The Journal of Experimental Biology 2, 2189 2195 (1997) Printed in Great Britain The Company of Biologists Limited 1997 JEB77 2189 MAXIMUM SPEED AND MECHANICAL POWER OUTPUT IN LIZARDS CLAIRE T. FARLEY* Department of Integrative Biology, University of California, Berkeley, CA 9472-314, USA Accepted 8 May 1997 The goal of the present study was to test the hypothesis that maximum running speed is limited by how much mechanical power the muscular system can produce. To test this hypothesis, two species of lizards, Coleonyx variegatus and Eumeces skiltonianus, sprinted on hills of different slopes. According to the hypothesis, maximum speed should decrease on steeper uphill slopes but mechanical power output at maximum speed should be independent of slope. For level sprinting, the external mechanical power output was determined from force platform data. For uphill sprinting, the mechanical power output was approximated as the power required to lift the center of mass vertically. When the slope increased from level to 4 uphill, maximum speed decreased by 28 % in C. variegatus and by 16 % in E. skiltonianus. At maximum speed on a 4 uphill slope in both species, the mechanical Summary power required to lift the body vertically was approximately 3.9 times greater than the external mechanical power output at maximum speed on the level. Because total limb mass is small in both species (6 16 % of body mass) and stride frequency is similar at maximum speed on all slopes, the internal mechanical power output is likely to be small and similar in magnitude on all slopes. I conclude that the muscular system is capable of producing substantially more power during locomotion than it actually produces during level sprinting. Thus, the capacity of the muscular system to produce power does not limit maximum running speed. Key words: locomotion, biomechanics, sprinting, muscle, running, lizard, Coleonyx variegatus, Eumeces skiltonianus. Introduction A 5 kg pronghorn antelope Antilocapra americana can run at 1 km h 1 (Garland, 1983), but other artiodactyls of similar body mass such as a roe deer Capreolus capreolus (Gambaryan, 1974), impala Aepyceros melampus (Alexander et al. 1977) or chamois Rupicapra rupicapra (Gambaryan, 1974) can only achieve approximately half of that speed. Because of the similarities in body form and size of all of these animals, it is surprising that the pronghorn antelope can run twice as fast as the others. It is not yet fully understood why some animals of a given body size can run so much faster than others. Some studies have demonstrated correlations between maximum speed and anatomical or physiological traits (Losos, 199; Garland and Janis, 1993; Garland and Adolph, 1994; Gleeson and Harrison, 1988; Marsh, 199). These correlations provide insight into the aspects of animal design that affect maximum speed but do not provide a full explanation of the mechanisms linking these traits to maximum speed. The goal of the present study was to examine the limitations to maximum speed in running animals using a biomechanical approach. The mechanical power required for running increases at higher speeds. As an animal runs, the center of mass of the body undergoes fluctuations in kinetic energy and gravitational potential energy with each footfall. During running at a constant speed, mechanical power is required to lift and accelerate the center of mass, to lift and accelerate the body segments relative to the center of mass and to overcome air resistance. Each component of the mechanical power required for locomotion increases with forward speed. This pattern of increasing mechanical power requirements with increasing speed is common to all of the legged animals studied to date, including humans, dogs, horses, kangaroos, lizards, cockroaches and ghost crabs (Cavagna et al. 1964; Heglund et al. 1982b; Blickhan and Full, 1987; Full and Tu, 199; Willems et al. 1995; Farley and Ko, 1997). Because running faster requires more mechanical power, it is reasonable to hypothesize that the maximum mechanical power that the muscular system can produce limits how fast an animal can run (Hill, 195). A powerful experimental approach to examining the limitations to maximum speed has involved manipulating the mechanical properties of the locomotor muscles by changing the body temperature of lizards. These experiments have been conducted on Dipsosaurus dorsalis and Sceloporus *Present address: Department of Integrative Biology, 36 Valley Life Sciences Building, University of California, Berkeley, CA 9472-314, USA (e-mail: cfarley@socrates.berkeley.edu).
