The Work and Energetic Cost of Locomotion: I. The Effects of Limb Mass Distribution in Quadrupeds

Locomotion is a critical aspect of the biology of any animal, yet the adaptive constraints associated with it are not well understood. Discussions of the selective forces likely to be acting on locomotor structures in mammals have focused on three major factors: mechanical resistance to the stresses induced by locomotion (McMahon, 1973; Lanyon and Baggott, 1976; Lanyon, 1981; Alexander, 1981, 1984; Biewener et al. 1983), generation of speed and/or power (Smith and Savage, 1955; Alexander, 1977; Steudel, 1981) and determination of the energetic cost of locomotion (Howell, 1944; Gray, 1968; Taylor et al. 1974; Alexander, 1982).

The significance of the last of these factors -the energetic cost of locomotion -has been seriously questioned as an important force shaping the evolution of limb Structure as a result of a study in which no difference in cost was detected in three species, cheetah, goat and gazelle, that differ substantially in limb morphology (Taylor et al. 1974). As a consequence, many workers have ruled out selection for energetic efficiency as an important design constraint on animal limb structure (Fleagle, 1979; Hurst etal. 1982; Williams, 1983). Other workers (Hildebrand and Hurley, 1985; Hildebrand, 1988), however, have resisted this conclusion.

To determine whether a controlled experiment could detect a difference in cost in response to differences in limb mass distribution, Myers and Steudel (1985) studied human subjects with externally applied loads. Their design allowed limb mass and its distribution to be altered in a system in which other factors that might influence locomotor energetics, such as differences in locomotor physiology and daily fluctuations within a subject, were minimized. The results showed a consistent, statistically significant, increase in the cost of locomotion when mass was added to the legs of a subject compared with the results when the same mass was added at the waist. Thus, it became clear that experimental alterations of limb mass and its distribution affect locomotor cost, at least in bipedal humans. Other experiments on human subjects have documented similar increases in cost as a result of externally applied limb loads (e.g. Martin, 1985; Claremont and Hall, 1988).

It is not clear, however, whether these results can be generalized to non-human locomotion (Cavanagh and Kram, 1985). The results of the comparative study of cost in the cheetah, goat and gazelle (Taylor et al. 1974) would seem to imply that they cannot. The bipedal gait of humans produces substantially different kinematic patterns from those of quadrupeds, with potentially different capacities for the storage and recovery of elastic strain energy and/or the transfer of energy between body segments or between kinetic and potential energy. Furthermore, humans do not show the pronounced morphological modifications of their limbs characteristic of many cursorial quadrupeds of similar mass. To date there has been no analogous experiment to determine whether the cost of locomotion in quadrupeds varies with differences in limb loading.

To remedy this situation, the present study measures changes in the energetic cost of locomotion of domestic dogs produced by experimentally adding mass either to the limbs or to the body center of mass. As in the experiment on human subjects (Myers and Steudel, 1985), this design allows experimental control of many variables other than limb inertia that might influence cost. The results of this study are used to evaluate the earlier conclusion that limb mass distribution has no apparent effect on the cost of locomotion.

The metabolic impact of adding mass to animals of different size in this and other studies are compared in order to investigate the scaling of the relationship between the mechanical work of locomotion and its energetic cost.

Three adult male dogs (20.0, 20.9 and 26.8 kg) were trained to run on a treadmill at 1.56 ms⁻¹, a slow trot, under three different loading conditions. In all trials the dogs wore a commercially available dog harness around their shoulders and specially constructed Neoprene casings on all four limbs. The two experimental conditions involved adding 0.77 kg of lead either to the dog’s harness or distributed equally on the four limbs. The casings were positioned so that the mass was added at the level of the radius and ulna on the forelimb and at the level of the metatarsals on the hindlimb. All loads were firmly attached to minimize extraneous movement, but were not so tight as to cause the animals any detectable discomfort. Runs in which the animals wore the harness and the casings with no added mass were used as a control. The purpose of the trials with the mass added to the harness was to provide a measure of the effect of a 0.77 kg mass affecting only the work done to raise and reaccelerate the center of mass of the body. Addition of mass to the limbs increased not only the total mass raised and reaccelerated, but also the work done to move the limbs relative to the center of mass.

The object of this experimental design was to alter the mass and inertia of the limbs to an extent similar to that which might occur during the evolution of a less cursorial locomotion, without producing any concomitant changes in limb length (which would be likely to change stride length and frequency), intrinsic speed of contraction of locomotor muscles, the capacity of the limbs to store energy elastically, and so forth. The fact that naturally evolved differences in limb mass and moment of inertia are likely to be accompanied by changes in these and other factors that may influence cost of locomotion make such natural variation unsuitable for investigating the specific effect of mass distribution on cost.

