Small animals use more metabolic energy per unit mass than large animals to run on a level surface. If the cost to lift one gram of mass one vertical meter is constant, small animals should require proportionally smaller increases in metabolic cost to run uphill. To test this hypothesis on very small animals possessing an exceptional capacity for ascending steep gradients, we measured the metabolic cost of locomotion in the cockroach, Periplaneta americana, running at angles of 0, 45 and 90° to the horizontal. Resting oxygen consumption was not affected by incline angle. Steady-state oxygen consumption increased linearly with speed at all angles of ascent. The minimum cost of locomotion (the slope of the versus speed function) increased with increasing angle of ascent. The minimum cost of locomotion on 45 and 90° inclines was two and three times greater, respectively, than the cost during horizontal running. The cockroach’s metabolic cost of ascent greatly exceeds that predicted from the hypothesis of a constant efficiency for vertical work. Variations in stride frequency and contact time cannot account for the high metabolic cost, because they were independent of incline angle. An increase in the metabolic cost or amount of force production may best explain the increase in metabolic cost. Small animals, such as P. americana, can easily scale vertical surfaces, but the energetic cost is considerable.

Many small animals appear to scale rocks, stalks, tree trunks and other vertical surfaces effortlessly. One frequently quoted explanation (e.g. in Calder, 1984; Schmidt-Nielsen, 1983, 1984; Vogel, 1988) for this capacity is that increases in metabolic cost for small animals running on inclines are relatively insignificant (Taylor et al. 1972). When moving vertically, a body acquires potential energy equal to its weight times the vertical distance traveled. Lifting 1 kg of body mass lm vertically will increase potential energy by 9.8 J. If muscular efficiency is constant (Hill, 1950), the amount of energy required to lift a 1kg body mass 1 vertical meter will be the same irrespective of animal size. In contrast, it is well established that small animals use more metabolic energy per unit mass than large animals to run on a level surface (Taylor et al. 1970,1982; Full, 1989). Therefore, if the vertical cost for moving 1 kg of body mass uphill is nearly constant, then the relative increase in metabolism needed for running up inclines will be much less for small animals. The fact that the energy demand for climbing in small animals is minimal could have profound effects on morphological and physiological design, ecology (e.g. habitat selection and foraging strategy) and evolution.

One alternative to the constant-efficiency hypothesis is based on the metabolic cost of muscle force production. Taylor et al. (1980) have suggested that the metabolic cost of locomotion depends directly on force production. Greater or more rapid force production appears to increase the metabolic cost of locomotion (Taylor, 1985). If the metabolic cost of force production increases during climbing, then oxygen consumption could show a substantial increase, even in small animals.

To test these hypotheses for very small animals possessing an exceptional capacity for running up very steep slopes, we measured the oxygen consumption of the American cockroach, Periplaneta americana, running on a miniature treadmill oriented at 0, 45 and 90°. This cockroach is ideal for studying the effect of size on the energetics of incline running. They are very small (less than 1g) and readily scale almost any vertical surface. If the constant vertical efficiency hypothesis is supported and small animals require very little additional metabolic energy to travel up inclines, then the minimum cost of transport (i.e. the energy required to transport 1 kg for 1 m, C) should be similar for incline and level running. Running animals at fast speeds on the steepest possible inclines should maximize any differences in metabolic cost (Wunder and Morrison, 1974; Taylor et al. 1972).

Animals

Periplaneta americana (0.78±0.09g, ±S.D.) were obtained from Carolina Biological Supply Company and from Dr Rody Pipa at the University of California at Berkeley. Cockroaches were housed in individual plastic containers with a layer of cedar shavings. Animals were given water and puppy chow ad libitum. All cockroaches were kept on a local photoperiod at ambient temperatures (24±2°C). All experiments were conducted during the daylight hours under ambient fight.

Oxygen consumption

Cockroaches were exercised on a treadmill enclosed in an airtight Lucite respirometer. The tread belt consisted of fine wire mesh that prevented slippage. The respirometer was mounted on a vice which could be oriented at angles from 0 to 90°. The respirometer and vice were placed in an incubator (Lab-Line, Ambi-Hi-Lo Chamber) to control ambient temperature at 23 °C. Oxygen consumption (VoJ was determined using open-flow respirometry (Herreid et al. 1981). We used a flow rate of 90 ml min−1 to measure oxygen consumption during exercise. To provide a detectable oxygen concentration difference, we used a lower flow rate of 35–50 ml min-1 to measure resting oxygen consumption . Air leaving the chamber passed through filters containing Drierite to remove water vapor. The oxygen concentration of air exiting the chamber was measured using an electrochemical oxygen analyzer (S-3A/II, Ametek), interfaced with a computer (IBM/AT) via an analog to digital converter (Cyborg).