219 C. T. FARLEY occidentalis. In spite of differences in morphology and phylogeny, the results for both species are remarkably similar (Marsh and Bennett, 1985, 1986a,b; Marsh, 199). When the body temperature of either species is manipulated in a range below 25 C, the maximum running speed and the maximum power output of the muscles both change substantially and nearly in parallel. In contrast, when the body temperature of either species is manipulated in a range above 25 C, the maximum mechanical power output of the muscles changes to a greater extent than does the maximum running speed. At first, this observation appears to contradict the hypothesis that the maximum power output of the muscular system limits maximum speed. However, because the mechanical power versus speed relationship is not known for the lizard species used in the body temperature manipulation studies, it is not possible to use these data for a definitive test of the hypothesis. There is as much as threefold variation in the mechanical cost of transport among animals of a given body size (Heglund et al. 1982a; Full, 1989) and, thus, it is important to measure the mechanical power output as a function of speed in each species in order to test the hypothesis rigorously. The goal of the present study was to test the hypothesis that the maximum power that the muscular system can produce limits maximum running speed. To test this hypothesis, maximum speed and mechanical power output were compared during sprinting on hills of different slopes in two species of small lizards, Eumeces skiltonianus and Coleonyx variegatus. According to the hypothesis, maximum speed should decrease on steeper uphill slopes, but mechanical power output at maximum speed should be independent of slope. The experiments were performed at a moderate body temperature (25 C) at which it seemed likely that mechanical power output would limit maximum speed on the basis of a previous study comparing stride frequency at maximum speed with the optimal frequency for mechanical power output by fast-twitch muscles (Swoap et al. 1993). E. skiltonianus and C. variegatus were used because of existing data describing the relationship between external mechanical power output and speed during their locomotion (Farley and Ko, 1997). Materials and methods Animals Five individuals of Eumeces skiltonianus (western skink) (Baird and Girard) were used, ranging in body mass from 4.3 g to 5.8 g (mean ± S.D. 5.24±.57 g) and with a snout vent length of approximately 5.2 cm. In addition, five individuals of Coleonyx variegatus (western banded gecko) (Baird) were used, ranging in body mass from 3.6 g to 5. g (mean ± S.D. 4.16±.61 g) and with a snout vent length of approximately 5.6 cm. Individuals of both species were obtained from a commercial collector. Individuals of E. skiltonianus were collected in San Bernardino County, CA, USA, and individuals of C. variegatus were collected in Riverside County, CA, USA. The lizards were housed in an environmental room (24 C) illuminated for 13 h per day. In addition, each cage containing an individual of C. variegatus had direct ultraviolet lighting from a fluorescent tanning lamp and a heat strip to allow behavioral thermoregulation over a gradient of 24 4 C. Both species were fed a diet of mealworms, crickets and a vitamin/mineral supplement, and they were given water daily. The animals were given no food for 24 h before experiments. Experimental design and protocol To test the hypothesis that the maximum mechanical power output of the muscular system limits maximum speed, I determined the maximum speed and mechanical power output of each animal on a level track, on a 2 uphill slope and on a 4 uphill slope. The experiments were performed at room temperature, which varied between 25 C and 26 C and represents a moderate body temperature for these species. The field active body temperature is 3 C for E. skiltonianus and approximately 23 C for C. variegatus (Brattstrom, 1965; Cunningham, 1966). The body temperature used in this study (25 C) is only slightly above the range ( 22 C) for which Swoap et al. (1993) found that the stride frequency was equal to the optimal frequency for power output by fast twitch muscle during work loops in D. dorsalis. Maximum speed on each slope was determined from trials in which the animals sprinted on a section of a 2 m track that had a fine sandpaper running surface. The animals were induced to sprint by the investigator prodding or gently pinching a hindlimb. In addition, a darkened box was placed at the end of the track to induce them to sprint into the box. The animals carried out 2 days of practice sprints on the track before data collection began in order to avoid any effects of behavioral accommodation (Bennett, 198). The animals were video-taped in lateral view at 6 fields s 1 during each trial. A small piece (approximately 1 cm 1 cm) of retroreflective tape was attached to the trunk of each animal. The retroreflective tape was positioned so as to be visible in lateral view and to be approximately halfway between the cranial and caudal ends of the trunk. This retroreflective tape, together with appropriate lighting during the trials, made it possible