Zoology 116 (2013) 67–74
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Zoology
journal homepage: www.elsevier.com/locate/zool
Symmetrical gaits and center of mass mechanics in small-bodied, primitive
mammals
Audrone R. Biknevicius a,∗ , Stephen M. Reilly b , Eric J. McElroy c , Michael B. Bennett d
a
Department of Biomedical Sciences, Ohio University Heritage College of Osteopathic Medicine, Athens, OH 45701, USA
Department of Biological Sciences, Ohio University College, Athens, OH 45701, USA
Department of Biology, College of Charleston, Charleston, SC 29401, USA
d
School of Biomedical Sciences, University of Queensland, St. Lucia, Qld 4072, Australia
b
c
a r t i c l e
i n f o
Article history:
Received 28 December 2011
Received in revised form 9 May 2012
Accepted 15 May 2012
Available online 26 November 2012
Keywords:
Locomotion
Center of mass mechanics
Symmetrical gaits
a b s t r a c t
Widely accepted relationships between gaits (footfall patterns) and center of mass mechanics have been
formulated from observations for cursorial mammals. However, sparse data on smaller or more generalized forms suggest a fundamentally different relationship. This study explores locomotor dynamics in one
eutherian and five metatherian (marsupials) mammals—all small-bodied (<2 kg) with generalized body
plans that utilize symmetrical gaits. Across our sample, trials conforming to vaulting mechanics occurred
least frequently (<10% of all trials) while bouncing mechanics was obtained most commonly (60%); the
remaining trials represented mixed mechanics. Contrary to the common situation in large mammals,
there was no evidence for discrete gait switching within symmetrical gaits as speed increased. This was
in part due to the common practice of grounded running. The adaptive advantage of different patterns of
center-of-mass motion and their putative energy savings remain questionable in small-bodied mammals.
© 2012 Elsevier GmbH. All rights reserved.
1. Introduction
Small mammals operate under different conditions during
terrestrial locomotion than do larger mammals. This can be summarized by the higher cost of transport incurred by small mammals
(less than about 1–5 kg; Fig. 1) and can be explained, in large part, by
higher muscular effort during terrestrial locomotion (reviewed in
Reilly et al., 2007). In order to cover an equivalent distance, small
mammals must take a greater number of strides at a higher frequency than large mammals (Kram and Taylor, 1990; Steudel and
Beattie, 1990; Pontzer, 2007); species that move with short stride
lengths and high frequencies perform a lot of internal mechanical
work simply to cycle the limbs (Van Damme et al., 1998). Furthermore, each phase of the stride cycle may be more costly for
small mammals. The crouched posture typical of small mammals is
related to poorer effective mechanical advantage for the antigravity
(extensor) muscles (Biewener, 1990); these muscles must be more
active during stance phase in small mammals to maintain locomotor posture. While the limited number of studies on the metabolic
costs of swing phase have found comparable levels in human and
avian bipedalism (Rubenson and Marsh, 2009; Doke et al., 2005),
on theoretical grounds, swing phase may be expected to be more
costly in small mammals: the passive forces of leg muscles are
∗ Corresponding author.
E-mail address: [email protected] (A.R. Biknevicius).
0944-2006/$ – see front matter © 2012 Elsevier GmbH. All rights reserved.
http://dx.doi.org/10.1016/j.zool.2012.05.005
relatively large compared with gravitational forces in animals with
low-weight limbs so that a larger percentage of swing may need to
be powered by muscle (Hooper et al., 2009).
It is also clear that large mammals have evolved morphological
specializations that enhance their capacity to recover energy during terrestrial locomotion. When running, large mammals cyclically
stretch and recoil elastic elements in their limbs and back (tendons, ligaments), thereby reducing the amount of muscular effort
required to maintain forward propulsion (Bennett et al., 1986;
Biewener and Baudinette, 1995). By comparison, the capacity to
recover elastic strain energy in small mammals is equivocal at best
(Bullimore and Burn, 2005). Meaningful energy savings via the
pendulum-like exchange of kinetic energy (Ek ) and gravitational
potential energy (Ep ) of the center of mass (COM) during walking
may also be more effective in large mammals (Reilly et al., 2007).
This is because external mechanical energy (i.e., the energy used
to move the COM which is recovered via the pendulum-like mechanisms) represents a substantial portion of the metabolic cost of
transport in large mammals whereas it is a trivial part of overall
costs in small mammals (horizontal dashed line in Fig. 1). Thus, if
the overall cost of transport and the capacity for saving energy differ between small and large mammals, then perhaps there is also a
different relationship between COM mechanics and gaits in these
mammals.
In the present study, we explicitly categorized COM mechanics
as either vaulting mechanics (inverted pendulum model), bouncing mechanics (spring–mass model) or mixed mechanics (having
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A.R. Biknevicius et al. / Zoology 116 (2013) 67–74
2.2. Kinetic data
Fig. 1. Relationship between cost of transport and body size in mammals (adapted
from Reilly et al., 2007). Symbols represent locomotor posture: , crouched limbs; ,
erect limbs. Overlying colored bars indicate the size range of mammals used in this
study. The horizontal dashed line represents the total external mechanical energy
of the center of mass (∼1.1 J kg−1 m−1 ; Full, 1991).
The mammals were encouraged to pass down a trackway into
which a force platform was integrated; the force platform was long
enough to capture the whole body forces of the animals as they
took several steps to cross the platform. Data capture on the New
World marsupials and the eutherian was conducted at Ohio University (USA). For Philander and Rattus, a Kistler force platform (Type
9281B; Kistler AG, Winterthur, Switzerland) was used in a 6-m-long
trackway. A 0.36-m-long custom-built force platform integrated
into a 2.44 m trackway was used for Monodelphis; the data for this
mammal had already been obtained by Parchmann et al. (2003).
