ABSTRACT
This series of four papers investigates the link between the energetics and the mechanics of terrestrial locomotion. Two experimental variables are used throughout the study : speed and body size. Mass-specific metabolic rates of running animals can be varied by about tenfold using either variable.
This first paper considers metabolic energy consumed during terrestrial locomotion. New data relating rate of oxygen consumption and speed are reported for: eight species of wild and domestic artiodactyls; seven species of carnivores ; four species of primates ; and one species of rodent. These are combined with previously published data to formulate a new allometric equation relating mass-specific rates of oxygen consumed during locomotion at a constant speed to speed and body mass (based on data from 62 avian and mammalian species):
where has the units ml O2 s−1 kg−1; Mb is in kg; and vg is in m s−1. This equation can be expressed in terms of mass-specific rates of energy consumption (Ėmetab/Mb) using the energetic equivalent of 1 ml O2 = 20·1 J because the contribution of anaerobic glycolysis was negligible :
where Ėmetab/Mb has the units watts/kg.
This new relationship applies equally well to bipeds and quadrupeds and differs little from the allometric equation reported 12 years ago by Taylor, Schmid-Nielsen & Raab (1970). Ninety per cent of the values calculated from this general equation for the diverse assortment of avian and mammalian species included in this regression fall within 25 % of the observed values at the middle of the speed range where measurements were made. This agreement is impressive when one considers that mass-specific rates of oxygen consumption differed by more than 1400% over this size range of animals.
INTRODUCTION
In this series of four papers we investigate the link between the energetics and the mechanics of terrestrial locomotion by measuring both the metabolic energy consumed and the mechanical energy changes that occur as birds and mammals move along the ground. We use two experimental variables throughout the study: speed and body size.
It is generally assumed that most of the energy consumed by the muscles of running animals is used in the transformation of chemical energy into mechanical energy (Hill, 1950; McMahon, 1975; Cavagna, Thys & Zamboni, 1976; Cavagna, Heglund & Taylor, 1977; Alexander, 1977; Alexander, 1980; Alexander, Jayes & Ker, 1980). A. V. Hill (1950) used dimensional analysis to predict how a variety of locomotory parameters, including rates at which muscles work and consume metabolic energy, change with body size. He limited his consideration to the peak performance of an animal moving at its top speed. He assumed that three properties were common to all vertebrate striated muscle, regardless of size : the maximal force developed per crosssectional area; the maximum work performed by each gram of muscle during a contraction; and the maximum efficiency with which muscles convert chemical energy into mechanical work. His analysis predicted that large and small animals would reach the same top speed, and at that speed the muscles of small animals would be working and consuming energy at much higher rates. A simple way of summarizing Hill’s logic is that each gram of muscle performs the same amount of work and consumes the same amount of energy during a step, but the small animals have to take many more steps to cover the same distance because of their shorter legs. Therefore when running at the same speed small animals should have higher stride frequencies and consume energy at higher rates.
Both of our experimental variables provide the potential for large changes in the rate of energy consumption. Aerobic metabolism of a running animal can be increased by about tenfold over resting rates. Also, mass-specific metabolic rates of animals running at the same speed vary by 10 to 15-fold over the size range of animals used in this study (Taylor, 1977). Tenfold differences in mass-specific metabolic rates should be large enough to overcome the uncertainties inherent in mechanical energy measurements and enable us to establish the link, if any, between metabolic and mechanical energy.
This first paper considers the metabolic energy consumed during terrestrial locomotion. More than 10 years ago, Taylor et al. (1970) developed a simple, empirically based equation that predicted the metabolic energy consumption by running mammals from two simple and easily measured parameters: speed and body mass. They found that metabolic cost of running increased linearly with speed over a wide range of speeds ; and that this relationship between metabolism and speed varied as a regular function of body mass. Measurements were made on six species of mammals ranging from 21 g to 18 kg. The results of this study have been substantiated by many measurements on a variety of mammalian species (Taylor, 1977). Recently, Fedak & Seeherman (1979) have reported that the energy cost of locomotion is the same for bipeds and quadrupeds regardless of size. However, an important gap in the literature is a lack of measurements from large wild animals.
