122
The Journal of Experimental Biology 214, 122-130
© 2011. Published by The Company of Biologists Ltd
doi:10.1242/jeb.045682
RESEARCH ARTICLE
Environmental differences in substrate mechanics do not affect sprinting
performance in sand lizards (Uma scoparia and Callisaurus draconoides)
Wyatt L. Korff1,* and Matthew J. McHenry2,†
1
Department of Integrative Biology, University of California, 3060 Valley Life Sciences Building, Berkeley, CA 94720-3140, USA and
2
Department of Ecology and Evolutionary Biology, University of California, 321 Steinhaus Hall, Irvine, CA 92697, USA
*Present address: Howard Hughes Medical Institute, Janelia Farm Research Campus, 19700 Helix Drive, Ashburn, VA 20147, USA
†
Author for correspondence ([email protected])
Accepted 4 October 2010
SUMMARY
Running performance depends on a mechanical interaction between the feet of an animal and the substrate. This interaction may
differ between two species of sand lizard from the Mojave Desert that have different locomotor morphologies and habitat
distributions. Uma scorparia possesses toe fringes and inhabits dunes, whereas the closely related Callisaurus draconoides lacks
fringes and is found on dune and wash habitats. The present study evaluated whether these distribution patterns are related to
differential locomotor performance on the fine sand of the dunes and the course sand of the wash habitat. We measured the
kinematics of sprinting and characterized differences in grain size distribution and surface strength of the soil in both habitats.
Although wash sand had a surface strength (15.4±6.2kPa) that was more than three times that of dune sand (4.7±2.1kPa), both
species ran with similar sprinting performance on the two types of soil. The broadly distributed C. draconoides ran with a slightly
(22%) faster maximum speed (2.2±0.2ms–1) than the dune-dwelling U. scorparia (1.8±0.2ms–1) on dune sand, but not on wash
sand. Furthermore, there were no significant differences in maximum acceleration or the time to attain maximum speed between
species or between substrates. These results suggest that differences in habitat distribution between these species are not
related to locomotor performance and that sprinting ability is dominated neither by environmental differences in substrate nor the
presence of toe fringes.
Key words: locomotion, biomechanics, running.
INTRODUCTION
Running performance depends on a mechanical interaction between
the feet of an animal and the substrate. Squamate reptiles in desert
habitats exemplify the importance of this interaction. These animals
accelerate rapidly to evade predators and capture prey, despite
moving along a sandy substrate that slips beneath their feet (Garland
and Losos, 1994; Huey and Hertz, 1984; Irschick and Jayne, 1998a;
Irschick and Jayne, 1999a; Irschick and Jayne, 1999b; Jayne and
Irschick, 2000). Some lineages of sand lizards that have migrated
into desert habitats have evolved elongated feet and toe fringes
(Kohlsdorf et al., 2001; Luke, 1986). Therefore, substrate mechanics
may have played in important role in the evolution of these traits
and in the locomotor performance of sand lizards.
The locomotor performance of a lizard species can influence its
habitat distribution. Irschick and Losos found that arboreal Anolis
species with a restricted distribution had a sprinting ability that
depended greatly on perch diameter (Irschick and Losos, 1999). This
contrasted with broadly distributed species that performed similarly
over a range of perch diameters (Irschick and Losos, 1999). The
authors proposed that locomotor performance might be a major
determinant of species distribution. It is possible that locomotion
may play a similar role in mediating the distribution of lizard species
in desert environments (Irschick and Jayne, 1998b; Luke, 1986).
The sand lizard Uma scoparia is a promising candidate for testing
whether habitat distribution is related to locomotor performance. This
species has toe fringes and is restricted to dune habitats in the Mojave
Desert, which are covered with fine-grained sand (Fig.1A,B). Ablating
the toe fringes causes a reduction in the maximum velocity and
acceleration of running, which suggests that the fringes function to
gain purchase in the sand (Carothers, 1986). However, toe fringes
may not help running in course-grained sand, such as that found in
wash habitats that neighbor the dunes in the Mojave. Despite a close
proximity to the dunes, U. scoparia is not found in wash habitats. It
is therefore reasonable to predict that U. scoparia will exhibit lower
running performance on wash sand than on the fine sand of the dunes.
It follows that a broadly distributed species, such as the closely related
Callisaurus draconoides, should exhibit running performance that is
less dependent on soil type. C. draconoides occurs in both dune and
wash habitats and has an ability to run on sand similar to that of U.
scoparia despite lacking toe fringes (Irschick and Jayne, 1998b). The
present study tested these predictions by measuring the running
performance of both species on dune and wash substrates in the field.
Furthermore, we evaluated the mechanical and morphological
differences between these sand types.
There are myriad factors that can influence the mechanics of sand.
