The alleged high net energy cost of running and low net energy cost of walking in humans have played an important role in the interpretation of the evolution of human bipedalism and the biomechanical determinants of the metabolic cost of locomotion. This study re-explores how the net metabolic energy cost of running and walking (J kg–1m–1) in humans compares to that of animals of similar mass using new allometric analyses of previously published data. Firstly, this study shows that the use of the slope of the regression between the rate of energy expenditure and speed to calculate the net energy cost of locomotion overestimates the net cost of human running. Also, the net energy cost of human running is only 17% higher than that predicted based on their mass. This value is not exceptional given that over a quarter of the previously examined mammals and birds have a net energy cost of running that is 17% or more above their allometrically predicted value. Using a new allometric equation for the net energy cost of walking, this study also shows that human walking is 20%less expensive than predicted for their mass. Of the animals used to generate this equation, 25% have a relatively lower net cost of walking compared with their allometrically predicted value. This new walking allometric analysis also indicates that the scaling of the net energy cost of locomotion with body mass is gait dependent. In conclusion, the net costs of running and walking in humans are moderately different from those predicted from allometry and are not remarkable for an animal of its size.

There is much interest in the comparative cost of human bipedal locomotion. Since the pioneering work of C. R. Taylor and colleagues(Taylor et al., 1970), it has generally been acknowledged that the net cost of running(Erun; J kg–1 m–1) in humans is considerably higher than predicted for an animal of a similar mass(Schmidt-Nielsen, 1975; Rodman and McHenry, 1980; Carrier, 1984; Taylor, 1994; Steudel, 1996; Leonard and Robertson, 1997; Aiello and Wells, 2002; Steudel-Numbers, 2003; Bramble and Lieberman, 2004). At the origin of this view is the allometric analysis of Erun in humans and other mammalian species performed by Taylor et al. (Taylor et al.,1970), where Erun in humans was shown to be twice (100% greater) that predicted for an animal of the same mass. Later work by the same research group, aimed at elucidating more precisely the scaling relationship of Erun, incorporated a large amount of data from several taxonomic groups (Taylor et al., 1982) and reported human Erun to be∼43% greater than predicted allometrically. It was also established in this study and the study of Fedak and Seeherman(Fedak and Seeherman, 1979)that the high cost of human running is not typical of bipedalism, since the cost of running in quadrupeds was found to be similar to that of bipeds.

These findings on the energy cost of human running have had important consequences for our understanding of human locomotion. Anthropologists, human biologists, ecologists and evolutionary theorists have often based their interpretations of the evolution of human bipedalism and the adaptive value of human locomotion on the studies of Taylor and colleagues(Taylor et al., 1970; Taylor et al., 1982) and have generated an impressive volume of studies in these areas (e.g. Rodman and McHenry, 1980; Carrier, 1984; Leonard and Robertson, 1997; Steudel-Numbers, 2001; Aiello and Wells, 2002; Bramble and Lieberman, 2004). The comparison of running costs between humans and other animal species has also been important for vertebrate morphologists, physiologists and biomechanists attempting to understand structure–function relationships amongst limbed vertebrates (Roberts et al., 1998).

One major limitation shared by most of the aforementioned studies addressing the biological significance of human Erun is that they have overlooked that the analyses of Taylor et al.(Taylor et al., 1970; Taylor et al., 1982) on which their interpretations are based were aimed at understanding how Erun scales with body mass rather than to specifically compare human Erun with those of other species. Because Taylor and colleagues were not interested in humans per se, their studies relied on data from a relatively small number of human studies. Although this is suitable for allometry studies involving a large number of species, the use of human data from only a small number of studies may not represent accurately the `average' Erun of humans since human Erun varies substantially between individuals and across studies (Daniels,1985). This is highlighted in a more recent allometry study on bipedal species (Roberts et al.,1998), where the Erun of a group of human subjects did not differ from the allometrically predicted value. This result is due to the Erun of their human subjects being among the lowest found in the literature. Another difficulty with comparing human Erun with that predicted from allometry is that Erun in allometric analyses is generally calculated from the slope of the linear relationship between the rate of energy expenditure(met; W kg–1) and speed. The limitation with this approach is that for the slope of metversus speed to be a valid measure of Erun, the y-intercept must coincide with the non-locomotor metabolic rate. Although a mismatch between the y-intercept and the non-locomotor metabolic rate is likely to have only a minor effect in allometric analyses of Erun based on a large number of animal species, such a mismatch in humans could affect significantly any estimate of their Erun relative to other species. Finally, another factor that has the potential to affect the comparison of Erun of humans with that predicted from allometric analyses is the fact that most previous allometry studies have been compiled from data in a manner that does not specifically distinguish between walking and running gaits, a potential difficulty given that walking and running elicit different costs of locomotion(Margaria et al., 1963; Minetti et al., 1999).

Given these difficulties shared by the studies using the findings of Taylor and colleagues (Taylor et al.,1970; Taylor et al.,1982) to compare Erun between humans and other species, the first aim of the present study was to examine specifically if humans have an atypically high net cost of running, relative to their mass,compared to other animal species. To this end, we used an allometric analysis that assesses how the Erun of humans compares to the predicted Erun for animals of similar mass not only by making a more extensive use of the human data available from the literature but also by adopting a more appropriate method of subtracting the experimental non-locomotor cost from the gross metabolic cost of locomotion and by restricting our analysis to studies where the net cost of locomotion can be determined specifically for running.

Our second aim follows from the observation that it is also unclear how the metabolic cost of walking in humans compares to that of other species, with some authors claiming that humans' cost of walking is lower than that of animals of similar mass (Steudel,1996; Steudel-Numbers,2003) while others claim that it is similar(Rodman and McHenry, 1980; Alexander, 1991; Alexander, 1992). Given that the comparative cost of human walking also has important biological and evolutionary significance (Alexander,1991; Steudel,1996; Leonard and Robertson,1997; Steudel-Numbers,2003), it was our objective to address this controversy by extending our analyses to specifically compare the net cost of walking(Ewalk; J kg–1 m–1)between humans and other species.

Comparison of human net metabolic cost of running and walking from literature

Published mean values of human metabolic energy costs of running from 20 sources (Table 1A,B) were compared to the metabolic energy cost of transport obtained from the allometric equation of Taylor et al.(Taylor et al., 1982):
(1)
where Mb is body mass in kg and Erunis in J kg–1 m–1. Published human values were compared to this equation in two ways. The first approach calculates Erun from the slope of the linear regression between the gross mass-specific rate of energy expenditure (met;W kg–1) and speed (slope method)(Table 1A). This approach has traditionally been used to represent Erun(Taylor et al., 1970; Full, 1991) and has the benefit of providing a single value for Erun. However, it assumes that the y-intercept of the linear regression between met and speed approximates the non-locomotor metabolic rate. The second approach calculates Erun by subtracting the measured non-locomotor metabolic rate from the gross metabolic rate at a given speed and dividing by that speed (subtraction method)(Table 1B). This latter approach assumes that the subtracted non-locomotor cost remains the same across exercise intensity. Although changes in energy use by non-locomotor tissues occur, studies on both humans and other animals indicate that these changes are small or negligible compared to the altered energy use by limb muscles (Poole et al., 1992; Musch et al., 2004; Ellerby et al., 2005; Marsh and Ellerby, 2006).
Table 1.

Human data (means) of net energy cost of running taken from the literature, used to compare with allometric predictions