To measure , an animal was placed in the respirometer oriented at 0, 45 or 90° and monitored for more than 1 h. was attained in approximately 15 min if the animal was not active (i.e. wandering around the chamber). All resting values were calculated from the second or third hour of the rest period. Resting rates for individual animals were calculated by averaging the over a 5–10 min period during which the animal remained motionless. If the animal would not rest for at least 10min, the results were discarded.

For each experiment measuring during exercise, cockroaches were weighed and given a 20 min rest period within the chamber prior to exercise. Following rest, animals were exercised for 10 min at four different speeds, and given a 10 min rest period between successive speeds. The multiple-speed protocol did not yield significantly different results from single-speed experiments in which animals were exercised at one speed daily. Animals attained steady-state oxygen consumption (, the rate at which varied by less than 5 % during exercise) in approximately 3 min. The experimental speeds were 0.07, 0.14, 0.22 and 0.29 km h−1. The slowest speed was chosen so that animals walked consistently without extraneous movements. The highest speed represented the rate at which animals could sustain during vertical running for 4–5 min, but fatigued within 10–15 min. Experiments were terminated if an animal could not sustain a certain speed or would not run consistently. Animals would occasionally cling to the sides of the chamber before climbing back onto the tread belt to resume exercise. Periods off the tread belt lasted less than 2 s. If there were more than five of these instances in one 10min exercise bout, the results were discarded. was calculated by averaging the for 4–6 min after an exercising animal had attained a steady state. Horizontal, 45° and vertical exercise bouts followed the same protocol, and individuals were tested only once a day. All values were corrected to STPD (Herreid et al. 1981).

Kinematic analysis

Cockroaches were video-taped with a high-speed camera (Video Logic CDR660) at 180 or 300 frames s−1 while running on a treadmill. Three animals were taped at four speeds (0.2,0.3,0.4 and 0.5 km h−1) for each of the three angles (0, 45 and 90°). Video frames were grabbed and digitized using a motion-analysis system (Peak Performance Tech. Inc.). Stride frequency and contact time (i.e. the duration of a stride a leg is in contact with the ground) were calculated from the digitized data.

Oxygen consumption during rest

Cockroaches were generally active for the first 1 h during measurements in the horizontal position, but became more quiescent in the second hour. Animals usually began resting within 20min at 45° and 5min at 90°. Three out of five animals at 45°, and five out of seven at 90°, oriented themselves with their heads pointing downwards. Body orientation did not affect was not statistically different for cockroaches resting horizontally, vertically or at 45° (Table 1; ANCOVA; F(242)=1.55: P=0.2).

Table 1.

Aerobic metabolism of Periplaneta americana at rest and during exercise as a function of angle of incline

Aerobic metabolism of Periplaneta americana at rest and during exercise as a function of angle of incline
Aerobic metabolism of Periplaneta americana at rest and during exercise as a function of angle of incline

Oxygen consumption during exercise

Steady-state oxygen consumption increased with speed during horizontal and incline running (Fig. 1; Table 1). Step-wise polynomial regression analysis showed that the next higher-order coefficient did not explain significantly more variation than that explained by a linear function (P<0.05). The linear regression equation relating speed and for horizontal locomotion obtained in the present study (Table 1) was not different from that found by Herreid and Full (1983). Moreover, the slope of the versus speed function for horizontal locomotion (Chor, the minimum cost of horizontal transport) was well within the 95 % confidence limits for insects and other pedestrians (Full, 1989). The slopes of the regressions relating speed and were statistically different for cockroaches running horizontally, at 45° and vertically (homogeneity of slopes: F(2,59)=12.9; P<0.001).

Fig. 1.

Steady-state oxygen consumption as a function of speed for three angles of incline, 0° (□), 45° (♦) and 90° (×). Steady-state oxygen consumption increased linearly with speed at each angle. Mass-specific metabolic power is represented on the right-hand ordinate and was calculated assuming 1 ml O2 =20.1 J.

Fig. 1.

Steady-state oxygen consumption as a function of speed for three angles of incline, 0° (□), 45° (♦) and 90° (×). Steady-state oxygen consumption increased linearly with speed at each angle. Mass-specific metabolic power is represented on the right-hand ordinate and was calculated assuming 1 ml O2 =20.1 J.