Data capture on the Australian marsupials was conducted at the
University of Queensland (Australia). For these studies the trackway was 4.2 m long with a 0.62-cm-long force platform designed
for larger-mass mammals. Analog data from the force platforms
were captured at 500 Hz. These were then converted into ground
reaction forces (GRFs) and filtered using two notch filters, at 60 Hz
and 150 Hz (5 Hz filter widths). Refer to Parchmann et al. (2003)
for details on the custom force platform design and the LabView
virtual instruments developed for data capture and filtering.
features of both vaulting and bouncing mechanics) (Cavagna et al.,
1977; Ahn et al., 2004). The inverted pendulum model of walking stipulates an exchange of Ek and Ep of the COM with every
step as a result of the out-of-phase cycle of Ek and Ep (phase difference of 135–180◦ ). By contrast, Ek and Ep cycle in-phase with
one another (0–45◦ ) in the spring–mass model of running, and the
limbs function like compressible springs that have the potential
for a return of elastic strain energy toward the end of the support
period. Mixed mechanics fall between these (45–135◦ ). Symmetrical gaits are footfall patterns that represent the slowest gaits used
by mammals as well as moderate to fast gaits (Hildebrand, 1976);
other running gaits use asymmetrical footfall patterns (Hildebrand,
1977). As walk–run transitions usually occur within symmetrical
gaits in large and small mammals alike (e.g., walk–trot transition;
Cavagna et al., 1977; Gatesy and Biewener, 1991; Minetti et al.,
1999; Griffin et al., 2004a), we focused our study on the relationship
between symmetrical gaits and COM mechanics in small mammals.
To this end, we tested the hypothesis that small-bodied mammals
exhibit a different relationship between gait and COM mechanics
than do large mammals.
Simultaneous video recordings (125 Hz; NAC camera; NAC
Image Technology, Tokyo, Japan), downloaded into the Ariel Performance Analysis System (Ariel Dynamics, Trabuco Canyon, CA,
USA), provided the following kinematic data (in ms): hindlimb support duration (time between touchdown and liftoff of a hindlimb),
hindlimb stride duration (time between subsequent touchdowns
of a hindlimb), and lateral advanced placement (time lag between
the touchdown of a hindlimb and its ipsilateral forelimb). Hind
limb phase (lateral advanced placement/stride duration) was used
to determine the symmetrical gait used in each trial (Hildebrand,
1976). Mean forward speed was calculated videographically using
the movement of the tip of the snout across a 10-cm grid across the
back wall of the trackway overlying the force platform. Only those
trials in which the animals did not alter velocity by more than 20%
when passing over the force platform were evaluated further. We
also independently tested the steadiness of the forward velocity for
each trial by noting balanced propulsive and braking components
of the craniocaudal force record (see Section 2.4).
2. Materials and methods
2.4. Center of mass (COM) mechanics
2.1. Study animals
Whole-body GRFs were used to estimate the fluctuations in
the external mechanical energies over a hindlimb step (hindlimb
touchdown to the contralateral hindlimb touchdown) (Cavagna
et al., 1977; Willey et al., 2004). Briefly, accelerations of the COM in
vertical, craniocaudal, and mediolateral directions were obtained
by dividing GRFs by body mass (body weight was first subtracted
in vertical records). Velocities of the COM for each direction were
estimated by taking the first integration of acceleration. While integration constants for the craniocaudal direction were set to mean
forward velocity (Blickhan and Full, 1992), the constants were
estimated as the mean value for the vertical and lateral records
(Donelan et al., 2002). These velocities were then used to calculate kinetic energies (EK = ½mv2 , where m is body mass in kg) in
the vertical (EK-V ), craniocaudal (EK-CC ), and mediolateral (EK-ML )
directions. Summing the three kinetic energies yielded the total
kinetic energy of the COM (EK ). Finally, changes in the vertical displacement of the center of mass (h) were determined by integrating
vertical velocity (integration constant estimated as the mean vertical record) and were used to determine changes in gravitational
potential energy during the step (EP = mgh, where g is gravitational
The mammalian species used in this study were chosen for
their small body mass (<2 kg), quadrupedal posture and fairly
unspecialized locomotor modes (Table 1). The marsupials included
three Australian species (Pseudocheirus peregrinus, Pseudocheiridae; Trichosurus vulpecula, Phalangeridae; Dasyurus hallucatus,
Dasyuridae) and two New World species (Monodelphis domestica,
Didelphidae; Philander opossum, Didelphidae). Rattus norvegicus
(Muridae) was the sole eutherian species. Monodelphis, Philander
and Rattus were obtained from breeding facilities in the United
States. Dasyurus and two of the Pseudocheirus individuals were
accessed from an educational organization in Australia. The other
two Pseudocheirus and all of the Trichosurus individuals were caught
in the wild in Queensland, Australia; these were collected under a
Queensland Environmental Protection Agency Scientific Purposes
Permit. All procedures with the animals were conducted under
an Ohio University Institutional Animal Care and Use Committee
approved protocol and a University of Queensland Animal Ethics
Approval Certificate.
2.3. Kinematic data
A.R. Biknevicius et al. / Zoology 116 (2013) 67–74
69
Table 1
Sample demographics and general ecology of species used in the study. Mean ± standard deviation for species with 3 or more individuals.
Wild-caught
Dasyurus hallucatus
(Northern quoll)
Pseudocheirus
peregrinus (Common
ringtail possum)
Trichosurus vulpecula
(Common brushtail
possum)
Monodelphis domestica
(Gray short-tailed
opossum)
Philander opossum
(Gray four-eyed
opossum)
Rattus norvegicus
(Norway rat)
2
Domestic bred
Body mass (kg)
Hip height (cm)
Ecology
2
0.58, 1.03
8.7, 9.9
2
Wild: 0.98, 1.03
Captive: 0.97, 1.27
11.4 ± 0.3
Primarily terrestrial
but able to climb;
carnivorousa
Scansorial;
herbivorousa
1.88 ± 0.53
17.2 ± 1.4
Arboreal; herbivorousa
7
0.11 ± 0.03
3.1 ± 0.1
2
0.82, 0.84
10.7, 11.7
5
0.45 ± 0.03
9.1 ± 0.6
Primarily terrestrial
but able to climb;
insectivorousa
Primarily terrestrial
but able to climb;
omnivorousa
Primarily terrestrial
but able to climb;
omnivorousb
5
Ecology references:
a
Nowak (2005).
b
Nowak (1991).
acceleration or 9.81 m s−2 ). The total external mechanical energy
(EM ) was computed as the sum of EK and EP .
