SUMMARY
Body mass is the primary determinant of an animal’s energy requirements. At their optimum walking speed, large animals have lower mass-specific 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 (COTmin) decreases with increasing body size roughly as COTmin∝body mass (Mb)–0.316±0.023 (95% CI). Typically, the variation of COTmin 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 mid-sized elephant, should be able to move its body approximately 23% cheaper than the smaller elephant. We sought to determine whether adult Asian and sub-adult African elephants follow a single quasi-intraspecific relationship, and extend the interspecific relationship between COTmin and body mass to 12-fold larger animals. Physiological and possibly geometric similarity between adult Asian elephants and sub-adult African elephants caused body mass to have a no effect on COTmin (COTmin∝Mb0.007±0.455). The COTmin 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 COTmin∝M –0.277±0.046b. The quasi-intraspecific relationship between body mass and COTmin among elephants caused the interspecific relationship to underestimate COTmin in larger elephants.
INTRODUCTION
Body mass is the primary determining factor of an animal’s total energy requirements (Calder, 1984; Schmidt-Nielsen, 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 well-trained 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 mass-specific total cost of transport (COTtot; 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 mid-range within a walking gait, where COTtot 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 (COTmin) 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 COTmin with increased body mass:
where Mb 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), COTmin=10.8M –0.32b. To extend the range of data towards the upper limits of body mass, Langman et al. (Langman et al., 1995) added sub-adult African elephants, with an average body mass six times that of the largest animal used in Taylor et al. (Taylor et al., 1982). The COTmin 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 COTmin in larger elephants should be reduced by approximately 23% when compared with COTmin in sub-adult 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 COTmin 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 COTmin and body mass is nearly flat (≈M 0b) 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 –0.316b (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 column-like 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). Sub-adult African and adult Asian elephants might be geometrically similar enough that they follow a quasi-intraspecific relationship, where the decrease in COTmin with increasing body mass is less than M –0.316b.
In this study, we first test the hypothesis that adult Asian elephants and sub-adult 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 COTmin. If elephants within a 2.5-fold range of body mass are physiologically and geometrically similar, then the slope of COTmin versus body mass will approach M 0b. 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 COTmin and body mass. If the intraspecific relationship applies to elephants, then COTmin measured in increasingly larger elephants will show sequentially greater deviation away from COTmin estimated using the interspecific relationship of M –0.316b. Therefore, we have measured the COTmin 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 loose-fitting mask that enclosed both the trunk and mouth for open-system 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%.
Characteristics and mean (±s.d.) resting mass-specific energy expenditure in two Asian elephants
Open-system measurement of resting oxygen consumption in a female Asian elephant prior to exercise at Audubon Zoo, New Orleans, LA, USA.
Data analyses
Mass-specific total energy expenditure (EEtot; 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 (Schmidt-Nielsen, 1972). The EEtot 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 O2 consumed.
Mass-specific net energy expenditure (EEnet) is the amount of energy required for locomotion above that required for the postural cost of standing (Schmidt-Nielsen, 1972). The EEnet was calculated by subtracting resting energy expenditure (Table 1) from EEtot 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 EEnet.
Minimum mass-specific total cost of transport (COTmin) recorded in elephants, the Froude number (Fr) at which COTmin occurred, second-order polynomial equations and estimated COTmin in three African and two Asian elephants
Range of Froude numbers (Fr), and mean (±s.d.) walking speed, mass-specific minimum cost of transport (COTmin), and whole-animal COTmin recorded in three African and two Asian elephants
Mass-specific COTtot was calculated by dividing the EEtot measured during exercise by the speed of locomotion (m s–1). The net cost of transport (COTnet) estimates the amount of energy required to move 1 kg of body mass over 1 m during locomotion above that required for standing quietly (Schmidt-Nielsen, 1972). COTnet was calculated by subtracting the average resting energy expenditure of individual elephants from EEtot prior to dividing by the speed of locomotion.
