The tale of the tail: limb function and locomotor mechanics in Alligator mississippiensis
1 Department of Biological Sciences, Ohio University College of Osteopathic
Medicine, Athens, OH 45701, USA
2 Department of Biomedical Sciences, Ohio University College of Osteopathic
Medicine, Athens, OH 45701, USA
Author for correspondence (e-mail:
biknevic{at}ohio.edu)
Accepted 29 October 2003
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Summary |
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Key words: locomotion, kinetics, limb function, tail-dragging, ground reaction force, Alligator mississippiensis
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Introduction |
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A tail may not always be a positive attribute during terrestrial
locomotion. Large tails may need to be elevated in order to avoid interfering
with hindlimb movements (Irschick and
Jayne, 1999) or to reduce rotational inertia when the animal
attempts a sharp turn (Carrier et al.,
2001
). Tails that provide propulsive power during swimming in
semiaquatic tetrapods may compromise terrestrial locomotion. The enlarged,
muscular tails of crocodilians, for example, are key to their predatory
success in aquatic attacks (Manter,
1940
) but these same tails presumably apply a constant
decelerative impulse to the center of mass during terrestrial locomotion
because they are typically not elevated off the ground. Yet, crocodilians
spend a substantial amount of time on dry land, periodically trekking long
distances between aquatic resources
(Tucker et al., 1997
), all the
while dragging their tails behind them.
Limbs must resist the force of gravity, modulate forward impulsion and
maintain lateral stability during terrestrial locomotion. These efforts are
energetically costly, but studies in bipedal and quadrupedal tetrapods have
shown that some external mechanical energy can be conserved by two
energy-saving mechanisms (Cavagna et al.,
1977). Inverse pendulum mechanics are employed at slower speeds,
when gravitational potential energy and kinetic energy cycle out-of-phase with
one another and therefore may be exchanged in a pendulum-like manner. At
higher speeds, spring mechanics may be used, where gravitational potential and
kinetic energies are exchanged with elastic strain energy through the
stretching and recoiling of spring elements in the limbs (e.g. tendons and
ligaments). These models have been documented for a wide array of terrestrial
vertebrates, including birds, humans and cursorial mammals
(Cavagna et al., 1977
).
However, the ubiquity of these models across terrestrial tetrapods may be
overstated and, furthermore, the effect of an unelevated tail on locomotor
mechanics has not been explored.
In the present study, we explore locomotor biodynamics in the American
alligator (Alligator mississippiensis) during high walking. The high
walk is the most common terrestrial locomotor behavior of extant crocodilians;
it is a trotting gait with a semi-erect locomotor posture (in which limb
orientation is between sprawling and erect grades during terrestrial
locomotion; Gatesy, 1991;
Reilly and Elias, 1998
).
Ground reaction forces are examined to address two fundamental questions.
First, how does Alligator partition the roles of body mass support,
braking and propulsive effort, and mediolateral stability among its supporting
limbs and tail? And, second, can high-walking, tail-dragging alligators
capitalize on the same energy-saving mechanisms found in more sprawling and
more erect animals (walking with inverse pendular mechanics or running with
spring-mass mechanics)?
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Materials and methods |
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The alligators were conditioned for terrestrial locomotion over three months. The animals were removed from their tanks regularly and were encouraged to walk repeatedly along a 5 m trackway as well as to walk freely in the holding room.
Data collection
Ground reaction force data were captured as the alligators moved across a
Kistler force platform (plate Type 9281B; Amherst, NY, USA) mounted flush with
the surface of a 6.1 m trackway. Force outputs were captured at 500 Hz and
resolved into vertical, craniocaudal and mediolateral force components using
the Kistler Bioware 2.0 software. Each animal was permitted to choose its own
locomotor speed, as attempts to encourage faster trials yielded unacceptable
behavior (reversing direction or attacking the encouraging hand). Each trial
was recorded at 250 frames s-1 using a MotionScope 500 camera
(Redlake Corp., San Diego, CA, USA). These recordings enabled the
identification of footfall patterns (gait), estimation of mean forward speed
(using a reference grid of 10-cm increments along the back wall of the
trackway), stride duration (elapsed time between ground strikes of individual
feet) and support duration (duration of foot contact with the ground). Duty
factor was computed as the quotient of stride duration to support duration.