to use automatic point-tracking software (Peak Performance Technologies, Inc.) to determine the instantaneous position and velocity of the animal throughout the trial. The maximum speed was determined for these species on a level track, a 2 uphill track and a 4 uphill track. Each animal participated in 5 days of experiments, with at least 2 days between them. On a given day, each animal performed four trials, separated by at least 3 min. Each animal performed a total of four trials on each slope, consisting of two trials on each of 2 days. The four trials on a given slope occurred in each position within the daily order of trials (i.e. first, second, third and fourth). On the first day that included trials on a given slope, the trials on that slope were the first and fourth trials performed by each animal. On the second day that included trials on a given slope, the trials on that slope were the second and third trials performed by each animal. This experimental design ensured that if fatigue did affect maximum speed, it would have equal effects on maximum speed on all slopes. The
Maximum speed and mechanical power 2191 results showed that the fastest trial for an individual on a given slope occurred as often on the last trial of the day as on the first trial of the day. This suggests that fatigue within a day did not slow down the animals. Determination of maximum speed Automatic point-tracking software (Peak Performance Technologies, Inc.) was used to track the movement of the retroreflective marker as the animal moved along the track. Parallax effects were negligible because the camera was placed a long distance from the track (6.1 m) relative to the width of the video field (approximately 1 m). Markers were placed a known distance apart within the video field for distance calibration. Thus, the instantaneous position of the animal could be determined from the digitized video data. The position data were low-pass filtered using a fourth-order zerolag Butterworth filter with a cut-off frequency of 1 Hz. This cut-off frequency was chosen using residual analysis as outlined in Winter (199). Subsequently, the velocity of the animal was calculated by taking the derivative of the displacement of the retroreflective marker with respect to time (Peak Performance Technologies, Inc.). The animals moved in bursts (Fig. 1), generally lasting.5 1 s, that were punctuated by brief pauses of approximately.1 s. The maximum velocity for a given trial was the average velocity for the fastest 1 cm traveled in which the velocity did not change by more than 5 % over the period. Over this period, the animals took approximately three steps. This criterion ensured that the maximum speed value was relatively unaffected by acceleration. For a given animal under a given condition, the maximum velocity was defined as the highest maximum velocity found for any of the four trials performed under that condition. Determination of mechanical power For sprinting on the level, data from Farley and Ko (1997) for E. skiltonianus and C. variegatus were used to determine the external mechanical power output at maximum speed. Farley and Ko (1997) calculated external mechanical power output at maximum speed from force platform measurements for E. skiltonianus. Although many trials at submaximal speeds were obtained for C. variegatus in that study, no constantspeed trials at maximum speed were obtained because C. variegatus moved in short bursts when sprinting maximally. However, the data for E. skiltonianus and C. variegatus were similar over the speed range covered by both. Whether the data for the two species were analyzed together or separately, the slope of the relationship between external mechanical power output and speed was 1.5 J kg 1 m 1 (Farley and Ko, 1997). This value that fell within the range (.5 1.8 J kg 1 m 1 ) previously determined for a variety of legged animals (Full, 1989). For the present study, the mass-specific external mechanical power output at maximum speed on a level surface (P ext, W kg 1 ) was calculated from the linear least-squares regression for external mechanical power output versus speed for the combined data from C. variegatus and E. skiltonianus: Velocity (m s 1 ) 1..8.6.4.2.2.4.6.8 Distance (m) Fig. 1. Instantaneous forward velocity as a function of distance traveled on the track for a typical level trial. Note that the animal tended to sprint for short bursts, interspersed with brief pauses. This pattern of bursts and pauses was typical for both species on all slopes. Maximum speed was the average velocity for the fastest 1 cm distance in which the velocity changed by less than 5 %. For this trial, maximum speed was the average velocity for the period outlined by a box. Each point represents the instantaneous velocity during a given field of video recorded at 6 fields s 1. P ext =.2 + 1.5v, (1) where v is forward velocity in m s 1 (r 2 =.86, P<.1; Farley and Ko, 1997). For sprinting on a 2 or 4 uphill slope, the mass-specific mechanical power required to lift the center of mass vertically (P uphill ) was calculated from equation 2: P uphill = gvsinθ, (2) where g is the gravitational acceleration and θ is the hill angle. The power required to