Energetic similarity between adult Asian and sub-adult African elephants was determined by plotting COTtot versus Froude number:
a dimensionless measure of speed calculated by dividing the squared forward velocity of locomotion (vf; m s–1) by gravitational acceleration (g; 9.8 m s–2) and hip height (hhip; m) (Alexander and Jayes, 1983). The COTmin for individual elephants was estimated from second-order polynomial equations that describe the relationship between COTtot and Froude number. The estimated COTmin was compared with minimum recorded COTmin (Table 2). However, because there was no clearly distinguishable COTmin in adult Asian elephant, we calculated the mean (±s.d.) COTmin by averaging the COTtot measured over the range of Froude numbers that minimized cost in individual elephants (Table 3). The calculated mean COTmin was used to develop intraspecific and interspecific allometric relationships between COTmin 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 EEtot for the larger Asian elephant, Panya, generally was less than that measured for the smaller elephant, Jean (Fig. 2). At the fastest walking speed, EEtot increased approximately 4.5-fold over resting measurements. Over approximately the same range of walking speeds, from 0.4 to 2.5 m s–1, the EEtot in sub-adult African elephants reported by Langman et al. (Langman et al., 1995) was comparable to EEtot measured in Asian elephants (Fig. 2). Similarly, EEnet (Fig. 2) tended to be lower in the larger elephant. At the fastest walking speed of 2.2 m s–1, EEnet increased approximately 11-fold over the slowest walking speed of 0.13 m s–1. The EEnet in Asian elephants was comparable to EEnet in sub-adult African elephants reported by Langman et al. (Langman et al., 1995).
Mass-specific total (solid symbols) and net energy expenditure (open symbols) (EEtot and EEnet; W kg–1) in two adult Asian elephants (Panya, red circles; Jean, blue squares) at walking speeds ranging from 0.13 to 2.2 m s–1. The equation describing the curvilinear increase in EEtot with walking speed is EEtot=0.35v 2f+0.42vf+0.75, where vf is walking speed (m s–1) (R2=0.88). The equation describing the curvilinear increase in EEnet with walking speed is EEnet=0.38v 2f+0.32vf+0.08 (R2=0.75). The mean EEtot and EEnet in three sub-adult African elephants (dashed lines) walking at speeds ranging from 0.44 to 2.5 m s–1 reported by Langman et al. (Langman et al., 1995) are presented for comparison.
Mass-specific total (solid symbols) and net cost of transport (open symbols) (COTtot and COTnet; J kg–1 m–1) in two Asian elephants (Panya, red circles; Jean, blue squares) at walking speeds from 0.13 to 2.2 m s–1. The equation describing the curvilinear relationship between COTtot and walking speed is COTtot=2.8v 2f–8.7vf+7.8, where vf is walking speed (m s–1) (R2=0.85). Note that the curve for Asian elephants is strongly affected by the high leverage of the data points at the exceptionally slow walking speed of 0.13 m s–1, and thus the walking speed for minimum COT (COTmin) is not clearly defined. The equation describing the curvilinear relationship between COTnet and body mass is COTnet=0.64v 2f–1.6vf+1.8 (R2=0.40). The mean COTtot and COTnet in three sub-adult African elephants (dashed lines) walking at speeds ranging from 0.44 to 2.5 m s–1 reported by Langman et al. (Langman et al., 1995) are presented for comparison.
Cost of transport
Over the range of walking speeds tested, the COTtot was generally lower in the larger Asian elephant, Panya (Fig. 3). COTmin values, calculated from the polynomial equation describing the relationship between COTtot and walking speed, in adult Asian elephants (Fig. 3) were less than recorded COTmin. Similarly, the larger elephant recorded lower COTnet. The COTnet recorded in Asian elephants in the present study was comparable to COTnet in African elephants reported by Langman et al. (Langman et al., 1995). The COTmin calculated from the polynomial equation describing the relationship between COTnet and walking speed of 0.80 J kg–1 m–1 recorded in Asian elephants (Fig. 3) was similar to the COTmin 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; Douglas-Hamilton 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 COTtot and COTnet using polynomial equations (Fig. 3) could not characterize optimum walking speed in Asian elephants because of the similarity in COTmin 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).
Second-order polynomial equations (Table 2) describing the quasi-intraspecific relationships between estimated total cost of transport (COTtot) and Froude number in two adult Asian elephants (Panya, red solid line; Jean, blue solid line) and three sub-adult African elephants (Kelly, dotted line; Tara, short dashed line; Dottie, long dashed line). The estimated minimum cost of transport occurred over a narrow range of Froude numbers, from 0.1 to 2.4.