The phase relationship between the fluctuation in the EK and
EP profiles across the step reflects the overall dynamics of the
COM. This phase shift was calculated by dividing the time difference between the minimum values of EK and EP by the duration
of the stride and then multiplying the value by 360◦ (Cavagna
et al., 1977). We distinguished three different categories. Phase
shifts of 180–135◦ or 45–0◦ signify that the animals were moving
with vaulting or bouncing mechanics, respectively, whereas phase
shifts between 135◦ and 45◦ represent mixed mechanics (Ahn et al.,
2004). Finally, recovery of mechanical energy due to pendulumlike exchange between EK and EP during a step was calculated as
(Blickhan and Full, 1992):
percent recovery =
(EK + EP − EM ) × 100
,
EK + EP
where EK , EP , and EM are the sum of the positive increments
of the EK , EP , and EM profiles, respectively.
In order to assess whether the mammals showed any preference
in moving with a particular mode of COM mechanics, Chi-squared
(2 ) goodness of fit tests were performed with the null expectation of 0.25 pendulum:0.5 mixed:0.25 spring-mass, based on the
phase shift ranges above. Non-significance (˛ > 0.05) indicates the
occurrence of all three forms of COM mechanics but with mixed
mechanics predominating, which is what is expected if animals
randomly use different phase shifts. A significant difference from
the null expectation suggests that the animal either is especially
biased toward mixed mechanics or is preferentially using pendulum or bouncing mechanics.
Finally, to evaluate whether or not there was a relationship
between gait and COM mechanics, phase shift (reflecting COM
mechanics) was regressed on limb phase (indicating symmetrical
gait) for each species using least-squares regression.
3. Results
Results for each species are shown in Fig. 2 and Table 2. The
small sample sizes for Dasyurus and Philander (two specimens each)
limit the confidence of our conclusions on these species; therefore, conclusions based on their results are necessarily considered
preliminary.
3.1. Findings for each species
The distribution of COM mechanics in Dasyurus was significantly
different from the null expectation (22 = 19.0, P < 0.001). Dasyurus overwhelmingly moved with bouncing mechanics (70.6% of all
symmetrical gaits) using diagonal-couplet gaits (lateral-sequence
diagonal-couplet, trot or diagonal-sequence diagonal-couplet); all
other trials followed mixed mechanics (23.5%) or, more rarely,
vaulting mechanics (5.9%). No significant relationship was found
between gait and COM mechanics (P = 0.775, r2 = 0.006). Maximum
recovery of mechanical energy via pendulum-like mechanisms
across all trials was nearly 52%.
Pseudocheirus showed a preference for moving with mixed
mechanics (59.2%); trials conforming to vaulting and bouncing
mechanics occurred with nearly equal frequencies (22.2% and
18.5%, respectively). This distribution matched the null expectation
(22 = 1.0, P = 0.607). Some tendency for speed-related changes in
gaits was noted, namely, there was a tendency for gaits to shift from
lateral-sequence diagonal-couplets and trots at high duty factors
to diagonal-sequence diagonal-couplets and diagonal-sequence
singlefoots at lower duty factors. The relationship between gait
and COM mechanics failed to reach a statistically significant level
(P = 0.056; r2 = 0.138). Maximum recovery of mechanical energy in
Pseudocheirus was 68%.
Trichosurus also primarily moved with mixed mechanics (59.1%)
but had a greater tendency to move with spring-like mechanics
(31.8%) than with vaulting mechanics (9.1%). This distribution was
marginally different from the null expectation (22 = 1.0, P = 0.05).
Unlike in Pseudocheirus, there was no evidence that Trichosurus
shifted gaits with decreasing duty factors (speed), with all trials
occurring with a diagonal-sequence diagonal-couplet or trot footfall pattern. Nor did Trichosurus alter COM mechanics with gait
(P = 0.187; r2 = 0.041). Maximum energy recovery in Trichosurus
was 33%.
Monodelphis almost exclusively moved with bouncing mechanics (96.7%) using diagonal-couplet gaits (lateral-sequence diagonalcouplet, trot or diagonal-sequence diagonal-couplet). Because
no vaulting mechanics were observed and rarely did Monodelphis use mixed mechanics, its COM mechanics differed from the
null expectation (22 = 162.45, P < 0.01) and there was no shift
with gait (P = 0.334; r2 = 0.011). Mechanical energy recovery via
pendulum-like mechanisms in Monodelphis was low (less than
10%).
70
A.R. Biknevicius et al. / Zoology 116 (2013) 67–74
Fig. 2. COM mechanics and symmetrical gait in the five marsupials and one eutherian mammal used in this study. Symbols indicate mechanics: 䊉, vaulting; , mixed; ,
bouncing.
Philander predominately used mixed mechanics (61.5%) but also
regularly moved with vaulting and bouncing mechanics (19.2% and
19.2%, respectively). This distribution matched the null expectation (22 = 1.385, P = 0.5). Although the mixed mechanics had a
tendency to shift across the diagonal-couplet gaits as duty factor decreased (from lateral-sequence diagonal-couplet to trot to
diagonal-sequence diagonal-couplet), there was no shift in gait
with speed in trials with vaulting or bouncing mechanics. Consequently, there was no significant relationship between gait and
COM mechanics (P = 0.40; r2 = 0.075). Mechanical energy recovery
in Philander maxed out at 59%.
