## ABSTRACT

The agamid lizard

*Stellio stellio*L. accelerates quickly and reaches maximum speed over short distances.Maximum speed on the level is proportional to body mass to the power. This relation differs from predictions based on an interspecific scaling model of “geometric” similarity (

*M*^{0}) and is intermediate between predictions based on interspecific scaling models of “elastic” similarity and of “static stress” similarity .Maximum speed was also measured on slopes ranging from –15° to + 60°. The effect of slope on speed varies with body mass. The maximum speed of large lizards decreases on steep slopes, but that of small lizards is remarkably independent of slope.

## INTRODUCTION

Many animal species have a remarkable ability to scamper quickly over nearly vertical surfaces on rocks or trees. Although the effect of body size and of slope on maximum sprint speed of terrestrial animals has been debated from a theoretical perspective (Hill, 1950; Henry & Trafton, 1951; Maynard Smith, 1968; Heglund, Taylor & McMahon, 1974; McMahon, 1975 ; Wilkie, 1977; Elliott, Cowan & Holling, 1977), empirical analyses bearing on this topic are rare (Hill, 1950). Indeed, the actual effect of slope on speed is apparently unstudied.

In this paper we examine how body mass and slope jointly affect maximum sprint speed of an agamid lizard [*Stellio (Agama) stellio* (Moody, 1980)]. These intraspecific results are compared with theoretical predictions based on interspecific scaling models.

Our investigation was prompted by the research of Taylor, Caldwell & Rowntree (1972) on the energetic cost of locomotion in mammals. Using steady-state aerobic metabolic rate as the metric of energetic cost, they found that cost increased with slope for large but not for small mammals. We wished to determine whether this result might pertain for lizards, a metabolically different group of terrestrial vertebrates. In contrast to mammals, most lizards are specialized for sprint (anaerobic) rather than endurance (aerobic) locomotion (Bennett, 1978). Consequently, maximum sprint speed (or acceleration) is an ecologically more relevant metric (Huey & Stevenson, 1979) for a parallel study of how size and slope affect locomotor performance.

We selected the lizard *Stellio stellio*, which is a moderate-sized (maximum mass about 125 g, maximum snout-to-vent length about 150 mm) insectivorous lizard that occupies diverse habitats in the Middle East. Because these lizards regularly live in complex microhabitats (rocks, boulders, walls) and because a large size range of individuals can be obtained, *Stellio* are ideally suited for a study of the effect of slope and size on sprint speed.

## MATERIALS AND METHODS

Lizards were collected at several localities in Israel in late June 1980, shipped to Seattle, acclimated for 10 days at 12:12 L;D and 34:26 °C (centred at 12·00 h local time), and used initially in a 3-week experiment on the thermal dependence of sprint speed (P. E. Hertz, R. B. Huey & E. Nevo, in preparation). Thus all lizards were well trained (see Bennett, 1980).

Subsequently, we selected 23 lizards for the present experiments. Beginning in mid-August 1980, lizards were raced daily (1 slope/day, 6 trials/lizard/day, about 1 trial every 45 min) in a 2·4 m × 20 cm racetrack with a rough, rubberized substrate that provided excellent traction. We induced a lizard to run by tapping its hindquarters and then chased it the length of the track. Speeds measured under these artificial conditions undoubtedly differ somewhat from those measured in nature: consequently, our results are relative, rather than absolute.

To measure speeds of lizards along the racetrack, 12 stacks of 4, vertically aligned photocells (height = 6 cm) were positioned at set intervals along the runway (total interval = 2 m) and connected to an AIM 65 microprocessor that produced a printed record of elapsed times, interval times, and interval speeds (Huey *et al*. 1981). Interval speeds were calculated to 0·01 m s^{−1} over each 0·5 m section of the track, and we report the maximum interval speed ever achieved by a given lizard for a given slope. Because maximum speed was unrelated to trial number for all slopes, the experimental regime of 6 trials per day did not fatigue lizards within days. Body temperature was controlled at about 34 °C, which approximates the mean *T*_{b} of active *Stellio stellio* in nature (P. E. Hertz & E. Nevo, in preparation) and is near the apparent ‘optimal’ *T*_{b} for sprint speed on the level (P. E. Hertz, R. B. Huey and E. Nevo, in preparation).