(A) Slope method
(B) Subtraction method
Mass (kg)Erun (net) (J kg-1 m-1)ReferenceMass (kg)Erun (net) (J kg-1 m-1)Reference
70.1 3.92 (Boje, 194472.7 3.15 (Bergh et al., 1991) BA 
53.7 3.66 (Bransford and Howley, 1977)FT 66.5 3.29 (Bergh et al., 1991) MR 
59.8 3.04 (Bransford and Howley, 1977)FU 51.7 3.61 (Bergh et al., 1991) FR 
67.0 4.08 (Bransford and Howley, 1977)MT 72.3 3.14 (Bergh et al., 1991) SO 
80.2 4.10 (Bransford and Howley, 1977)MU 70.1 3.75 (Boje, 1944
64.6 4.20 (Conley and Krahenbuhl, 198053.7 3.56 (Bransford and Howley, 1977)FT 
63.1 4.19 (Costill and Fox, 196959.8 3.51 (Bransford and Howley, 1977)FU 
63.7 5.07 (Costill et al., 197367.0 3.43 (Bransford and Howley, 1977)MT 
65.4 4.82 (Daniels and Daniels, 199280.2 3.57 (Bransford and Howley, 1977)MU 
58.9 4.24 (Daniels et al., 197764.6 3.44 (Conley and Krahenbuhl, 1980
65.1 3.18 (Dressendorfer et al., 197763.1 3.42 (Costill and Fox, 1969
65.4 4.70 (Hagan et al., 198063.7 3.56 (Costill et al., 1973
73.8 4.18 (Knuttgen, 196165.4 3.49 (Daniels and Daniels, 1992
68.8 4.02 (Margaria et al., 196358.9 3.39 (Daniels et al., 1977
67.5 4.19 (Mayhew, 197765.1 3.31 (Dressendorfer et al., 1977
66.1 3.46 (Mckicken and Daniels, 197665.4 4.48 (Hagan et al., 1980
69.9 3.77 (Menier and Pugh, 196873.8 3.82 (Knuttgen, 1961
61.4 3.59 (Pugh, 197168.8 4.23 (Margaria et al., 1963
78.8 2.75 (Roberts et al., 199867.5 3.59 (Mayhew, 1977
66.4 3.99 (Saunders et al., 2004a66.1 3.54 (Mckicken and Daniels, 1976
65.7 4.63 (Saunders et al., 2004b69.9 3.45 (Menier and Pugh, 1968
70.0 3.46 (Sheppard, 196961.4 3.24 (Pugh, 1971
70.0 2.94 (Wright and Weyand, 200166.4 3.48 (Saunders et al., 2004a
   65.7 3.77 (Saunders et al., 2004b
   70.0 3.73 (Sheppard, 1969
   70.0 3.22 (Wright and Weyand, 2001
Mean   Mean   
66.8 3.92  66.1 3.55  
(A) Slope method
(B) Subtraction method
Mass (kg)Erun (net) (J kg-1 m-1)ReferenceMass (kg)Erun (net) (J kg-1 m-1)Reference
70.1 3.92 (Boje, 194472.7 3.15 (Bergh et al., 1991) BA 
53.7 3.66 (Bransford and Howley, 1977)FT 66.5 3.29 (Bergh et al., 1991) MR 
59.8 3.04 (Bransford and Howley, 1977)FU 51.7 3.61 (Bergh et al., 1991) FR 
67.0 4.08 (Bransford and Howley, 1977)MT 72.3 3.14 (Bergh et al., 1991) SO 
80.2 4.10 (Bransford and Howley, 1977)MU 70.1 3.75 (Boje, 1944
64.6 4.20 (Conley and Krahenbuhl, 198053.7 3.56 (Bransford and Howley, 1977)FT 
63.1 4.19 (Costill and Fox, 196959.8 3.51 (Bransford and Howley, 1977)FU 
63.7 5.07 (Costill et al., 197367.0 3.43 (Bransford and Howley, 1977)MT 
65.4 4.82 (Daniels and Daniels, 199280.2 3.57 (Bransford and Howley, 1977)MU 
58.9 4.24 (Daniels et al., 197764.6 3.44 (Conley and Krahenbuhl, 1980
65.1 3.18 (Dressendorfer et al., 197763.1 3.42 (Costill and Fox, 1969
65.4 4.70 (Hagan et al., 198063.7 3.56 (Costill et al., 1973
73.8 4.18 (Knuttgen, 196165.4 3.49 (Daniels and Daniels, 1992
68.8 4.02 (Margaria et al., 196358.9 3.39 (Daniels et al., 1977
67.5 4.19 (Mayhew, 197765.1 3.31 (Dressendorfer et al., 1977
66.1 3.46 (Mckicken and Daniels, 197665.4 4.48 (Hagan et al., 1980
69.9 3.77 (Menier and Pugh, 196873.8 3.82 (Knuttgen, 1961
61.4 3.59 (Pugh, 197168.8 4.23 (Margaria et al., 1963
78.8 2.75 (Roberts et al., 199867.5 3.59 (Mayhew, 1977
66.4 3.99 (Saunders et al., 2004a66.1 3.54 (Mckicken and Daniels, 1976
65.7 4.63 (Saunders et al., 2004b69.9 3.45 (Menier and Pugh, 1968
70.0 3.46 (Sheppard, 196961.4 3.24 (Pugh, 1971
70.0 2.94 (Wright and Weyand, 200166.4 3.48 (Saunders et al., 2004a
   65.7 3.77 (Saunders et al., 2004b
   70.0 3.73 (Sheppard, 1969
   70.0 3.22 (Wright and Weyand, 2001
Mean   Mean   
66.8 3.92  66.1 3.55  

(A) Net energy cost of running calculated using the slope method. (B) Net energy cost of running calculated using the subtraction method

For studies where multiple values exist, symbols represent groups: BA(biathletes), MR (male runners), FR (female runners), SO (ski orienteers), FT(female trained), FU (female untrained), MT (male trained), MU (male untrained)

Gross metabolic rates were obtained either from published regression equations or from single (mean) published values. For studies where only rates of oxygen consumption were presented, energy expenditure was calculated using an energy equivalent of 20.1 J ml–1 O2. Non-locomotor metabolic rates in humans were either published values of standing metabolic rate or, when unavailable, assumed to be equal to 1.5 W kg–1, a representative value based on data from the literature (Burdett et al.,1983; Farley and McMahon,1992; Martin et al.,1992; Waters and Mulroy,1999; Bastien et al.,2005; Browning et al.,2006). Because Erun calculated using the subtraction method has no unique value over a range of speeds, calculations were made close to the middle of the speed range examined in each study (these were generally between 3.0 and 4.5 m s–1, common speeds for recreational runners).

Since differences in Erun based on these two approaches(slope method and subtraction method) may also be present in other species, it is possible that they also affect the scaling relationship of Erun and body mass. For this reason, we have also generated a new allometric equation for Erun from existing data from studies where both experimental values of non-locomotor metabolic rates and gross running metabolic rates are provided(Table 3). Our analyses included 17 of the 95 animals in the data set of Taylor et al.(Taylor et al., 1982) and 14 additional species from other studies. Calculations were made close to the middle of the speed range of each animal examined. In order to ensure further that the selected animals were running over the targeted speed range, gait criteria were either based on existing published reports on gait mechanics(e.g. Cavagna et al., 1977; Fedak et al., 1982; Gatesy and Biewener, 1991) or an estimate of the animals' Froude number (see Alexander, 1989). The transition from walking to running has generally been found to occur at a Froude number of approximately 0.5 in a large range of vertebrate species(Alexander, 1989; Kram et al., 1997). We only accepted conservative values (above 0.6 for running). The allometric equation developed from these data provided a means to compare human net cost of running using the subtraction method with an allometrically predicted value of Erun based on the same approach.

Table 3.

Data from the literature used to construct the allometric equation(Eqn 2) for the net energy cost of running based on the subtraction method