Sand is a granular medium that may resist loads like a solid or a
fluid, depending on loading conditions. The moisture content, the
shape and size of the grains, and their spatial distribution are but
some of the additional factors that influence the mechanics of
granular media (Corwin et al., 2005; Jaeger et al., 1996; Mehta and
Barker, 1994). In contrast to the classical mathematics that accurately
predicts the behavior of fluid flow (Lamb, 1945), the theoretical
foundation for granular dynamics remains a frontier for investigation
(Ciamarra et al., 2004; Goldman et al., 2003; Li et al., 2009; Maladen
THE JOURNAL OF EXPERIMENTAL BIOLOGY
Running in sand lizards
A
Dune
Uma scorparia
B
123
Fig.1. Substrate type and the ecological distribution
of two species of sand lizard. (A)The Kelso Dunes in
the Mojave Desert illustrate the spatial distribution of
dune and wash habitats. (B)The Mojave fringe-toed
lizard (Uma scorparia) is distributed in dune habitat,
whereas (C) the zebra-tailed lizard (Callisauris
draconoides) is found in both dune and wash
habitats.
Wash
Callisaurus draconoides
C
et al., 2009). As a consequence, no suite of materials tests
comprehensively characterizes the mechanics of a soil. Nonetheless,
there are a few metrics that provide a gross description of a soil’s
properties and allow comparisons between similar soils. Grain size
distribution provides a starting point for describing sand and is easily
measured by passing a sample through a series of sieves of varying
mesh size (Nichols, 1999). Grain size distribution affects the
cohesion between particles (Mehta and Barker, 1994) and
consequently affects the resistance of the soil to compression. This
resistance is measured as the pressure required to deform the surface,
known as the surface strength. We used grain size distribution and
the surface strength to characterize the gross differences between
sand in the dune and wash habitats.
Numerous studies on lizards include measurements of the velocity
and acceleration of sprinting from video recordings (e.g. Bennett,
1980; Garland, 1985; Huey and Hertz, 1984; Irschick and Jayne,
1998a; Irschick and Jayne, 1998b; Sinervo, 1990). Among such
studies, the different approaches for acquiring coordinates of body
landmarks are likely similar in their accuracy for position
measurements. However, different methods for calculating velocity
and acceleration from these measurements can produce substantially
different values. The accuracy of these analytical methods has been
shown to depend on the spatial and temporal resolution of a video
recording and rates of motion (Harper and Blake, 1990; Rayner and
Aldridge, 1985; Walker, 1998). The present investigation included
an error analysis of these analytical methods to determine the
accuracy of methods for estimating the velocity and acceleration of
a lizard’s sprint.
MATERIALS AND METHODS
Animals
Zebra-tailed lizards (Callisaurus draconoides Blainville 1835) and
Mojave fringe-toed lizards (Uma scoparia Cope 1894) were caught
by noose on and around the Kelso dunes in the Mojave Desert (San
Bernardino County, CA, USA). At the time of capture, we measured
the body weight with a spring scale (Pesola, Kapuskasing, ON,
Canada) and the snout-vent length (SVL) with digital calipers.
Among the lizards captured, we retained the five individuals for
each species that presented the narrowest range in SVL. There were
no significant differences in length (unpaired t-tests, P>0.05)
between the two species, with U. scoparia ranging from 6.9 to 8.8cm
SVL (mean ± 1 s.d.7.1±1.5cm) and C. draconoides ranging from
7.3 to 8.8cm SVL (7.4±1.3cm). These species were also similar in
mass, with U. scoparia ranging from 8.0g to 14.5g (11.9±3.4g)
and C. draconoides from 8.3 to 16.7g (13.6±3.4g) in mass. After
experimentation, animals were returned to the exact location of
collection as determined with GPS coordinates (Garmin eTrex,
Olathe, KS, USA).
Body temperature was carefully monitored and controlled
throughout our investigation because locomotor performance in
lizards is highly temperature-dependent (Bennett, 1990; Huey and
Bennett, 1987; Jayne et al., 1990). This was measured by reading
temperature on the ventral surface with an infrared non-contact
thermometer (Raytek Raynger ST, Raytek, Santa Cruz, CA, USA).
The lizards were transported to a nearby field station (Granites
Mountain Desert Research Station) after capture, where they were
held at >27°C for less than 24h before using them in an
experiment. At the time of an experiment, each lizard was placed
in a 19l bucket filled with a 15cm depth of dune sand that was
partially shaded to allow the animals to behaviorally
thermoregulate. Lizards were held until they reached their fieldactive temperature (between 39 and 40°C for these species)
(Irschick and Jayne, 1999c; Jayne and Ellis, 1998). During
experiments, the surface temperature of the sand was monitored
and reduced by shading the track when temperatures exceeded
46°C.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
124
W. L. Koff and M. J. McHenry
collection site, the surface strength was measured with a highly
sensitive penetrometer (model 49015 with a disk diameter of
2.54cm; Ben Meadows Co., Janesville, WI, USA). The surface
strength was measured as the load at which the surface was visibly
compressed by the disk of the penetrometer when loaded slowly
(~0.5mms–1).
A
Dark box
Observation wall
Mesh netting
High-speed
video camera
3
1
Uncorrected field of view
1
B
Kinematics recording
2
1
3
2
1
0.4
0.3
0.1
0.2
0.2
1
0.
Corrected field of view
0.1
C
0.
2
0.1
0.2
0.1
0.