lift the center of mass vertically is equal to the product of vertical force and vertical velocity. The average force acting vertically is body weight (mg, where m is body mass), and the vertical velocity is equal to the product of the animal s running velocity (v) and the sine of the hill angle (sinθ). Because P uphill is the mass-specific mechanical power, the mass term (m) cancels out, leaving the expression in equation 2. The mass-specific mechanical power required to lift the center of mass up each hill was compared with the mass-specific external mechanical power output at maximum speed on a level surface. This analysis included two simplifications. First, for uphill sprinting, the analysis only included the mechanical power required to lift the center of mass vertically. The actual external mechanical power required for uphill sprinting is likely to be higher because the center of mass undergoes fluctuations in velocity and displacement that are not associated with lifting the center of mass vertically up the hill. As shown in Farley and Ko (1997), each step of locomotion on a level surface involves fluctuations in the kinetic energy and gravitational potential energy of the center of mass due to cyclic movements of the center of mass in the horizontal (fore aft), vertical and lateral directions. The present analysis of uphill sprinting only considered the average vertical velocity of the center of mass
2192 C. T. FARLEY in the estimation of external power output (equation 2). However, the results show that the mechanical power associated with lifting the body vertically up an incline is approximately four times greater than the external mechanical power required during level sprinting; our simplified analysis is therefore adequate to provide a strong test of the hypothesis. The second simplification was that the internal mechanical power associated with lifting and accelerating the body segments relative to the center of mass was not included in the analysis of either level or uphill sprinting. However, the following observations suggest that the magnitude of the internal mechanical power is likely to be similar for all slopes and is small compared with the external mechanical power. First, the stride frequency at maximum speed was similar on a level surface (12 strides s 1 ) to that on a 4 uphill slope (11 strides s 1 ), suggesting that the magnitude of the internal mechanical power output would also be similar on all slopes. Second, the limbs are relatively small in both species. The total mass of the four limbs is 6 % of body mass in E. skiltonianus and 16 % of body mass in C. variegatus. As a result, the power required to lift and accelerate the limbs relative to the center of mass is likely to be low. The cockroach Blaberus discoidalis has a similar body mass with lightweight limbs (13 % of body mass), and its internal mechanical power is only 13 % of the external mechanical power (Kram et al. 1997). In addition, because the external mechanical power output in the present study is approximately fourfold greater during uphill sprinting than during level sprinting, the general conclusions are not likely to be changed by inclusion of the internal mechanical power output. Maximum speed and mechanical power output were compared for the level, 2 uphill, and 4 uphill slopes using a repeated-measures analysis of variance (ANOVA). Results The animals moved in bursts, generally lasting.5 1 s, punctuated by brief pauses of less than.1 s (Fig. 1). This general pattern was similar for both species and on all slopes. The maximum speed of both species decreased significantly on steeper uphill slopes (P=.71; Fig. 2). For E. skiltonianus, maximum speed (v max ) was 16 % lower on a 4 uphill slope than on a level surface (level v max =.76±.6 m s 1, mean ± S.E.M.). For C. variegatus, the maximum speed was 28 % lower on a 4 uphill slope than on a level surface (level v max =.87±.5 m s 1 ). There were no significant differences among the individuals of each species (P=.16). On each uphill slope, the lizards were able to achieve a higher maximum speed than was predicted by the powerlimitation hypothesis (Fig. 2). On the 4 uphill slope, E. skiltonianus and C. variegatus achieved maximum speeds that were approximately 3.9 times greater than predicted by the power-limitation hypothesis. For example, the predicted maximum speed for E. skiltonianus on the 4 slope was.15 m s 1 and the actual maximum speed was.64 m s 1. Both species required substantially more mechanical power Maximum speed (m s 1 ) 1..8.6.4.2 1..8.6.4.2 A B Predicted E. skiltonianus C. variegatus 2 4 Uphill angle (degrees) Fig. 2. Measured maximum speed (shaded bars) and predicted maximum speed (open bars) for sprinting on a level surface, 2 uphill and 4 uphill for the gecko Coleonyx variegatus (A) and the skink Eumeces skiltonianus (B). The predicted maximum speed was calculated from the mechanical power-limitation hypothesis. For 2 and 4 uphill slopes, the predicted maximum speed is the maximum speed that the animals would have achieved if the mechanical power output associated with lifting the center of mass vertically were the same as the external mechanical power output on the level. Values