Lizards were raced at the following sequence of slopes: 0°, 15°, – 15°, 30°, 45° and 60°. Because this sequence was non-random, observed changes in speed during the experiment could be due to factors other than slope. To guard against this possibility, we re-ran all lizards at a slope of 0° on the day after the 60° run and eliminated four lizards that failed to run at least 90% as fast as the maximum speed in the initial series at 0° (an *a priori* criterion for elimination). Consequently, this analysis is based only on lizards that maintained sprint capacity during the entire experiment and for which the regime of daily trials did not induce cumulative fatigue.

*v*

_{m}= maximum speed (m s

^{−1}),

*t =*time (s), and

*k =*a constant. This curve was fitted using Marquardt’s algorithm (SPSS). Progressive differentiation permits specifications of speed and acceleration as functions of time.

## RESULTS

### Speed profile during a run

Lizards in nature appear to have high initial rates of acceleration and to reach maximum speed quickly. This subjective impression is supported in Fig. 1, which shows distance, speed, and acceleration as functions of time for a 65 g 5. *stellio* running up a 60° slope. Even on this acute slope, the lizard achieved 95% of *v*_{m} (2·9 m s^{−1}) within the first 0·4 m (or in 0·2 s).

### Maximum speed -versus body mass on level slope

Maximum speed on a level slope varies considerably among individuals (1·7–4·0 m s^{−1}). However, most of the variation in log *v*_{m} is accounted for by log body mass (*r*^{2} = 0·575, *P*< 0·001, Fig. 2); and *v*_{m} can be predicted from mass by the following relationship :

### Maximum speed versus slope

To examine the effect of slope on sprint speed, slopes were first transformed to sint θ to generate a linear measure of the vertical displacement of a lizard running a distance of 1 m on a slope of θ degrees; the linear regression of *v*_{m} versus sin θ was then determined for each lizard (Fig. 3). The effect of slope on *v*_{m} is demonstrated by determining from these regressions the predicted difference in *v*_{m} of a lizard running on slopes of 0° and + 60°.

The effect of slope on speed (*v*_{0°}–*v*_{60°}) is strongly and inversely related to body mass *(r* = –0·590, *P <* 0·01, Fig. 4). Large lizards run much slower up a 60° slope than on the level. Remarkably, however, some small and medium-sized lizards (Figs. 3 and 4) appear to run as fast up steep slopes as on the level.

### Speed versus mass, slope variable

The patterns in Figs. 2–4 raise the question of whether large lizards can always outrun small lizards even on steep slopes. In other words, is there an uphill slope at which speed is independent of mass? To investigate this question we calculated the exponential relationship for *v*_{m} versus body mass [see equation (3)] at each slope. The effect of mass on *v*_{m} (Fig. 5) is progressively reduced as slope increases (Spearman rank correlation of exponent of the above equation versus slope = – 0·943, *P <* 0·01), but large lizards still run slightly faster on average than do small lizards even on slopes as steep as 60°, where *v*_{m} ∝ *M*^{0·16}. However, information on speeds at steeper slopes would be of interest.

## DISCUSSION

In the following Discussion the results of our experiments on the effects of size and slope on sprint of *Stellio stellio* are first described with reference to theoretical models of sprint locomotion. Our comparisons of intraspecific trends with several theoretical scaling models do not, however, constitute an empirical test of those models, which are more appropriately tested by interspecific data from individuals at a particular growth stage (Gould, 1975; Sweet, 1980).

### Scaling spring speed with body mass

The theoretical basis of scaling top speed with mass of quadrupedal animals has a controversial history. Hill’s pioneering model (Furusawa, Hill & Parkinson, 1928; Hill, 1950; Wilkie, 1977) is based on the assumption that small and large animals are geometrically similar [i.e. the length (Z) of every anatomical element is maintained proportional to diameter (d), thus 1∝ *d*]. This static model predicts that speed is independent of size (∝ M°). In other words, small and large animals should run equally fast. McMahon (1974, 1975) has proposed two dynamic scaling models which assume that animals maintain either ‘elastic’ similarity or ‘static stress’ similarity These models predict that maximum speed is proportion to and respectively. Thus, unlike Hill’s static model, both of McMahon’s dynamic models predict that speed increases with size.

