Brief Communication: Stand and Shuffle: When Does itMake Energetic Sense?

Adam D. Sylvester1 and Patricia A. Kramer2*

1Department of Mechanical, Aerospace and Biomedical Engineering, The University of Tennessee,Knoxville, TN 379962Department of Anthropology, University of Washington, Seattle, WA 98195-3100

KEY WORDS mechanical modeling; bipedalism; locomotion

ABSTRACT Many reasons for the emergence of biped-alism have been proposed, including postural argumentswhich highlight that a sub-optimal form of bipedalism(‘‘shuffling’’) might have been used by protohominids tocover short distances between resources that require bi-pedal standing. Bipedal shuffling may have been employedbecause it avoids the cost of raising the trunk from thequadrupedal orientation, which we assume is the habituallocomotor stance of protohominids. To date, these posturalproposals have not been analytically assessed, a lack we rec-

tify herein. Our model seeks to specify a threshold distance,below which bipedal shuffling uses less energy than quad-rupedalism. Parameters for the model include the mechani-cal cost of transport, the ratio of bipedal to quadrupedalcost, and the cost associated with raising the trunk. Wefound that, using reasonable model parameters, open dis-tances of �9–16 m support the use of bipedal shuffling. Pro-tohominids may have used shuffling as an energeticallyeffective way to traverse between resource patches. Am JPhys Anthropol 135:484–488, 2008. VVC 2007 Wiley-Liss, Inc.

Of the many questions that vex paleoanthropologists,the origin of bipedalism is among the most persistent.Numerous theories have been proposed to account forour curious form of locomotion, although none hasreceived universal support. Several selective pressureshave been suggested, including: vigilance (Dart, 1925),provisioning (Lovejoy, 1981), behavioral displays (Tanner,1981; Jablonski and Chaplin, 1993), thermoregulation(Wheeler, 1991), locomotor decoupling (Sylvester, 2006),food transportation (Hewes, 1961), as well as increasedlocomotor efficiency (Rodman and McHenry, 1980; Foley,1992). Locomotor energetic arguments are particularlycompelling because of the patent advantage, to an indi-vidual’s survival and reproduction, of savings in meta-bolic energy. They are, however, problematic because oneassumes that, when switching to a new method of loco-motion, a period of sub-optimality precedes the develop-ment of effective movement. Evolution cannot act to pro-duce future gains, so a selective pressure other thanfuture energetic efficacy must be present. Postural argu-ments (Wrangham, 1980; Rose, 1991; Hunt, 1994) haveavoided this problem, however, by highlighting that atransitional form of bipedalism (‘‘shuffling’’) might haveevolved to cover short distances between resources thatrequire bipedal standing, because it avoids the cost ofraising the trunk after moving between those resourcepatches. The logic underlying the postural feedinghypotheses is both undeniable and appealing because, asHunt (1998) stresses, ‘‘[the] hominoid body is a food-get-ting machine’’ and, thus, there is strong selective pressureon hominoid anatomy to optimize food-getting behaviors.In order for the postural arguments to work, the

energy required to raise and lower the trunk mustexceed the additional energy required to travel a dis-tance bipedally instead of quadrupedally. Althoughbipedalism avoids the cost of raising the trunk, it islikely that protohominids required more energy to walkbipedally than to walk quadrupedally, thereby accruingadditional locomotor cost. Quadrupedalism, while less

costly for travel, requires the additional cost of raisingthe trunk. When the cost of raising the trunk exceedsthe additional cost of walking bipedally for a given dis-tance, spontaneous bipedalism should occur. Thus, thecritical elements of the postural feeding hypotheses arethe energetic costs of the locomotor forms (bipedalism vs.quadrupedalism) and the magnitude of the energy costassociated with raising the trunk. The purpose of thisproject is to model the mechanical energy associatedwith moving between resources that require bipedalstanding in an effort to predict the threshold distance ofprimate bipedalism.To develop our model, we first assumed that limiting

energetic expenditure is the ‘‘goal’’ of selection. Weacknowledge that locomotor form and anatomy are verylikely affected by selective pressures other than reducingenergy expenditure (Hunt, 1994; Pontzer and Wrang-ham, 2004). Bipedal shuffling hypotheses (Wrangham,1980; Rose, 1991; Hunt, 1994), however, identify anexplicit link between energetic optimization and bipedal-ism, and the popularity of these ideas provides the impe-tus for the model. Our goal is to develop a prediction forthe threshold distance to bipedalism, under the premiseof these hypotheses, which can be tested using primateobservational data.Given the energy optimization premise, if the proto-

hominid’s bipedalism used less (or equivalent) energyas other locomotor forms, then bipedalism arose to re-duce locomotor energy expenditure (e.g., Rodman and

