SUMMARY
Body mass is the primary determinant of an animal’s energy requirements. At their optimum walking speed, large animals have lower massspecific energy requirements for locomotion than small ones. In animals ranging in size from 0.8 g (roach) to 260 kg (zebu steer), the minimum cost of transport (COT_{min}) decreases with increasing body size roughly as COT_{min}∝body mass (M_{b})^{–0.316±0.023} (95% CI). Typically, the variation of COT_{min} with body mass is weaker at the intraspecific level as a result of physiological and geometric similarity within closely related species. The interspecific relationship estimates that an adult elephant, with twice the body mass of a midsized elephant, should be able to move its body approximately 23% cheaper than the smaller elephant. We sought to determine whether adult Asian and subadult African elephants follow a single quasiintraspecific relationship, and extend the interspecific relationship between COT_{min} and body mass to 12fold larger animals. Physiological and possibly geometric similarity between adult Asian elephants and subadult African elephants caused body mass to have a no effect on COT_{min} (COT_{min}∝M_{b}^{0.007±0.455}). The COT_{min} in elephants occurred at walking speeds between 1.3 and ∼1.5 m s^{–1}, and at Froude numbers between 0.10 and 0.24. The addition of adult Asian elephants to the interspecific relationship resulted in COT_{min}∝M ^{–0.277±0.046}_{b}. The quasiintraspecific relationship between body mass and COT_{min} among elephants caused the interspecific relationship to underestimate COT_{min} in larger elephants.
INTRODUCTION
Body mass is the primary determining factor of an animal’s total energy requirements (Calder, 1984; SchmidtNielsen, 1984; West and Brown, 2005; McNab, 2008). Large animals use less energy per kilogram body mass for locomotion than small animals. African (Loxodonta africana) and Asian elephants (Elephas maximus) represent the upper limit of body mass in extant terrestrial mammals, and large bulls can weigh up to 7500 kg (Nowak, 1999). Although physiological measurements on elephants are technically challenging, experiments using welltrained captive elephants allow modeling of the biomechanical and energetic characteristics of locomotion in the largest terrestrial mammals (Alexander et al., 1979; Langman et al., 1995; Hutchinson et al., 2003; Hutchinson et al., 2006; Ren and Hutchinson, 2008; Ren et al., 2010; Genin et al., 2010).
The massspecific total cost of transport (COT_{tot}; J kg^{–1} m^{–1}) is the amount of energy required to move 1 kg of body mass over 1 m. Animals, including elephants, prefer to walk at a speed near the midrange within a walking gait, where COT_{tot} is minimized (Pennycuik, 1975; Hoyt and Taylor, 1981; Taylor et al., 1982; Alexander, 1989; Full and Tu, 1991; Griffin et al., 2004; Rubenson et al., 2007; Maloiy et al., 2009). Because the minimum total cost of transport (COT_{min}) provides a biologically meaningful parameter for comparison, Taylor et al. (Taylor et al., 1982) used data from approximately 90 species of mammals ranging in size from 7 g (pygmy mouse) to 260 kg (zebu steer) to develop an interspecific allometric equation that describes the decrease in COT_{min} with increased body mass: where M_{b} is body mass (kg) [values shown are presented ±95% confidence intervals (CIs)]. To extend the range of data towards the lower limits of body mass, Full and Tu (Full and Tu, 1991) added reptiles, crustaceans, myriapods and insects with body mass as low as 0.8 g and obtained approximately the same equation as that reported by Taylor et al. (Taylor et al., 1982), COT_{min}=10.8M ^{–0.32}_{b}. To extend the range of data towards the upper limits of body mass, Langman et al. (Langman et al., 1995) added subadult African elephants, with an average body mass six times that of the largest animal used in Taylor et al. (Taylor et al., 1982). The COT_{min} of young African elephants were within the 95% CIs of Eqn 1. The application of Eqn 1 to adult Asian elephants, twice the size of the elephants reported by Langman et al. (Langman et al., 1995), estimates that COT_{min} in larger elephants should be reduced by approximately 23% when compared with COT_{min} in subadult African elephants.