AnimalMass (kg)Erun (net) (J kg-1 m-1)Non-locomotor cost (W kg-1)Speed (m s-1)Reference
Mammals      
   White mouse 0.021 85.56 12.67 0.21 (Taylor et al., 1970
   Deer mouse 0.022 65.08 8.25 0.56 (Chappel et al., 2004) 
   Kangaroo rat* 0.041 45.23 8.43 0.28 (Taylor et al., 1970
   Merriam's chipmunk 0.075 36.10 8.21 0.67 (Wundur, 1970) 
   Kangaroo rat 0.100 31.69 6.37 0.42 (Taylor et al., 1970
   Ground squirrel 0.236 14.67 6.31 0.56 (Taylor et al., 1970
   Red squirrel 0.252 17.80 12.06 0.58 (Wunder and Morrison, 1974
   White rat 0.384 27.19 5.67 0.49 (Taylor et al., 1970
   Bettong rat kangaroo 0.97 10.85 2.61 4.00 (Webster and Dawson, 2003
   Brush-tailed possum 1.95 11.38 4.41 1.49 (Baudinette et al., 1978
   Mongrel dog 2.6 7.24 3.40 1.94 (Taylor et al., 1970
   Patas monkey 3.8 6.29 3.00 3.47 (Mahoney, 1980
   Tammar wallaby 4.68 4.29 1.94 4.50 (Baudinette et al., 1987
   Hunting dog 8.75 6.17 4.07 2.78 (Taylor et al., 1971a
   River otter 11.1 6.71 3.34 1.40 (Williams et al., 2002
   Walker foxhound 18.0 4.36 1.79 1.94 (Taylor et al., 1970
   Elk calf 50.0 4.30 2.74 2.22 (Cohen et al., 1978
   Human 66.1 3.55 1.5 3.0–4.5 Mean data (see Table 1B
   Miniature horse 121 2.07 1.34 1.70 (Griffin et al., 2004), T. M. Griffin (personal communication) 
   Shetland pony 140 1.72 1.35 3.06 (Hoyt and Taylor, 1981), D. F. Hoyt (personal communication) 
   Arabian horse 448 1.63 1.29 2.70 (Griffin et al., 2004), T. M. Griffin (personal communication) 
   Camel 477 1.33 0.54 6.00 (Evans et al., 1994
   Standardbred horse 515 1.98 0.65 3.50 (Minetti et al., 1999
   Draft horse 715 1.93 1.38 3.00 (Griffin et al., 2004), T. M. Griffin (personal communication) 
Birds      
   Painted quail 0.042 26.63 11.61 0.56 (Fedak et al., 1974
   Bob-white quail 0.194 18.57 7.48 0.69 (Fedak et al., 1974
   Chuckar partridge 0.489 14.74 7.54 0.83 (Fedak et al., 1974
   Guinea fowl 1.45 9.14 6.37 2.50 (Ellerby et al., 2003
   Wild turkey 4.31 8.47 3.13 2.22 (Fedak et al., 1974
   Rhea 22.0 6.85 2.12 2.78 (Taylor et al., 1971b
   Ostrich 66.1 2.45 1.81 2.5–4.0 (Rubenson et al., 2004
AnimalMass (kg)Erun (net) (J kg-1 m-1)Non-locomotor cost (W kg-1)Speed (m s-1)Reference
Mammals      
   White mouse 0.021 85.56 12.67 0.21 (Taylor et al., 1970
   Deer mouse 0.022 65.08 8.25 0.56 (Chappel et al., 2004) 
   Kangaroo rat* 0.041 45.23 8.43 0.28 (Taylor et al., 1970
   Merriam's chipmunk 0.075 36.10 8.21 0.67 (Wundur, 1970) 
   Kangaroo rat 0.100 31.69 6.37 0.42 (Taylor et al., 1970
   Ground squirrel 0.236 14.67 6.31 0.56 (Taylor et al., 1970
   Red squirrel 0.252 17.80 12.06 0.58 (Wunder and Morrison, 1974
   White rat 0.384 27.19 5.67 0.49 (Taylor et al., 1970
   Bettong rat kangaroo 0.97 10.85 2.61 4.00 (Webster and Dawson, 2003
   Brush-tailed possum 1.95 11.38 4.41 1.49 (Baudinette et al., 1978
   Mongrel dog 2.6 7.24 3.40 1.94 (Taylor et al., 1970
   Patas monkey 3.8 6.29 3.00 3.47 (Mahoney, 1980
   Tammar wallaby 4.68 4.29 1.94 4.50 (Baudinette et al., 1987
   Hunting dog 8.75 6.17 4.07 2.78 (Taylor et al., 1971a
   River otter 11.1 6.71 3.34 1.40 (Williams et al., 2002
   Walker foxhound 18.0 4.36 1.79 1.94 (Taylor et al., 1970
   Elk calf 50.0 4.30 2.74 2.22 (Cohen et al., 1978
   Human 66.1 3.55 1.5 3.0–4.5 Mean data (see Table 1B
   Miniature horse 121 2.07 1.34 1.70 (Griffin et al., 2004), T. M. Griffin (personal communication) 
   Shetland pony 140 1.72 1.35 3.06 (Hoyt and Taylor, 1981), D. F. Hoyt (personal communication) 
   Arabian horse 448 1.63 1.29 2.70 (Griffin et al., 2004), T. M. Griffin (personal communication) 
   Camel 477 1.33 0.54 6.00 (Evans et al., 1994
   Standardbred horse 515 1.98 0.65 3.50 (Minetti et al., 1999
   Draft horse 715 1.93 1.38 3.00 (Griffin et al., 2004), T. M. Griffin (personal communication) 
Birds      
   Painted quail 0.042 26.63 11.61 0.56 (Fedak et al., 1974
   Bob-white quail 0.194 18.57 7.48 0.69 (Fedak et al., 1974
   Chuckar partridge 0.489 14.74 7.54 0.83 (Fedak et al., 1974
   Guinea fowl 1.45 9.14 6.37 2.50 (Ellerby et al., 2003
   Wild turkey 4.31 8.47 3.13 2.22 (Fedak et al., 1974
   Rhea 22.0 6.85 2.12 2.78 (Taylor et al., 1971b
   Ostrich 66.1 2.45 1.81 2.5–4.0 (Rubenson et al., 2004
*

Dipodomys merriami

Dipodomys spectabilis

The mean Erun over the running speed range is used

A new allometric relationship between the net minimum energy cost of walking and body mass was also constructed based on the subtraction method. Our analysis focused on the minimum net cost of walking because Ewalk is speed-dependent in certain species [e.g. humans(Margaria, 1976); horses(Minetti et al., 1999)]. We performed one analysis that included only those studies where an estimate of minimum Ewalk could be provided from the Ewalk determined over a range of walking speeds (denoted Ewalk,min). In addition, we performed an analysis that also included Ewalk of species determined at a self-selected speed, since these speeds are thought to coincide with the minimum Ewalk speed(Hoyt and Taylor, 1981). Because the fraction of the non-locomotor rate of energy expenditure accounts for a greater percentage of the exercising metabolic rate during walking compared to running, all studies selected for our allometric analyses had to provide a measurement of standing metabolic rate. Finally, in order to ensure further that the animals selected for our study were actually walking, walking gait criteria were based either on previously published reports on gait mechanics in the animal under consideration (e.g Gatesy and Biewener, 1991; Cavagna et al., 1977; Fedak et al., 1982) or, where gait mechanics were not available, on an estimate of the animal's Froude number at the speed being examined. Only speeds where the Froude number was below 0.4 were included. Metabolic rates presented as rates of oxygen consumption were converted to a rate of energy expenditure as described above. Because of the strict criteria set for our walking allometry, a large body of literature reporting walking metabolic rates in animals had to be excluded,and for this reason our analysis included 21 species of mammals and birds ranging in mass from 300 g to 1500 kg (see Table 4). Finally, the minimum net energy costs of human walking (at speeds approximating 1.25 m s–1) were taken from 20 previously published sources(Table 2) and calculated as described above for Erun.

Table 4.

Data from the literature used to construct the allometric equations(Eqn3and4) for the net energy cost of walking

AnimalMass (kg)Ewalk (net) (J kg-1 m-1)Non-locomotor (standing) cost (W kg-1)Minimum examinedSpeed (m s-1)Reference
Mammals       
   Granadia goat 35.4 3.37 1.93 Yes 0.17 (Lachica et al., 1997
   Red deer 68.3 2.56 2.07 Self-selected 1.67 (Brockway and Gessaman, 1977
   Human 69.5 2.06 1.50 Yes 1.20 Mean data (see Table 2
   Reindeer 92.8 2.38 1.92 Self-selected 0.83 (White and Yousef, 1978
   Caribou 102.1 1.71 * Yes 1.00 (Fancy and White, 1987
   Shetland pony 140 0.82 1.35 Yes 0.64 (Hoyt and Taylor, 1981), D. F. Hoyt (personal communication) 
   Miniature horse 121 1.37 1.34 Yes 0.9 (Griffin et al., 2004), T. M. Griffin (personal communication) 
   Bunaji bulls 378 1.47 * Self-selected 0.97 (Dijkman and Lawrence, 1997
   Arabian horse 448 1.08 1.29 Yes 1.05 (Griffin et al., 2004), T. M. Griffin (personal communication) 
   Brahman cattle 501.3 1.27 * Self-selected 1.23 (Dijkman and Lawrence, 1997
   Standardbred horse 515.0 1.49 0.65 Yes 1.20 (Minetti et al., 1999
   Camel 582.5 0.68 0.63 Self-selected 1.12 (Yousef et al., 1989
   Brahman × Friesen cattle 660 1.05 * Self-selected 1.06 (Dijkman and Lawrence, 1997
   Draft horse 715 1.05 1.38 Yes 1.55 (Griffin et al., 2004), T. M. Griffin (personal communication) 
   Water buffalo 811.3 1.56 * Self-selected 1.01 (Dijkman and Lawrence, 1997
   Elephant 1542 0.78 0.92 Yes 1.00 (Langman et al., 1995
Birds       
   Moorhen 0.29 29.89 5.67 Yes 0.33 J. A. Carr and R. L. Marsh (personal communication) 
   Duck 1.15 31.03 6.67 Yes 0.33 J. A. Carr and R. L. Marsh (personal communication) 
   Guinea fowl 1.45 14.63 6.37 Yes 0.50 (Marsh et al., 2004; Marsh et al., 2006), T. J. McPherson and R. L. Marsh (personal communication) 
   Marabou stork 4.50 8.26 3.81 Yes 1.02 (Bamford and Maloiy, 1980
   Ostrich 66.1 1.85 1.8 Yes 0.97 (Rubenson et al., 2004
AnimalMass (kg)Ewalk (net) (J kg-1 m-1)Non-locomotor (standing) cost (W kg-1)Minimum examinedSpeed (m s-1)Reference
Mammals       
   Granadia goat 35.4 3.37 1.93 Yes 0.17 (Lachica et al., 1997
   Red deer 68.3 2.56 2.07 Self-selected 1.67 (Brockway and Gessaman, 1977
   Human 69.5 2.06 1.50 Yes 1.20 Mean data (see Table 2
   Reindeer 92.8 2.38 1.92 Self-selected 0.83 (White and Yousef, 1978
   Caribou 102.1 1.71 * Yes 1.00 (Fancy and White, 1987
   Shetland pony 140 0.82 1.35 Yes 0.64 (Hoyt and Taylor, 1981), D. F. Hoyt (personal communication) 
   Miniature horse 121 1.37 1.34 Yes 0.9 (Griffin et al., 2004), T. M. Griffin (personal communication) 
   Bunaji bulls 378 1.47 * Self-selected 0.97 (Dijkman and Lawrence, 1997
   Arabian horse 448 1.08 1.29 Yes 1.05 (Griffin et al., 2004), T. M. Griffin (personal communication) 
   Brahman cattle 501.3 1.27 * Self-selected 1.23 (Dijkman and Lawrence, 1997
   Standardbred horse 515.0 1.49 0.65 Yes 1.20 (Minetti et al., 1999
   Camel 582.5 0.68 0.63 Self-selected 1.12 (Yousef et al., 1989
   Brahman × Friesen cattle 660 1.05 * Self-selected 1.06 (Dijkman and Lawrence, 1997
   Draft horse 715 1.05 1.38 Yes 1.55 (Griffin et al., 2004), T. M. Griffin (personal communication) 
   Water buffalo 811.3 1.56 * Self-selected 1.01 (Dijkman and Lawrence, 1997
   Elephant 1542 0.78 0.92 Yes 1.00 (Langman et al., 1995
Birds       
   Moorhen 0.29 29.89 5.67 Yes 0.33 J. A. Carr and R. L. Marsh (personal communication) 
   Duck 1.15 31.03 6.67 Yes 0.33 J. A. Carr and R. L. Marsh (personal communication) 
   Guinea fowl 1.45 14.63 6.37 Yes 0.50 (Marsh et al., 2004; Marsh et al., 2006), T. J. McPherson and R. L. Marsh (personal communication) 
   Marabou stork 4.50 8.26 3.81 Yes 1.02 (Bamford and Maloiy, 1980
   Ostrich 66.1 1.85 1.8 Yes 0.97 (Rubenson et al., 2004