Kinematic gait was determined with the Hildebrand
(1976) gait graph by plotting
limb phase, or the percent of the stride that the ipsilateral forelimb lands
after the reference hindlimb, against duty factor.
Individual limb and tail kinetics
In order to optimize the capture of force records for individual limb
strikes, a triangular insert (244.25 cm2) was firmly affixed to the
surface of the force platform (Fig.
1A); the uninstrumented part of the runway covered the remainder
of the force platform. Video reviews eliminated trials that lacked clean
footfalls, i.e. partial or overlapping. Forward speed was also determined
videographically using the 10 cm grid along the back wall of the trackway.
Trials in which the animals were clearly accelerating or decelerating were not
analyzed. This was assessed by comparing forward velocity estimated
immediately over the force platform to the mean velocity determined over a
longer distance (70 cm); trials for which the central velocity differed from
the mean velocity by greater than 5% were dropped from the analysis.
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Ground reaction force records for individual limbs were evaluated for peak forces (maximum displacement of a force record) and impulses (area under a force profile). The vertical component of force was analyzed as the peak vertical force and vertical impulse, measuring the role of the limbs in body mass support. Horizontal forces were distinguished into craniocaudal and mediolateral components. Net craniocaudal impulse reflected the overall role of the limb in controlling forward momentum; negative values reflected overall braking efforts whereas propulsive efforts were positive. The craniocaudal records were further subdivided into the braking (negative) and propulsive (positive) components, and impulses for each were calculated. Net mediolateral impulses were standardized so that negative values reflected an overall lateral push by the limb on the ground (i.e. a medially directed ground reaction force). The units for force and impulses are body weight units (BWU) and BWU·s, respectively, in order to adjust for differences in body size across individuals.
The entire surface of the Kistler force platform (60 cm x 40 cm) was used to obtain ground reaction forces from the tail (Fig. 1B). The tail was dragged behind the animal, so that pure tail records were obtained once the animal completely stepped off the plate. Peak forces were thus obtained for the tail. However, because the hindlimb record overlapped the initial segment of the tail record, precise determination of impulses over the entire support phase of the tail could not be determined. Rather, we estimated tail impulses over the mean step duration of the fore- and hindlimbs (1.54 s).
Vertical impulse (Qz) was used to estimate the role of
each limb and the tail in body mass support. The relative role of the forelimb
in body support (%Qz,fore, or relative support impulse)
during the high walk was calculated using an equation modified from Jayes and
Alexander (1980):
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Using the criteria described previously for assessing steady speed,
analysis of individual foot function was conducted on 60 trials (12 trials per
animal). A repeated-measures analysis of variance (SYSTAT 9) was used to
evaluate differences between forelimbs and hindlimbs in speed, support
duration, peak forces, impulses, time to peak vertical force, and timing of
the shift from braking to propulsion in the craniocaudal force record. Limb
pairs were treated as independent factors crossed with the five subjects. No
individual effects were found within the timing and kinetic variables for each
limb; hence, the data from all individuals were pooled. Sequential Bonferroni
corrections were made for multiple comparisons (following
Rice, 1989). Additionally,
reduced major axis regression evaluated speed effects on support duration,
peak vertical force, and craniocaudal and mediolateral impulses (SYSTAT
9).
Whole-body mechanics
The entire surface of the Kistler force platform (60 cm x 40 cm) was
also used for the whole-body mechanics study
(Fig. 1C). The alligators
typically took one full and two partial steps as they crossed the force
platform. Analysis focused on a single step (forelimb strike to contralateral
forelimb strike). Valid trials for this analysis were identified as those for
which craniocaudal velocity, determined by the first integration of the
craniocaudal force, was fairly well balanced about mean forward velocity
(determined videographically), indicating that the animal was neither strongly
decelerating nor accelerating during the step. Only 15 out of nearly 500
trials from four alligators met both criteria and were used in this analysis.
