were most marked for bites made with the molars,
where peak stresses in the polar bear were up to 408% those of the
brown bear (Table 3). Similarly strain energy values were higher in
the polar bear cranium than for the brown bear for all bites
(Table 2; Fig. 2b), indicating that the polar bear skull undergoes
more deformation in producing similar bite forces. Again,
differences between the polar and brown bear crania were most
pronounced for bites made with the post-canine dentition, the
main site for processing of ingested food. Our model results are
unvalidated by in vivo data and should be treated as estimates only.
However, based on our findings, it appears that although the two
species are similar in cranial size and have similar muscle leverage
potential, the polar bear’s skull is a weaker, less work-efficient
structure, and does not appear well suited to dealing with large
Figure 1. Time-calibrated ursid phylogeny used for assessing
rates of cranial shape evolution. Node numbers correspond to
those used for evolutionary contrasts (see Table 1).
Table 1. Mulitvariate evolutionary contrasts for ursid cranial
Contrast mulitvariate rate
A. melanoleuca / node 10.025
T. ornatus / node 2 0.013
U.ursinus / node 30.023
U. arctos / node 40.032
U.malayanus / node 50.030
U. thibethanus / U.americanus0.018
Ursid mean (sd)0.024 (0.007)
U.maritimus / node 70.059
Node numbers refer to nodes in Fig. 1.
Figure 2. Performance metrics assessed for four different bite
positions in the polar bear (blue symbols) and brown bear (red
symbols) FE models. The X axis corresponds to bite point, with
anterior bites towards the left and posterior bites to the right. Panel A
shows bite forces, panel B shows cranial strain energy. Note that bite
forces are similar in both species for all bites, while strain energies are
uniformly lower in the brown bear.
Table 2. Bite forces and strain energy density (SED) values for
the two models under four simulated bites.
Bite Force right1939.96 3798.694481.55 5041.65
Bite Force left2302.09 3882.044426.24 5127.36
mean Bite force2121.02 3840.364453.90 5084.50
SED right2.382.36 1.912.03
SED left- 1.98 2.17 2.03
mean SED2.382.172.04 2.03
brown bearBite Force right1731.923832.534197.82 4570.43
Bite Force left1630.84 3644.364119.48 4768.38
mean Bite force 1681.383738.454158.65 4669.41
SED right1.861.31 1.25 1.52
SED left- 1.35 1.341.35
mean SED1.861.331.30 1.44
Values are given for FE analyses conducted with bite points on the right and left
sides, as well as means over both sides.
Polar Bear Feeding Performance
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The transition to an arctic environment and hypercarnivorous
diet resulted in extremely rapid morphological evolution in the
polar bear lineage. Our results indicate that the rate of cranial
shape evolution in the polar bear lineage was at least twice as fast
as in other branches of ursid phylogeny. Our estimate is probably
conservative; while the phylogeny that we used for rate estimates
dates the polar bear/brown bear split at ,700 kya , recent
analysis of sub-fossil polar bear remains suggests that polar bears
diverged from brown bears as recently as 150 kya, and that the
modern polar bear morphology was present by 130 kya .