Error (pixels)
0
1
2
3
4
D
20
300
Filtered
position
Position (pixels)
10
200
Extrapolated
padding
Measurement
0
15
0
30
100
Zero padding
0
0
40
80
120
Time (ms)
160
Fig.2. Experimental setup for field recordings of running kinematics.
(A)The 4-m-long portable trackway used to enclose a lizard while it was
running was recorded with high-speed video (1000framess–1). This camera
setup generates errors in position that we measured from recordings of a
grid. Errors in the field of view are color-coded before (B) and after (C)
correcting for optical distortions (see Materials and methods for details).
Contour lines denote differences in error in intervals of 1 and 0.1 pixels in
panels B and C, respectively. (D)Representative position recording during
a sprint (gray points) and the filtered version (red line) with padding added
before and after the recording.
Substrate morphology and mechanics
We measured grain sizes and surface strength of sand from the dune
and wash habitats where lizards were collected. To measure grain
size, single representative samples (~300ml) from dune and wash
habitats were desiccated in an oven to minimize particle clumping.
The samples were poured into a stacked set of sieves (W. S. Tylor,
Mentor, OH, USA) with 4.0, 2.0, 1.0, 0.5, 0.25, 0.125 and 0.062mm
openings and placed in a sieve shaker (Ro-Tap model RX-29,
W. S. Tyler) for 30min. The contents of each sieve were weighed
to determine grain distribution by mass (Pettijohn, 1957). At each
We measured the kinematics of running within a trackway that was
placed on a flat section of sand close to where the lizards were
collected. This trackway (4m long⫻0.25m wide⫻40cm tall)
included a nylon mesh enclosure and an acrylic observation window
(Fig.2A), but possessed no floor so that the lizards could run on
the natural substrate. We selected one location to set up the
trackway on a section of a dune and another on a portion of wash.
Each site was representative of the two types of substrate observed
where the lizards were collected, as determined by penetrometer
measurements. A black box was located at one end of the trackway
to provide a darkened exit to entice animals in that direction. To
minimize substrate variation between trials, the region of trackway
visible to the video cameras was raked (3cm tine spacing) and
sprayed with dry compressed air to minimize compaction from
repeated trials of running and to eliminate moisture from raking.
We recorded running with high-speed video from a lateral
perspective as a lizard accelerated from a standstill (Fig.2A).
Animals were placed on the trackway (where they assumed a
sprawling posture) and were then induced to run by the extended
hand of an investigator. Trials were only deemed acceptable if the
animal ran parallel to the trackway for a distance beyond the
camera’s field of view. Each individual successfully ran five to eight
trials on each type of substrate. Between each trial, animals were
allowed to rest in the dark box at the end of the trackway for a
minimum of 5min. The camera (Redlake MotionMeter, DEL
Imaging Systems, Cheshire, CT, USA; with a 8.5mm c-mount lens,
Computar, Commack, NY, USA) was set up approximately 3m from
the trackway to provide an effective field of view (~1.2m) that
spanned the observation window of the trackway. The camera
captured a lateral view of the animals as they accelerated from rest
at 1000framess–1 (with 0.2ms exposure and an effective spatial
resolution of 658⫻496pixels) and recordings were digitized with
a camcorder (JVC DVL-9800U) from which they could be
transferred to a computer for subsequent analysis.
We measured the kinematics of running by automated position
tracking of the anterior margin of the snout with custom software.
As for all software developed for the present study, this code was
written and executed in Matlab (v. 6.5, MathWorks Inc., Natick,
MA, USA). This program de-interlaced the images and then applied
an adaptive image histogram equalization to provide uniform
contrast among video recordings (Gonzalez et al., 2004). It then
traced the peripheral shape of the lizard’s body by identifying the
pixel values that changed over time. This was achieved with a
hysteresis thresholding algorithm (Canny, 1987) that was adjusted
to find changes in pixel intensity beyond 2.85 standard deviations
from mean values over the duration of the recording.
To correct for lens distortion that could affect kinematic
measurements, we analyzed how our lens and camera altered the
kinematics of a calibration image. This image was a two-dimensional
grid (with 3cm squares) that we recorded as it was translated across
and into the camera’s field of view for the camera and lens settings
that we used to record the lizards. We used an open source software
package (Bouguet, 2009) that implemented a series of algorithms
(Heikkila, 2000; Heikkila and Silven, 1997) to correct for distortions
THE JOURNAL OF EXPERIMENTAL BIOLOGY
Running in sand lizards
in the spacing of line intersections in the grid. This software found
distortion errors that exceeded 4pixels in some regions of the field
of view (Fig.2B) and was able to perform a correction to reduce
these errors by approximately an order of magnitude (Fig.2C).
running analyses over a range of cut-off frequencies and determining
which cut-off frequency minimized errors in estimating velocity.