Rattus in this study never used vaulting mechanics, and thus
its COM mechanics differed from the null expectation (22 =
162.45, P < 0.01). Rattus overwhelmingly preferred moving with
spring-like mechanics (90.7%); all other trials (9.3%) occurred with
mixed mechanics. There was a slight tendency for limb phase to
increase with duty factor so that slower trials corresponded to
lateral-sequence diagonal-couplets, intermediate speed trials to
trots, and the fastest trials to diagonal-sequence diagonal-couplets.
Furthermore, shifts in gait were associated with a phase shift (COM
mechanics) (P = 0.045). Maximum recovery of mechanical energy
in Rattus was 24.5%.
Three of the six species were observed using asymmetrical gaits;
Dasyurus, Trichosurus and Rattus used half-bounds and gallops in
addition to their symmetrical gaits.
3.2. General findings
Several global tendencies could be seen when the data for all
six species were combined and sorted into vaulting, mixed and
bouncing mechanics (Fig. 3):
1. Most of the mammalian species evaluated in this study displayed an ability to move with vaulting, mixed and bouncing
mechanics when using symmetrical gaits; only Monodelphis and
Rattus failed to display all three modes. However, all mammals
we studied tended to avoid vaulting mechanics when moving at
steady speeds (only 26 of the 268 trials; Table 2). Instead, they
Table 2
Distribution of trials conforming to vaulting (phase shift = 135–180◦ ), mixed (45–135◦ ) and bouncing mechanics (45–0◦ ) among small-bodied mammals; values in parentheses
represent the mean ± standard deviation of the phase shifts within each category for each species. Percent recovery reflects the capacity to recover external mechanical energy
via pendulum-like mechanisms during symmetrical gaits. Asymmetrical gaits observed for some species include half bounds (½ B) and gallops (G).
Steady speed
trials
Speed (m s−1 )
Symmetrical gaits only
Vaulting
Dasyurus hallucatus
Pseudocheirus peregrinus
Trichosurus vulpecula
Monodelphis domestica
Philander opossum
Rattus norvegicus
Overall
17
37
44
90
26
54
268
0.36–0.63
0.38–1.90
0.31–2.77
0.32–1.79
0.15–3.5
0.30–0.67
Mixed
◦
Percent recovery
Asymmetrical
gaits observed
0–51.7%
3.3–67.9%
2.4–33.0%
0–9.4%
1.5–59.02%
0–24.5%
½ B, G
–
½ B, G
–
–
½ B, G
Bouncing
◦
5.9% (160 )
22.2% (154.1 ± 16.3◦ )
9.1% (142.0 ± 10.3◦ )
–
19.2% (148.2 ± 9.5◦ )
–
23.5% (115.9 ± 8.9 )
59.3% (84.5 ± 28.2◦ )
59.1% (93.7 ± 26.2◦ )
3.3% (46.5 ± 0.4◦ )
61.5% (81.6 ± 24.5◦ )
9.3% (101.9 ± 22.3◦ )
70.6% (16.6 ± 16.8◦ )
18.5% (16.3 ± 8.1◦ )
31.8% (18.5 ± 11.2◦ )
96.7% (19.1 ± 13.4◦ )
19.2% (39.4 ± 19.5◦ )
90.7% (11.3 ± 8.6◦ )
10.1%
28.9%
61.0%
A.R. Biknevicius et al. / Zoology 116 (2013) 67–74
Fig. 3. Vaulting mechanics (top), mixed mechanics (middle) and bouncing mechanics (bottom) plotted.
preferentially moved with bouncing mechanics (61%) or mixed
mechanics (28.9%).
2. Across a large range of duty factors (0.45–0.70), these mammals
interchangeably used vaulting, mixed and bouncing mechanics while predominately using diagonal-couplet gaits (i.e., trot
or its imprecise variants: lateral-sequence diagonal-couplet and
diagonal-sequence diagonal-couplet). Consequently, there was
little fidelity between symmetrical gait and COM mechanics.
3. Most symmetrical gaits were grounded, that is, they occurred
without an aerial phase. As aerial phases are impossible at high
duty factors (>0.5), all trials with vaulting and mixed mechanics were grounded as were over half of the bouncing mechanics
trials.
4. Discussion
The small-bodied mammals in this study are clearly predisposed away from moving with vaulting mechanics (Fig. 3, top).
A survey of other small mammals indicates a similar bias. It is
not surprising that mammals that favor asymmetrical gaits have
this bias since these running gaits occur with mixed mechanics that have a predominant influence of bouncing mechanics
(Cavagna et al., 1977). These mammals include the bipedal hoppers,
such as Pedetes (springhare) and Dipodomys (kangaroo rat), and
quadrupedal bounding or galloping species, such as Tamias (chipmunk), Spermophilus (ground squirrel) and Antechinus (marsupial
mouse) (Cavagna et al., 1977; Heglund et al., 1982; Biknevicius,
pers. obs.). Although we did not evaluate the COM mechanics
of the half bounds and gallops recorded in Dasyurus, Trichosurus and Rattus, it is likely that these trials displayed mixed or
bouncing mechanics. Small mammals using symmetrical gaits are
only slightly more likely to employ vaulting mechanics. The three
Australian marsupials (Dasyurus, Pseudocheirus, and Trichosurus)
and one of the New World marsupials (Philander) occasionally
move with vaulting mechanics but vastly prefer either bouncing
or mixed mechanics. Monodelphis virtually avoided using anything
but bouncing mechanics. While that was also true of Rattus in this
71
study, another study obtained occasional trials in Rattus that were
consistent with vaulting mechanics (Horner et al., 2011). Finally,
a study of Mustela (ferret) also reported a dominance of bouncing
mechanics (71%) over mixed (18%) and vaulting (11%) mechanics
(Horner and Biknevicius, 2010).