Compared with other ursids, polar bears possess low flat skulls
with elevated orbits , consistent with both semi-aquatic  and
faunivorous  adaptations. This morphology might also increase
hunting efficiency by allowing bears to thrust their heads into
breathing holes or pupping dens. Polar bear evolution was
facilitated by the expansion of polar ice sheets and floes in the
late Pleistocene . If polar bears evolved from coastal
populations of brown bears , as molecular evidence now
suggests [3–5], , then rapid evolution of adaptations for semi-
aquatic life and hypercarnivory could have occurred to facilitate
foraging over wider areas. Polar bears have denser fore- and
hindlimb bones, a common adaptation of aquatic mammals, than
closely related brown bears, further supporting this interpretation
Although polar bears possess mechanically efficient skulls, as
indicated by larger bite forces for a given muscle effort (Fig. 2A),
we found that they also possess energetically inefficient and
structurally weaker skulls (Fig. 2b; Fig. 3). This initially seems
somewhat counterintuitive; among other carnivoran families,
more carnivorous taxa tend to have stronger skulls , ,
. However, polar bears feed almost exclusively on young
ringed (Pusa hispida) and bearded (Erignatus barbatus) seals, which, at
68–250kg, are small prey in comparison to a ,500 kg adult polar
bear , . As a result, cranial reinforcement may not be
necessary as in hypercarnivores such as lions or wolves that
regularly take prey larger than themselves , , . The
performance of the polar bear skull is particularly poor during
bites with the post-canine dentition. (Fig 2b; Fig 3b–d; f–h). Polar
bears exhibit reduced premolars and molars in comparison with
most other ursids  but also lack the well-developed shearing
blade-like teeth of hypercarnivores , . In this respect they
parallel insectivorous carnivorans, such as aardwolf (Proteles
cristata), bat-eared fox (Otocyon megalotis) and sloth bear (Ursus
ursinus) , . Although convergence between a carnivore and
Figure 3. FE models showing von Mises stresses in the polar bear (left) and brown bear (right) skulls during bilateral canine biting
(A,E), and unilateral PM4 (B,F), M1 (C,G), and M2 (D,H) biting.
Polar Bear Feeding Performance
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insectivores also appears surprising, consideration of food material
properties sheds light on this finding. Polar bears feed as almost
exclusively on blubber and flesh that, unlike bone, require little or
no processing prior to swallowing. If there is no selective
advantage to maintaining large molars, they can be rapidly lost
through the action of a few small mutations  or simple
developmental mechanisms , . Brown bears, in contrast,
are generalized omnivores with unreduced dentitions , .
Although they consume animal protein when available, brown
bears seasonally consume large amounts of plant material,
including grasses, which require extensive mechanical breakdown
and repeated skull loading prior to swallowing . This is
reflected in their larger molar grinding area, similar to other
omnivorous ursids . The lower peak stresses and higher work
efficiency of the the brown bear cranium may result in part from
the species’ deep, vaulted and pneumatized forehead (see Fig. 3), a
morphology that is characteristic of all herbivorous and omniv-
orous ursids . Although pneumatized spaces are associated with
reduced structural strength of the cranium , their presence is
also associated with dissipation of regular, large peak masticatory
loads in bone-cracking hyaenas and fossil canids [29–32]. The low,
flat head of the polar bear, while advantageous for its semi-aquatic
lifestyle and hunting behavior, reduces the ability of the cranium
to withstand repeated large loads generated by bites made with the
The polar bear has become a flagship species for global climate
change in recent years. Projected climate trends in coming decades
will have profound effects on polar bear populations by decreasing
the availability of suitable denning sites as well as eliminating
much of the polar sea ice over which this specialized ursid forages
for its seal prey . Furthermore, climate-driven northward
expansion of temperate ecosystems and their associated faunas
 has already begun to facilitate the movement of brown bears
into polar bear territory . The continued survival of the polar
bear in the face of global climate change will ultimately depend on
a range of factors, including behavioral and physiological
flexibility. Our findings, combined with those of earlier studies,
shed some light on the potential dietary flexibility of polar bear. In
response to a specialized diet of seal blubber, polar bears rapidly
lost the large grinding molars and deep vaulted skull that
characterize omnivorous ursids. This has not only resulted in a
dentition that is less suited to diets requiring high levels of oral food
processing but also, based on our results, a cranium that is less
suited to bearing the associated loads. Small differences in cranial
stress and strain are probably not alone sufficient to force a species
to extinction. However, increased competition from northward
advancing brown bear populations will also present a significant
challenge. In areas where specialized arctic foxes (Vulpes lagopus)
overlap with more generalized red foxes (Vulpes vulpes), red foxes
actively displace arctic foxes and control prime feeding and
denning areas , . In this context, even the slight selective
advantage provided by the superior mechanical performance of
the brown bear’s cranial shape, combined with a loss of molar
grinding area, could be enough in such a setting to contribute to
the exclusion of the polar bear. As a consequence of exceptional
rapid specialization to a high arctic diet of seal flesh, the polar bear
appears to have lost the generalized feeding abilities of its close
relative. As a result, if current climate trends continue, one of the
most striking examples of rapid phenotypic evolution may be lost
as quickly as it appeared.