We found that the optimal cutoff frequency (fcut) could be
approximated by the following formula:
fcut =
Velocity and acceleration analysis
We conducted an error analysis to evaluate the accuracy of a variety
of methods for calculating the velocity and acceleration from video
recordings of an animal’s position. This was first achieved by
modeling the velocity of a sprinting animal over time, v(t), as the
sum of two terms:
v(t)  vmax(1 – e–t/) + voe–t/sin(t / )2 ,
(1)
where the first term describes the net increase that asymptotically
approaches vmax at a rate determined by the time constant , and
the second term characterizes the oscillations in speed created by
individual steps with an initial velocity of vo and step period . We
used this equation to generate a series of simulations that tested
methods of analysis by first evaluating position (i.e. integrating Eqn
1) at regular intervals (corresponding to frame rates of 250, 500,
1000, 2500 and 5000framess–1). These position data were generated
for parameter values that approximated the kinematics of C.
draconoides and U. scoparia, as determined from previous work
(Irschick and Jayne, 1998b) and our own preliminary analysis of
the present experiments. The pixel displacements achieved by this
motion corresponded to what could reasonably be attained using a
high-speed video camera with a spatial resolution equal to that
of the present experiments (658⫻496pixels). These parameters
were: 40frames, vmax2pixelsframe–1, vo1pixelframe–1 and
20frames. We added noise (Gaussian distributed) (Crenshaw et
al., 2000) to the position data with an amplitude of 1pixel to simulate
digitizing error and applied each method of analysis to calculate
velocity and acceleration. These estimates of velocity and
acceleration were then compared to the values generated by Eqn 1
to evaluate their accuracy. Comparisons were repeated 1000 times
with different values for noise to assess the random variability
anticipated for each method. All considerations of analytical methods
were performed using programming within Matlab.
Each simulated and experimental position recording was preprocessed prior to calculating velocity and acceleration. This
consisted of first reducing high-frequency digitizing noise by
filtering each kinematic sequence with a fourth-order, zero-lag
recursive Butterworth digital filter (cutoff frequency of 80Hz,
determined by residual analysis) (Winter, 1990). Position data were
then padded before and after the period analyzed to avoid edge
effects. Zero values were included for the position prior to motion
over a duration of half the period of motion (Smith, 1989). Padding
after the period of motion was added for the same duration, but we
extrapolated from the rate of change in the position with a leastsquares fit of a second-order polynomial to a duration corresponding
to the last 20ms of the sequence and extrapolated along that function
in time (Fig. 2D).
We evaluated five methods for estimating the velocity and
acceleration of a running animal. Two of these methods used a bform smoothing spline (SPAPS) (Reinsch, 1967) that was fit to the
data (with a single pixel tolerance) to minimize the squared
differences with the data. The first and second derivatives of these
splines provided estimates of velocity (vSPAPS) and acceleration
(aSPAPS). The remaining methods involved filtering the data and then
discretely calculating velocity and acceleration. Filtering was
achieved with a fourth-order, zero-lag low-pass Butterworth filter.
We determined the optimal cut-off frequency at each frame rate by
125
1.5
F
+
,
τ
300
(2)
where F is the frame rate (framess–1) and  is the step period (s).
We therefore used this equation to determine the best cut-off
frequency for each analyzed sequence.
The velocity and acceleration of filtered data were calculated
discretely with three different methods. First, velocity was calculated
with forward differentiation (vFD):
vFD =
xi+1− xi
,
Δt
(3)
where xi is the position of sample i and ⌬t is the time difference
between samples. The second method, first-order central difference
(1-CD), was calculated with the following equation:
v1-CD =
xi+1 − xi−1
.
2Δt
(4)
The third method used fourth-order central difference (4-CD),
according to the equation (Biewener and Full, 1992):
v4-CD =
xi+2 + 8xi+1 − 8xi−1 − xi−2
.
12Δt
(5)
Accelerations were calculated using the same equations, with
velocity values used in place of position data. As described in the
Results, we found that a smoothing spline fit to filtered data provided
the most accurate estimates of velocity and acceleration. We
therefore applied this method to our analysis of field recordings.
In comparisons between estimated and known values of velocity
and acceleration, we calculated error in two ways. An average
measure of error in velocity (vRMS) was provided by the normalized
root mean square (RMS) error (Ev,RMS) with the following equation
(Taylor, 1982; Walker, 1998):
n
Ev,RMS =
∑ ( v̂i − vi )
i=1
2
n
∑ vi2
× 100% ,
(6)
i=1
where vi is the true velocity of sample i (found by evaluating the
first position of the cubic spline for position), n is the number of
samples and vi is the estimated velocity at the same instant of time.
This indicates the accuracy of instantaneous estimates of velocity.
Error in the estimate of maximum velocity (vmax) was evaluated
with the following calculation (Walker, 1998):
Ev,max =
v̂max − vmax
vmax
× 100% ,
(7)
where vmax and vmax are the maximum velocities in estimated and
true data, respectively. We used the same equations to calculate the
RMS error and error in maximum values for acceleration (aRMS and
amax, respectively) and determined true acceleration by evaluating
the second derivative of velocity (Eqn 1).