Although the platform surface was sufficiently long to obtain a complete step
with all limbs over the platform, it could not simultaneously support the
entire tail. Therefore, force records produced by the tail alone (see above)
were added to those of the limbs at equivalent speeds to obtain whole-body
records. This was possible because the force records of the tail were
non-oscillating.
Force data for single steps were imported into a LabView (National
Instruments, Austin, TX, USA) virtual instrument in order to determine
fluctuations of external mechanical energy, following the method described by
Blickhan and Full (1992) and
Donelan et al. (2002
). Because
the high walk of alligators has some temporal irregularities in footfalls
(i.e. they are somewhat `sloppy' trotters), a step is defined as the time
between the touchdown of the first limb in a diagonal couplet to the touchdown
of the first limb of the opposite couplet. Accelerations of the center of mass
in vertical, craniocaudal and mediolateral directions were obtained by
dividing the forces by body mass; body weight was first subtracted from the
vertical forces. Velocities of the center of mass for each direction were then
estimated by taking the first integration of acceleration. While the
integration constant for the craniocaudal direction was set to mean forward
velocity (Blickhan and Full,
1992
), the constants were estimated as the mean value for the
vertical and mediolateral records (Donelan
et al., 2002
). Velocities (v) were used to calculate
kinetic energies (Ek=GMv2,
where M is body mass in kg) in the vertical
(Ek,V), craniocaudal (Ek,CC)
and mediolateral (Ek,ML) directions. Total kinetic energy
of the center of mass (Ek,tot) during the step was then
calculated as the sum of all three components
(Ek,V+Ek,CC+Ek,ML).
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). Changes in vertical
displacement were used to determine changes in gravitational potential energy
(Ep=Mgh, where
g is gravitational acceleration or 9.81 m s-2)
during the step.
Phase-shifts between total kinetic energy
(Ek,tot) and gravitational potential energy
(Ep) during a step were calculated as the difference
between when Ek,tot and Ep reached
their minimal values relative to the duration of the stride multiplied by
360° (Farley and Ko,
1997). Perfect inverted-pendulum mechanics are characterized by
180° phase shift between Ek,tot and
Ep so that Ek,tot is at its minimum
when Ep is maximum (i.e. Ek,tot and
Ep are out-of-phase). By contrast,
Ek,tot and Ep are in-phase (phase
shift=0°) in spring-mass mechanics because Ek,tot and
Ep each reach their minimal values simultaneously during
the step. These energy patterns have been used to distinguish walks from runs
from the whole-body perspective (Cavagna et
al., 1977
). We specify these as mechanical walks and runs, because
movements of the center of mass are determined through force data, as a
contrast to the kinematic walks and runs determined by footfall patterns
(gaits) alone.
Recovery of mechanical energy (%R) due to pendulum-like exchange
between Ek,tot and Ep during a step
was calculated according to Blickhan and Full
(1992):
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Finally, the positive work done against gravity was computed as the sum of the positive increments of (Ep+Ek,V). Similarly, summing the positive increments of Ek,CC and Ek,ML provides the positive work done to accelerate the body forward and laterally, respectively.
Center of gravity
At the completion of the study, all alligators were euthanised with an
overdose of sodium pentobarbital, and the craniocaudal and dorsoventral
positions of their centers of gravity were determined using the reaction board
method (Ozkaya and Nordin,
1999). Three conditions were evaluated. First, centers of gravity
were determined in intact animals with limbs replicating a midstance
semi-erect posture. Second, shifts in the center of gravity were recorded when
the diagonal limbs were fully protracted and then fully retracted (replicating
limb movements during a trot). Finally, tails were removed at the first caudal
vertebra in order to assess the impact of the tail on the craniocaudal
positioning of the center of gravity. The craniocaudal position of the center
of gravity was determined relative to the distance between the scapular
glenoid fossa and the acetabulum, so that 0% and 100% reflect glenoid and
acetabular locations of the center of gravity, respectively.