*Correspondence to: Patricia A. Kramer, Department of Anthro-pology, University of Washington, Box 353100, Seattle, WA 98195-3100, USA. E-mail: pakramer@u.washington.edu

Received 13 April 2007; accepted 27 September 2007

DOI 10.1002/ajpa.20752Published online 13 November 2007 in Wiley InterScience

(www.interscience.wiley.com).

VVC 2007 WILEY-LISS, INC.

AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 135:484–488 (2008)

McHenry, 1980; Foley, 1992) and no further explanationof bipedalism is required. As this has not been demon-strated, we assumed that the protohominid’s habitualform of terrestrial locomotion (a version of quadrupedal-ism) uses less energy than its bipedalism (shuffling).Although the number of limbs used for locomotion doesnot affect the cost of transport when comparing acrossspecies (Herreid et al., 1981; Taylor et al., 1982), thismay not be the case when comparing a single individualusing different locomotor modes, one of which is its nor-mal form and one which is used infrequently. Taylor andRowntree (1973) suggest that bipedalism and quadru-pedalism are energetically equivalent in (juvenile) chim-panzees, but recently Sockol et al. (2007) have demon-strated that bipedalism is more costly than quadrupedal-ism in some mature chimpanzees. Nakatsukasa et al.(2006) also found that bipedalism was more costly thanquadrupedalism in macaques. Additionally, kinematicsare known to affect energy consumption (Ishida, 1991)and abnormal gait parameters increase energetic costs(Carey and Crompton, 2005). Bipedalism could be consid-ered ‘‘abnormal’’ for a predominately quadrupedal pri-mate. Consequently, we assume that bipedalism is morecostly than quadrupedalism for a quadruped based notonly on the recent chimpanzee and macaque data, butalso on this theoretical proposition.Next, we assumed that an unspecified activity (al-

though feeding is a likely candidate) requires a bipedalposture and that this activity occurs in discrete areasthat are separated by distances that must be traversed.Finally, we assumed that calculations based on me-

chanical energy expenditure reflect metabolic require-ments. Although it is clear that the ratio of mechanicalenergy output to metabolic energy input, known as effi-ciency, is dependent on the activity and can vary from0.25 to 0.70 (Heglund et al., 1982; Heglund and Cava-gna, 1985), precisely how this variation accrues in vari-ous activities is unknown. Efficiencies for single musclefibers can approach 50%, if the fibers are stretched priorto contraction, while that for muscle contraction from anisometric state hover in the range of 20–25% (Heglundand Cavagna, 1985). Efficiencies above this level [e.g.,that of large mammals while running which approach70% (Heglund et al., 1982)] are thought to be the prod-uct of elastic energy storage in tendons and muscles. Ifthe efficiencies of the two activities that we consider,shuffling and raising the trunk, were known at thistime, we could incorporate them directly into the model,but because they are not known, we consider the effectof muscle efficiencies after calculating the distancethresholds. The model is generic, but here we use themorphology of Pan troglodytes as a surrogate for thehominid/hominoid last common ancestor, as is often done(Hunt, 1994, 1998; Marchant, 1996; Pontzer and Wrang-ham, 2004).

MATERIALS AND METHODS

We modeled the total mechanical cost of locomotionbetween two resources which require bipedal standing.The quadrupedal cost was the cost of traversing a spe-cific distance using quadrupedism plus the cost of raisingthe trunk. The bipedal cost was calculated simply as thecost of traversing the same distance using bipedalism.The mechanical cost (MCmode) of traversing a distanceusing a specific mode of locomotion can be calculated asthe product of the mass specific mechanical cost of trans-

port for that mode of locomotion (CoTmode, J/kg/m), thedistance (d, in m) and mass (m, in kg).