We performed a sensitivity analysis to determine how individual
kinematic parameters affect the accuracy of velocity and acceleration
calculations. This was achieved by running simulations that
individually varied the parameters in our model of sprinting
THE JOURNAL OF EXPERIMENTAL BIOLOGY
126
W. L. Koff and M. J. McHenry
0.6
Dune
A
30
Wash
0.25≤g<0.5
0.5≤g<1
0.4
1≤g<2
0.3
2≤g<4
0.2
g>4
0.1
Surface strength (kPa)
Proportion of mass
0.5
20
10
B
Fig.3. Differences in grain size and the surface
strength of dune (black bars) and wash (gray bars)
sands. (A)The mass distribution of grain sizes for
representative samples of each soil type, as
measured with a series of sieves. The range of
grain sizes (g, in mm) for each bin is provided
above the bars. (B)The mean surface strength
(+1 s.e.m.) for dune and wash sands (N5) was
measured with a penetrometer. The surface
strength of wash sand was significantly greater
than that of dune sand (t-test, P<0.001).
0.063≤g<0.25
g<0.063
0
0
Grain size (mm)
kinematics (vmax, , vo and  in Eqn 1). These changes in parameter
values ranged between 0.25 and 1.75 times the values for each
parameter used in our consideration of methods of analysis:
40frames, vmax2pixelsframe–1, vo1pixelframe–1 and
20frames. For each set of parameter values, 1000 simulations
were analyzed with differing values of pixelation noise to consider
the variation in error created by random noise. This sensitivity
analysis focused on calculations that used the smoothing spline
approach because a preliminary analysis found this method to be
the most accurate.
Statistical analysis
We used a two-factor ANOVA to evaluate differences in the
kinematics between species and substrate. A Kolmogorov–Smirnov
test found that our measurements failed to conform to a normal
distribution, as assumed by ANOVA analysis (Sokal and Rohlf,
1995). A normal distribution was therefore achieved by a log10transformation of our measurements prior to analysis. We used post
hoc tests (Tukey–Kramer method) (Sokal and Rohlf, 1995) to
determine which species and substrates differed significantly. Onetailed Students’ t-tests were used to evaluate differences in the
surface strength of dune and wash sands. All statistical analyses
were implemented in Matlab.
RESULTS
Substrate mechanics
Dune and wash sands differed in grain size and surface strength.
Dune sand was dominated by medium (0.25mm≤g<0.5mm, where
g is grain size) and coarse (0.5mm≤g<1.0mm) particles, which
collectively accounted for 92% of its mass (Fig.3A). By contrast,
these grain sizes comprised only 39% of wash sand, which was also
largely composed of very coarse grains (1.0mm≤g<2.0mm, 29%),
granules (2.0mm≤g<4.0mm, 17%) or pebbles (g>4.0mm, 11%).
Therefore, wash sand included a more broad distribution of grain
sizes, which correlated with a greater resistance to compression.
The surface strength of wash sand (15.4±6.2kPa, N5) was more
than three times that of dune sand (4.7±2.1kPa, N5) (Fig.3B),
which was a highly significant difference (unpaired t-test, P<0.001).
Methods for estimating velocity and acceleration
We used simulated kinematics to evaluate the accuracy of methods
for estimating the velocity and acceleration of a sprinting animal.
Our results (Fig.4) should be applicable to the kinematics of any
animal that accelerates with oscillations that decrease over time,
within the limits of the range of pixel displacement, velocity and
acceleration (Fig.4A–C) and parameter values (Fig.4H–K)
considered. Within those bounds, estimates of maximum velocity
were found to be highly inaccurate (>25%) for frame rates below
500framess–1 (Fig.4E), and the method of analysis had a large effect
on RMS error in velocity at these low frame rates (Fig.4D). For
example, only the smoothing spline methods produced RMS error
values below 10% at 250framess–1. Accuracy in velocity improved
at higher frame rates and by 2500framess–1, all methods yielded
highly accurate results (<5% error; Fig.4D,E). However, even at
the highest frame rates, RMS errors for acceleration were found to
be large (Fig.4F). Again, the smoothing spline produced the best
results, but did not produce errors below 25% at any frame rate.
This suggests suggest that calculations of instantaneous acceleration
from digital video recordings exhibit a high degree of inaccuracy
that could be improved with a camera having higher spatial
resolution. In contrast to RMS error, maximum acceleration can
reasonably (<25% error) be approximated at the frame rates used
presently (1000framess–1) by all methods.
A sensitivity analysis of simulated recordings examined how
kinematic parameters individually affected the accuracy of velocity
and acceleration calculations (Fig.4H–K). Reducing the step period
to 25% of the default value (20frames) produced RMS and
maximal errors for acceleration that approached 100% (Fig.4J) and
90% (Fig.4K), respectively. All other parameters had a relatively
small influence on errors in estimating velocity and acceleration.
Sprinting velocity and acceleration
Both species exhibited a great capacity to sprint forward from a
standstill. Using either one or two pairs of legs, lizards initiated
running with an acceleration that typically displaced the body by
one-half its length (~3.6cm) within 70ms (Fig.5A). In this period,
lizards commonly attained speeds exceeding 1ms–1 and virtually
all individuals moved even faster in the subsequent 100ms, as
footfalls continued to generate positive accelerations with decreasing
magnitude over time (Fig.5B). In both species, the variation in
kinematics between trials (e.g. Fig.5A,B) generally exceeded the
variation in mean kinematics between individuals (Fig.5C,D).