Comparison with predictions based on a constant-efficiency hypothesis

To test if results from the present study on incline running support the hypothesis based on constant vertical efficiency, we compared the observed oxygen consumption rates of P. americana with predicted rates. We based our predictions on the equation:
formula
(Taylor et al. 1972), where Chor is the measured value of the minimum cost of locomotion (i.e. the slope of the vs speed function) for horizontal running in J kg−1m−1, Cin is the minimum cost of locomotion for incline running in J kg −1m−1, fi is the angle of incline in degrees, and 15.5 J kg−1 m−1 is the constant for the additional amount of energy required to lift 1 kg for 1 vertical meter found empirically by Taylor et al. (1972). Sinβ is the fraction of a meter climbed vertically per meter of run. For β we used 45 and 90°. Observed costs for cockroaches running on 45 and 90° inclines fall well above those predicted using the constant vertical efficiency hypothesis. When running at 0.15–0.30 km h−1 on inclines of 45 and 90°, values for P. americana were 60–120% greater than those predicted if vertical efficiency were constant.

To test the generality of the constant-efficiency hypothesis, we plotted the relationship of Cin/Chor and body mass on logarithmic coordinates for a variety of animals running on inclines ranging from 3 to 90°. The ratio of Cin/Chor represents the factorial increase in energy cost during incline running. For comparison with actual factorial increases in energy cost, we generated a family of curves (i.e. isopleths) that represent the predicted ratios of Cin/Chor for a given body mass and angle, based on the assumption that mass-specific vertical work is nearly constant (Fig. 2). To predict values of Chor, we used the equation:

Fig. 2.

Factorial increase in metabolic cost of incline running, relative to running on the horizontal, as a function of ascent angle and body mass on logarithmic coordinates for several species. The ratio of the metabolic cost of locomotion during incline running (Cin, the slope of the V˙O2ssvs speed function for a given angle of ascent) to the metabolic cost of locomotion during horizontal running (Chor, the slope of the V˙O2ssvs speed function at a zero angle of ascent) is shown for values predicted on the basis of a constant efficiency of vertical work (vertical work=15.5 Jkg−1m−1). Curved lines represent these predicted Cin/Chor ratios as isopleths of a constant incline angle. Predicted Cin/Chor ratios (open squares) for individual species are plotted with respect to body mass and their actual angle of ascent. Actual ratios, obtained from literature values of Chor and Cin (closed squares), are plotted with respect to body mass (rat, Armstrong et al. 1983; elk calf, Cohen et al. 1978; dog, Raab et al. 1976; mouse and chimpanzee, Taylor et al. 1972; quail, Wamcke el al. 1988; squirrel, Wunder and Morrison, 1974; lion cub, sheep, elk calf, man, reindeer and burro, see Cohen et al. 1978 for references).

Fig. 2.

Factorial increase in metabolic cost of incline running, relative to running on the horizontal, as a function of ascent angle and body mass on logarithmic coordinates for several species. The ratio of the metabolic cost of locomotion during incline running (Cin, the slope of the V˙O2ssvs speed function for a given angle of ascent) to the metabolic cost of locomotion during horizontal running (Chor, the slope of the V˙O2ssvs speed function at a zero angle of ascent) is shown for values predicted on the basis of a constant efficiency of vertical work (vertical work=15.5 Jkg−1m−1). Curved lines represent these predicted Cin/Chor ratios as isopleths of a constant incline angle. Predicted Cin/Chor ratios (open squares) for individual species are plotted with respect to body mass and their actual angle of ascent. Actual ratios, obtained from literature values of Chor and Cin (closed squares), are plotted with respect to body mass (rat, Armstrong et al. 1983; elk calf, Cohen et al. 1978; dog, Raab et al. 1976; mouse and chimpanzee, Taylor et al. 1972; quail, Wamcke el al. 1988; squirrel, Wunder and Morrison, 1974; lion cub, sheep, elk calf, man, reindeer and burro, see Cohen et al. 1978 for references).

formula
(Full, 1989) in which m represents body mass in kg. To generate predicted values of Cin, we used equations 1 and 2 and solved for Cin:
formula
The ratio can be calculated as follows:
formula
By varying β and m in equation 4, we obtained predicted values for factorial increases in metabolic cost of animals running on inclines ranging from 3 to 90° and varying in body mass by seven orders of magnitude. Fig. 2 shows the results of this analysis. Each isopleth in this figure represents a different angle of ascent. Superimposed on this graph are both predicted and observed Cin/Chor ratios for various animals running on different inclines. We used the animal’s mass and angle of ascent to calculate predicted ratios based on a constant vertical efficiency (equation 4). For observed ratios, we used literature values for both Cin and Chor. The length of the vertical bar for each species represents the difference between actual and predicted increases in metabolic cost. For example, the predicted increase in metabolic cost of a 250 kg burro running on a 9° incline is somewhat over twofold, whereas the actual increase in cost is over sixfold.