MCmode ¼ CoTmodedm

To estimate the mechanical energy expenditure of proto-hominids, we used mechanical estimates for human loco-motion from the literature, because, unfortunately, thereare no published values for the mechanical cost of adultchimpanzee bipedal or quadrupedal locomotion. We usedthe range reported by Wang et al. (2003) for the massspecific mechanical cost of transport for bipedal walkingof between 0.3 and 0.5 J/kg/stride, which includes avalue of 0.38 J/kg/stride for ‘‘bent-hip, bent-knee’’ walk-ing. Using these values and an estimated stride lengthof 1.5 m/stride (Wang et al., 2003), we arrived at a costof transport of 0.2–0.33 J/kg/m. We extended this rangeup to 1.0 J/kg/m based on values reported by Kramerand Eck (2000). Metabolic cost of transport for humansis �3 J/kg/m [calculated from Steudel-Numbers and Tilk-ens (2004)]. If the efficiency of muscle contractions froman isometric state (0.25) is applied to the human empiri-cal costs, a mechanical cost of transport of 0.75 J/kg/m isobtained, which is within our range. Interestingly, themetabolic cost of transport of five chimpanzees fromSockol et al. (2007) is reported to range from 3 to 5.6 J/kg/m for bipedal walking and 2.8–5.8 J/kg/m quadrupe-dal walking, but, as previously indicated, no mechanicalmodel of chimpanzee locomotion exists. Because the effi-ciency of raising the trunk is unknown, we cannot usemetabolic energy to calculate MCmode.We modeled the quadrupedal cost of transport as a

percentage (between 0.9 and 0.5) of the bipedal costunder the assumption that the protohominid uses lessenergy during quadrupedal locomotion than duringbipedal shuffling. This translates into protohominidbipedalism being between 1.1 and 2 times more energeti-cally expensive compared to quadrupedalism, a rangethat encompasses the bipedal/quadrupedal relative costsof 1.42–1.55 reported for chimpanzees (Sockol et al.,2007) and 1.2421.38, reported for macaques (Nakatsu-kasa et al., 2006). We represented this energetic scalingfactor as X and all results are given in these terms.

CoTbiped ¼ XCoTquad

The mechanical energy requirement of raising the trunkwas calculated as the change in the potential energy ofthe total body center of gravity (CG) between quadrupe-dal and bipedal standing. Potential energy is the productof mass, height and gravity, thus change in potentialenergy is the product of the mass, gravity (g, 9.81 m/s2)and the change in height (Dh, in m).

DPE ¼ mgDh

The change in the height of the CG between stanceswas calculated from trunk angles and the distancebetween the hip joint and the CG in chimpanzees (seeFig. 1). Alexander (2004), in a review of bipedal kinemat-ics, reports a trunk angle of 308 (to horizontal) for chim-panzees during quadrupedal standing and 708 duringbipedal standing. The distance between the hip and theCG was estimated to be between 15 and 30 cm (Sylves-ter, 2004) resulting in a change in CG vertical height of

485MODELING LOCOMOTOR ENERGETICS

American Journal of Physical Anthropology

between 6 and 13 cm. Although D’Aout et al. (2002)report no significant change in knee flexion betweenqudrupedal and bipedal stances in bonobos, Sockol et al.(2007) do report a significant change in knee angleof �108. This potential height change would add 2 cm.We used, therefore, CG height change values of 5 and15 cm.We did not model the energy of lowering the trunk. In

mechanical terms, this would be an energy gain to thesystem from the change in potential energy that accom-panies lowering the CG. Lowering and then raising thetrunk would have no energetic consequences if theenergy to lower the trunk could be stored. This energy,however, cannot be stored and used to raise the trunk ata later time and, thus, is lost to the environment. Also,lowering the trunk may require energy to control themotion. Consequently, our value is the lower bound ofmechanical energy usage needed for this activity.We calculated the threshold distance of protohominid

bipedalism as the distance at which the cost of movingas a biped is equal to the cost of traveling as a quadru-ped plus raising the trunk. At open distances thatexceed the threshold, the cost of shuffling exceeds thecost of quadrupedalism and raising the trunk, makingquadrupedalism energetically optimal. At distancesbelow this threshold, bipedalism is energetically less ex-pensive. The relationship between quadrupedal andbipedal costs expressed mathematically is:

CoTquaddmþmgDh ¼ CoTbipeddm

After rearrangement, this becomes:

d ¼ gDh�

CoTbiped � CoTquad

� �

We calculated the threshold distances for all combina-tions of: the two values of change in the vertical heightof CG associated with raising the trunk (5 and 15 cm),

Fig. 1. Calculation of Change in CG Height. The change inthe height of CG can be calculated as the difference between h2and h1. Both h1 and h2 are easily calculated from the distancebetween the hip (filled circle) and the CG (cross-circle) and thetrunk angles.