We found minor differences in sprinting performance between
the species for running on the two sand types. Mean trajectories
overlapped substantially between the two species running on both
substrates (Fig.6A,B). The maximum acceleration was
indistinguishable between species and between substrates (Table1,
Fig.6C). Only the maximum velocity for running on dune sand was
THE JOURNAL OF EXPERIMENTAL BIOLOGY
Running in sand lizards
50
A
40
Ev,RMS
Position (pixels)
400
300
100
0
50
Ev,max
I
30
20
10
2
0
Fourth-order central difference
1
First-order central difference
Forward differentiation
100
0.2
80
C
0
Ea,RMS
0
80
0
Step period, τ
Smoothing spline
Initial velocity, vo
Maximum velocity, vmax
Time constant, λ
40
0
100
–0.2
0.2
Filtered smoothing spline
60
20
Ea,max
Velocity (pixels frame–1)
40
Acceleration (pixels frame–2)
E
20
10
B
H
30
200
0
3
D
127
F
J
G
K
60
40
20
–0.2
0
50
100
Time (frames)
150
0
250 1000 2500
5000 0.25
0.75
1.25
1.75
500
Frame rate (frames s–1)
Normalized parameter value
Fig.4. Error analysis of methods for calculating the velocity and acceleration of a sprinting animal from digital video recordings. (A)Representative simulated
trajectories illustrate changes in position with pixelation noise that were determined by a velocity function (Eqn 1) with different parameter values (black line:
40frames, vmax2pixelsframe–1, vo1pixelframe–1, 20frames; red line: 40frames, vmax3pixelsframe–1, vo1.5pixelsframe–1, 15frames). The
velocity (B) and acceleration (C) of these trajectories (heavy solid lines) are shown in comparison to estimates calculated from the position data using two
different analytical methods. A smoothing spline (dotted line) generally provided the best estimates and the fourth-order central difference method (light solid
line) was the least accurate. (D–G) A series of such simulations allowed for measurements of error (mean ± 1 s.d.) in estimates by five analytical methods
(line colors defined in panel F). All simulations used identical parameter values (black lines in A, C), repeated in 1000 simulations at each frame rate with
different values for pixelation noise. (D)Calculations of root-mean squared error velocity (Ev,RMS; Eqn 6) approximate the average accuracy over the course
of a simulation, and (E) error in maximum velocity (Ev,max; Eqn 7) indicates the accuracy of the fastest event in a sequence. (F)Root-mean squared (Ea,RMS)
and (G) maximum (Ea,max) errors in acceleration were calculated in the same manner but are plotted over a greater range because of the large inaccuracy
of all methods in estimating acceleration. (H–K) A sensitivity analysis considered the errors in the smoothing spline method sampled at 1000framess–1 (as
in the present experiments) for individually varied parameters (using Eqn 1; line colors defined in panel J). Each point is the mean value (±1 s.d.) for 1000
simulations with the same parameter values, but different values for pixelation noise. Parameter values are shown normalized by their default value (the
same values as the black lines in A–C).
found to be significantly different (Fig.6D). On average, the dunedwelling U. scoparia sprinted to a maximum speed (1.8±0.2ms–1,
N5) that was 22% slower than C. draconoides (2.2±0.2ms–1, N5).
However, the species were indistinguishable in the duration of time
necessary to achieve maximum speed (Fig.6E).
DISCUSSION
Environmental variation in substrate mechanics
It is not surprising that wash sand exhibited a greater surface strength
than dune sand. The broad grain size range of wash sand (Fig.3A),
allows small grains to fill the gaps between the contact surfaces of
larger grains. This contrasts the more uniformly distributed particles
of dune sand that stack with its gaps unfilled, which generates less
resistance to deformation (Jaeger and Nagel, 1997; Jaeger et al.,
1996). As a consequence, wash sand exhibits a surface strength that
is more than threefold greater than dune sand and, therefore, has a
superior capacity to resist compression (Fig.3B).
Because of these differences in soil mechanics, it is surprising
that sprinting performance was indistinguishable between the
two substrates (Fig.6). Although dune and wash sands are
substantially different in surface strength, they may offer similar
resistance to the motion of a lizard’s foot. This is the case for sea
turtles, which move along stiff and compliant sand at similar speeds.
Mazouchova et al. suggested that the forces generated by the flippers
of hatchling sea turtles on two substrates (hard ground and loosely
packed sand) are below the yield threshold, where soil transitions
THE JOURNAL OF EXPERIMENTAL BIOLOGY
128
W. L. Koff and M. J. McHenry
Position (m)
0.4
0.4
A
0.3
0.3
0.2
0.2
0.1
0.1
5
5
6
0
0
0
100
200
0
B
2.0
Velocity (m s–1)
C
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0
0
0
100
200
100
200
100
200
D
0
Time (ms)
Fig.5. Representative recordings of position and velocity for Uma scorparia
sprinting on dune sand. (A)Position recordings and (B) calculations of
velocity are shown for separate trials for an individual [snout-vent length
(SVL)7.7cm]. Each colored line in B was calculated from the recording in
A of the same color. (C–D) Mean (±1 s.d.) position and velocity from
multiple trials for three representative individuals (blue line: SVL7.7cm;
red line: SVL8.7cm; purple line: SVL7.3cm; the number of trials for each
is given in C).
from solid to fluid-like behavior (Mazouchova et al., 2010).