An analysis of intraspecific variability is complementary to interspecific analyses (Bennett, 1987). Because of geometric and physiological similarity, body mass does not have the same effect on COT_{min} at the intraspecific level, or between closely related species, as it does at the interspecific level. In geometrically similar species, juveniles have the same relative dimensions as adults, just on a smaller scale. As a result, muscle and skeletal morphology of small and large individuals are similar. Both equines and camels show intraspecific geometric similarity. The slope of the intraspecific relationship between COT_{min} and body mass is nearly flat (≈M ^{0}_{b}) in both horses from 90 to 720 kg (Griffin et al., 2004) and camels from 240 to 580 kg (Yousef et al., 1989; Maloiy et al., 2009) compared with the interspecific relationship M ^{–0.316}_{b} (Eqn 1). African and Asian elephants, along with extinct mammoths (Mammuthus), comprise the family Elephantidae and share common ancestry (Haynes, 1991; Krause et al., 2006). All elephants are graviportal species, i.e. species with columnlike limbs and a bone structure that distributes their enormous body mass across a sizeable foot surface (Gray, 1968; Coombs, 1978; Yates and Kitching, 2003). However, subtle differences in limb geometry exist between African and Asian elephants (Kokshenev and Christiansen, 2010). Subadult African and adult Asian elephants might be geometrically similar enough that they follow a quasiintraspecific relationship, where the decrease in COT_{min} with increasing body mass is less than M ^{–0.316}_{b}.
In this study, we first test the hypothesis that adult Asian elephants and subadult African elephants are physiologically similar and geometrically similar enough, as reported in horses and camels, that larger body mass will not bring about a reduction in COT_{min}. If elephants within a 2.5fold range of body mass are physiologically and geometrically similar, then the slope of COT_{min} versus body mass will approach M ^{0}_{b}. Second, we discuss the effect that the addition of elephants, with 12 times the body mass of the largest animal used by Taylor et al. (Taylor et al., 1982), has on the interspecific relationship between COT_{min} and body mass. If the intraspecific relationship applies to elephants, then COT_{min} measured in increasingly larger elephants will show sequentially greater deviation away from COT_{min} estimated using the interspecific relationship of M ^{–0.316}_{b}. Therefore, we have measured the COT_{min} in adult Asian elephants and combined these results with those for smaller African elephants reported by Langman et al. (Langman et al., 1995).
MATERIALS AND METHODS
Elephants
Two adult female Asian elephants Elephas maximus Linnaeus 1758 (Panya and Jean; Table 1) housed at the Audubon Zoo in New Orleans, LA, USA, were used for all of the metabolic measurements. Both elephants were very tractable and well trained by their keepers. Their feeding schedule was unaltered and water was available ad libitum except during the exercise trials. All methods were approved by the Audubon Zoo Institutional Animal Care and Use Committee.
Experimental procedure
Oxygen consumption was measured using the techniques reported by Langman et al. (Langman et al., 1995) to quantify metabolic rates at rest and during exercise from African elephants. The elephants were trained, for 1 week prior to measurements, to wear a loosefitting mask that enclosed both the trunk and mouth for opensystem oxygen consumption measurements. The elephants were fitted with the mask, and metabolic measurements then made while the elephants stood quietly or walked up to three laps around the level 0.5 km oval track in the interior of the zoo (Fig. 1). The mask was connected to a 1 hp industrial blower (Dayton, Niles, IL, USA) mounted on a motorized golf cart that was fitted with a bicycle wheel equipped with a calibrated electronic speedometer to record speed. The blower was previously calibrated in laboratory conditions to meter air flow through the mask at a rate of 108 l s^{–1}, a flow rate that ensured the elephants’ exhaled air was drawn through the mask. The elephants walked the first lap at a slow pace and sequentially increased speed on the following laps. A small sample of the air flow exiting the mask was collected in a 200 l Douglas bag (Harvard Apparatus, Holliston, MA, USA) over a 5 min period in the later stages of walks. The sample was analyzed for oxygen concentration with a paramagnetic oxygen analyzer (Taylor Servomex OA272, Woburn, MA, USA). The entire system was calibrated by metering nitrogen into the mask (Fedak et al., 1981) and the accuracy was better than ±2%.