are means + S.E.M. (N=5). to overcome gravity during uphill sprinting than was required to lift and accelerate the center of mass during level sprinting (P<.1; Fig. 3). On average for both species, the mechanical power required to lift the center of mass up a 4 hill at maximum speed was 3.9 times higher than the external mechanical power output on a level surface at maximum speed. For example, in E. skiltonianus, the mechanical power required to overcome gravity at maximum speed up a 4 hill was 4. W kg 1, whereas the external mechanical power output was.94 W kg 1 at maximum speed on a level surface. Discussion The present study shows that the muscular systems of E. skiltonianus and C. variegatus are capable of producing substantially more power than they actually produce during maximum-speed running on a level surface. The mechanical power required to lift the center of mass up a 4 hill at maximum speed is 3.9 times greater than the external Actual
Maximum speed and mechanical power 2193 Power (W kg 1 ) 5 4 3 2 1 2 E. skiltonianus 4 mechanical power required for running at maximum speed on a level surface. The findings are nearly identical for E. skiltonianus and C. variegatus in spite of their morphological and phylogenetic differences. These findings show that the maximum mechanical power that the muscular system can produce does not limit maximum running speed in either species. Previous research has revealed that uphill slope has a relatively small effect on sprinting speed in a faster lizard species, Stellio stellio (Huey and Hertz, 1982). This observation suggests that the muscular system of Stellio stellio is able to produce more power during uphill sprinting than during level sprinting. To test further whether the maximum power output of the muscular system limits maximum speed in lizards, it would be useful to apply the approach used in the present study to some of the fastest lizard species. Previous research has shown that the metabolic energetic cost of low-speed sustained level and uphill locomotion is 4 5 % lower in C. variegatus than in other diurnal lizards, including E. skiltonianus (Farley and Emshwiller, 1996; Autumn et al. 1997). The similarity in maximum speed between the two species suggests that the physiological traits associated with a very low cost of locomotion in C. variegatus do not necessarily lead to reduced performance in burst locomotion, as has been speculated previously (Woledge, 1989). In lizards, as in other animals, primarily slow oxidative muscle fibers are active during low-speed sustained locomotion, and fast glycolytic fibers are active during highspeed locomotion (Jayne et al. 199). Because different muscle fiber populations are active in low- versus high-speed locomotion, it is possible that unusual physiological characteristics of slow muscle fibers could lead to a low energetic cost of sustained locomotion without leading to a reduced maximum speed in C. variegatus. However, it is also important to note that other differences between C. variegatus and E. skiltonianus, such as the reduced limbs of E. skiltonianus, may offset the effects of postulated differences in skeletal muscle properties during maximum-speed running. 2 C. variegatus Fig. 3. The mechanical power required to lift the center of mass vertically at maximum speed on a 2 or 4 uphill slope and the external mechanical power output during maximum-speed running on a level surface for C. variegatus and E. skiltonianus. Values are means + S.E.M. (N=5). 4 Previous studies suggest that muscle power output is more likely to limit maximum running speed in the lizards Sceloporus occidentalis and Dipsosaurus dorsalis at body temperatures below 25 C than above 25 C (Marsh and Bennett, 1985, 1986a,b; Marsh, 199; Swoap et al. 1993). When body temperature is varied between 15 C and 25 C in these species, maximum speed changes in parallel with maximum muscle power output (Marsh and Bennett, 1985, 1986a,b; Marsh, 199). In contrast, when body temperature is varied between 25 C and 44 C, sprint speed only changes slightly in spite of large changes in the ability of the muscles to produce power. In addition, a recent study compared the stride frequency used by D. dorsalis at maximum speed with the optimum frequency for mechanical power output by fast twitch muscle fibers during work loops (Swoap et al. 1993). The findings show that the stride frequency used at maximum speed is the optimum frequency for muscle power output at body temperatures of 15 C and 22 C (Swoap et al.1993). However, at body temperatures of 35 C and 42 C, the stride frequency used at maximum speed is lower than the frequency that maximizes muscle power output. Thus, although these studies do not provide a direct test of whether the maximum mechanical power output of muscle limits maximum speed, they suggest that the maximum mechanical power output of muscle is more likely to limit maximum speed at body temperatures at or below 25 C than at higher body temperatures. The present study examined mechanical power output at maximum speed on different slopes in E. skiltonianus and C. variegatus at a body temperature of 25 C. For D. dorsalis and S. occidentalis, a body temperature of 25 C is