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Results |
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Individual limb and tail kinetics
Alligator chose to high walk within a speed range of
0.16±0.01 m s-1 (0.07-0.26 m s-1). Support
durations were, on average, comparable between forelimbs and hindlimbs
(Table 1), and speed-related
increases in support duration were observed in both limb pairs
(Table 2).
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Peak vertical forces were significantly higher for the hindlimbs than for the forelimbs (Fig. 3A,B; Table 1). Hindlimb vertical force records were also distinctive because they usually displayed a brief impact spike and because the peak vertical force of the hindlimbs occurred significantly earlier in the support phase than that of the forelimbs (Fig. 3A; Table 1). Significant speed-related increases in peak vertical force were found for the hindlimb only (Table 2). Vertical forces applied by the tail were substantial (0.08±0.02 BWU); these forces were, on average, 18.5% and 14.4% of fore- and hindlimb values, respectively.
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Although both limbs displayed an initial braking effort followed by a propulsive effort (Fig. 3A), braking impulses were significantly greater in the forelimbs whereas greater propulsive impulses were generated by the hindlimbs (Table 1). The high braking impulses of the forelimbs were due to the lengthened braking phase in the forelimb records (68% of support phase compared with only 15% in hindlimbs), whereas the high propulsive impulses in the hindlimb records were reflective of the greater peak propulsive forces (Table 1). Hence, net craniocaudal impulses were negative (braking) in forelimbs but positive (propulsive) in hindlimbs (Fig. 3C). Net craniocaudal impulses for both forelimbs and hindlimbs decreased with speed (Table 2), driven by reductions in braking impulses by the forelimbs and in propulsive impulses by the hindlimbs. The tail's craniocaudal impulse (estimated over the mean support duration of the limbs, or 1.54 s) was -0.02±0.02 BWU · s, reflecting a constant braking impulse.
Both forelimbs and hindlimbs consistently pushed laterally on the ground during the support phase (as shown by the medially directed ground reaction forces; Fig. 3A). Although hindlimb mediolateral impulses tended to be greater than those of the forelimbs, the difference was not significant (Table 1). Peak mediolateral forces were high in Alligator (Table 1), averaging 16.1% and 19.1% of peak vertical forces in the fore- and hindlimb, respectively. More striking, however, are the ratios of peak mediolateral force to peak craniocaudal force, which reached 137.5% in the forelimb and 144.3% in the hindlimb. Both fore- and hindlimb mediolateral impulses decreased significantly with speed (Table 2). Negligible mediolateral forces were recorded for the tail.
Body weight support and center of gravity
Using relative vertical impulse (%Q) to reflect the role of the
limbs and tail in body weight support, it was estimated that the diagonal
forelimb and hindlimb in a walking trot support 36.8±1.6% and
51.3±1.5% of body weight, respectively. The remainder,
11.8±0.5%, was supported by the alligator's tail.
The center of gravity of alligator carcasses with limbs approximating standing posture was found to be located at 70.0±0.1% of the gleno-acetabular distance, i.e. closer to the hip joint than the shoulder joint. Simultaneous protraction of diagonal limbs (i.e. replicating touchdown of fore- and hindlimbs in a trot) shifted the center of gravity cranially by only 0.3±0.1%. By contrast, removal of the tail (which represented 27.8±0.1% of total body mass) relocated the center of gravity cranially to a position 28.2±0.1% of the gleno-acetabular distance.
The dorsoventral position of the center of gravity of alligators with limbs approximating a standing posture was located 3.70±0.20 cm inferior to the dorsal surface of the animals. Maximal protraction of a fore- and hindlimb pair shifted the center of gravity by 1.1 cm dorsally, on average.
