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.
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 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
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 field-active 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.
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 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).
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 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).
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: (1) where the first term describes the net increase that asymptotically approaches vmax at a rate determined by the time constant λ, and the second term characterizes the oscillations in speed created by individual steps with an initial velocity of vo and step period τ. 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: λ=40 frames, vmax=2 pixels frame–1, vo=1 pixel frame–1 and τ=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 pre-processed 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 least-squares 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 b-form 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 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: (2) where F is the frame rate (frames s–1) and τ 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): (3) where xi is the position of sample i and Δt is the time difference between samples. The second method, first-order central difference (1-CD), was calculated with the following equation: (4)
The third method used fourth-order central difference (4-CD), according to the equation (Biewener and Full, 1992): (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): (6) 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): (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 kinematics (vmax, λ, vo and τ 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: λ=40 frames, vmax=2 pixels frame–1, vo=1 pixel frame–1 and τ=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.
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 log10-transformation 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. One-tailed Students' t-tests were used to evaluate differences in the surface strength of dune and wash sands. All statistical analyses were implemented in Matlab.
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 (τ=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 found to be significantly different (Fig. 6D). On average, the dune-dwelling 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).
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 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 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 laboratory- and 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 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 (τ<20 frames for a frame rate of 1000 frames s–1) than what we observed in these sand lizards (Fig. 4J–K).
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.
Marvalee Wake provided essential guidance and support. The Biomechanics Group and Museum of Vertebrate Zoology (MVZ) at UC Berkeley offered 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.
↵* Present address: Howard Hughes Medical Institute, Janelia Farm Research Campus, 19700 Helix Drive, Ashburn, VA 20147, USA
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).
- © 2011.