Materials and Methods
Rates of Cranial Shape Evolution
We computed multivariate rates of cranial shape evolution
following . Our morphometric data comprised mean principal
component scores from a previous study of cranial shape variation
across all extant ursid species . We calculated rates of evolution
from these data on an ursid phylogeny (Fig. 1) with topology and
branch lengths from . The rate of cranial shape evolution in the
polar bear lineage was compared to the distribution of rates in
other ursids using a one-tailed T-test. Analyses were conducted
with R 2.10.1  using custom-written scripts and functions from
the APE  and Geiger  packages.
Creating skull models
Dry skulls of one adult male polar bear (Illinois State Museum
H001-05) and one adult male brown bear (United States National
Museum 82003) were CT scanned at the High Resolution CT
facility at the University of Texas, Austin. Slice thickness/inter-
slice spacing was 0.75mm (polar bear) and 1mm (brown bear).
Both scans are available via the digital morphology website
(http://www.digimorph.org). Due to the high cost of CT scanning
and the time consuming nature of FE model construction, only
Table 3. Peak Von mises stress for homologous cranial
regions in the polar and brown bear models for the four
bite position skull region polar bearbrown bear
bilateral caninert zygoma 29.13 (7.95)26.46 (6.73)
lt zygoma 34.77(8.45)27.08 (6.60)
palate24.49 (5.66) 10.50 (2.94)
snout13.49 (4.51) 10.66 (4.59)
frontal 31.53 (6.32)11.66 (4.84)
rt orbit27.72 (6.85)15.75 (5.13)
lt orbit 19.88 (7.32)21.40 (3.80)
PM4rt zygoma 29.92 (9.30) 21.02 (6.93)
lt zygoma 25.27 (5.65)19.17 (4.54)
palate 21.20 (5.12) 9.94 (2.74)
snout20.39 (2.76)14.41 (2.58)
frontal 24.39 (4.65)10.49 (4.03)
rt orbit62.31 (15.37)20.23 (8.64)
lt orbit 14.07 (3.75) 11.63 (2.02)
M1rt zygoma 38.15 (9.79) 22.84 (7.04)
lt zygoma25.23 (6.08)19.16 (4.61)
palate52.84 (6.76)16.10 (3.24)
snout 13.81 (2.66) 13.94 (2.14)
frontal22.9 (4.03) 10.47 (3.85)
rt orbit 114.18 (23.22)27.93 (11.03)
lt orbit 21.84 (3.55)9.87 (1.84)
M2rt zygoma 38.81 (9.92) 27.26 (7.66)
lt zygoma 24.75 (4.63)18.80 (4.58)
palate 52.93 (6.51)17.93 (3.37)
snout 13.36 (2.63)10.99 (1.77)
frontal 22.92 (3.64)11.09 (3.83)
rt orbit 114.63 (23.16)45.72 (15.62)
lt orbit 22.09 (3.63)11.58 (1.81)
Average brick stress for each region is also given in parentheses.
Polar Bear Feeding Performance
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one specimen per species was used. Both specimens were
quantitatively typical for their species based analysis of landmark
data following . Skulls were assessed as adult based on tooth
eruption and full closure of the basilar synchondrosis.