Therefore, wash and dune sands may provide similar resistance if
the yield strength for both exceeds the forces generated by a lizard
A
Wash
Callisaurus Wash
draconoides
0.2
Dune
Uma
scorparia
Dune
0.1
0
0
100
150
200
250
B
1.5
Time to vmax (ms)
Velocity (m s–1)
2.0
50
vmax (m s–1)
Position (m)
0.3
amax (m s–1)
70
1.0
0.5
0
0
50
100
150
200
Time (ms)
250
foot. Testing this hypothesis requires measurements of these forces
and their respective yield strengths under loading conditions that
are similar to what is generated by a lizard’s foot.
Until recently, studies on terrestrial locomotion rarely considered
the effects of soil differences on performance. Those that did
indicated that performance may be greatly affected by the mechanics
of the substrate. In humans, reductions in the compliance of a
substrate cause proportionate increases in the leg stiffness to
maintain consistent center-of-mass dynamics (Ferris et al., 1998;
Kerdok et al., 2002). A human running on sand requires 20 to 60%
more energy than on firm ground (Lejeune et al., 1998). Such effects
account for some of the reported discrepancies between laboratoryand field-based measures of performance in lizards. For example,
U. scoparia has been recorded in the laboratory to run at 75% of
the maximum speed recorded in the field (Jayne and Ellis, 1998;
Carothers, 1986). By contrast, many Anolis and lacertid lizards run
at higher velocity in the laboratory than in the field (Irschick et al.,
2005).
Recent attempts to understand the mechanical interactions
between an animal’s body and the substrate have yielded some
surprising results. For example, a modified version of resistive force
theory that was developed for the hydrodynamics of spermatozoa
can successfully predict the speed of sandfish lizards (Scincus
scincus) that undulate through soil (Maladen et al., 2009). However,
the mechanics of moving in sand also depends on factors that do
not play a role in a fluid, like the depth of the body and the packing
of particles, as measured by the volume fraction. The volume fraction
(the ratio of grain volume to total volume) is a major factor in how
quickly a crab-like robot can run on sand (Li et al., 2009) and is
likely an important variable for sand lizards as well.
Differences in running performance between species
Our results are consistent with prior studies on the sprinting
kinematics of sand lizards. Prior experiments established that
Fig.6. Sprint kinematics for Uma scoparia (purple) and Callisauris
draconoides (green) on different substrate types. (A,B)Mean (±1
s.d.) position and velocity for running on dune (solid lines) and
wash (dashed lines) sands among all individuals (N5) of each
species. Mean (±1 s.d.) values of (C) maximum acceleration
(amax), (D) maximum velocity (vmax) and (E) time to vmax for all
sprinting sequences. The only significant difference (*) was in the
vmax between species for sprinting on dune sand (see Table1).
C
50
30
10
2.5
D
2.0
*
1.5
300
E
250
200
150
Dune
sand
Wash
sand
THE JOURNAL OF EXPERIMENTAL BIOLOGY
Running in sand lizards
129
Table 1. Sprinting performance of Uma scoparia and Callisaurus draconoides on dune and wash substrates
Uma scoparia
Performance variable
Maximum acceleration
Normalized maximum acceleration
Maximum velocity
Normalized maximum velocity
Time to maximum velocity
Callisaurus draconoides
Units
Dune
Wash
Dune
Wash
m s–2
SVL s–2
m s–1
SVL s–1
ms
41±13
600±200
1.8±0.2*
28±10
230±20
31±13
450±200
1.9±0.2
28±6
211±23
47±13
630±220
2.2±0.2*
29±7
221±20
51±18
710±340
2.1±0.3
21±3
221±30
Data are means ± 1 s.d., N5 lizards in both species.
SVL, snout-vent length; *, P0.04, two-factor ANOVA with Tukey–Kramer post hoc comparison.
C. draconoides initiates sprinting on dune sand with the same
acceleration as U. scorparia (Irschick and Jayne, 1998b). This was
surprising, given that C. draconoides was reported to have a hind
limb length almost one-third longer than that of U. scorparia of
comparable size. However, the more elongated limbs of C.
draconoides traversed a greater stride length in subsequent strides,
which allowed this species to achieve a greater maximum velocity
than U. scorparia. We reached the same conclusions for dune sand,
but found that running on wash sand neutralized any differences in
sprint performance between the two species (Fig.6D–F).
Our results provide the opportunity to consider whether locomotor
performance is a dominant factor in the habitat distribution of sand
lizards. Arboreal Anolis lizards distribute in accordance with their
locomotor abilities (Irschick and Losos, 1999). Specifically, species
with a sprinting performance that is highly dependent on perch
diameter have a relatively restricted distribution. This principle, the
habitat constraint hypothesis, predicts that U. scorparia should
perform better on dune sand because this species inhabits only dunes.