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 COTtot between slow-walking 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 pendulum-like 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 stiff-legged 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 second-order polynomial equation relating EEtot to walking speed (R2=0.88; Fig. 2), we estimate that it would require a 26-fold increase EEtot above rest (Table 1) for the Asian elephants reported here to walk at 6.8 m s–1. The estimated increase in EEtot in fast-walking elephants is comparable to near-maximum increases in energy expenditure recorded in donkeys and camels of 22- and 32-fold, respectively (Evans et al., 1994; Mueller et al., 1994).
Interspecific relationship between minimum cost of transport (COTmin;, J kg–1 m–1) and body mass (Mb; kg) in terrestrial animals ranging in size from 0.8 g to 3545 kg. The relationship between COTmin and body mass in reptiles, amphibians, crustaceans, myriapods and insects ranging in size from 0.8 g to approximately 1 kg is represented by the allometric equation COTmin=10.8M –0.32b (dotted line) (Full and Tu, 1991). The relationship between COTmin and body mass in mammals ranging in size from 7 g to 260 kg is represented by the allometric equation COTmin=10.7±0.663M –0.316±0.023b (95% CI) (solid line) (Taylor et al., 1982). The addition of adult Asian elephants and sub-adult African elephants (blue circles) to data from Taylor et al. (Taylor et al., 1982) produced the equation COTmin=11.9±3.30M –0.277±0.046b (long dashed line). The quasi-intraspecific relationship within elephants is described by the allometric equation COTmin=1.43±0.07M 0.007±0.455b (short dashed line). We estimate the COTmin in a large (7500 kg) elephant (red diamond) to be approximately 1.52 J kg–1 m–1.
Physiological similarity between adult Asian and sub-adult African elephants
African and Asian elephants ranging in body mass from 1435 to 3545 kg are physiologically similar and geometrically similar enough that mass-specific COTmin among individual elephants is similar (Table 3, Fig. 4). However, it should be noted that the whole-animal COTmin (J m–1), the ecologically relevant level of analyses, indicates that the two larger Asian elephants would require 1.6- to 2.4-fold 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 whole-animal COTtot between adult and sub-adult elephants, migration might result in differential intraspecific energetic challenges, a topic worthy of further investigation.
The recorded mean (±s.d.) COTmin in all elephants occurred over a narrow range of Froude numbers (Table 3, Fig. 4). The equation describing the quasi-intraspecific relationship between COTmin and body mass within elephants is COTmin=1.44±0.07M 0.007±0.455b (R2=0.01; Fig. 5). Within elephants, the COTmin is not a function of M –0.316b, as is characteristic of the interspecific relationship (Eqn 1) reported by Taylor et al. (Taylor et al., 1982), but is a function of ≈M 0b, 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 sub-adult African elephants are physiologically similar and geometrically similar enough to influence the interspecific relationship between COTmin and body mass. The addition of Asian elephants, with a 12-fold 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 (COTmin=11.9±3.30M –0.277±0.046b; Fig. 5).
The mean COTmin in two adult Asian elephants (Table 3) was approximately the same as the mean COTmin in three sub-adult African elephants reported by Langman et al. (Langman et al., 1995), not 23% lower as estimated by Eqn 1. The difference between COTmin measured in elephants and that predicted by Eqn 1 was due to the influence of physiological similarity within elephants. The mean COTmin 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 COTmin 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 COTmin and body mass within elephants, i.e. M 0.007b, and that of the interspecific relationship, i.e. M –0.316b, the COTmin 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
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FUNDING
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
LIST OF SYMBOLS
- COTmin
- Mass-specific minimum cost of transport (J kg–1 m–1)
- COTnet
- Mass-specific net cost of transport (J kg–1 m–1)
- COTtot
- Mass-specific total cost of transport (J kg–1 m–1)
- EEnet
- Mass-specific net energy expenditure (W kg–1)
- EEtot
- Mass-specific energy expenditure (W kg–1)
- Fr
- Froude number (dimensionless speed)
- g
- Gravitational acceleration (9.8 m s–2)
- Mb
- Body mass (kg)
- vf
- Walking speed (m s–1)
- © 2012.
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