In this paper, we extend the data on energetic cost of locomotion to include: (1) a greater diversity of animals; (2) a greater range of running speeds from individual animals; and (3) a greater size range of animals. Then we calculate a revised allometric equation for energy cost of locomotion. We compare the metabolic rates calculated using the revised equation with the observed rates at the middle of the speed range obtained for each animal. Additionally, we formulate allometric equations for taxonomically related groups of animals (where the data base is sufficient) and compare these equations with the general equation for birds and mammals. This analysis should enable us to find out whether costs vary from group to group. The equations are used in the subsequent papers for comparison with similar equations describing mechanical energy changes within an animal.
MATERIALS AND METHODS
Experimental approach
Energy consumption as a function of treadspeed
To obtain a reproducible relationship between rate of energy consumption and speed for animals running on a treadmill, we have: (1) used ‘trained’ animals; (2) made the measurements at each speed over a long enough interval to be certain that a steady-state oxygen consumption was achieved; and (3) ascertained that the energy was being derived primarily from aerobic metabolism over the entire range of speeds.
Training animals to run on the treadmill required a period of weeks to months, depending on the species and the individual animal. Two factors seemed important in the training. First, the animals were frightened when first introduced to the treadmill and did not run with normal gaits or stride frequencies at a given speed. Trained animals had the same gait and stride frequency for a given speed on the treadmill and on the ground. Second, the oxygen-consumption experiments required far greater endurance than would normally be required in nature. We have found that when a human or animal begins to tire, its oxygen consumption increases. As the training progressed, animals were able to run much longer without tiring, and oxygen consumption remained constant during the run. Rate of oxygen consumption was measured while the animals were being trained. We considered that the animals were trained once we were able to obtain reproducible values for at any speed.
To achieve a steady-state we measured of the trained animals for 15–30 min at each speed. Frequently, was higher during the first 2–3 min of a run. We did not include these higher values, but used an average over the remainder of the run. We assumed these higher values were either the result of repayment of an anaerobic ‘start-up cost’ or due to an abnormal gait as the animal adjusted to the tread speed at the beginning of a run.
To ensure that all of the energy was being provided aerobically, R values were determined during the run, and blood lactate values were determined at the beginning and end of the runs at the highest speeds. We selected our top speeds so that R values were less than 1·0 and less than 1 % of the total energy consumed could be attributed to anaerobic glycolysis on the basis of the energy derived from the lactic did that accumulated during the run (Seeherman et al. 1981).
Energetic cost of locomotion as a function of body size
In order for allometry to yield meaningful results, both the range of body mass and the number of animals must be great enough to yield small 95 % confidence limits.
Animals
A review of existing data (Taylor, 1977) indicates that the principal gaps on energetic cost of locomotion are for large wild mammals. Therefore, we decided to take advantage of the diversity of large wild mammals living in Africa and carried out a major part of this work in Kenya. We obtained eight species of wild and domestic artiodactyls and three species of carnivores by capture or purchase. The wild artiodactyls in order of increasing body mass were: 2 suni (Nesotragus moschatus, av. body mass 3·50 kg); 2 dik-diks (Madoqua kirkii, av. body mass 4·35 kg); 2 wildebeest (Connochaetes taurinus, av. body mass 92·0 kg) ; 2 waterbucks (Kobus defassa, av. body mass 114 kg) ; and 2 elands (Tauro tragus oryx, av. body mass 213 kg). The domestic artiodactyls in order of increasing body mass were: 2 African goats (Capra hircus, av. body mass 20·0 kg) ; 2 African sheep (Ovis aries, av. body mass 23·0 kg) ; 2 zebu cattle (Bos indicus, av. body mass 254 kg). We also obtained three species of the small carnivores. In order of increasing body mass they were : 3 dwarf mongooses (Helogale pervula, av. body mass 0·583 kg); 2 banded mongooses (Mungos mungo, av. body mass 1·15 kg); 2 genet cats (Genetta tigrina, av. body mass 1·46 kg). The bovids were housed in facilities provided by the East African Veterinary Research Organization at Muguga. Muguga is in the Kenya highlands and a little over 2000 m above sea level. The average barometric pressure at Muguga during these experiments was 787 mbar (590 Torr). The viverrids were housed at the University of Nairobi, in Nairobi. This is also in the Kenyan highlands and a little less than 2000 m above sea level. The average barometric pressure during these experiments was 835 mbar (626 Torr).