Net costs of walking are either from studies where a minimum cost could be assessed or from studies examining self-selected speeds and are calculated using the subtraction method (see Materials and methods)

*

Standing cost was not reported in these studies but was used by the authors(Fancy and White, 1987); Dijkman and Lawrence, 1997) to compute Ewalk

Preliminary data from guinea fowl indicate that the minimum Ewalk is not statistically different from that observed at 0.5 m s-1 (T. J. McPherson and R. L. Marsh, personal communication)

The metabolic data (fig. 2 in Bamford and Maloiy, 1980) was scanned, digitized and fit with a 2nd order polynomial (y=1.20x2-0.65x+1.29; y is in ml O2 s-1, x is in m s-1). This equation fitted the data better than a linear relationship, as indicated by the higher r (0.85 vs 0.65). A minimum Ewalk is evident at ∼1 m s-1

Table 2.

Human data (means) of net energy cost of walking taken from the literature, used to compare with allometric predictions

Mass (kg)Ewalk (net) (J kg-1 m-1)Reference
67.0 1.91 (Bastien et al., 2005
56.8 2.45 (Booyens and Keatinge, 1957
58.7 1.98 (Browning and Kram, 2005
74.7 1.80 (Browning et al., 2006
65.2 2.31 (Burdett et al., 1983
59.0 1.91 (Dolgener, 1982
70.4 2.59 (Duggan and Haisman, 1992
65.0 2.12 (Farley and McMahon, 1992
66.7 2.00 (Gottschall and Kram, 2003
70.8 2.06 (Howley and Glover, 1974
63.2 2.22 (Martin et al., 1992
72.0 2.15 (McCann and Williams, 2002
84.1 2.15 (Minetti et al., 1995
66.1 1.80 (Ortega and Farley, 2005
76.3 1.71 (Pearce et al., 1983
76.0 2.37 (Ralston, 1958
75.8 2.24 (van der Walt and Wyndham,1973
72.8 1.91 (Waters et al., 1988
70.0 1.86 (Waters et al., 1983
80.0 1.77 (Yousef et al., 1989
Mean   
69.5 2.06  
Mass (kg)Ewalk (net) (J kg-1 m-1)Reference
67.0 1.91 (Bastien et al., 2005
56.8 2.45 (Booyens and Keatinge, 1957
58.7 1.98 (Browning and Kram, 2005
74.7 1.80 (Browning et al., 2006
65.2 2.31 (Burdett et al., 1983
59.0 1.91 (Dolgener, 1982
70.4 2.59 (Duggan and Haisman, 1992
65.0 2.12 (Farley and McMahon, 1992
66.7 2.00 (Gottschall and Kram, 2003
70.8 2.06 (Howley and Glover, 1974
63.2 2.22 (Martin et al., 1992
72.0 2.15 (McCann and Williams, 2002
84.1 2.15 (Minetti et al., 1995
66.1 1.80 (Ortega and Farley, 2005
76.3 1.71 (Pearce et al., 1983
76.0 2.37 (Ralston, 1958
75.8 2.24 (van der Walt and Wyndham,1973
72.8 1.91 (Waters et al., 1988
70.0 1.86 (Waters et al., 1983
80.0 1.77 (Yousef et al., 1989
Mean   
69.5 2.06  

Values were calculated using the subtraction method

Statistical analysis

In order to determine whether the slope and subtraction methods for calculating Erun yield significantly different allometric relationships, we first tabulated the data from Taylor et al.(Taylor et al., 1982) and included in our analysis those animals that were used to develop their allometric equation (N=89). We estimated a regression with Erun (log-transformed) from both Taylor et al.(Taylor et al., 1982) and our new data set (Table 3) as the dependent variable, a categorical variable for the slope or subtraction method as a fixed factor, and body mass (log-transformed) as a covariate (General Linear Model using SPSS version 13). We also performed a similar analysis on log-transformed data to determine whether the allometric relationship of the net cost of locomotion is different for running and walking gaits. We used cost (Erun and Ewalk) as the dependent variable, a categorical variable for gait (walking vs running) as a fixed factor, and body mass as a covariate. Main and interaction effects were analyzed at a significance level of P<0.05.

Fig. 1.

Double logarithmic plot of the net energy cost of human running(Erun) versus body mass calculated from the slope method (A) and subtraction method (B) (see Materials and methods for explanation). The shaded circles represent human data from 20 previously published sources (see Table 1Aand Table 1B for corresponding data), and the solid circle represents the mean value from these studies. The solid line in A and the broken line in B correspond to Erun predicted from the allometric equation of Taylor et al. (Taylor et al., 1982)(Eqn 1). The solid line in B corresponds to Erun predicted from the new allometric equation from the present study (Eqn 2).

Fig. 1.

Double logarithmic plot of the net energy cost of human running(Erun) versus body mass calculated from the slope method (A) and subtraction method (B) (see Materials and methods for explanation). The shaded circles represent human data from 20 previously published sources (see Table 1Aand Table 1B for corresponding data), and the solid circle represents the mean value from these studies. The solid line in A and the broken line in B correspond to Erun predicted from the allometric equation of Taylor et al. (Taylor et al., 1982)(Eqn 1). The solid line in B corresponds to Erun predicted from the new allometric equation from the present study (Eqn 2).

Fig. 2.

Double logarithmic plot of the net energy cost of running(Erun) versus body mass for humans and other mammalian and avian species. The shaded circles represent human data from 20 previously published sources (calculated from the subtraction method; see Materials and methods) (Table 1B), and the solid circle represents the mean value from these studies. The solid diamonds represent the other animals (see Table 3) used to generate the allometric equation for Erun using the subtraction method(Eqn 2). The solid line corresponds to the predicted Erun from this equation. For comparison, we have included the data points used by Taylor et al.(Taylor et al., 1982) (shaded diamonds; used to generate their allometric equation for Erun (Eqn 1;slope method). The broken line corresponds to the predicted Erun from Eqn 1.

Fig. 2.

Double logarithmic plot of the net energy cost of running(Erun) versus body mass for humans and other mammalian and avian species. The shaded circles represent human data from 20 previously published sources (calculated from the subtraction method; see Materials and methods) (Table 1B), and the solid circle represents the mean value from these studies. The solid diamonds represent the other animals (see Table 3) used to generate the allometric equation for Erun using the subtraction method(Eqn 2). The solid line corresponds to the predicted Erun from this equation. For comparison, we have included the data points used by Taylor et al.(Taylor et al., 1982) (shaded diamonds; used to generate their allometric equation for Erun (Eqn 1;slope method). The broken line corresponds to the predicted Erun from Eqn 1.

Comparison of human net cost of running and walking from literature

Using the slope of the regression between met and running speed in humans (slope method) to calculate Erun,the mean Erun from 20 previously published studies was 38±21% (s.d.) above the predicted cost from the allometric equation of Taylor et al. (Taylor et al.,1982) (Eqn 1) and within the 95% confidence interval for this equation. The study with the highest cost of running was 75% above the predicted cost whereas the lowest was 2% above (Fig. 1A).

Using the gross metabolic cost minus the non-locomotor cost (subtraction method) to calculate Erun in humans, the mean Erun obtained from the published studies was 25±11%(s.d.) above the predicted cost using the allometric equation of Taylor et al.(Taylor et al., 1982) and was within the 95% confidence interval of the equation. The study with the highest cost of running using the subtraction method was 57% above the predicted cost from Taylor et al. (Taylor et al.,1982) whereas the lowest was 11% above(Fig. 1B).

Fig. 3.