Whole-body ground reaction forces
Steady speed high walks in the whole-body mechanics study ranged from 0.10
m s-1 to 0.20 m s-1 (mean 0.16 m s-1).
Whole-body vertical ground reaction forces fluctuated around body weight
(Fig. 4). A large vertical
spike (in excess of 1 BWU), developed early in the step, represented the
touchdown of the step-initiating limb superimposed over the terminal portion
of the stance phase of the previous step's diagonal limbs. The ground reaction
force records of the diagonal limbs were superimposed because only
0.05±0.01 s separated each footstrike (equivalent to 5.58±1.14%
of step duration; see Fig.
2B).
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Both horizontal ground reaction forces were much smaller in magnitude than the vertical forces in alligators (Fig. 4A). Whole-body craniocaudal forces changed sense (braking versus propulsion) several times during the stance phase because steps overlapped temporally. An early cranially directed ground reaction force represented the greater propulsive effort of the previous step's diagonal limbs. Soon thereafter, however, a braking effort of the step of interest dominated as the limbs of the previous step prepared for and completed lift-off. During the remainder of the step, the animal's center of mass accelerated forward. In contrast to the consistently high mediolateral forces of individual limbs, mediolateral ground reaction forces of the whole body were small in magnitude and fluctuated around zero with no consistent pattern.
Fluctuations in the velocity and vertical displacement of the center of mass
Velocity fluctuations were comparable in magnitude in all three directions
(Fig. 4A). Initial negative
values in vertical velocity reflect a brief downward movement of the center of
mass. Subsequently, vertical velocity followed a bell-shaped curve: increasing
as the center of mass moved upwards, then decreasing with the falling of the
center of mass. In all trials, the center of mass was lowest at the beginning
and end of the step, reaching its greatest height at midstep. The fluctuation
in vertical displacement of the center of mass during a walking trot was
1.0±0.1 cm. Craniocaudal velocity fluctuated about the mean forward
velocity. The high forward velocity at the onset of the step represented the
end of the propulsive effort of the previous step's diagonal limbs. This was
consistently followed by a sinusoidal decrease (braking) and then increase
(propulsion) in forward velocity. The profiles for the mediolateral velocities
were somewhat more variable, although all patterns fluctuated about zero; the
most common pattern displayed a single change in direction at midstep.
Fluctuations in the mechanical energy of the center of mass
Kinetic energy curves in the three orthogonal directions reached their
minimum values at approximately midstep
(Fig. 4B). The magnitude of the
fluctuations in craniocaudal kinetic energy was greater than for the vertical
and mediolateral directions. The profiles of total kinetic energy were
U-shaped, with minimum values at midstep. By contrast, the profiles of the
gravitational potential energy were consistently bell-shaped, so that
gravitational potential energy was lowest at the beginning and the end of the
step and reached its maximal values at midstep
(Fig. 4B). In general, the
magnitude of gravitational potential energy fluctuations was much greater than
that of total kinetic energy.
Only one pattern of external mechanical energy fluctuations was found for Alligator. Total kinetic and gravitational potential energies were consistently out-of-phase: total kinetic energy was near its minimal values at midstep as gravitational potential energy was approaching its maximum (Fig. 4B). The relative phase relationship for the minima of gravitational potential and kinetic energy curves was 177.9±11.9° (Fig. 5A).
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Alligator did recover some external mechanical energy by
pendulum-like mechanisms across each step, with percent energy recoveries
ranging from 7.6% to 32.4% (mean 19.8±2.0%;
Fig. 5B). Energy recovery was
significantly correlated with speed (r=0.657, P=0.04). When
total kinetic energies were recomputed without the lateral component, mean
percent recovery dropped by 6.9±2.0%
(Fig. 5B).
Vertical work in high walking significantly exceeded work in the craniocaudal and mediolateral directions (Table 3). Significant speed effects were only observed in vertical work, which was found to decrease with speed.