3D surface models of the crania were rendered in AMIRA
v.4.1.2-1 (Visualization Sciences Group, Massachusetts, USA). An
automated thresholding tool was initially used to delimit bone
surfaces. We then manually edited the slices. At this stage we made
a number of simplifying steps to reduce model complexity. First,
we omitted the complex turbinal bones within the nasal cavity and
semi-circular canals of the middle ear, as these presumably do not
function in load bearing. We also simplified the morphology of
complex structures that can be problematic in FE modeling, such
as the perforated cribriform plate of the ethmoid. Second, we
modeled teeth as continuous with surrounding maxillary bone as
in other FE studies [9–11], , , . Although tooth roots
and periodontal ligaments (PDL) play important roles in
transmitting and absorbing forces, recent work suggests that
inclusion of the PDL in finite element models affects only local
strain in the region of the alveolus  and so presumably does
not affect global patterns of performance. Third, we ignored the
distribution of trabecular bone and modeled the entire cranium as
continuous cortical bone. Although this will over-stiffen the
models, both contained similar amounts of cancellous bone and
so are presumably affected in similar ways. Finally, we omitted to
model the intricate three-dimensional morphology of cranial
sutures. Recent FE work suggests that sutures may play important
roles in locally reducing strain in non-mammalian tetrapod skulls
,  but their significance in mammalian cranial function
remains to be explored. Internal cavities, such as the frontal
sinuses and tympanic bulla cavity were modeled as hollow,
preserving potential biomechanical function. Simplified skull
models were imported into Geomagic Studio v.10. (Geomagic
Corp. North Carolina, USA), where we manually edited the
surfaces to correct artifacts of the reconstruction process and patch
holes. Once watertight surface models of the two skulls had been
created, we re-exported them for FE modeling.
Finite Element models
The complete, simplified skull models were imported into
Strand7 (Strand7 Pty. Ltd., Sydney, Australia) for FE analysis. We
created Finite Element meshes of the cranium only (the mandible
was retained only for positioning muscle vectors) using 4-noded
tetrahedral elements. The final models comprised 841,531
elements for the polar bear and 984,184 elements for the brown
bear. Complete finite element models have been deposited with,
and are available for download from Biomesh (http://www.
biomesh.org/models). Ideally, we would have assigned complex
material properties to our models to account for regional variation
in the distribution of cortical and cancellous bone, and the
orthotropic material behavior of bone. Because the use of
homogenous material properties in FEMs has been shown to
produce surface strains that fall within the range of values of
obtained from in vivo strain gauge studies  and material
properties are currently not available for polar or brown bear
cranial bone, we made the simplifying assumption here to assign
homogeneous isotropic material properties based on values for
domestic dog cortical bone, following ,  (E=13.7 GPA,
n=0.3). Our study is not validated and thus absolute values of
results should be treated with caution. However, as the aim of our
study is comparative and both skulls were modeled in identical
ways, we should still be able to draw broad conclusions regarding
comparative performance of the skulls of the two species from the
We applied muscle forces over the origins of the temporalis,
masseter and pterygoideus (internal+external) muscles using the
tangential-plus-normal traction model in the program BoneLoad
. This method incorporates the effects of muscle wrapping
around curved bone surfaces and eliminates artifacts caused by
point loads in areas of muscle insertion. A thin layer of plates
(1024mm) was applied over the entire area of muscle origin for
each muscle. The plates were assigned the same material
properties as the tetrahedral elements forming the cranium.
Muscle forces were then applied to the plate surfaces. To provide
focal points for the muscle forces to act towards, we identified the
x,y,z coordinates of nodes on the mandibles representing the
estimated center points of the temporalis, masseter, and pterygoi-
deus insertion areas. We subsequently deleted the plates
constituting the mandibles and, in their place, created six nodes
at the exact co-ordinates of the previously identified focal positions
for the muscles. These newly created nodes were used as focal
points for the action of the muscle forces. For example, all left
temporalis forces pulled towards a focal node representing the
center point of temporalis insertion on the left mandible.
Measurements of cross section area of the jaw muscles were not
available for the species modeled here. Instead, a total amount of
muscle force (see below) was distributed in each model according
to percentage contribution of temporalis (65.17%), masseter
(28.08%) and pterygoideus (6.75%) to total jaw muscle mass in
the closely related American black bear Ursus americanus .
Available evidence suggests that these values are consistent across
such disparate carnivoran families as felids and canids , .