Double logarithmic plot of the net energy cost of walking versusbody mass (calculated from the subtraction method; see Materials and methods). The shaded circles represent human data from 20 previously published sources(calculated from the subtraction method, see Materials and methods)(Table 2), and the solid circle represents the mean value from these studies. The solid diamonds represent the other animals (see Table 4)used to generate the allometric equations for the net cost of walking. The solid line represents the predicted net cost of walking from the allometric equation based on animals for which either a minimum net cost of walking could be assessed or for which the net cost of walking was measured at a self-selected walking speed (Ewalk; Eqn 4). The broken line represents the predicted net cost of walking from the allometric equation based only on animals for which a minimum net cost of walking could be assessed (Ewalk,min; Eqn 3).

Fig. 3.

Double logarithmic plot of the net energy cost of walking versusbody mass (calculated from the subtraction method; see Materials and methods). The shaded circles represent human data from 20 previously published sources(calculated from the subtraction method, see Materials and methods)(Table 2), and the solid circle represents the mean value from these studies. The solid diamonds represent the other animals (see Table 4)used to generate the allometric equations for the net cost of walking. The solid line represents the predicted net cost of walking from the allometric equation based on animals for which either a minimum net cost of walking could be assessed or for which the net cost of walking was measured at a self-selected walking speed (Ewalk; Eqn 4). The broken line represents the predicted net cost of walking from the allometric equation based only on animals for which a minimum net cost of walking could be assessed (Ewalk,min; Eqn 3).

The new allometric equation predicting the net energy cost of running based on the Erun of 31 animals ranging in mass from 21 g to 715 kg and calculated using the subtraction method is:
(2)
where Mb is body mass in kg and Erunhas the units J kg–1 m–1 (see Fig. 2). Values are means± s.e.m. and r2=0.941. The mean Erun of humans based on the subtraction method was 17±11% (s.d.) above the predicted cost from Eqn 2 and fell within the 95%confidence interval of this equation. The human values ranged 4–47%above the predicted cost using Eqn 2 (Fig. 1B). Our statistical analysis revealed a significant main effect (P<0.001)between the method used for calculating Erun (slope method, N=89 vs subtraction method, N=31). This represents a significant difference in the constant term of the allometric equations.
The allometric equation predicting minimum net cost of walking using the subtraction method and relying only on those data for which a minimum net cost of walking can be assessed (N=15) is:
(3)
where Ewalk has the units J kg–1m–1 (see Fig. 3). Values are means ± s.e.m. and r2=0.927.
By including data of the net cost of walking at preferred speeds, the resulting allometric equation predicting the net energy cost of walking using the subtraction method (N=21 with mass ranging from 290 g to 1524 kg)is:
(4)
Values are means ± s.e.m. and r2=0.911. A significant main effect for gait (walking vs running) was observed(P<0.001) when Ewalk was compared to Erun using either the data from Taylor et al.(Taylor et al., 1982) (slope method) or Erun calculated from the 31 animals using the subtraction method (P<0.001). The interaction effect between body mass and gait (walking vs running) was also significant(P<0.001) using either Erun from Taylor et al.(Taylor et al., 1982) (slope method) or Erun calculated from 31 animals using the subtraction method. (P<0.001). The tests of significance remained the same when Ewalk,min was used in place of Ewalk.

The difference between the mean human Ewalk obtained from 20 previously published studies and the net energy cost of walking predicted using Eqn 3 and Eqn 4 were –15±10%and –20±9% (s.d.), respectively, and fell within the 95%confidence interval for these equations. The data used for establishing the allometric equation for Ewalk and Ewalk,min are presented in Table 4 and shown in Fig. 3.

This study re-explores how the net metabolic energy cost of human running and walking compares to those of animals of similar mass. From an extensive comparison of published human data and the adoption of a more appropriate approach to compare the net energy cost of locomotion of humans with other animal species, this study shows that the difference between the net energy cost of human running and that predicted for an animal of similar mass is much smaller (17%) than previously estimated (∼43–100%). The relative difference between humans' Erun and their allometrically predicted cost is comparable to or less than those of many other species, some of which are regarded as economical runners. This study also indicates that humans' net cost of walking is 20% lower than predicted for their mass. Nevertheless, this difference is not atypical given that 25% of the species examined here have a similar or lower relative cost of walking compared to that predicted for their mass.

Comparative cost of human running

It is difficult to establish definitively when the Erunof an animal should be regarded as atypical for its mass and, to the best of our knowledge, there is no golden standard upon which to make such a decision. Our allometric analysis nevertheless reveals that the 17% higher than predicted cost of human running is unremarkable and, in comparison with previous studies, does not warrant the labelling of humans as particularly uneconomical runners. One simple approach to gauge the cost of human running is to compare the relative difference between their measured and allometrically predicted Erun to those observed in other species. With respect to the allometric equation of Taylor et al.(Eqn 1), 22% of the animals used to generate this equation have an equal or greater relative difference between their measured and predicted Erun compared to humans (Figs 2, 4). With our new allometric equation for Erun using the subtraction method, 27% of the animals examined have an equal or greater relative difference between their measured and predicted Erun compared to humans (Figs 2, 4). Interestingly, among the animal species that have a greater relative difference between their measured and allometrically predicted Erun compared to humans there are several `athletic' cursorial runners, including horses and antelope. It is also worth considering that the 17% higher than predicted cost of Erun reported here in humans is not only much smaller than previously reported in the literature (43–100%)(Taylor et al., 1970; Taylor et al., 1982; Taylor, 1994) but also modest relative to the 20–27% inter-individual variation in the cost of human running (Daniels, 1985) and more than one order of magnitude smaller than the sixfold interspecies variation in the net cost of locomotion that has been reported by Full et al.(Full et al., 1990) to exist at any given body mass. Overall, given our findings and assuming that the animal species used in our allometric analysis are representative, it would be difficult to uphold that humans have an atypically high Erun.

Fig. 4.

Histogram of the percentage difference between the measured and allometrically predicted net cost of running (Erun) using(A) the animal data from Taylor et al.(Taylor et al., 1982)(N=95) and the allometric equation(Eqn 1) developed in their study(where Erun is computed using the slope method; see Materials and methods) and (B) 31 animals for which Erunwas computed using the subtraction method and the allometric equation developed from these data (Eqn 2). The position of the mean human Erun based on the subtraction method from 20 previously published studies is represented by the black bars.

Fig. 4.

Histogram of the percentage difference between the measured and allometrically predicted net cost of running (Erun) using(A) the animal data from Taylor et al.(Taylor et al., 1982)(N=95) and the allometric equation(Eqn 1) developed in their study(where Erun is computed using the slope method; see Materials and methods) and (B) 31 animals for which Erunwas computed using the subtraction method and the allometric equation developed from these data (Eqn 2). The position of the mean human Erun based on the subtraction method from 20 previously published studies is represented by the black bars.

Fig. 5.

The predicted net cost of running (Erun) and walking(Ewalk) using the new allometric equation of the net cost of running (Eqn 2; solid line)and the new allometric equation of the net cost of walking(Eqn 4; broken line). The point where these relationships intersect (∼20 kg) represents the theoretical mass where the net cost of walking and running are equivalent. Above this mass, the net cost of walking is predicted to be greater than the net cost of running, and below this mass the opposite is predicted.

Fig. 5.

The predicted net cost of running (Erun) and walking(Ewalk) using the new allometric equation of the net cost of running (Eqn 2; solid line)and the new allometric equation of the net cost of walking(Eqn 4; broken line). The point where these relationships intersect (∼20 kg) represents the theoretical mass where the net cost of walking and running are equivalent. Above this mass, the net cost of walking is predicted to be greater than the net cost of running, and below this mass the opposite is predicted.

The smaller differences found here between the measured and predicted Erun for humans compared to previously reported values is best explained on the basis of the following factors. Firstly, the higher than predicted Erun values for humans in the work of Taylor and colleagues (Taylor et al.,1970; Taylor et al.,1982) stems in part from the much smaller sample of human data selected for their allometric analyses. In particular, the human Erun values used in these analyses are among the higher values published for humans. However, it must be stressed in defence of Taylor and colleagues (Taylor et al.,1970; Taylor et al.,1982) that the purpose of their studies was not to specifically compare human Erun with other species but to perform an allometric analysis of Erun across species. Even the selection of non-representative human data would be expected to have a negligible effect on the overall scaling relationship based on a large animal sample. Secondly, another factor contributing to the higher Erun in humans in the allometric analyses of Taylor and colleagues is the approach adopted to calculate Erun. As mentioned earlier, Erun in allometry studies is generally estimated from the slope of the linear regression between the rate of energy expenditure and speed. This method has the advantage that it provides a single value for Erun that is independent of speed, a benefit that has proven very useful for establishing general allometric scaling relationships between a large number of species moving at very different speeds. Here, we show that the use of the slope method provides a mean Erun that is 38% above predicted Erunin humans, a value similar to the 43% difference reported by Taylor et al.(Taylor et al., 1982). However, with the subtraction method to evaluate Erun in humans, the combined mean Erun from 20 previous studies falls only 25% above that predicted from the allometric equation of Taylor and colleagues (Taylor et al.,1982) and 17% above our new Erun allometric equation based on the subtraction method.