Data analyses
Massspecific total energy expenditure (EE_{tot}; W kg^{–1}) is the amount of energy expended per kilogram body mass for both the postural cost of standing, i.e. standing metabolic rate, and the energy expended to move the body’s center of mass both horizontally and vertically during locomotion (SchmidtNielsen, 1972). The EE_{tot} in the elephants was calculated from the rate of oxygen consumption recorded during exercise and applying an energetic equivalent of 20.1 J to 1 ml O_{2} consumed.
Massspecific net energy expenditure (EE_{net}) is the amount of energy required for locomotion above that required for the postural cost of standing (SchmidtNielsen, 1972). The EE_{net} was calculated by subtracting resting energy expenditure (Table 1) from EE_{tot} recorded during exercise. It was not always possible to make resting measurements prior to each exercise trial or make an equal number of trials at each walking speed. Therefore, the mean resting energy expenditure recorded for individual elephants was used to calculate EE_{net}.
Massspecific COT_{tot} was calculated by dividing the EE_{tot} measured during exercise by the speed of locomotion (m s^{–1}). The net cost of transport (COT_{net}) estimates the amount of energy required to move 1 kg of body mass over 1 m during locomotion above that required for standing quietly (SchmidtNielsen, 1972). COT_{net} was calculated by subtracting the average resting energy expenditure of individual elephants from EE_{tot} prior to dividing by the speed of locomotion.
Energetic similarity between adult Asian and subadult African elephants was determined by plotting COT_{tot} versus Froude number: a dimensionless measure of speed calculated by dividing the squared forward velocity of locomotion (v_{f}; m s^{–1}) by gravitational acceleration (g; 9.8 m s^{–2}) and hip height (h_{hip}; m) (Alexander and Jayes, 1983). The COT_{min} for individual elephants was estimated from secondorder polynomial equations that describe the relationship between COT_{tot} and Froude number. The estimated COT_{min} was compared with minimum recorded COT_{min} (Table 2). However, because there was no clearly distinguishable COT_{min} in adult Asian elephant, we calculated the mean (±s.d.) COT_{min} by averaging the COT_{tot} measured over the range of Froude numbers that minimized cost in individual elephants (Table 3). The calculated mean COT_{min} was used to develop intraspecific and interspecific allometric relationships between COT_{min} and body mass.
Studies of animal energetics are usually conducted by subjecting animals to evenly spaced increases in treadmill speed (Hoyt and Taylor, 1981; Taylor et al., 1982; Full and Tu, 1991; Griffin et al., 2004; Rubenson et al., 2007; Maloiy et al., 2009). These conditions allow for equal sample sizes of repeated trials at each tread speed, i.e. treatment groups. However, treadmills suitable for elephants are rare, and so our data and those reported by Langman et al. (Langman et al., 1995) were obtained by walking zoo elephants on an outdoor track. The resulting small sample size and unpaired continuous data reduced the power of our statistical analyses (Sokal and Rohlf, 1995). KaleidaGraph 4.03 (Synergy Software, Reading, PA, USA) was used for graphing and statistical analyses.
RESULTS
Energy expenditure
The results of our measurements of resting energy expenditure in Asian elephants (Table 1) were similar to those reported by Benedict (Benedict, 1936). During locomotion at speeds ranging from 0.13 to 2.2 m s^{–1}, the EE_{tot} for the larger Asian elephant, Panya, generally was less than that measured for the smaller elephant, Jean (Fig. 2). At the fastest walking speed, EE_{tot} increased approximately 4.5fold over resting measurements. Over approximately the same range of walking speeds, from 0.4 to 2.5 m s^{–1}, the EE_{tot} in subadult African elephants reported by Langman et al. (Langman et al., 1995) was comparable to EE_{tot} measured in Asian elephants (Fig. 2). Similarly, EE_{net} (Fig. 2) tended to be lower in the larger elephant. At the fastest walking speed of 2.2 m s^{–1}, EE_{net} increased approximately 11fold over the slowest walking speed of 0.13 m s^{–1}. The EE_{net} in Asian elephants was comparable to EE_{net} in subadult African elephants reported by Langman et al. (Langman et al., 1995).