Kinematics

Stride frequency increased with speed at all angles of ascent (ANOVA, F(1,98)=368; P<0.001; Fig. 3A). Angle of ascent had no significant effect on stride frequency when the effect of speed was removed (ANCOVA, F(2,98)=2-7; P=0.07). Contact time decreased with speed at all angles of ascent (ANOVA, F(1,98)=437; P<0.001; Fig. 3B). Angle of ascent had no significant effect on contact time when the effect of speed was removed (ANCOVA, F(2,98)=2.6; P=0.08).

Fig. 3.

Kinematics of locomotion as a function of speed and angle of ascent. (A) Mean stride frequency as a function of speed. Stride frequency increased with speed, but was not significantly different for angles of ascent of 0 (□), 45 (♦) and 90° (×). (B) Contact time (i.e. duration of a stride a leg was in contact with the ground) as a function of speed. Contact time decreased with speed, but was not significantly different for angles of ascent of 0 (□), 45 (♦) and 90° (×). Bars represent ±1S.E.

Fig. 3.

Kinematics of locomotion as a function of speed and angle of ascent. (A) Mean stride frequency as a function of speed. Stride frequency increased with speed, but was not significantly different for angles of ascent of 0 (□), 45 (♦) and 90° (×). (B) Contact time (i.e. duration of a stride a leg was in contact with the ground) as a function of speed. Contact time decreased with speed, but was not significantly different for angles of ascent of 0 (□), 45 (♦) and 90° (×). Bars represent ±1S.E.

Resting oxygen consumption

Oxygen consumption was similar for P. americana resting at 0, 45 and 90° (Table 1). Yox et al. (1982) found that passive resting tension in the leg muscles of arthropods maintains limb position. This passive tension in the limbs of quiescent cockroaches could provide an energetically inexpensive mechanism for maintaining posture, regardless of the resting angle. Alternatively, it is possible that pretarsal claws along with other skeletal elements provide support on 45 and 90° inclines. Use of skeletal structures to maintain position would require no additional muscle force production, making any added gravitational effects energetically insignificant. More studies determining muscle activity need to be performed to give us a better understanding of posture.

Oxygen consumption during exercise

P. americana showed a linear increase in with speed when running horizontally and on 45 and 90° inclines (Herreid and Full, 1983; Fig. 1). A linear increase in with speed during incline running is also typical of mammals and birds (Taylor et al. 1972; Wunder and Morrison, 1974; Raab et al. 1976; Cohen et al. 1978; Armstrong et al. 1983; Wamcke et al. 1988).

The minimum cost of transport (C, represented by the slope of the versus speed function; Cin for the cost on an incline and Chor for the cost on the horizontal) for cockroaches running on inclines increased with increasing angle of ascent. Cockroaches running at 45 and 90° had Cin values approximately two-and threefold higher, respectively, than Chor for cockroaches moving at 0° (Fig. 1; Table 1). Most other animals show a substantial increase in C with increasing incline angle. For example, C for 250 g red squirrels increases 123 % when running on a 37° incline relative to horizontal running (Wunder and Morrison, 1974). When running on a 24 % slope, dogs (17.3 and 6.7 kg) had a 179 % increase in Cinover Chor (Raab et al. 1916). For 350 g rats running on a 16° incline, Cin increased 42% over ChOr (Armstrong et al. 1983).

There are, however, at least two exceptions to this trend. Taylor et al. (1972) found that 30 g mice did not show a significant increase in C when running up a 15° incline compared to running on the level. Herreid et al. (1981) found that the Madagascar hissing cockroach, Gromphadorina portentosa, did not use significantly more oxygen when running on 5, 15 and 25° inclines than when running on the level. One possible explanation for a lack of a significant increase in in that the variability in prevents the resolution of any increases in cost when speeds are very slow and low angles of incline are used, as was the case for G. portentosa.

Cost of incline running

The hypothesis of a constant vertical efficiency for animals that vary in body mass offers one reason why small animals can easily run up inclines. Taylor et al. (1972) found that 30 g mice have the same C running on a 15° incline as they do running on the level. Chimpanzees (17.5 kg), however, show a twofold increase in C when running on a 15° incline. From their study, along with data on sheep and man, Taylor et al. (1972) suggested that the metabolic energy needed to lift 1 kg of body mass 1 vertical meter may be similar for animals that differ in body mass. They empirically derived an estimate of 15.5 J kg−1m−1 for the metabolic energy needed to lift 1 kg of body mass 1 vertical meter. In contrast to vertical cost, massspecific Chor scales with body mass to the −0.30 power (equation 2; Full, 1989; Taylor et al. 1970). Compared to large animals, small animals have relatively high costs for horizontal running. Therefore, if the work required to lift 1 kg for 1 vertical meter is similar in animals that differ in mass, small animals running uphill should require proportionally smaller increases in energy over that used during horizontal running than would larger animals (Taylor et al. 1972).