at the upper end of the temperature range for which power output is more likely to limit maximum speed than at higher temperatures (see above). It is not clear to what extent previous findings about the thermal sensitivity of sprint speed and muscle power output in D. dorsalis and S. occidentalis apply to E. skiltonianus and C. variegatus, because of differences in their field active body temperatures and phylogeny. However, the relationship between maximum speed and body temperature is remarkably similar among C. variegatus (Huey et al. 1989), D. dorsalis and S. occidentalis (Marsh and Bennett, 1985, 1986b) in spite of the substantially lower field active body temperature in C. variegatus (Brattstrom, 1965; Cunningham, 1966) and phylogenetic differences among the species. This observation suggests that similar mechanisms may link the thermally sensitive muscle properties and sprinting speed in all of these species. Further insight into the limitations to maximum speed may be gained by comparing the mechanical power output of the muscular system during sprinting on different slopes over a range of body temperatures. In addition, examining other lizard species with a range of phylogenetic histories and sprinting abilities may provide insight. Several studies suggest that animals covering a range of body sizes may not operate at the limit for mechanical power production during maximum-speed running. First, the stride frequency used at maximum speed by D. dorsalis at a body
2194 C. T. FARLEY temperature of 35 C is lower than the optimum frequency for mechanical power output by its fast twitch muscle fibers in individuals spanning a 1-fold range of body mass (Johnson et al. 1993). Second, earlier studies suggest that human sprinters with a 1-fold higher body mass than the lizards in the present study also appear not to use their full capacity for mechanical power production during sprinting. When humans run at maximum speed up a slight hill while carrying an extra load, they produce approximately 28 % more power to lift their center of mass vertically than at their maximum speed without an extra load (Kyle and Caiozza, 1986). In addition, a comparison of separate studies on human running suggests that acceleration from a standstill to a high speed (7.5 m s 1 ; Cavagna et al. 1971) requires nearly twice as much external mechanical power as running steadily at the high speed (Willems et al. 1995). In spite of body form and phylogenetic differences between lizards and humans, both use kinetically similar bouncing gaits that are typical of high-speed legged locomotion, suggesting that the fundamental constraints on running speed may be similar for both (Farley and Ko, 1997). Finally, it is interesting to note that one study shows that sprinting performance is more greatly affected by slope in larger lizards (Huey and Hertz, 1982). This finding suggests that larger lizards may operate closer to their limit for mechanical power output during sprinting than do smaller lizards. Future research should examine this issue as it may give insight into the link between musculoskeletal design and maximum speed. If the maximum mechanical power output of the muscular system does not limit maximum speed, what does limit it? One promising hypothesis is that an animal s maximum speed is limited by the minimum ground contact time that the animal is capable of using (McMahon and Greene, 1979). As running animals increase their forward speed, the time that each foot is in contact with the ground decreases, reaching its minimum value at maximum speed. In lizards at low body temperatures (15 25 C), the minimum possible ground contact time may be determined by the minimum time required for force generation by the muscles (Marsh, 199). Over this temperature range, the twitch time of muscle is approximately the same as the ground contact time at maximum speed. In contrast, in lizards at higher body temperatures, the twitch time of muscle is substantially shorter than the ground contact time at maximum speed, and thus does not limit the minimum ground contact time (Marsh, 199). In lizards at higher body temperatures and in mammals, the minimum ground contact time is likely to be determined by the spring-like properties of the musculoskeletal system. Running, hopping and trotting animals, including lizards, use bouncing gaits (Cavagna et al. 1977; Heglund et al. 1982a; Blickhan and Full, 1993; Farley et al. 1993; Farley and Ko, 1997). These bouncing gaits have been modeled with a simple spring mass system in which the stiffness of the integrated musculoskeletal system is represented by a single spring and the mass of the body is represented by a point mass. In these gaits, the minimum ground contact time primarily depends on the maximum vertical stiffness of the animal s spring mass system relative to its body mass (Blickhan, 1989; He et al. 1991; Farley et al. 1991, 1993; McMahon and Cheng, 199; Farley and Gonzalez, 1996). Thus, maximum running speed may be limited by the maximum stiffness of an animal s spring mass system. The author thanks K. Autumn, R. J. Full, D. Moran and M. Emshwiller for their input to this project. 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