Some non-mammalian tetrapods also limit the use of vaulting mechanics during steady speed locomotion, but this is by
no means ubiquitous (Table 3). Indeed, the finding that Sphenodon (tuatara), a generalized amniote, uses vaulting, bouncing and
mixed mechanics with near-equal frequencies (Reilly et al., 2006)
might lead one to expect little preference across tetrapods. Yet
among the two amphibians evaluated to date, Kassina (frog) clearly
prefers bouncing mechanics, whereas Ambystoma (salamander) is
slightly more partial to vaulting mechanics (Ahn et al., 2004; Reilly
et al., 2006). Bouncing mechanics is most commonly used among
squamates although there is some variation within the clade.
Many lizards avoid vaulting mechanics completely (Hemidactylus,
Laudakia, Leiocephalus, Cordylus, Eulamprus, Lepidophyma, Oplurus,
Sceloporus, and Tropidurus), while others sporadically move with
vaulting mechanics (Coleonyx, Plestiodon, Varanus, and Acanthodactylus) (Farley and Ko, 1997; Chen et al., 2006; McElroy et al.,
2008). For both groups of lizards, the predominant mode is bouncing mechanics with occasional use of mixed mechanics. Only
two species of lizards make substantial use of vaulting mechanics during terrestrial locomotion (Trachelopthychus and Eumeces)
(McElroy et al., 2008), and both of these are as likely or more
to employ mixed mechanics. Finally, crocodilians (Alligator) are
biased toward vaulting mechanics (Willey et al., 2004). All of the
non-mammalian tetrapod trials described above occurred with
symmetrical gaits.
Why are so many small-bodied tetrapods biased away from
vaulting mechanics when using symmetrical gaits? One possible explanation is founded on locomotor energetics. The cost of
transport reflects the external mechanical energy used to move
the COM as well as internal energies used to move body segments. The pendulum-like exchange of EP and EK that occurs
during vaulting mechanics only impacts the external mechanical
energy requirements. The maximum recovery of external mechanical energy via pendulum-like mechanisms in the present study
was comparable to that reported for cursorial mammals (∼60%)
(Griffin et al., 2004b). Yet these savings may be inconsequential
to the true cost of transport in small mammals because these
species are in the size range where external mechanical energy
of the COM represents a small component of the total cost of
transport (Fig. 1). In Monodelphis, the smallest mammal in the
study, external mechanical energy only represents about 3% of
the total energy required to move the body. Even though external mechanical energy becomes a more substantial component
of the cost of transport as body size increases, it still only represents about 20% of energy needs for the largest mammal in
our study (Trichosurus). In other words, even if small mammals
had 100% recoveries of external mechanical energies, they would
still have to pay for the bulk of their locomotor costs via muscular effort. A comparable situation is found in penguins, which
recover as much as 80% of mechanical energy via pendulum-like
mechanisms yet have very high metabolic costs for terrestrial
locomotion (Pinshow et al., 1977; Griffin and Kram, 2000); the
mismatch in penguins is explained by the shortness of their limbs
and the greater muscular effort required to drive their stride frequencies. Admittedly, directly linking COM mechanics with cost
of transport has proven to be difficult to accomplish and, in some
studies, both have not been found to be tightly coupled (Heglund
et al., 1982; Griffin et al., 2003; Usherwood et al., 2007); yet
the substantial difference between the cost of transport in small
versus large mammals – paired with the near equity in total
external mechanical energy for terrestrial locomotion across the
72
A.R. Biknevicius et al. / Zoology 116 (2013) 67–74
Table 3
Percentage of trials conforming to vaulting (phase shift = 135–180◦ ), mixed (45–135◦ ) and bouncing mechanics (45–0◦ ) across quadrupedal amniotes. N, number of specimens
per species.
Sphenodon punctatus (Tuatara)
Ambystoma tigrinum (Tiger salamander)
Kassina maculata (Red-legged running frog)
Coleonyx variegatus (Western banded gecko)
Plestiodon (Eumeces) skiltonianus (Western skink)
Hemidactylus garnoti (Indo-Pacific gecko)
Tracheloptychus petersi (Malagasy plated lizard)
Varanus exanthematicus (Savannah monitor)
Ameiva ameiva (Common ameiva)
Eublepharis macularius (Leopard gecko)
Eumeces schneideri (Schneider’s skink)
Tupinambis teguixin (Gold tegu)
Acanthodactylus boskianus (Daudin’s fringe-toed lizard)
Laudakia (Agama) stellio (Stellion/star lizard)
Leiocephalus schreibersi (Red-sided curly-tailed lizard)
Cordylus warreni (Warren’s girdled lizard)
Eulamprus quoyii (Eastern water skink)
Lepidophyma flavimaculatum (Yellow-spotted night lizard)
Oplurus cuvieri (Collared iguana)
Sceloporus malachiticus (Emerald swift)
Tropidurus torquatus (Amazon lava lizard)
Alligator mississippiensis (American alligator)
Blaberus discoidalis (Discoid cockroach)
Periplaneta americana (American cockroach)
Ocypode quadrata (Ghost crab)
N
Vaulting
Mixed
Bouncing
Source
3
6
12
4
3
5
2
3
3
1
3
2
8
2
3
4
3
3
3
4
3
5
13
8
?
38.5
44.8
12.5
18.2
22.2
0
34.6
6.9
11.8
31.6
43.2
33.3
4.0
0
0
0
0
0
0
0
0
73.3
2.1
0
B
23.0
31.0
21.9
0
7.4
0
50
15.8
61.8
47.4
48.6
37.0
16.0
8.7
8.8
31.8
10.0
33.3
0
12.5
6.5
26.7
32.6
A
B
38.5
24.1
65.6
81.8
70.4
100
15.4
77.2
26.3
21.0
8.1
29.6
80.0
91.3
91.2
68.2
90.0
66.7
100.0
87.5
93.5
0
65.2
A
B
Reilly et al. (2006)
Reilly et al. (2006)
Ahn et al. (2004)
Farley and Ko (1997)
Farley and Ko (1997)
Chen et al. (2006)
McElroy et al. (2008)
McElroy et al. (2008)
McElroy et al. (2008)
McElroy et al. (2008)
McElroy et al. (2008)
McElroy et al. (2008)
McElroy et al. (2008)
McElroy et al. (2008)
McElroy et al. (2008)
McElroy et al. (2008)
McElroy et al. (2008)
McElroy et al. (2008)
McElroy et al. (2008)
McElroy et al. (2008)
McElroy et al. (2008)
Willey et al. (2004)
Full and Tu (1990)
Full and Tu (1991)
Blickhan and Full (1987)
A – Full and Tu (1991) only noted phase shifts of 46 ± 9.06◦ (mean ± S.E.M.), indicating that only bouncing and mixed mechanics occurred in Periplaneta.