Cost of transport
Over the range of walking speeds tested, the COT_{tot} was generally lower in the larger Asian elephant, Panya (Fig. 3). COT_{min} values, calculated from the polynomial equation describing the relationship between COT_{tot} and walking speed, in adult Asian elephants (Fig. 3) were less than recorded COT_{min}. Similarly, the larger elephant recorded lower COT_{net}. The COT_{net} recorded in Asian elephants in the present study was comparable to COT_{net} in African elephants reported by Langman et al. (Langman et al., 1995). The COT_{min} calculated from the polynomial equation describing the relationship between COT_{net} and walking speed of 0.80 J kg^{–1} m^{–1} recorded in Asian elephants (Fig. 3) was similar to the COT_{min} of 0.78 J kg^{–1} m^{–1} reported in African elephants (Langman et al., 1995).
DISCUSSION
Optimum walking speed in Asian elephants
Elephants in nature generally choose to walk at a slow pace and only use fast locomotion when disturbed (Moss, 1988; DouglasHamilton et al., 2005; Joshi, 2009). At slow walking speeds, kinematic and kinetic variables that define the walking gait in African and Asian elephants are quite similar (Hutchinson et al., 2006; Ren and Hutchinson, 2008; Genin et al., 2010). Analyses of COT_{tot} and COT_{net} using polynomial equations (Fig. 3) could not characterize optimum walking speed in Asian elephants because of the similarity in COT_{min} measurements recorded at speeds between 0.5 and 2.2 m s^{–1}. However, recorded and estimated minimum total cost of transport (Table 2, Fig. 4) occurred at speeds and Froude numbers similar to the biomechanical optimum walking speed of approximately 1.3 m s^{–1} and a Froude number of 0.09 reported by Ren and Hutchinson (Ren and Hutchinson, 2008) and Genin et al. (Genin et al., 2010).
The minimum walking speed reported here of 0.13 m s^{–1} was the result of the Asian elephants’ willingness to walk at an extremely slow pace, in comparison to the reluctance of young African elephants to walk slower than 0.44 m s^{–1} (Langman et al., 1995). Therefore, the large difference in COT_{tot} between slowwalking Asian and African elephants (Fig. 3) is the result of different sampling intervals and not physiological differences between species. The maximum walking speed of Asian and African elephants, 2.2 and 2.5 m s^{–1}, respectively, was limited by the maximum speed of the golf cart when heavily loaded with respirometry equipment (Fig. 1), not by the ability of the elephants to walk faster.
Indeed, elephants are capable of fast locomotion; they have a maximum recorded walking speed of 6.8 m s^{–1} (Hutchinson et al., 2003). However, fast locomotion comes with a high energetic cost (Fig. 2). At fast speeds of locomotion, nearly all animals switch from the pendulumlike mechanism characteristic of the walking gait to a more elastic mechanism characteristic of a running gait (Alexander, 1991). Elephants differ somewhat from this pattern. Elephants exhibit substantial limb compliance during the walking gait (Ren et al., 2010), which defies the characterization of elephants as stifflegged graviportal species (Gray, 1968; Coombs, 1978; Yates and Kitching, 2003). In elephants, limb compliance increases with locomotion speed, which results in increased joint flexion and dampening of ground forces on the limbs (Ren et al., 2010). However, as joint flexion increases a greater muscle volume is required to support the great body mass of elephants (Ren et al., 2010). In response, elephants may experience a linear increase in energy expenditure at walking speeds greater than the maximum we report in the present study. Although we acknowledge the dangers of extrapolation, using the secondorder polynomial equation relating EE_{tot} to walking speed (R^{2}=0.88; Fig. 2), we estimate that it would require a 26fold increase EE_{tot} above rest (Table 1) for the Asian elephants reported here to walk at 6.8 m s^{–1}. The estimated increase in EE_{tot} in fastwalking elephants is comparable to nearmaximum increases in energy expenditure recorded in donkeys and camels of 22 and 32fold, respectively (Evans et al., 1994; Mueller et al., 1994).