Available data on the maximum speeds of mammals (Howell, 1944; Hill, 1950; Layne & Benton, 1954; Hildebrand, 1974) roughly support Hill’s prediction (1950) only for mammals ranging in size from a whippet ( ∼ 9 kg) to a horse. Unfortunately, a variety of different and often inaccurate methods were used to estimate speed (Hill, 1950). Heglund *et al*. (1974) found that running speeds of mammals (a 30 g mouse to a 680 kg horse) at the trot-gallop transition was proportional to M^{0·24}, supporting the model of elastic similarity (Heglund *et al*. 1974; McMahon, 1975). However, the phyletic diversity in the above experiments somewhat weakens the comparative strength of the conclusions : scaling models assume that the body form of species being compared are structurally similar.

Our data for a single species of lizard demonstrate that maximum speed on the level is proportional to (Fig. 2). Indeed, manipulation of equation (3) suggests that a 100 g *Stellio* should run about 2·2 × faster than a 10 g individual. This general result differs strikingly from that predicted for interspecific comparisons by a model of geometric similarity (*M°*), but is roughly intermediate between those predicted for models of elastic and static stress similarity.

### Size, slope, and maximum speed

The work against gravity in running uphill is proportional to slope (sin θ*)* and mass. Consequently, maximum speed should be inversely proportional to sin θ for a given sized animal. However, because the power output of muscles increases with whereas the work expended increases with *M*^{1}, steep slopes should slow large animals more severely than small animals (Hill, 1950; Maynard Smith, 1968).

Our results confirm the prediction that maximum speed of large lizards is negatively related to slope (Figs. 3 and 4). Indeed, a 100 g *Stellio* will run only about 30% as fast on a 60° slope as on a 0° slope.

Our results also confirm the prediction (Hill, 1950; Maynard Smith, 1968) that maximum speed of small lizards is less affected by slope than that of large lizards (Figs. 3 and 4). This pattern neatly complements the demonstration by Taylor *et al*. (1972) that the incremental metabolic cost of running uphill is significant for large but not for small mammals (Reichman & Aitchison, 1981 ; but see Cohen, Robbins & Davitt, 1978).

We were surprised, however, to find that maximum speed of small *Stellio* is essentially independent of slope. Indeed, some small lizards actually run as fast up 60° slopes as on the level (Figs. 3 and 4). Perhaps small lizards that have evolved to live in structurally complex microhabitats might have morphological specializations (e.g. body proportions, patterns of muscle recruitment) that can compensate for the effects of slope (Armstrong & Taylor, 1980). We leave this as an open problem.

### Ecological implications of scaling speed with size and slope

Differences in maximum sprint speed influence an animal’s ability to capture prey, to avoid becoming prey for another animal, and to interact socially (Howland 1974; Webb, 1976; Elliott *et al*. 1977). Consequently, our results on changes in speed with size and slope have significant implications for the behavioural ecology of S. *stellio* and potentially other species that occupy habitats with high structural complexity.

The observed effects of size and slope on maximum speed (Fig. 4 and 5) suggest, for example, that the orientation of predatory lizards lying in ambush should vary with body size : large lizards should preferentially attack on level or downhill slopes, whereas small lizards might attack on any slope. (Similarly, the distance a lizard might venture from its retreat should vary with size and slope.) Data on attack angles of *Stellio* in nature are unavailable, but T. C. Moermond (personal communication) notes that the predicted patterns hold for some arboreal lizards of the genus *Anolis*.

## ACKNOWLEDGEMENTS

This research was supported by the National Science Foundation under grants DEB 78-12024 and DEB 78-12024-03, the Dorothy Spivack Fund and the Research and Travel Fund of Barnard College, the Graduate School Research Fund of the University of Washington, and the United States-Israel Binational Science Foundation (BSF, Jerusalem). We thank J. A. Nelson, A. M. Hawkins, T. A. MacMahon, S. M. Moody, T. W. Schoener, R. D. Stevenson and C. R. Tracy for assistance and discussion. Field research in Israel was made possible by the generous help of E. Nevo and the Institute of Evolution, University of Haifa.

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