Fig. 2. Threshold Distances for Bipedalism Model. Thegraphs provide the threshold distances (meters) to bipedalismusing the trunk proportions of chimpanzees. The x-axis in eachgraph is the energetic scaling factor (e.g. 1.1 models the cost ofbipedalism as 1.1 times that of quadrupedalism). Each graphshows threshold distances for different cost of transport values(0.2, 0.3, 0.5 and 1 J/kg/m). Squares 5 Dh CG 5 cm; Diamonds5 Dh CG 15 cm.

486 A.D. SYLVESTER AND P.A. KRAMER

American Journal of Physical Anthropology

the 10 different values cost of transport scaling fac-tor (1.1–2 at 0.1 increments), and the four valuesfor the mass specific cost of transport (0.2, 0.3, 0.5, and1 J/kg/m).

RESULTS

Values for the threshold distance varied widelydepending on the parameters used in the model and arepresented in Figure 2 and Table 1. The shortest distancewas 0.98 m, assuming a cost of transport of 1 J/kg/m,that bipedalism carries twice the cost of quadrupedismand a 5 cm gain in vertical height associated with stand-ing. The largest threshold distance was �80 m assuminga cost of transport for quadrupedalism of 0.2 J/kg/m,that bipedalism requires 1.1 times the amount of energyof quadrupedalism and that the CG must be raised 15cm to transition between quadrupedal and bipedalstanding.

DISCUSSION

As dictated by the model, as the vertical distance thatthe CG must be raised to stand bipedally increases sodoes the threshold distance. This accrues because a keyfactor in determining the threshold distance is the mag-nitude of the energy cost associated with raising thetrunk. Larger deviations of the CG create a greater ener-getic cost to raise the trunk and, hence, increase thethreshold distance. For instance, our mechanical cost forraising the trunk is 15 J for raising the trunk 5 cm, butis 44 J for raising the trunk 15 cm (both for a 30 kg indi-vidual). To put in biologically relevant terms, after con-verting from joules to kilocalories (1 kilocalorie 5 4,184joules) and including the effect of the mechanical/meta-bolic efficiency (0.25–0.70), the metabolic cost rangesfrom 0.005 to 0.042 Kcal per standing episode.Increasing the cost of transport scaling factor or the

absolute magnitude of the cost of transport has the oppo-site effect. As bipedalism becomes more costly comparedto quadrupedalism, it takes less distance to counter theeffect of raising the CG and the threshold distance de-creases. Similarly, increasing the absolute cost of trans-port reduces the relative magnitude of the cost of raisingthe CG.These results provide a theoretical basis for evaluating

chimpanzee bipedal behavior. At the extreme, our resultssuggest that chimpanzees should strongly prefer to shuf-fle, if already standing bipedally, for distances less than

1 m, and that they should rarely, if ever, use bipedalismfor distances greater than 80 m. The mechanical cost oftransport of humans is, however, almost certainly lowerthan that of chimpanzees because, as numerous authorshave suggested (Rodman and McHenry, 1980; Steudel-Numbers, 2003; Sockol et al., 2007), human bipedalismuses less energy than chimpanzee quadrupedalism orbipedalism. Consequently, it seems likely that the highercost of transport values used here are more probable. Ifonly the largest mechanical cost of transport is consid-ered (1.0 J/kg/m) and the ratio of the average values ofmetabolic cost of transport for bipedalism and quadru-pedalism (1.1) from Sockol et al. (2007) is used, then themaximum threshold distance drops from �80 to 16 m. Ifthe average cost of macaque bipedalism to quadrupedal-ism of 1.2 (Nakatsukasa et al., 2006) is used, the thresh-old distance drops to just short of 9 m. As research onprimate energetics provides better estimates for the pa-rameters of our model, we will be able to narrow therange of threshold distances further.A potentially complicating factor that is likely to affect