The larger difference between predicted and measured human Erun determined using the slope method compared to the subtraction method is primarily due to the marked differences between the y-intercepts of the regression equations and actual non-locomotor rates of energy expenditure. Interestingly, out of those human studies that we examined (Table 1A,B), the majority reporting steep slopes of metvsspeed (high net energy costs of running) were found to have intercepts much lower than non-locomotor metabolic rates, with some of those studies reporting negative intercepts that do not correspond to any resting physiological state(e.g. Sheppard et al., 1969; Bransford and Howley, 1977; Saunders et al.,2004b), thus resulting in an overestimation of Erun. Conversely, those studies reporting shallow slopes of metvs speed (low net energy costs of running) generally have intercepts greater than non-locomotor metabolic rates. The mismatch between y-intercepts and non-locomotor metabolic rates explains, in part, the observation that there is a 70% difference in human Erun across studies using the slope method, with values as low as 2% above those predicted from allometry to values as high as 75% above the allometric prediction (Fig. 1A). This variability is far greater than the upper limit of 20–27% inter-individual difference in running economy in humans(Daniels, 1985). By contrast,the variability in Erun in humans is reduced when using the subtraction method (Fig. 1B). These findings are not surprising because the relationship between met and speed is not linear through walking speeds in humans, with intercepts from running data in the literature(Table 1A,B) fluctuating by as much as 150%.

It is important to point out that the errors in determining Erun resulting from the disparity between the y-intercept and actual non-locomotor metabolic rates also affect the calculation of the net cost of running in other animal species. Perhaps the most explicit example of the unsuitability of using the slope method is the case of hopping kangaroos, where a negative slope of the linear regression between the rate of energy expenditure and speed has been reported(Dawson and Taylor, 1973). It is interesting to note that these errors have a small but statistically significant effect on the scaling relationship between Erun and body mass, with the slope method resulting in a lower Erun compared to the subtraction method(Eqn 2). This difference could be explained on the basis of a general overestimate of the non-locomotor metabolic rate using the y-intercept of the regression between metabolic rate and speed. The general scaling relationship for Erun (the scaling exponent) is, however, not different when using the two methods. This absence of difference is possibly because the error between the y-intercept and the actual non-locomotor cost in many animals is a small fraction of the gross metabolic rate during running and may be relatively consistent across body mass. Therefore, since only a small difference exists between the allometric equations for Erun based on the subtraction and slope methods, the use of the slope method appears to be appropriate for general scaling analyses of Erun.

Comparative cost of human walking

Unlike running, the Ewalk for humans falls moderately below the predicted values for their body mass using our new allometric analysis of Ewalk. The lower than predicted Ewalk in humans is also not atypical compared to the other species examined here, given that a quarter of these animals have a relatively lower Ewalk compared to their allometrically predicted value. Also, the Ewalk of humans is comparable to those of animals that share a similar mass, such as ostriches, caribou and deer. That there is little difference between Ewalk in humans and these animals is somewhat surprising given that they do not possess a graviportal (straight) limb posture. Other factors that can reduce the metabolic cost of walking may balance any disadvantage that a more bent joint posture imposes on walking animals.

An unexpected and interesting finding arising from our allometric analyses is the marked significant (P<0.001) interaction effect between body mass and gait (walking vs running) on the net energy cost of locomotion. This interaction effect is reflected by the different exponents of the allometric relationship of the net energy cost of running [–0.316(Taylor et al., 1982);–0.336 (present study)] and walking (–0.449) and highlights for the first time the importance of using a walk-specific allometric equation to predict the net energy costs of walking. More importantly, these results also indicate that the relative differences between Ewalk and Erun in animals vary across body mass. According to our walking allometric analysis, the net energy cost of walking should be lower than that of running for large animals, but the converse for small animals(Fig. 5), and at a mass of∼20 kg, where the walking and running regression lines intersect, an animal's Ewalk and Erun should in theory be equivalent. In support of this view, large animal species have an Ewalk considerably lower than their Erun, as found in humans(Margaria, 1976), Shetland ponies (Hoyt and Taylor, 1981)(D. F. Hoyt, personal communication), Arabian, Draft and Miniature horses(Griffin et al., 2004) (T. M. Griffin, personal communication), Standardbred horses(Minetti et al., 1999),ostriches (Rubenson et al.,2004) and camels (Yousef et al., 1989; Evans et al.,1994) (see Tables 3and 4) despite the gross energy cost of walking and running in several of these species being the same(Hoyt and Taylor, 1981; Griffin et al., 2004). By contrast, Ewalk is higher compared to Erun in all but two of the 13 small mammal and bird species (0.021–22 kg) studied by Taylor et al.(Taylor et al., 1970) and Fedak et al. (Fedak et al.,1974). Ground squirrels (0.23 kg)(Hoyt and Kenagy, 1988) and mink (∼1 kg) (Williams,1983) also expend more energy to travel a given distance when walking compared to running. Unfortunately, the mechanisms underlying our observation that the relative differences between Ewalkand Erun in animals vary across body mass remain unclear,although differences in the effectiveness of pendular and elastic energy saving strategies between large and small animals are a possible candidate(Cavagna et al., 1977). Clearly, the finding that large animals are expected to have lower walking than running net locomotor cost, and vice versa for small animals,requires further corroboration and raises the question of whether this can explain some of the differences in locomotor behaviour between large and small animals.

It must be stressed that a number of precautions were taken to construct our new allometric scaling relationship for the net energy cost of walking. First, because non-locomotor rates of energy expenditure account for a greater percentage of gross metabolic rates during walking compared to running, we have used only those studies where an experimental standing non-locomotor value is provided. A second potential confounding factor relates to the fact that Ewalk is not constant across speed for all animals. For this reason, we have computed the allometric equation for the net energy cost of walking using either only those studies where a net minimum cost of walking can be assessed (Ewalk,min; N=15) or including also those studies reporting values at self-selected speeds(Ewalk; N=21), as these are believed to correspond to the animals' minimum net cost of walking(Hoyt and Taylor, 1981). Our results show that both approaches yield similar findings. Given our low sample size, we also performed further analyses to determine how sensitive our allometric analysis is to the removal of data obtained from animals with either a dissimilar gait pattern (duck with their waddling gait) or leg length(stork). We found that the removal of the duck or stork from our data set did not affect significantly the scaling relationship between the net cost of walking and body mass for either Ewalk or Ewalk,min. Nevertheless, it is important to stress that since there are only a few studies providing data for non-locomotor and gross costs from which a minimum net cost of walking can be assessed, the scaling relationship between Ewalk and body mass determined here suffers from the limitation that it is based on a small number of animal species. Clearly, such an allometric analysis would benefit from the inclusion of many more species.

In conclusion, by performing an extensive allometric analysis using data from the literature, we conclude that human net costs of running and walking relative to those predicted on the basis of their body mass are unremarkable compared to those of other species. For this reason, it is recommended that earlier interpretations based on the viewpoint that human locomotion is energetically atypical should be reconsidered.

This research was supported by an Australian Research Council grant to P.A.F. and D.G.L. The authors thank Jen Carr, Jade McPherson, Richard Marsh,Donald Hoyt and Timothy Griffin for kindly providing data used in establishing the new allometric equations for the net energy cost of walking. The authors also thank Richard Marsh for commenting on an earlier version of this work and Rodger Kram for useful insights into the different scaling relationships between the net energy cost of walking and running. Finally, the authors wish to thank two anonymous reviewers for their valuable comments and criticisms.