During biting with the post-canine dentition, jaw muscles are likely
to differ in activity patterns on working and balancing sides of the
jaw. To ensure that the assumption of maximal muscle activity did
not bias our results, we conducted analyses at the post-canine
dentition with forces allocated at a 1:0.66 ratio between working
and balancing sides, based on electromyographic work on the
domestic dog  and subsequent FE studies of carnivoran
To prevent free-body rotation (unconstrained movement of
models in space), we followed protocols described in . We
constrained a single node at each glenoid fossa, creating a virtual
axis of rotation with the ventrally directed muscle forces rotating
the cranium about the temporal-mandibular joint. To simulate
biting behavior and measure feeding performance (i.e. bite force,
cranial stress and strain), we applied additional single node
constraints at teeth involved in the simulated biting behaviors.
This added a virtual bite point, with the rotating skull meeting a
point of resistance at the bite point and a resultant virtual bite
force generated. From this action, resultant stresses and strain can
be calculated and visualized. We simulated four bite scenarios that
ursids use when feeding: a bilateral canine bite (one constrained
node at the tip of each canine); and unilateral bites at the fourth
upper premolar - the ‘‘carnassial’’ (a single constrained node at the
carnassial notch); upper first molar (a single constrained node at
the protocone); and upper second molar (a single constrained node
at the protocone). To ensure that asymmetries in the models and
placement of constraints did not influence results, we repeated
analyses for both left and right teeth and averaged subsequent bite
force and strain energy results (Table 2).
Scaling and Assessing Performance
We controlled for differences in size between the models using a
recently developed method for comparing FE models . In order
Polar Bear Feeding Performance
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to ensure that stress values are comparable among models of
different sizes, it is important that force to surface area ratios are
constant among finite element models. Therefore, prior to analysis,
both models were scaled to common surface area corresponding to
that of the polar bear model (1,209,042 mm2). To produce realistic
estimates of bite force we used the total muscle force derived from a
dry skull estimate of the cross sectional area of temporalis and
masseter plus pterygoideus muscles in the polar bear (18069.6 N -
). For bilateral canine bites, this total muscle force was
distributed according to proportions described above from the
black bear. For unilateral post-canine bites, we reduced the
balancing side muscle forces by 2/3, resulting in a working side
total of 9034.8 N and a balancing side total of 6023.2 N.
We evaluated performance of the models based on three
criteria. First, we determined how skull shape affects bite
performance by comparing bite forces at the constrained nodes
on the teeth. Because all models were scaled to a common surface
area and used equal muscle forces, our null hypothesis was that
bite forces should be identical among the models. Any differences
in bite forces could then be interpreted as the result of differences
in skull geometry alone . Second, we assessed strength of the
skull models by comparing model stress, measured as Von Mises
stress . Bone is an elastic material and therefore fails under a
ductile, rather than brittle model of fracture . Von Mises stress
is a scalar function of the principle stresses at each element and
provides a good predictor of failure due to ductile fracture .
Lower peak stress values and more even stress distributions were
interpreted as indicating a stronger structure for a given loading
condition. Finally, we assessed the work efficiency of the skull
models by comparing total strain energy values, a measure of
energy lost to deformation. In terms of work efficiency, efficient
structures are those that maximize stiffness for a given volume of
material . Lower strain energy values indicate stiffer structures
and therefore greater work efficiency. Strain energy values were
corrected for differences in volumes of the models using Equation
5 from Dumont et al. . Our null hypotheses for all analyses
were that stress and strain energy values should be identical among
scaled models. All FE analyses were linear static and were
completed in Strand7.
We thank Mark McPeek for checking our rate results against his own code,
Dan Pulaski for technical assistance, and the University of Texas High
Resolution X-ray CT Scanning Facility for scanning specimens. We also
thank Academic Editor Andrew Farke, Deborah Bird, Anthony Friscia,
Betsy Dumont, Paul Palmqvist, Shauna Price, Sharlene Santana, David
Strait, Robert Wayne, and an anonymous reviewer for thoughtful and
helpful comments on previous versions of the manuscript.
Conceived and designed the experiments: GJS. Performed the experi-
ments: GJS LL PY. Analyzed the data: GJS BF LL PY. Contributed
reagents/materials/analysis tools: GJS BF BVV. Wrote the paper: GJS BF
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