The training period in which the animals were accustomed to the treadmill, the weighting system and an open-circuit respiratory gas analysis system lasted 4 months. The rate of oxygen consumption under the various loading conditions gradually declined over the training period. The animals were considered trained when the values for each animal under each test condition no longer decreased with training. All data used in the analysis were taken after the animals had reached the trained state.

Rates of oxygen consumption were measured using an Applied Electrochemistry S-3A/1 oxygen analyzer in an open-circuit system. The animals wore loose-fitting masks through which room air was pulled at rates of 120–1501 min⁻¹. I initially tested for leaks by bleeding nitrogen directly on to all joints while monitoring the fractional concentration of oxygen in the air being pulled through the system. Any leaks were revealed by a drop in the readings on the oxygen analyzer and could then be effectively sealed. To test for leaks in the overall system with the animal in place, oxygen consumption was monitored while the flow rate was decreased by 10%. This fluctuation in flow rate did not change observed rates of oxygen consumption under equivalent conditions, indicating that all expired air was being recovered.

The analyzer and flow meters were calibrated at the beginning and end of every test session using the one-step N₂ dilution technique described by Fedak et al. (1981), which has been found to be accurate to better than ±3 %. A small stream of the expired gases was removed from the main flow downstream from the flow meter and diverted through Ascarite and Drierite to the oxygen analyzer for continuous monitoring of its fractional concentration of oxygen. Runs continued until values leveled off, between 7 and 20min into a run, signalling that a steady state had been achieved. values for the last three successful runs for each dog under each of the three test conditions were used for data analysis.

These experiments tested whether an increase in limb mass produced an increase in the cost of locomotion when other physiological variables were held constant. To evaluate the significance of any increase in ⁠, it is useful to assess the extent to which the limb loads alter the inertial properties of the limbs.

Consequently, the effect on limb mass distribution of the loads added to the distal limb segments has been estimated by calculating I_p as though the limb was a single rigid body arranged with segments extended -a single, standardized configuration. The alteration in I_p produced as a result of the addition of mass at a measured distance from the proximal point of rotation (the shoulder or hip joint) was calculated as described below. Estimation of limb moment of inertia based on particular segment configurations has also been used by Jayes and Alexander (1982).

Limb moments of inertia about the point of rotation have been determined experimentally for a sample of 12 dead dogs on which total body mass and a series of variables describing limb morphology have also been measured (K. Steudel and M. J. Myers, in preparation). Limb length was found to be an excellent predictor of limb inertia in the forelimb and the hindlimb, which both have coefficients of determination (r²) of 0.97. These regression equations were used to estimate unloaded limb moments of inertia for the three dogs used in this study based on measurements of their limb lengths.

All trials were videotaped at 200 frames s⁻¹ using a NAC high-speed video camera. Stride frequency was measured for each trial by counting the number of fields per stride and averaging over 10 strides. Knowing the tape speed allowed conversion to strides per minute.

Rates of oxygen consumption for unloaded dogs were similar to those observed by previous investigators. Expected values calculated from data reported by Taylor et al. (1970) for an 18 kg dog were slightly higher than those obtained here, while expected values calculated from data reported by Cerretelli et al. (1964) for a 24 kg dog were slightly lower.

values for each subject under each of the three loading conditions are given in Table 1. In all subjects, trials with limb loads produced significant increases in cost compared with back-loaded runs and control runs (P<0.001, N=6, two-tailed t-test). There was no significant difference between back-loaded trials and control runs (P=0.344).

That the effect of the loads was similar in the three dogs tested can be verified using analysis of variance (ANOVA) with as the dependent variable and dog and loading condition as independent variables. Both dog and loading condition had significant individual effects on (P<0.001), but there was no significant interaction (P=0.472). This indicates that, although the dogs differed in (due substantially to differences in their mass), they did not differ in the nature of their responses to the loads.

The estimated limb moments of inertia about the proximal joint for the loaded and unloaded limbs of the three dogs are shown in Table 2. The addition of the loads, representing between 2.9 and 3.9% increases in body mass, produced increases in moment of inertia of between 19 and 26% in the forelimb and between 25 and 40% in the hindlimb.

The dogs responded to the limb loads with a small decrease in stride frequency. The stride frequencies observed in the limb-loaded trials were significantly lower than those in control (P<0.001) or back-loaded trials (P<0.002). No significant difference was observed between stride frequencies in back-loaded and control trials (P=0.432). Stride frequency in the limb-loaded trials averaged 103.8 strides min⁻¹ (S.E.=2.24, N=9), 96% of that seen in both the control (average= 107.74 strides min⁻¹, S.E.=2.57, N=9) and back-loaded (average=108.34 strides min⁻¹, S.E.=3.07, N=9) trials.