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Discussion |
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Effects of tails on body weight support and forward impulsion
The most potent factor that explains the crocodilian pattern of hindlimb
dominance in body weight support is likely to be the alligator's massive tail,
which accounts for a substantial percentage of body weight (nearly 28%;
Fig. 6). That the tail
effectively draws the center of mass caudally towards the hindlimbs in
Alligator is supported by the cranial shift in center of mass with
postmortem removal of its tail. Removal of the tail repositioned the center of
mass from 70% of the gleno-acetabular distance to 28%, realigning it closer to
the 30-40% position noted for most mammals
(Kimura and Endo, 1972;
Demes et al., 1994
).
Relatively high hindlimb vertical forces have also been reported in the lizard
Varanus (Christian,
1995
), which also sports a large tail. The torso and hindlimbs
support a substantial portion of the proximal tail in high-walking alligators
since vertical impulses of the tail represent only 12% of total vertical
impulses even though the tail represents 28% of the total body mass. Finally,
Gray (1968
) concluded that
hindlimbs should support an increased percentage of weight when a quadruped is
working against a drag. Hence, the constant braking impulse of the tail may
further contribute to hindlimb vertical forces and impulses.
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High vertical forces and relative support impulses in the hindlimbs are
also characteristics of higher primates
(Demes et al., 1994;
Schmitt, 1994
). Unlike
alligators, mass distribution cannot explain the primate condition because
cadaveric specimens of primates and other mammals alike tend to have cranially
displaced centers of gravity (closer to the forelimbs than the hindlimbs;
Vilensky, 1979
). Rather, it
appears that the activity of hindlimb retractor muscles in primates
effectively draws the center of mass caudally, thereby reducing the
compressive load on the forelimbs
(Vilensky, 1979
). This
characteristic of primate kinetics has been associated with the more upright
trunk (orthograde posture) of higher primates and has been suggested as a
prerequisite for the evolution of bipedality (e.g.
Kimura et al., 1979
). Because
basal crocodilians have been reconstructed as cursorial bipeds
(Sennikov, 1989
; Parrish,
1987
,
1988
;
Gomani, 1997
), it may be
tempting to ascribe the hindlimb dominance in vertical force generation in
extant alligators to historical baggage. But Caluromys philander (the
highly arboreal wooly opossum) was recently found to replicate the vertical
force patterns of primates, strongly indicating that the hindlimb dominance in
body mass support in primates primarily reflects arboreal ancestry more so
than orthograde posture (Schmitt and
Lemelin, 2002
). To date, no one has credibly suggested that
arboreality plays a role in crocodilian evolution and, so, a caudally
positioned center of mass remains the most convincing factor determining limb
function in body mass support in alligators.
Vertical force is not the only aspect of individual limb function that is
affected by the tail in alligators. While both braking and propulsive impulses
are exerted by limbs in walking tetrapods, one function typically dominates:
forelimbs tend to be net braking and hindlimbs are net propulsive
(Demes et al., 1994).
Furthermore, quadrupeds moving at near-constant forward velocity should have
balanced propulsive and braking impulses across their four limbs. In
Alligator, the craniocaudal records of the limbs are strongly
unbalanced because of the exceptionally propulsive hindlimbs
(Fig. 6). The ratio of
propulsive impulse to braking impulse for the hindlimbs of mammals usually
falls below 5 (see fig. 11 in Demes et
al., 1994
) whereas alligators have an extraordinarily high value
of 9.4. This great forward propulsive effort by hindlimbs appears to be
necessary for counteracting the constant braking effect of the tail.
Sprawling and semi-erect tetrapods have large mediolateral ground reaction
forces that have a distinct polarity indicative of a net lateral push by the
limbs. By contrast, mediolateral forces of individual limbs in cursorial
mammals are sufficiently small and irregular that they are commonly ignored in
locomotion studies (e.g. comprising only about 6% of vertical force and 40% of
braking force in walking and trotting dogs;
Budsberg et al., 1987;
Rumph et al., 1994
).