At our laboratory in the United States, we purchased four species of primates, one species of rodent, and four species of carnivores. The primates in order of increasing mass were: 3 tree shrews (Tupaia glis, av. body mass 0·124 kg); 3 bush babies (Galago senegalensis, av. body mass 0·240 kg); 3 stump-tailed macaques (Macaca speciosa, av. body mass 5·10 kg); and 2 hamadryas baboons (Papio hamadryas, av. body mass 8·50 kg). The rodent was the flying squirrel (3 individuals, Glaucomys volans, av. body mass 0 063 kg). The carnivores in order of increasing size were : 1 ferret (Mustela nigripes, av. body mass 0·542 kg); 2 domestic cats (Felis catus, av. body mass 3·90 kg 2 domestic dogs (Canis familiaris, av. body mass 4·36 kg); and 2 wolves (Canis lupus, av. body mass 23·1 kg).
Methods
The face mask system gave 95% response in 1 min for a step reduction in the oxygen content of the air from 20·94 to 19·94%. The enclosed treadmill system gave a 95% time response in less than 2 min for the same step change in the oxygen content of the air.
Systems which utilize loose-fitting face masks require large flow rates in order to ensure that all expired air is collected. Increasing the flow should decrease the magnitude of any leak, and decreasing the flow should increase the magnitude of any leak. We found no difference in the rate of oxygen consumption when the flow rate was changed by 25% and were therefore confident that we were recovering all of the expired air.
Net rates of energy derived from anaerobic glycolysis (of the whole animal) were calculated from rates of change in lactate concentration in the blood during the runs by assuming a P/lactate ratio of 1·5 (Seeherman et al. 1981). Blood samples were obtained by cardiac puncture in the small animals and through catheters that had been chronically implanted in the external jugular vein in the larger animals. The lactate concentrations of blood samples were analysed using Boehringer Mannheim Lactate Test Combinations and a Beckman u.v. Spectrophotometer (model 24). Fifty /d samples of blood were used for the analysis with small animals and | ml samples for the larger animals.
RESULTS
Oxygen consumption as a function of speed
Steady-state oxygen consumption of the 20 species investigated in this study increased linearly with tread speed over a wide range of speeds (Fig. 1A-C). We found it convenient to use mass-specific oxygen consumption (rate of oxygen consumption divided by body mass) for comparing animals of diffeient size because this enabled us to plot the data for the entire size range on the same co-ordinates.
The linear increase in oxygen consumption with speed makes it possible to express the relationship between oxygen consumption and speed for each animal by a linear-equation of the form
Oxygen consumption accounted for the major part of the metabolic energy consumption over the range of speeds used in this study. At the maximum speeds reported in Table 1, R values were less than 1·0 and the rate of accumulation of lactate during the run accounted for less than 1 % of the energy available from the oxygen consumption.
Energetic cost of locomotion as a function of body size
There are two components to the energetic cost of locomotion (measured as ):an extrapolated zero speed cost (the Y intercept) and an incremental cost (the slope) (see equation 6). Both are constant for an individual animal because the Relationship between energy consumption and speed is linear. However, both change with body size. Fig. 1(A–C) are organized in terms of increasing body mass for primates, carnivores, and artiodactyls. It is obvious from looking at these graphs that both the Y intercept and the slope decrease with increasing body size. This decrease is very general, being found among all the taxonomic groups of mammals and birds (Table 1).
Fig. 2 plots the Y intercept (top) and the slope (bottom) of the equations relating and speed against body mass on logarithmic co-ordinates. The solid points represent new data and the open points previously published data. Both visual comparison of the open and closed points, and linear regression analysis show there is no significant difference between the new data presented in this paper and the data in the literature. However, the new data reduces the 95 % confidence intervals for the constants and the scaling factors. Therefore, we will limit our discussion of the allometric equations to those for the combined data.
(where is the mass-specific oxygen consumption of an animal running at speed vo). The Y intercept is proportional to the −0·303 power of body mass and the slope proportional to −0·316 power. See equations (7) and (8) of the text for the allometric equations representing Y intercept and slope calculated by linear regression analysis from the data presented here. Open symbols represent data from the literature ; closed symbols represent new data from this paper; circles represent data from wild species; and triangles represent laboratory/ domestic species.
The lion, red kangaroo and the waddlers (ducks, geese and penguins) were not included in our allometric equations because either their energy consumption did not increase linearly with speed over a wide range of speeds (lion and big red kangaroo : Chassin et al. 1976 ; Dawson & Taylor, 1973) or there was a large additional component to the energetics that was unique (waddlers: Pinshow, Fedak & Schmidt-Nielsen, 1977).