The addition of 0.77 kg of mass (2.9–3.9% of body mass) to the limbs of the dogs produced increases in that are qualitatively similar to those obtained in analogous experiments on human subjects. In the current experiments, the average 3.5% increase in mass produced by the limb loads increased by an average of 9.9% over control values. In human subjects, the addition of a mass equivalent to 1.4–5.4 % of body mass resulted in increases in of between 5.4 and 12.1% (Myers and Steudel, 1985; Martin, 1985; Claremont and Hall, 1988). Thus, increasing limb moment of inertia by using externally applied loads produces generally similar effects on cost in bipedal humans and quadrupedal dogs.

In the present study, the dogs showed a decrease in stride frequency with limb loading. The various experiments involving limb loads on human subjects have reported dissimilar effects of the loads on stride frequency. Martin (1985) reported a slight reduction in stride frequency, similar to that seen in these dogs, but Claremont and Hall (1988) noted the opposite -a slight increase in stride frequency in their limb-loaded human subjects.

The observation that the relatively small amount of mass added in the present experiments did not produce a detectable effect on when added to the back is consistent with previous findings. Taylor etal. (1980) measured the effect on of adding mass equivalent to 22 % and 27 % of body mass to the backs of dogs traveling at three different speeds. Calculation of the expected effect on of adding 0.77 kg of mass to the backs of dogs based on the data of Taylor et al. (1980) indicates that the expected increase would be of the order of 0.5 ml O₂S⁻¹, within the range of experimental error. Cureton et al. (1978) found that the addition of a load equal to 10 % of body mass to the backs of human subjects did not have a significant effect on ⁠. Nielsen et al. (1982) found that even a 25 % increase in mass obtained with back loads did not produce a significant effect on in ants.

Are the experimental changes in limb moment of inertia induced in this study of a magnitude that one might reasonably expect to see within natural populations? Limb moments in domestic dogs of similar body mass have been shown to vary by 3.4-fold in the hindlimb and 4.0-fold in the forelimb of domestic dogs of similar body mass (K. Steudel and M. J. Myers, in preparation). Owing to artificial selection, domestic dogs show greater morphological variation than will be found in most natural populations. Yet even dogs of the same breed (beagle) and similar mass showed 2.6-fold variation in moment of inertia in the hindlimb and 3.1-fold in the forelimb. Thus, the vastly smaller changes in limb moments produced in this study, between 19 and 40%, seem well within the range likely to be available for natural selection. This is especially true because measurement of I_p with the limb segments extended will tend to magnify the percentage change in I_p produced by the loads because it assesses I_p when the added mass is at its most distant from the proximal point of rotation.

That the addition of 0.77 kg (3–4% of body mass) to the limbs of trotting dogs produced a 7–22 % increase in the rate of oxygen consumption while a similar load on the back produced no detectable effect demonstrates that mass distribution influences locomotor cost. But will these increased locomotor costs influence the total energy budget of an animal to such an extent that they create significant selection for more economical limb design?

Garland (1983) has estimated that the ecological cost of transport (the percentage of an animal’s daily energy budget allotted to locomotion) should be approximately 10% for dogs of this size. The mass added in the present experiments would, therefore, increase the daily energy budget by approximately 1 %. Could such an increment in an organism’s energy budget result in effective selection pressure?

I know of no studies that answer this question directly. That small changes in locomotor efficiency are detected and responded to by animals is suggested by data on the cost of locomotion in ponies. Rigorous training of the experimental animals coupled with data collection under very controlled conditions allowed Hoyt and Taylor (1981) to detect curvilinearity of the relationship between and speed within gaits. The deviation from linearity was slight (r²=0.98), implying only slightly lower cost to move a given distance when moving at speeds near the midpoint of a gait range. Nevertheless, animals allowed to move freely selected speeds within each gait near the energetically optimal speed (Hoyt and Taylor, 1981).

Furthermore, several recent studies, albeit in completely different systems, suggest that energetic effects of very small magnitude can result in significant selection pressures. For example, Cowan and Farquhar (1977) found that timevarying adjustments of stomatal conductance in plants quantitatively match those predicted by an optimization model, and yet increase photosynthesis by only 2 % relative to a pattern of constant stomatal conductance. Givnish (1986) showed that leaf branching angles in the forest herb Podophyllum match the quantitative predictions of a model for minimum support costs, even though the variation in those costs within ±5° of the predicted and observed angle is considerably less than 1 % of the total biomass allocated to leaf, stem and vein tissue. Furthermore, Lande (1976) has shown that very weak selection (two selective deaths per million individuals per generation) can account for the evolutionary changes in paracone height and ectoloph length in the evolution of equids.