Mediolateral forces represent
20% of vertical force values in the fore-
and hindlimbs of Alligator, Iguana and Varanus
(Christian, 1995
;
Blob and Biewener, 2001
). More
striking is the magnitude of mediolateral force relative to craniocaudal
force, with ratios of mediolateral force to craniocaudal force of
100%
for the hindlimb of Iguana (Blob
and Biewener, 2001
) and reaching 140% in the fore- and hindlimbs
of Alligator. This indicates that the limbs of sprawling and
semi-erect tetrapods apply as much, if not greater, effort in pushing
laterally than they do craniocaudally with each step. The tail's mediolateral
forces are trivially small so that the large lateral push by each limb is
unlikely to be a response to the tail. That lateral bending of the axial
skeleton alone is an inadequate explanation is borne out by turtles, which are
clearly incapable of laterally bending the thoracic and lumbar spine yet show
subequal craniocaudal and mediolateral force magnitudes
(Jayes and Alexander, 1980
;
Moon, 1999
). Consequently,
high mediolateral forces in non-erect tetrapods are probably due to a
combination of factors, including sprawling posture, nonparasagittal limb
movements and proximal limb bone rotation as well as possibly lateral bending
(Gatesy, 1991
;
Reilly and Elias, 1998
;
Blob and Biewener, 2001
).
Thus, the hindlimbs of alligators assume a large role in body mass support
and forward impulsion because these animals drag long and muscular tails.
While this may be viewed as an unavoidable consequence of powering aquatic
locomotion with the tail, and therefore comparable to other morphological and
energetic compromises found in semiaquatic animals
(Fish et al., 2001;
Williams et al., 2002
), it is
important to recall that dragging a long and heavy tail behind the body is
also the ancestral condition of tetrapods. Hence, the differential limb
function noted for alligators may replicate the basal condition for
terrestrial quadrupeds.
Effect of tails on pendular mechanics
What determines the efficacy of pendulum-like recovery during terrestrial
walking is the phase relationship between total kinetic energy and
gravitational potential energy as well as the magnitudes of the fluctuations
in the energy profiles (Cavagna et al.,
1977). With phase relationships averaging nearly 178°,
Alligator fulfills the first criterion for efficient energy recovery;
that is, the minimum kinetic energy and the maximum gravitational potential
energy occur nearly synchronously. However, kinetic energy and gravitational
potential energy profiles, although out-of-phase with one another, are not
mirror images of each other in Alligator as the kinetic energy
profiles are demonstrably flatter than those of potential energy. As a result,
high walks are not particularly efficient mechanical walks because, on
average, 80% of the mechanical energy of each walking step must be supplied by
the muscles (compared with less than 65%, on average, in birds and mammals;
Cavagna et al., 1977
). Modest
energy recoveries were also found in Coleonyx variegatus (western
banded gecko) and Eumeces skiltonianus (western skink;
Farley and Ko, 1997
),
tetrapods that similarly drag their tails when walking. While large-mass tails
that remain in contact with the ground and limited energy recovery appear to
be coupled, other features of alligator locomotor behavior, such as lateral
forces, locomotor posture, footfall patterns and locomotor speed, may also
contribute to reductions in energy recovery.
Should one assume that large mediolateral limb forces in non-erect
tetrapods necessarily equate to locomotor inefficiency? The answer, provided
by whole-body mechanics, is a resounding "no". In
Alligator, the large laterally directed applied forces of
contralateral limbs during high walks (walking trots) largely counteract each
other, so that moderate mediolateral movements of the center of mass result.
Rather than degrading energy recovery by pendulum mechanics, these residual
mediolateral movements actually improve energy recovery in high walking
Alligator (by nearly 7%, on average). This is consistent with results
found for the penguin: although they move with substantial side-to-side
waddling, penguins are capable of recovering up to 80% of mechanical energy by
pendular mechanics and this recovery is actually aided by waddling
(Griffin and Kram, 2000).