DISCUSSION
Oxygen consumption as a function of speed
The nearly linear increase in oxygen consumption as a function of speed observed in this study is in agreement with the findings of previous studies (Taylor et al. 1970; Taylor, 1977; Taylor, 1980). One of the reasons for initiating this series of studies was to find out whether the linear increase could be explained by the mechanical energy changes that occur within an animal. We will therefore defer the discussion of the linear increase to the subsequent papers where both metabolic and mechanical energies can be compared.
Energetics of locomotion as a function of size
This equation is very general. Table 2 compares the constants and scaling factors for both terms of the general equation for birds and mammals with various groupings of species: all mammals, all birds, all wild animals, all domestic animals, Marsupials, Insectivores, Artiodactyla, Carnivora, Rodentia, and Primates. None of the groups differed from the general equation at the 95 % level of confidence. The major difference is wider confidence intervals of the smaller groups because both the number of species and range in body mass are smaller.
How well does the general equation estimate the oxygen consumption observed for individual animals ? For each of the species included in the regression analysis, we present the percentage deviation between the values calculated from the general equation and the observed value for the middle of the speed range for which oxygen consumption data were available. At the mid-speed, 90 % of the calculations for species included in the regression fall within 25 % of the observed value. This agreement is impressive when one considers that mass-specific oxygen consumption changes by more than 1400% over this size range of animals.
Energy consumption per step at equivalent speeds
A. V. Hill’s dimensional arguments outlined in the introduction of this paper predicted that, in mass-specific terms, muscles of small animals would be working and consuming energy at much highei rates than those of large animals.
The findings of this paper are in general agreement with Hill’s predictions for how rates of energy consumption should change with size. Hill’s analysis, however, was limited to top speed, which he used as an equivalent speed for comparing animals of different body size. Measurements of energy consumption at top speed are not available, but comparisons can be made for quadrupeds at the speed where they change gaits from a trot to a gallop. Heglund, Taylor & McMahon (1974) have proposed that this is a ‘physiologically similar speed’ for quadrupeds of different size. Both the speed at which quadrupeds change from a trot to a gallop, and the stride frequency at this speed, change in a regular manner with body mass and can be estimated using allometric equations given by Heglund et al. (1974). Table 3 gives the trot-gallop transition speed and the stride frequency at this speed calculated for a 10 g, 1 kg, and 100 kg animal using these equations. The amount of energy consumed at this speed was calculated using eq. 10, and cost per stride was obtained by dividing the rate of energy consumption by stride frequency. This analysis reveals that the amount of metabolic energy consumed per stride by each gram of muscle at this speed remains almost constant (5 J stride−1 kg−1) over a change in Mb of 4 orders of magnitude.
The finding that energy cost per stride by each gram of muscle at an equivalent speed is almost the same for large and small animals seems to indicate that Hill’s logic is correct, i.e. the work performed per stride and the efficiency with which muscles perform this work are constant. We will return to this matter in the fourth and final paper of this series where it is possible to compare these assumptions with measurements of the rate at which mechanical work is performed by an animal’s muscles as it runs at a constant average speed.
The essential part of this work depended on a field study on wild animals in Kenya. It would not have been possible without the support of various Kenyan authorities. We thank particularly the Kenyan Minister of Wildlife and Tourism for providing permits and for helping to obtain animals ; Dr Walter Masiga, Director, East African Veterinary Research Organization, Muguga, Kenya, for making the excellent large animal facilities of his organization available to us for these studies. This study would not have been feasible without the most generous support of the School of Veterinary Medicine at the University of Nairobi; we thank the authorities of the University of Nairobi for all the encouragement and material help received during planning and Execution of the study.
ACKNOWLEDGEMENTS
We thank Garth Ballantyne, Rusa Baudinette, Daphne Cooke, Vaughn Langman, Timothy Lay, Victoria Rowntree, Emmett Schmidt, Howard Seeherman and Tom Shatten who all helped acquire the new data reported here.
We also gratefully acknowledge the excellent technical assistance received from Ms Gayle Kaufman and Ms Margaret McCutchin.
We finally acknowledge the financial support received for this study through the following grants: U.S. National Science Foundation (PCM75-22684 & PCM78-23319 to C. R. Taylor); National Institutes of Health (AM 18140 & AM 18123 to C. R. Taylor) ; National Geographic Society grant to C. R. Taylor ; Guggenheim Foundation grant to C. R. Taylor; Nuffield Foundation grant to G. M. O. Maloiy; Wellcome Trust grant to G. M. O. Maloiy.