B – Blickhan and Full (1987) do not report phase shift values but note that both out-of-phase and in-phase relationships were obtained for Ocypode.
mammalian size range (∼1.1 J kg−1 m−1 ; Full, 1991) and similarly
low muscle efficiencies (∼25%; Hill, 1938; Cavagna and Kaneko,
1977) – is strongly suggestive of a real difference in the energysaving capacity of pendulum-like mechanisms when small and
large mammals walk, even if the true magnitudes of these differences are uncertain.
Another factor limiting the use of vaulting mechanics in small
mammals may be their tendency to move with intermittent locomotion, a locomotor behavior characterized by brief locomotor
bouts interspersed with periods of rest or pauses (reviewed in
Kramer and McLaughlin, 2001). These locomotor bouts are flanked
by rapid accelerations and decelerations and, therefore, locomotor
intermittency predisposes tetrapods against moving with slow and
steady speeds. Several functions have been proposed for intermittent locomotion, including antipredatory strategy, improved visual
surveillance and energetic economy (Kramer and McLaughlin,
2001). Interestingly, a recent study found that vaulting mechanics are extremely common in armored mammals (Tachyglossus,
echidna; Atelerix, hedgehog), leading the authors to conclude
that the release of predatory pressures allows these mammals to
move at slow and steady speeds conducive to vaulting mechanics (Biknevicius, unpubl. data). Therefore, whether driven by
an ambivalence towards the low energetic rewards of vaulting
mechanics or by behavioral tendencies to move intermittently with
quick but short bouts, many small mammals appear to curb the use
of vaulting mechanics during terrestrial locomotion.
However, it would be inappropriate to conclude that our limited
observations of vaulting mechanics suggest that walking is not an
important part of the locomotor repertoire in small animals. Small
mammals moving particularly slowly, as when foraging in a safe
area (Kenagy and Hoyt, 1989), are almost certainly vaulting at least
sometimes. Accordingly, slow-moving gaits have been observed
in many small mammals (Dagg, 1973; Hildebrand, 1976). These
slow-moving events are traditionally characterized as walking gaits
because of their high duty factors (<0.5) and the lack of an aerial
phase (Hildebrand, 1976), but these criteria do not exclude the possibility that some of these observations are actually grounded runs
(Biknevicius and Reilly, 2006) nor do they prove that any of the trials consisted of vaulting mechanics. The real challenge for future
research is to recreate more realistic conditions with the goal of
coaxing small animals to move with their full range of locomotor
behaviors, including very slow speeds. Of course, this would also
require methods to evaluate COM mechanics at non-steady speeds.
The reason for preferring bouncing mechanics is also unclear.
Bouncing mechanics may not provide an energetic boost to small
mammals when they run. Small mammals have a contradictory
relationship between the stiffness of their limbs and the stiffness
of the biological springs within their limbs. Leg stiffness is low in
small mammals (Farley et al., 1993), which might lead one to expect
that they are stretching their tendons during the first half of stance
phase and then recovering elastic strain energy during the latter
half of stance as a means for reducing the metabolic cost of running.
However, the tendons of small mammals tend to be too short and
thick to provide meaningful elastic strain energy storage and recovery (Biewener et al., 1981; Pollock and Shadwick, 1994; Bennett
and Taylor, 1995). The ecomorphological significance of low leg
stiffness may instead be related to the crouched posture of small
mammals and the high degree of maneuverability that is associated
with moving with flexed limbs. Tendons with high stiffness more
perfectly transmit muscular forces to the skeleton (i.e., avoiding a
long “toe region” in their mechanical behavior under tension), a
useful feature for the rapid and powerful accelerative efforts associated with intermittent locomotion (Biewener and Blickhan, 1988;
Biewener et al., 1988). Furthermore, running with compliant limbs
may provide improved stability when passing over uneven terrain
(Daley and Usherwood, 2010).
Therefore, the energy-saving aspects of both vaulting mechanics
and bouncing mechanics confer questionable physiological advantages for small-bodied mammals. This may explain the lack of
fidelity between COM mechanics and gaits noted in this study, as
exemplified by the use of a single gait (diagonal-sequence diagonalcouplet) with vaulting, bouncing and mixed mechanics in Dasyurus
(at duty factor 0.64), Pseudocheirus (0.56) and Trichosurus (0.51). In
other words, these mammals moved at a particular speed with a
A.R. Biknevicius et al. / Zoology 116 (2013) 67–74
particular gait and interchangeably used different COM mechanics.
Not surprisingly, therefore, ascertaining a walk or a run based on
footfall patterns alone is often difficult, if not impossible, in small
mammals. The task is further confounded by the common use of
grounded runs in small mammals (Biknevicius and Reilly, 2006).
These features of terrestrial locomotion in small mammals are
sharply contrasted by the condition in large, more cursorially
adapted mammals, such as dogs, horses and humans. Walks and
runs typically involve different gaits that are correlated to vaulting and bouncing mechanics (Cavagna et al., 1977; Minetti et al.,
1999; Griffin et al., 2004b); consequently, the natural walk–run
transitions are discrete events with a concurrent shift in gait
and mechanics. Only elephants and Icelandic horses have been
shown to use a more seamless transition between walks and runs
(Hutchinson et al., 2003; Biknevicius et al., 2006). Perhaps it is
because the recovery of external energy by pendulum-like mechanisms when vaulting or elastic strain energy when bouncing is
energetically meaningful for large mammals so that they may be
more careful at matching speed and gait. For these mammals, moving faster or slower than preferred speeds reduces the efficiency of
vaulting mechanics (Griffin et al., 2004b). Similarly, matching step
frequency with the resonant frequency of the limb–body system
helps to moderate muscular effort when bouncing (Farley et al.,
1993; Cavagna et al., 1997).