Aiello, L. C. and Wells, J. C. K. (
2002
). Energetics and the evolution of the genus
Homo. Annu. Rev. Anthropol.
31
,
323
-338.
Alexander, R. M. (
1989
). Optimization and gaits in the locomotion of vertebrates.
Physiol. Rev.
69
,
1199
-1227.
Alexander, R. M. (
1991
). Characteristics and advantages of human bipedalism. In
Biomechanics in Evolution
(ed. J. M. V. Raynor and R. J. Wooton), pp.
225
-266. Cambridge: Cambridge University Press.
Alexander, R. M. (
1992
). Comparative aspects of human activity. In
Physical Activity and Health, 34th Symposium Volume of the Society for the Study of Human Biology
(ed. N. G. Norgan), pp.
7
-19. Cambridge: Cambridge University Press.
Bamford, O. S. and Maloiy, G. M. (
1980
). Energy metabolism and heart rate during treadmill exercise in the Marabou stork.
J. Appl. Physiol.
49
,
491
-496.
Bastien, G. J., Willems, P. A., Schepens, B. and Heglund, N. C. (
2005
). Effect of load and speed on the energetic cost of human walking.
Eur. J. Appl. Physiol.
94
,
76
-83.
Baudinette, R. V., Seymor, S. R. and Orback, J.(
1978
). Cardiovascular responses to exercise in the brush-tailed possum.
J. Comp. Physiol.
124
,
143
-147.
Baudinette, R. V., Seymor, S. R. and Orback, J.(
1987
). Do cardiorespiratory frequencies show entrainment with hopping in the tammar wallaby?
J. Exp. Biol.
129
,
251
-263.
Bergh, U., Sjodin, B., Forsberg, A. and Svedenhag, J.(
1991
). The relationship between body mass and oxygen consumption during running in humans.
Med. Sci. Sports Exerc.
23
,
205
-211.
Boje, O. (
1944
). Energy production, pulmonary ventilation, and length of steps in well-trained runners working on a treadmill.
Acta Physiol. Scand.
7
,
362
-375.
Booyens, J. and Keatinge, W. R. (
1957
). The expenditure of energy by men and women walking.
J. Physiol.
138
,
165
-171.
Bramble, D. M. and Lieberman, D. E. (
2004
). Endurance running and the evolution of Homo.
Nature
432
,
345
-352.
Bransford, D. R. and Howley, E. T. (
1977
). Oxygen cost of running in trained and untrained men and women.
Med. Sci. Sports. Exerc.
9
,
41
-44.
Brockway, J. M. and Gessaman, J. A. (
1977
). The energy cost of locomotion on the level and on gradients for the red deer(Cervus elaphus).
Q. J. Exp. Physiol.
62
,
333
-339.
Browning, R. C. and Kram, R. (
2005
). Energetic cost and preferred speed of walking in obese vs. normal weight women.
Obes. Res.
13
,
891
-899.
Browning, R. C., Baker, E. A., Herron, J. A. and Kram, R.(
2006
). Effects of obesity and sex on the energetic cost and preferred speed of walking.
J. Appl. Physiol.
100
,
390
-398.
Burdett, R. G., Skrinar, G. S. and Simon, S. R.(
1983
). Comparison of mechanical work and metabolic energy consumption during normal gait.
J. Orthop. Res.
1
,
63
-72.
Carrier, D. R. (
1984
). The energetic paradox of human running and hominid evolution.
Curr. Anthropol.
24
,
483
-495.
Cavagna, G. A., Heglund, N. C. and Taylor, C. R.(
1977
). Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure.
Am. J. Physiol.
233
,
R243
-R261.
Chappell, M. A., Garland, T., Jr, Rezende, E. L. and Gomes, F. R. (
2004
). Voluntary running in deer mice: speed, distance,energy cost and temperature effects.
J. Exp. Biol.
207
,
3839
-3854.
Cohen, Y., Robbins, C. T. and Davitt, B. B.(
1978
). Oxygen utilization by elk calves during horizontal and vertical locomotion compared to other species.
Comp. Biochem. Physiol.
61A
,
43
-48.
Conley, D. L. and Krahenbuhl, G. S. (
1980
). Running economy and distance running performance of highly trained athletes.
Med. Sci. Sports Exerc.
12
,
357
-360.
Costill, D. L. and Fox, E. L. (
1969
). Energetics of marathon running.
Med. Sci. Sports Exerc.
1
,
81
-86.
Costill, D. L., Thomson, H. and Roberts, E.(
1973
). Fractional utilization of the aerobic capacity during distance running.
Med. Sci. Sports
5
,
248
-252.
Daniels, J. (
1985
). A physiologist's view of running economy.
Med. Sci. Sports Exerc.
17
,
332
-338.
Daniels, J. and Daniels, N. (
1992
). Running economy of elite male and elite female runners.
Med. Sci. Sports Exerc.
24
,
483
-489.
Daniels, J., Krahenbuhl, G., Foster, C., Gilbert, J. and Daniels, S. (
1977
). Aerobic responses of female distance runners to submaximal and maximal exercise.
Ann. N. Y. Acad. Sci.
301
,
726
-733.
Dawson, T. J. and Taylor, C. R. (
1973
). Energetic cost of locomotion in kangaroos.
Nature
246
,
313
-314.
Dijkman, J. T. and Lawrence, P. R. (
1997
). The energy expenditure of cattle and buffaloes walking and working in different soil conditions.
J. Agric. Sci.
128
,
95
-103.
Dolgener, F. (
1982
). Oxygen cost of walking and running in untrained, sprint trained, and endurance trained females.
J. Sports Med. Phys. Fitness
22
,
60
-65.
Dressendorfer, R. H., Scaff, J. H. J., Wagner, J. O. and Gallup,J. D. (
1977
). Metabolic adjustments to marathon running in coronary patients.
Ann. N. Y. Acad. Sci.
301
,
466
-483.
Duggan, A. and Haisman, M. F. (
1992
). Prediction of the metabolic cost of walking with and without loads.
Ergonomics
35
,
417
-426.
Ellerby, D. J., Cleary, M., Marsh, R. L. and Buchanan, C. I.(
2003
). Measurement of maximum oxygen consumption in Guinea fowl Numida meleagris indicates that birds and mammals display a similar diversity of aerobic scopes during running.
Physiol. Biochem. Zool.
76
,
695
-703.
Ellerby, D. J., Henry, H. T., Carr, J. A., Buchanan, C. I. and Marsh, R. L. (
2005
). Blood flow in guinea fowl numida meleagris as an indicator of energy expenditure by individual muscles during walking and running.
J. Physiol.
564
,
631
-648.
Evans, D. L., Rose, R. J., Knight, P. K., Cluer, D. and Saltin,B. (
1994
). Oxygen uptake in the racing camel at rest and during treadmill exercise.
Acta Physiol. Scand. Suppl.
617
,
41
-48.
Fancy, S. G. and White, R. G. (
1987
). Energy expenditure for locomotion by barren-grounded caribou.
Can. J. Zool.
65
,
122
-128.
Farley, C. T. and McMahon, T. A. (
1992
). Energetics of walking and running: insights from simulated reduced-gravity experiments.
J. Appl. Physiol.
73
,
2709
-2712.
Fedak, M. A. and Seeherman, H. J. (
1979
). Reappraisal of energetics of locomotion shows identical cost in bipeds and quadrupeds including ostrich and horse.
Nature
282
,
713
-716.
Fedak, M. A., Pinshow, B. and Schmidt-Nielsen. K.(
1974
). Energy cost of bipedal running.
Am. J. Physiol.
227
,
1038
-1044.
Fedak, M. A., Heglund, N. C. and Taylor, C. R.(
1982
). Energetics and mechanics of terrestrial locomotion. II. Kinetic energy changes of the limbs and body as a function of speed and body size in birds and mammals.
J. Exp. Biol.
97
,
23
-40.
Full, R. J. (
1991
). The concepts of efficiency and economy in land locomotion. In
Efficiency and Economy in Animal Locomotion
(ed. R. W. Blake), pp.
97
-131. Cambridge: Cambridge University Press.
Full, R. J., Zuccarello, D. A. and Tullis, A.(
1990
). Effect of variation in form on the cost of terrestrial locomotion.
J. Exp. Biol.
150
,
233
-246.
Gatesy, S. M. and Biewener, A. A. (
1991
). Bipedal locomotion effects of speed size and limb posture in birds and humans.
J. Zool. Lond.
224
,
127
-148.
Gottschall, J. S. and Kram, R. (
2003
). Energy cost and muscular activity required for propulsion during walking.
J. Appl. Physiol.
94
,
1766
-1772.
Griffin, T. M., Kram, R., Wickler, S. J. and Hoyt, D. F.(
2004
). Biomechanical and energetic determinants of the walk–trot transition in horses.
J. Exp. Biol.
207
,
4215
-4223.
Hagan, R. D., Strathman, T., Strathman, L. and Gettman, L. R. (
1980
). Oxygen uptake and energy expenditure during horizontal treadmill running.
J. Appl. Physiol.
49
,
571
-575.
Howley, E. T. and Glover, M. E. (
1974
). The caloric costs of running and walking one mile for men and women.
Med. Sci. Sports
6
,
235
-237.
Hoyt, D. F. and Kenagy, G. J. (
1988
). Energy costs of walking and running gaits and their aerobic limits in Golden-Mantled ground squirrels.
Physiol. Zool.
61
,
34
-40.
Hoyt, D. F. and Taylor, C. R. (
1981
). Gait and energetics of locomotion in horses.
Nature
292
,
239
-240.
Knuttgen, H. G. (
1961
). Oxygen uptake and pulse rate while running with undetermined and determined stride lengths at different speeds.
Acta Physiol. Scand.
52
,
366
-371.
Kram, R., Domingo, A. and Ferris, D. P. (
1997
). Effect of reduced gravity on the preferred walk-run transition speed.