It should also be noted that Altmann (1987) has recently questioned the adequacy of the estimates of the distance moved daily on which Garland (1983) based estimates of the amount of energy allocated to locomotion as a percentage of the total. Altmann suggests that the energy required for locomotion might be several times higher than implied by the data on the ecological cost of transport quoted above. It seems, therefore, that variations in the cost of locomotion resulting from modest changes in limb mass distribution, such as those used in the present experiments, could indeed be the subject of selection to minimize daily energetic expenditures.

The economy of locomotion may also be important if energetically less efficient limbs limit the duration of a bout of exercise to such an extent that the probability of successful prey capture or predator escape is reduced. In situations where a substantial component of the energy needed for locomotion comes from anaerobic sources, a discrete, localized stockpile of ATP, creatine phosphate and muscle glucose will be depleted at a rate dependent on the intensity of the exercise. Less economical locomotion would tend to deplete these stores more rapidly, leading to an earlier onset of fatigue. High-intensity locomotion, such as that involved in prey capture or predator escape, may involve a substantial anaerobic component. This may result in animals with less economical locomotion being restricted to behavioral strategies that limit the duration of a bout of intense exercise. Alternatively, behavioral strategies that result in short bouts of exercise may allow less economical limb design. Certainly lions, which capture prey after a long stalk and short rush (Kruuk and Turner, 1967), have heavier limbs and higher locomotor costs (Chassin et al. 1976) than cheetahs, which capture prey after longer chases (Taylor et al. 1974), an observation consistent with this interpretation. More data are required, however, before this argument can be seriously evaluated.

Taylor et al. (1980) analyzed their data on back loads by comparing the proportional increase in with the proportional increase in mass. Table 3 shows the results of an analogous approach to the limb load data from the present study. The proportional increase in for a given proportional increase in mass is generally similar across dogs and speeds. The ratio /((M+M_L)/M), where M is the mass of the animal, is the mass of the load and L is the rate of oxygen consumption of limb-loaded animals, averages 1.06 (±0.02, N=9) from the limb load data in the present study. This is significantly different (Student’s r-test, P<0.05) from the average of 1.01 for dogs running with back loads sufficiently large to produce an effect on (Taylor et al. 1980).

Although the double ratio tends to minimize the contribution of the increase in due to the loads and the mass of the load by adding these effects to the unloaded values and then dividing by the unloaded value, it is useful for comparisons among species that differ widely in body size. Fig. 1 summarizes the results from a variety of studies in which varying amounts of mass were added to the limbs or backs of animals with a wide range of body mass. The line indicates the values that would be seen if the proportional increase in were directly proportional to the proportional increase in mass. It is apparent that adding mass to the limbs produces increases in that fall consistently above this line. Several studies in which loads have been added to the backs of animals have produced a range of results. The results of Taylor et al. (1980) from rats, dogs, humans and horses all fall on or near the 1:1 line, as do the back loading data on humans from Myers and Steudel (1985). When very large loads (1.5–1.9 times body mass) were added in human subjects, however, increased faster than mass, producing values that fell above the 1:1 line (data from Soule etal. 1978). Very small animals, however, such as hermit crabs (Herreid and Full, 1986) and ants (Nielsen et al. 1982), showed a different pattern. In these animals, adding substantial load increased ⁠, but the increase was not proportional to the increase in mass (Herreid and Full, 1986). Thus, it appears that, at very small body sizes, an increase in the total work done in locomotion produced by increasing mass does not cause proportionate increases in cost, while a substantial linkage between increase in work and increase in cost holds for larger animals. Similarly Taylor et al. (1972) found that increasing work by making animals run up and down inclines produced negligible effects on cost in small animals (mice) but very substantial effects in large animals (chimpanzees). Again, the relationship between cost and work observed in large animals is not apparent in small animals. These observations suggest that there may be a qualitative difference between large and small animals in the factors underlying the energetic cost of locomotion.

In conclusion, increases in limb mass result in substantially greater increases in cost than those that occur when the same amount of mass is added on the trunk. The magnitude of this effect is similar in quadrupedal dogs and bipedal humans. Comparison of the effects on cost of back loads on species showing a wide range of body size suggests substantial differences in the response of large and small animals.

I would like to thank Paula Kroma, Karla Pecelunas, Cynthia Dott, Patricia Breen, Phillip Gilson, Allen Caviles and Julie Cherney for help with the training and care of the dogs. I am especially grateful to two of my graduate students, Marcella Myers and Kevin Strang, for useful discussions about the determinants of the cost of locomotion and to Ted Garland, Tom Givnish, Kevin Strang and Marcella Myers for helpful criticism of the manuscripts. Cheryl Hughes drew the figure.