Our data illuminate the fundamentally different ways that gait
and COM mechanics interface during small mammal locomotion
and show that there is substantial variation across the six smallbodied species examined in this study. Overall, these findings
suggest few generalizations can be made across mammals, largely
because body size and limb posture have a major impact on locomotor mechanics.
Acknowledgements
We thank Martin Fingland at Geckoes Wildlife Presentations
(Queensland, Australia) for access to Dasyurus, Pseudocheirus and
Trichosurus specimens in his care. We also acknowledge the assistance provided by Amy Back, Jennifer Hancock, Kristin Stover, and
Celeste Taylor during the data capture phase of the study. The study
was supported by a United States National Science Foundation
grant (IOB 0520100).
References
Ahn, A.N., Furrow, E., Biewener, A., 2004. Walking and running in the red-legged
running frog, Kassina maculata. J. Exp. Biol. 207, 399–410.
Bennett, M.B., Taylor, G.C., 1995. Scaling of elastic strain energy in kangaroos and
the benefits of being big. Nature 378, 56–59.
Bennett, M.B., Ker, R.F., Dimery, N.J., Alexander, R.M., 1986. Mechanical properties
of various mammalian tendons. J. Zool. (London) 209, 537–548.
Biewener, A.A., 1990. Biomechanics of mammalian terrestrial locomotion. Science
250, 1097–1103.
Biewener, A.A., Baudinette, R.V., 1995. In vivo force and elastic energy storage during
steady-speed hopping of tammar wallabies (Macropus eugenii). J. Exp. Biol. 198,
1829–1841.
Biewener, A.A., Blickhan, R., 1988. Kangaroo rat locomotion: design for elastic energy
storage or acceleration? J. Exp. Biol. 140, 243–255.
Biewener, A., Alexander, R.M., Heglund, N.C., 1981. Elastic energy storage in the
hopping of kangaroo rats (Dipodomys spectabilis). J. Zool. (London) 195, 369–383.
Biewener, A.A., Blickhan, R., Perry, A.K., Heglund, N.C., Taylor, C.R., 1988. Muscle
forces during locomotion in kangaroo rats: force platform and tendon buckle
measurements compared. J. Exp. Biol. 137, 191–205.
Biknevicius, A.R., Reilly, S.M., 2006. Correlation of symmetrical gaits and whole
body mechanics: debunking myths in locomotor biodynamics. J. Exp. Zool. 305,
923–934.
Biknevicius, A.R., Mullineaux, D.R., Clayton, H.R., 2006. Locomotor mechanics of the
tolt in Icelandic horses. Am. J. Vet. Res. 2006, 1505–1510.
Blickhan, R., Full, R.J., 1987. Locomotion energetics of the ghost crab. II. Mechanics
of the center of mass. J. Exp. Biol. 130, 155–174.
Blickhan, R., Full, R.J., 1992. Mechanical work in terrestrial locomotion. In: Biewener,
A.A. (Ed.), Biomechanics: Structures and Systems, A Practical Approach. IRL Press
at Oxford University Press, Oxford, pp. 75–96.
73
Bullimore, S., Burn, J.F., 2005. Scaling of elastic energy storage in mammalian limb
tendons: do small mammals really lose out? Biol. Lett. 1, 57–59.
Cavagna, G.A., Kaneko, M., 1977. Mechanical work and efficiency in level walking
and running. J. Physiol. (London) 268, 467–481.
Cavagna, G.A., Heglund, N.C., Taylor, C.R., 1977. Mechanical work in terrestrial
locomotion: two basic mechanisms for minimizing energy expenditure. Am.
J. Physiol. 233, R243–R261.
Cavagna, G.A., Mantovani, M., Willems, M., Musch, G., 1997. The resonant step frequency in human running. Eur. J. Physiol. 434, 678–684.
Chen, J.J., Peattie, A.M., Autumn, K., Full, R.J., 2006. Differential leg function in a
sprawled-posture quadrupedal trotter. J. Exp. Biol. 209, 249–259.
Dagg, A.I., 1973. Gaits in mammals. Mamm. Rev. 3, 135–154.
Daley, M.A., Usherwood, J.R., 2010. Two explanations for the compliant running paradox: reduced work of bouncing viscera and increased stability in uneven terrain.
Biol. Lett. 6, 418–421.
Doke, J., Donelan, J.M., Kuo, A.D., 2005. Mechanics and energetics of swinging the
human leg. J. Exp. Biol. 208, 439–445.
Donelan, J.M., Kram, R., Kuo, A.D., 2002. Simultaneous positive and negative external
mechanical work in human walking. J. Biomech. 35, 117–124.
Farley, C.T., Ko, T.C., 1997. Mechanics of locomotion in lizards. J. Exp. Biol. 200,
2177–2188.
Farley, C.T., Glasheen, J., McMahon, T.A., 1993. Running springs: speed and animal
size. J. Exp. Biol. 185, 71–86.
Full, R.J., 1991. The concepts of efficiency and economy in land locomotion. In: Blake,
R.W. (Ed.), Efficiency and Economy in Animal Physiology. Cambridge University
Press, Cambridge, pp. 97–131.
Full, R.J., Tu, M.S., 1990. Mechanics of six-legged runners. J. Exp. Biol. 148, 129–146.
Full, R.J., Tu, M.S., 1991. Mechanics of a rapid running insect: two-, four-, and sixlegged locomotion. J. Exp. Biol. 156, 215–231.
Gatesy, S.M., Biewener, A.A., 1991. Bipedal locomotion: effects of speed, size and
limb posture in birds and humans. J. Zool. (London) 224, 127–147.