J. Exp. Biol.
200
,
821
-826.
Lachica, M., Prieto, C. and Aguilera, J. F.(
1997
). The energy cost of walking on the level and on negative and positive slopes in the Granadina goat (Capara hircus).
Br. J. Nutr.
77
,
73
-81.
Langman, V. A., Roberts, T. J., Black, J., Maloiy, G. M.,Heglund, N. C., Weber, J. M., Kram, R. and Taylor, C. R.(
1995
). Moving cheaply: energetics of walking in the African elephant.
J. Exp. Biol.
198
,
629
-632.
Leonard, R. and Robertson, M. L. (
1997
). Rethinking the energetics of bipedality.
Curr. Anthropol.
38
,
304
-309.
Mahoney, S. A. (
1980
). Cost of locomotion and heat balance during rest and running from 0 to 50°C in a patas monkey.
J Appl. Physiol.
49
,
789
-800.
Margaria, R. (
1976
).
Biomechanics and Energetics of Muscular Exercise
. Oxford: Clarendon Press.
Margaria, R., Cerretelli, P., Aghemo, P. and Sassi, G.(
1963
). Energy cost of running.
J. Appl. Physiol.
18
,
367
-370.
Marsh, R. L. and Ellerby, D. J. (
2006
). Partitioning locomotor energy use among and within muscles. Muscle blood flow as a measure of muscle oxygen consumption.
J. Exp. Biol.
209
,
2385
-2394.
Marsh, R. L., Ellerby, D. J., Carr, J. A., Henry, H. T. and Buchanan, C. I. (
2004
). Partitioning the energetics of walking and running: swinging the limbs is expensive.
Science
303
,
80
-83.
Marsh, R. L., Ellerby, D. J., Henry, H. T. and Rubenson, J.(
2006
). The energetic cost of trunk and distal-limb loading during walking and running in guinea fowl Numida meleagris. I. Organismal metabolism and biomechanics.
J. Exp. Biol.
209
,
2050
-2063.
Martin, P. E., Rothstein, D. E. and Larish, D. D.(
1992
). Effects of age and physical activity status on the speed-aerobic demand relationship of walking.
J. Appl. Physiol.
73
,
200
-206.
Mayhew, J. L. (
1977
). Oxygen cost and energy expenditure of running in trained runners.
Br. J. Sports Med.
11
,
116
-121.
McCann, D. J. and Williams, C. A. (
2002
). A dimensional paradigm for identifying the size-independent cost of walking.
Med. Sci. Sports Exerc.
34
,
1009
-1017.
Mckicken, D. F. and Daniels, J. T. (
1976
). Aerobic requirements and maximum aerobic power in treadmill and track running.
Med. Sci. Sports
8
,
14
-17.
Menier, D. R. and Pugh, L. G. (
1968
). The relation of oxygen intake and velocity of walking and running, in competition walkers.
J. Physiol.
197
,
717
-721.
Minetti, A. E., Capelli, C., Zamparo, P., di Prampero, P. E. and Saibene, F. (
1995
). Effects of stride frequency on mechanical power and energy expenditure of walking.
Med. Sci. Sports Exerc.
27
,
1194
-1202.
Minetti, A. E., Ardig, O. L., Reinach, E. and Saibene, F.(
1999
). The relationship between mechanical work and energy expenditure of locomotion in horses.
J. Exp. Biol.
202
,
2329
-2338.
Musch, T. I., Eklund, K. E., Hageman, K. S. and Poole, D. C.(
2004
). Altered regional blood flow response to submaximal exercise in older rats.
J. Appl. Physiol.
96
,
81
-88.
Ortega, J. D. and Farley, C. T. (
2005
). Minimizing center of mass vertical movement increases metabolic cost in walking.
J. Appl. Physiol.
99
,
2099
-2107.
Pearce, M. E., Cunningham, D. A., Donner, A. P., Rechnitzer, P. A., Fullerton, G. M. and Howard, J. H. (
1983
). Energy cost of treadmill and floor walking at self-selected paces.
Eur. J. Appl. Physiol. Occup. Physiol.
52
,
115
-119.
Poole, D. C., Gaesser, G. A., Hogan, M. C., Knight, D. R. and Wagner, P. D. (
1992
). Pulmonary and leg VO2 during submaximal exercise: implications for muscular efficiency.
J. Appl. Physiol.
72
,
805
-810.
Pugh, L. G. (
1971
). The influence of wind resistance in running and walking and the mechanical efficiency of work against horizontal or vertical forces.
J. Physiol. Lond.
213
,
255
-276.
Ralston, H. J. (
1958
). Energy-speed relation and optimal speed during level walking.
Int. Z. Angew. Physiol.
17
,
277
-283.
Roberts, T. J., Kram, R., Weyand, P. G. and Taylor, C. R.(
1998
). Energetics of bipedal running. I. Metabolic cost of generating force.
J. Exp. Biol.
201
,
2745
-2751.
Rodman, P. S. and McHenry, H. M. (
1980
). Bioenergetics and the origin of human bipedalism.
Am. J. Phys. Anthropol.
52
,
103
-106.
Rubenson, J., Heliams, D. B., Lloyd, D. G. and Fournier, P. A. (
2004
). Gait selection in the ostrich: mechanical and metabolic characteristics of walking and running with and without an aerial phase.
Proc. R. Soc. Lond. B Biol. Sci.
271
,
1091
-1099.
Saunders, P. U., Pyne, D. B., Telford, R. D. and Hawley, J. A. (
2004a
). Reliability and variability of running economy in elite distance runners.
Med. Sci. Sports Exerc.
36
,
1972
-1976.
Saunders, P. U., Telford, R. D., Pyne, D. B., Cunningham, R. B.,Gore, C. J., Hahn, A. G. and Hawley, J. A. (
2004b
). Improved running economy in elite runners after 20 days of simulated moderate-altitude exposure.
J. Appl. Physiol.
96
,
931
-937.
Schmidt-Nielsen, K. (
1975
). Scaling in biology:the consequences of size.
J. Exp. Zool.
194
,
287
-307.
Sheppard, R. J. (
1969
). A nomogram to calculate the oxygen-cost of running at slow speeds.
J. Sports Med. Phys. Fitness
9
,
10
-16.
Steudel, K. (
1996
). Limb morphology, bipedal gait, and the energetics of hominid locomotion.
Am. J. Phys. Anthropol.
99
,
345
-355.
Steudel-Numbers, K. L. (
2001
). Role of locomotor economy in the origin of bipedal posture and gait.
Am. J. Phys. Anthropol.
116
,
171
-173.
Steudel-Numbers, K. L. (
2003
). The energetic cost of locomotion: humans and primates compared to generalized endotherms.
J. Hum. Evol.
44
,
255
-262.
Taylor, C. R. (
1994
). Relating mechanics and energetics during exercise.
Adv. Vet. Sci. Comp. Med. A
38
,
181
-215.
Taylor, C. R., Schmidt-Nielsen, K. and Raab, J. L.(
1970
). Scaling of energetic cost of running to body size in mammals.
Am. J. Physiol.
219
,
1104
-1107.
Taylor, C. R., Dmi'el, R., Fedak, M. and Schmidt-Nielsen, K.(
1971a
). Effect of hyperthermia on heat balance during running in the African hunting dog.
Am. J. Physiol.
220
,
823
-827.
Taylor, C. R., Dmi'el, R., Fedak, M. and Schmidt-Nielsen, K.(
1971b
). Energetic cost of running and heat balance in a large bird, the rhea.
Am. J. Physiol.
221
,
597
-601.
Taylor, C. R., Heglund, N. C. and Maloiy, G. M.(
1982
). Energetics and mechanics of terrestrial locomotion. I. Metabolic energy consumption as a function of speed and body size in birds and mammals.
J. Exp. Biol.
97
,
1
-21.
van der Walt, W. H. and Wyndham, C. H. (
1973
). An equation for prediction of energy expenditure of walking and running.
J. Appl. Physiol.
34
,
559
-563.
Waters, R. L. and Mulroy, S. (
1999
). The energy expenditure of normal and pathologic gait.
Gait Posture
9
,
207
-231.
Waters, R. L., Hislop, H. J., Perry, J., Thomas, L. and Campbell, J. (
1983
). Comparative cost of walking in young and old adults.
J. Orthop. Res.
1
,
73
-76.
Waters, R. L., Lunsford, B. R., Perry, J. and Byrd, R.(
1988
). Energy-speed relationship of walking: standard tables.
J. Orthop. Res.
6
,
215
-222.
Webster, K. N. and Dawson, T. J. (
2003
). Locomotion energetics and gait characteristics of a rat-kangaroo, Bettongia penicillata, have some kangaroo-like features.
J. Comp. Physiol. B.
173
,
549
-557.
White, R. G. and Yousef, M. K. (
1978
). Energy expenditure in reindeer walking on roads and on tundra.
Can. J. Zool.
56
,
215
-223.
Williams, T. M. (
1983
). Locomotion in the North American mink, a semi-aquatic mammal: the effect of an elongated body on running energetics and gait patterns.
J. Exp. Biol.
105
,
283
-295.
Williams, T. M., Ben-David, M., Noren, S., Rutishauser, M.,McDonald, K. and Heyward, W. (
2002
). Running energetics of North American river otter: do short legs necessarily reduce efficiency on land?
Comp. Biochem. Physiol. A
113
,
203
-213.
Wright, S. and Weyand, P. G. (
2001
). The application of ground force explains the energetic cost of running backward and forward.
J. Exp. Biol.
204
,
1805
-1815.
Wunder, B. A. (
1970
). Energetics of running activity in Merriam's chipmunk, Eutamias merriami.
Comp. Biochem. Physiol.
33
,
821
-836.
Wunder, B. A. and Morrison, P. R. (
1974
). Red squirrel metabolism during incline running.
Comp. Biochem. Physiol.
48A
,
153
-161.
Yousef, M. K., Webster, M. E. D. and Yousef, O. M.(
1989
). Energy cost of walking in camels, Camelus dromedarius.
Physiol. Zool.
62
,
1080
-1088.