Locomotor efficiency does appear to be associated with locomotor posture
when walking. Bipeds tend to exceed quadrupeds in maximum mechanical energy
recovery (maximum values at 70% versus 50%, respectively;
Cavagna et al., 1977
), probably
because two limbs are less likely to impede pendular mechanics than are four.
Furthermore, there is a tendency for animals with erect postures (birds,
cursorial mammals) to recover, on average, more mechanical energy by
inverse-pendulum mechanisms than do more sprawling animals
(Cavagna et al., 1977
;
Farley and Ko, 1997
;
Griffin et al., 1999
;
Muir et al., 1996
;
Tesio et al., 1998
). Although
a semi-erect posture clearly does not provide alligators with the energy
savings typical of more erect tetrapods, this posture probably serves to lower
the overall cost of terrestrial locomotion by increasing effective limb length
(hip to substrate length). Again, the contrast with penguins illuminates this
point: the high cost of locomotion in penguins has been ascribed to their
short legs not to their waddling gait
(Griffin and Kram, 2000
).
Footfall patterns may also affect the efficiency of inverse-pendulum
mechanisms. While the expectation that the footfalls of a diagonal couplet are
well synchronized in trots was confirmed in dogs
(Bertram et al., 1997), no such
precision of footfalls was found in Alligator even though high walks
are walking trots (diagonal couplet walks with
50% duty factor and
50±10% limb phase; Farley and Ko,
1997
). In alligators, the forelimbs usually landed before the
contralateral hindlimb (by as much as 9% of support duration); in a minority
of the steps, hindlimb footfalls slightly preceded the forelimb. High-walking
alligators also failed to consistently elevate the feet off the ground during
the swing phase, with the toes of a protracting foot dragging forward more
frequently in hindlimbs than forelimbs.
Finally, the efficiency of a pendulum-like exchange of gravitational
potential energy and kinetic energy is well-known to be speed dependent. In
animals as diverse as rheas and rams, the greatest energy recovery occurs at a
narrow range of speeds, with lower recoveries at slower or faster speeds
(Cavagna et al., 1977). The
inverted-pendulum model applies best to intermediate walking speeds when the
positive work to increase forward speed of the center of mass
(Wf) is most similar to that used to lift the center of
mass (Wv). At low speeds, energy recovery is reduced
because Wv increasingly exceeds Wf
(Cavagna et al., 1977
). It is,
therefore, not surprising that inverted-pendulum mechanics fails to provide
great energy recovery in Alligator given that its positive work
against gravity is almost an order of magnitude greater than that for forward
propulsion. Energy recovery in Alligator was seen to increase with
speed (Fig. 5B), so it is
possible that captured speeds simply fell short of that required for peak
energy recovery. The alligators in the present study chose to walk steadily at
0.102-0.195 m s-1, speeds comparable with those obtained by Gatesy
(1997
) and Reilly and Elias
(1998
). Our top speed was
nearly half that achieved by Blob and Biewener
(1999
; 0.37 m s-1),
suggesting that higher speeds may be possible. However, neither our animals
nor those used by Gatesy
(1997
) could maintain a steady
gait at higher speeds.
Therefore, relatively low locomotor speeds together with a semi-erect
quadrupedal posture and an irregular trotting gait appear to degrade the
ability of alligators to capitalize on pendular mechanics as a means of
reducing locomotor costs for terrestrial locomotion. The effect of
tail-dragging on pendular mechanics, however, remains questionable. The tail
posture in other gaits and in lizards suggests that dragging heavy tails
terrestrially may reduce locomotor efficiency. For example, while crocodilians
typically walk with tail in tow, Crocodylus elevates its tail during
quick galloping bouts (Renous et al.,
2002), presumably to improve its running mechanics (e.g. by
offsetting the tail's decelerative effect for the duration of this high-speed
locomotor event).
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Acknowledgments |
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References |
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