Griffin, T.M., Kram, R., 2000. Penguin waddling is not wasteful. Nature 408, 929.
Griffin, T.M., Roberts, T.J., Kram, R., 2003. Metabolic cost of generating muscular force
in human walking: insights from load-carrying and speed experiments. J. Appl.
Physiol. 95, 172–183.
Griffin, T.M., Kram, R., Wickler, S.J., Hoyt, D.F., 2004a. Biomechanical and energetic determinants of the walk–trot transition in horses. J. Exp. Biol. 207,
4215–4223.
Griffin, T.M., Main, R.P., Farley, C.T., 2004b. Biomechanics of quadrupedal walking:
how do four-legged animals achieve inverted pendulum-like movements? J.
Exp. Biol. 207, 3545–3558.
Heglund, N.C., Fedak, M.A., Taylor, C.R., Cavagna, G.A., 1982. Energetics and mechanics of terrestrial locomotion. IV. Total mechanical energy changes as a function
of speed and body size in birds and mammals. J. Exp. Biol. 97, 57–66.
Hildebrand, M., 1976. Analysis of tetrapod gaits: general considerations and symmetrical gaits. In: Herman, R.M., Grillner, S., Stein, P.S.G., Stuart, D.G. (Eds.),
Neural Control of Locomotion. Plenum Press, New York, pp. 203–236.
Hildebrand, M., 1977. Analysis of asymmetrical gaits. J. Mammal. 58, 131–156.
Hill, A.V., 1938. The heat of shortening and the dynamic constants of muscle. Proc.
R. Soc. London 126, 136–195.
Hooper, S.L., Guschlbauer, C., Blumel, M., Rosenbaum, P., Gruhn, M., Akay, T.,
Buschges, A., 2009. Neural control of unloaded leg posture and of leg swing in
stick insect, cockroach, and mouse differs from that in larger animals. J. Neurosci.
29, 4109–4119.
Horner, A.M., Biknevicius, A.R., 2010. A comparison of epigean and subterranean
locomotion in the domestic ferret (Mustela putorius furo: Mustelidae: Carnivora).
Zoology 113, 189–197.
Horner, A.M., Russ, D.W., Biknevicius, A.R., 2011. Effects of aging on locomotor
dynamics and hindlimb muscle force production in the rat. J. Exp. Biol. 214,
3588–3595.
Hutchinson, J.R., Famini, D., Lair, R., Kram, R., 2003. Are fast-moving elephants really
running? Nature 422, 493–494.
Kenagy, G.J., Hoyt, D.F., 1989. Speed and time–energy budget for locomotion in goldmantled ground squirrels. Ecology 70, 1834–1839.
Kram, R., Taylor, C.R., 1990. Energetics of running: a new perspective. Nature 346,
265–267.
Kramer, D.L., McLaughlin, R.L., 2001. The behavioral ecology of intermittent locomotion. Am. Zool. 41, 137–153.
McElroy, E.J., Hickey, K.L., Reilly, S.M., 2008. The correlated evolution of biomechanics, gait and foraging mode in lizards. J. Exp. Biol. 211, 1029–1040.
Minetti, A.E., Ardigo, L.P., Reinach, E., Saibene, F., 1999. The relationship between
mechanical work and energy expenditure of locomotion in horses. J. Exp. Biol.
202, 2329–2338.
Nowak, R.M., 1991. Walker’s Mammals of the World. The Johns Hopkins University
Press, Baltimore.
Nowak, R.M., 2005. Walker’s Marsupials of the World. The Johns Hopkins University
Press, Baltimore.
Parchmann, A.J., Reilly, S.M., Biknevicius, A.R., 2003. Whole-body mechanics and
gaits in the gray short-tailed opossum Monodelphis domestica: integrating patterns of locomotion in a semi-erect mammal. J. Exp. Biol. 206, 1379–1388.
Pinshow, B., Fedak, M.A., Schmidt-Nielsen, K., 1977. Terrestrial locomotion in penguins: it costs most to waddle. Science 195, 592–594.
Pollock, C.M., Shadwick, R.E., 1994. Allometry of muscle, tendon and elastic energy
storage capacity in mammals. Am. J. Physiol. 226, R1022–R1031.
Pontzer, H., 2007. Predicting the energy cost of terrestrial locomotion: a test of the
LiMb model in humans and quadrupeds. J. Exp. Biol. 210, 484–494.
74
A.R. Biknevicius et al. / Zoology 116 (2013) 67–74
Reilly, S.M., McElroy, E.J., Odum, R.A., Hornyak, V.A., 2006. Tuataras and salamanders show that walking and running mechanics are ancient features of tetrapod
locomotion. Proc. R. Soc. B 273, 1563–1568.
Reilly, S.M., McElroy, E.J., Biknevicius, A.R., 2007. Posture, gait and the ecological relevance of locomotor costs and energy-saving mechanisms in tetrapods. Zoology
110, 271–289.
Rubenson, J., Marsh, R.L., 2009. Mechanical efficiency of limb swing during walking
and running in guinea fowl (Numida meleagris). J. Appl. Physiol. 106, 1618–1630.
Steudel, K., Beattie, J., 1990. Scaling of cursoriality in mammals. J. Morphol. 217,
55–63.
Usherwood, J.R., Williams, S.B., Wilson, A.M., 2007. Mechanics of dog walking compared with a passive, stiff-limbed, 4-bar linkage model, and their collisional
implications. J. Exp. Biol. 210, 533–540.
Van Damme, R., Aerts, P., Vanhooydonck, B., 1998. Variation in the morphology, gait
characteristics and speed of locomotion in two populations of lizards. Biol. J.
Linnean Soc. 63, 409–427.
Willey, J.S., Biknevicius, A.R., Reilly, S.M., Earls, K.D., 2004. The tale of the tail: limb
function and locomotor mechanics in Alligator mississippiensis. J. Exp. Biol. 207,
553–563.