By contrast, substrate type did not affect initial acceleration or
maximum velocity, and the broadly distributed species, U. scorparia,
attained a higher top speed than U. scorparia (Fig.6C,D, Table1).
Therefore, the restricted distribution of U. scorparia cannot be
explained by the habitat constraint hypothesis.
In contrast to U. scorparia, C. draconoides is broadly distributed
in dune and wash habitats. The habitat breadth hypothesis (Irschick
and Losos, 1999) predicts that the performance of such species
should be relatively less sensitive to substrate type. In favor of this
hypothesis, we found substrate type to have no effect on sprinting
performance in C. draconoides (Fig.6D,F, Table1). However, U.
scorparia also was not significantly affected by substrate type.
Furthermore, we found that C. draconoides achieved a higher
maximum speed than U. scorparia when running on dune sand, but
not on wash sand (Fig.6D). Therefore, the more broad distribution
of C. draconoides does not appear to be related to a lower sensitivity
of their performance to differences in substrate.
The morphological differences between these species may be
more meaningful in providing crypsis than locomotor specialization
for substrate type. We found that the fringes of U. scorparia do not
endow the species with a competitive advantage over C. draconoides
for sprinting on the dunes. However, the fringes may aid the ability
of U. scoparia to vibrate its body to bury itself in the sand (Arnold,
1995; Jayne and Daggy, 2000; Stebbins, 1944). This ability is
unlikely to be possible in wash sand because of its greater surface
strength (Fig.4B), which could therefore deter U. scoparia from
wash habitats. U. scoparia also possesses a coloration pattern that
is cryptic on dune but not wash sand (Norris, 1958) (Fig.1). In
contrast, C. draconoides is more cryptic on wash sand and likely
benefits from the protection offered by the vegetation in the wash
habitat (Fig.1A) (Irschick and Jayne, 1999a). Toe fringes may also
help in thermoregulation as increased surface area conduits to
transfer heat from the body to the environment, much like radiator
fins.
Measuring sprint performance
The present study considered methods for enhancing the accuracy
of measurements of sprinting performance from video recordings.
Optical distortions generate errors that depend on the lenses used
and the proximity of the camera to the subject. The optics in our
setup produced errors in position that approached 4pixels (Fig.2B),
but could be reduced to an order of magnitude less (Fig.2C) with
a careful calibration (described in the Materials and methods). An
uncorrected image appears capable of introducing substantial errors,
considering that our analysis found that errors exceeding 100% (e.g.
Fig.4F) could be generated by single-pixel noise.
Temporal and spatial resolution are major considerations for
enhancing the accuracy of velocity and acceleration measurements.
Depending on the resolution of the camera and rate of motion
measured, it is possible to measure maximum acceleration with error
below 10% at a frame rate of 250framess–1 in human running (Chau,
2001; Giakas et al., 2000) and accelerating fish (Walker, 1998).
However, instantaneous measurements of acceleration are more
difficult to acquire accurately. As reported previously (Walker,
1998), we found exceedingly high errors for instantaneous
acceleration, even at exceedingly high frame rates (e.g.
5000framess–1; Fig.4F). The method of calculation can a have a
large effect on the accuracy of both acceleration and velocity
measurements, particularly at low frame rates (e.g. 250 and
500framess–1; Fig.4D–F). As explored by our sensitivity analysis,
the accuracy of these measurements also depends on the animal’s
rate of motion. This is particularly true of the step period, which
has a strong effect on the errors in acceleration for motion more
rapid (<20 frames for a frame rate of 1000framess–1) than what
we observed in these sand lizards (Fig.4J–K).
CONCLUSIONS
In summary, our results suggest that natural variation in substrate
mechanics do not greatly affect sprinting performance in either C.
draconoides or U. scorparia. Despite a more than threefold disparity
in the surface strength of dune and wash sands, most measures of
sprinting performance were statistically indistinguishable between
these substrates. The subtle differences found between species ran
counter to expectation from their habitat distribution. Therefore, the
difference in distribution between these species does not appear to
be dictated by sprinting ability.
ACKNOWLEDGEMENTS
Marvalee Wake provided essential guidance and support. The Biomechanics
Group and Museum of Vertebrate Zoology (MVZ) at UC Berkeley offered
THE JOURNAL OF EXPERIMENTAL BIOLOGY
130
W. L. Koff and M. J. McHenry
numerous suggestions. Sheila Patek and Bob Full provided feedback on very
early incarnations of this manuscript. Fieldwork in the Mojave Desert would not
have been possible without the help of Rob Bingham and Nichole Danos. Jim
André and the Granite Mountains Desert Research Center provided a wonderful
respite from the heat. Lizards were collected under National Park Service permit
no. MOJA-2002-SCI-0017 and CA Fish and Game permit no. 801100-01. W.L.K.
was supported by the NSF DDIG (IBN-0309307) and the Annie Alexander
Fellowship through the MVZ. M.J.M. was supported by the NSF (IOS-0952344).
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