Physiological similarity between adult Asian and subadult African elephants
African and Asian elephants ranging in body mass from 1435 to 3545 kg are physiologically similar and geometrically similar enough that massspecific COT_{min} among individual elephants is similar (Table 3, Fig. 4). However, it should be noted that the wholeanimal COT_{min} (J m^{–1}), the ecologically relevant level of analyses, indicates that the two larger Asian elephants would require 1.6 to 2.4fold more energy for locomotion than the three smaller African elephants (Table 3). Some populations of both African and Asian elephants engage in seasonal migrations (Guy, 1976; Sukumar, 1989; Tchamba, 1993; Thouless, 1995; Joshi, 2009). As a result of variations in wholeanimal COT_{tot} between adult and subadult elephants, migration might result in differential intraspecific energetic challenges, a topic worthy of further investigation.
The recorded mean (±s.d.) COT_{min} in all elephants occurred over a narrow range of Froude numbers (Table 3, Fig. 4). The equation describing the quasiintraspecific relationship between COT_{min} and body mass within elephants is COT_{min}=1.44±0.07M ^{0.007±0.455}_{b} (R^{2}=0.01; Fig. 5). Within elephants, the COT_{min} is not a function of M ^{–0.316}_{b}, as is characteristic of the interspecific relationship (Eqn 1) reported by Taylor et al. (Taylor et al., 1982), but is a function of ≈M ^{0}_{b}, characteristic of the intraspecific relationship reported in horses and camels (Yousef et al., 1989; Griffin et al., 2004; Maloiy et al., 2009).
Do we really need a bigger elephant?
Adult Asian and subadult African elephants are physiologically similar and geometrically similar enough to influence the interspecific relationship between COT_{min} and body mass. The addition of Asian elephants, with a 12fold increase in body mass over the largest animal used by Taylor et al. (Taylor et al., 1982), produced an allometric relationship for mammals ranging in size from 7 g to 3545 kg (COT_{min}=11.9±3.30M ^{–0.277±0.046}_{b}; Fig. 5).
The mean COT_{min} in two adult Asian elephants (Table 3) was approximately the same as the mean COT_{min} in three subadult African elephants reported by Langman et al. (Langman et al., 1995), not 23% lower as estimated by Eqn 1. The difference between COT_{min} measured in elephants and that predicted by Eqn 1 was due to the influence of physiological similarity within elephants. The mean COT_{min} in individual elephants (Table 3) ranged from 27 to 88% above that predicted by Eqn 1. If the intraspecific relationship is extrapolated to even larger elephants, physiological similarity will cause greater divergence from the Taylor et al. (Taylor et al., 1982) equation. It is unlikely that the COT_{min} in a larger elephant (with a body mass of 7500 kg) would be significantly lower than the values we report here. Based on the slopes of the relationship between COT_{min} and body mass within elephants, i.e. M ^{0.007}_{b}, and that of the interspecific relationship, i.e. M ^{–0.316}_{b}, the COT_{min} of large bull elephants will be approximately 138% above that predicted by Eqn 1.
ACKNOWLEDGEMENTS
This manuscript is dedicated in memoriam to C. R. ‘Dick’ Taylor, who continues to contribute to our increased understanding of animal physiology. The authors thank Roger Ilse, the curator of mammals, and Dan Maloney, the assistant curator of the Asian domain at Audubon Zoo. We greatly appreciate the help of the Audubon Zoo elephant staff – James Holsten, Eiler McGuin and Jimmy Pitts – who made this study possible. The authors thank George S. Bakken for his thoughtful suggestions on an earlier version of this manuscript. We also thank the editor and two anonymous reviewers for their helpful comments and criticisms.
FOOTNOTES

FUNDING
This research received no specific grant from any funding agency in the public, commercial, or notforprofit sectors.
LIST OF SYMBOLS
 COT_{min}
 Massspecific minimum cost of transport (J kg^{–1} m^{–1})
 COT_{net}
 Massspecific net cost of transport (J kg^{–1} m^{–1})
 COT_{tot}
 Massspecific total cost of transport (J kg^{–1} m^{–1})
 EE_{net}
 Massspecific net energy expenditure (W kg^{–1})
 EE_{tot}
 Massspecific energy expenditure (W kg^{–1})
 Fr
 Froude number (dimensionless speed)
 g
 Gravitational acceleration (9.8 m s^{–2})
 M_{b}
 Body mass (kg)
 v_{f}
 Walking speed (m s^{–1})
 © 2012.