Results from the present study on insects ascending steep angles do not support the hypothesis based on a constant efficiency for vertical work (Fig. 2). When running on 45 and 90° inclines, P. americana, an animal weighing less than 1 g, had approximately a two-and threefold elevation, respectively, in Cin over Chor (Table 1). These increases correspond to values of 223 and 290 J kg−1 m−1, respectively, for the metabolic work needed to lift 1kg of cockroach mass 1 vertical meter. These values yield efficiencies of only 3–4% (Table 1).

When data on the energy required during running up slopes are viewed collectively, considerable variability is apparent (Fig. 2). Excluding results on cockroaches obtained in the present study, observed values of Cin/Chor for birds and mammals range from 35.7% below (53.5 kg lion cub on a 17.7° incline) to 162% above (253.5 kg burro on a 9.6° incline) values predicted by Taylor et al. 1972. Cohen et al. 1978 found that the mean value representing the amount of metabolic energy used to lift a 1 kg mass 1 vertical meter is closer to 27 J kg−1 m−1. If the value for vertical work is increased from 15.5 J kg−1 m−1 (Taylor et al. 1972) to 27 J kg−1 m−1 (Cohen et al. 1978), observed Cin values for cockroaches running at 45 and 90° are still 80 and 146%, respectively, above predicted values. If a constant of 27 J kg−1 m−1 is used to predict the cost of incline running for other animals, predicted costs considerably underestimate some observed costs (e.g. by 55 % in lion cubs, Chassin et al. 1976; and 31 % in chimpanzees, Taylor et al. 1972) and substantially overestimate others (e.g. by 85 % in burros, Cohen et al. 1978; and 65% in quails, Warncke et al. 1988).

The added cost of incline running appears to be highly variable and not a simple function of angle and body mass. One alternative explanation to the constantefficiency hypothesis is based on the metabolic cost of force production. Taylor et al. (1980) tested the hypothesis that the metabolic cost of force production determines the metabolic cost of locomotion by loading animals with back-packs while they ran on a treadmill. No change in acceleration of the center of mass was observed between loaded and unloaded animals. Thus, muscle force increased in direct proportion to the load added. Oxygen consumption also rose in direct proportion to the added load. Therefore, metabolic cost increased directly with muscle force production for animals ranging in mass from a rat to a horse. Taylor (1985) suggested that both greater force and a higher rate of force generation can increase metabolic cost. Larger forces will increase the volume of muscle active and result in a higher cost. Likewise, activation of the same volume of muscle, but at higher rates, can lead to a higher metabolic cost because faster fibers are recruited.

Loading studies on insects show an increase in proportional to the load carried (Nielsen et al. 1982; Lighton et al. 1987). As in mammals, the metabolic cost for insects may increase directly with muscle force production. Therefore, the greater metabolic cost of locomotion for incline running in P. americana may have resulted from a twofold increase in the cost of force production at 45° and a threefold increase at 90°. The lack of change in stride frequency and contact time with angle of ascent does not support the hypothesis that the cost of muscle force production is elevated because of higher rates of force development (Fig. 3). The greater metabolic cost of running on steeper inclines was not associated with higher stride frequencies or shorter contact times, which would have led to a higher cost of force production. However, changes in leg kinematics other than stride frequency and contact time, such as the orientation of the limb relative to the running surface, could result in an alteration of the mechanical advantage of the limb possibly affecting metabolic cost by increasing the amount of force production. Finally, an increased metabolic cost of force production could result from the substitution of less expensive eccentric contractions (i.e. contraction during muscle stretching) used in level running with more costly concentric contractions (i.e. contraction producing muscle shortening) necessary for climbing (Margaria, 1938).

Insects cannot easily walk up steep inclines simply because of a relatively low energy expenditure. Variables other than energy cost need to be considered, such as adaptations for grasping. Added work or force production during incline running for small animals does result in significant increases in metabolic cost. Although P. americana can scale vertical surfaces with remarkable ease, the energetic cost is considerable.

We thank C. R. Taylor for reading the manuscript critically. Supported by NSF grant DCB 8904586 and the University of California at Berkeley Committee on Research 1987–88.

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