the distance threshold is muscular efficiencies dur-ing different activities. Because animals use metabolic(chemical) energy, and not mechanical energy, the ‘‘deci-sion’’ to shuffle or to lower to the ground and walk quad-rupedally will be made based on metabolic requirementsnot mechanical ones. The connection between the me-chanical work accomplished and the metabolic energyrequired is a complicated one, mediated by many factors.As a result, different activities could have different effi-ciencies. Muscular efficiency for contraction from an iso-metric state is in the 20–25% range, while that of pre-stretched muscles may be as high as 50% (Heglund andCavagna, 1985). Locomotor efficiencies can be as high as70% when the gait allows the use of structures thatstore elastic energy. Storage of elastic energy is generallyaccepted as critical in running gaits, but less importantin walking (Saibene and Minetti, 2003). Thus, it may bethat efficiencies for raising the trunk and walking arevery similar—especially if raising the trunk is precededby stretch of the pertinent muscles and the efficiency ofwalking is in the 30–40% range. Higher locomotor effi-ciencies, or lower efficiencies for raising the trunk, wouldincrease the threshold distance. Further investigationsinto muscular efficiencies will help refine the predictedthreshold distances.An important aspect of this model is that it can be

tested. Using chimpanzee bipedal behavior and the high-est estimate for cost of transport, we would predict that

TABLE 1. Threshold distances for bipedalism

Scaling Factor

0.2 J/kg/m 0.3 J/kg/m 0.5 J/kg/m 1.0 J/kg/m

15 cm 5 cm 15 cm 5 cm 15 cm 5 cm 15 cm 5 cm

1.1 80.93 26.98 53.96 17.99 32.37 10.79 16.19 5.401.2 44.15 14.72 29.43 9.81 17.66 5.89 8.83 2.941.3 31.88 10.63 21.26 7.09 12.75 4.25 6.38 2.131.4 25.75 8.58 17.17 5.72 10.30 3.43 5.15 1.721.5 22.07 7.36 14.72 4.91 8.83 2.94 4.41 1.471.6 19.62 6.54 13.08 4.36 7.85 2.62 3.92 1.311.7 17.87 5.96 11.91 3.97 7.15 2.38 3.57 1.191.8 16.55 5.52 11.04 3.68 6.62 2.21 3.31 1.101.9 15.53 5.18 10.36 3.45 6.21 2.07 3.11 1.042 14.72 4.91 9.81 3.27 5.89 1.96 2.94 0.98

The table provides the threshold distance (meters) to bipedalism assuming chimpanzee trunk proportions. Each row represents adifferent energetic scaling factor (X). The columns represent combinations of the different values for the mechanical energetic costof locomotion (upper row 0.2, 0.3, 0.5, and 1 J/kg/m) with the two different values for change in CG (5 and 15 cm).

487MODELING LOCOMOTOR ENERGETICS

American Journal of Physical Anthropology

chimpanzees would rarely used bipedalism for distancesgreater than 16 m, that most bouts of bipedalism wouldbe less than 9 m, and that bipedalism would be used fre-quently at distances less than 1 m. Such a test wouldindicate if minimizing energy expenditure is the limitingfactor to chimpanzee bipedalism or if other factors, suchas muscle fatigue, are of equal or greater importance.This might indicate the cause of the evolutionary barrierto chimpanzee bipedalism, and in turn provide importantinsight into what selective pressure may have been im-portant in overcoming the barrier to bipedalism in earlyhominid evolution.Another crucial aspect of this model is that it can be

generalized to all primates. The transition betweenbipedalism and quadrupedalism can be modeled for anyspecies, including Japanese macaques, in which the costsof bipedalism and quadrupedalism have been studied(Nakatsukasa et al., 2004, 2006). It could even be usedto estimate the threshold distance of adult human crawl-ing, using an energetic scaling factor less than one. Thethreshold distance to crawling would be dictated by thecost of raising the body between bouts. While perhapsnot of specific interest, such a test could be used to vali-date the model.

CONCLUSIONS

The results presented here provide a theoretical modelfor testing primate locomotor behavior and suggest athreshold distance for chimpanzee bipedalism of 9–16 m.As more primate data becomes available, refined predic-tions of the threshold distance will be possible and thesepredictions can be compared to observational data. Themodel can be generalized to all primates, including mod-ern humans and fossil hominids, by varying the ratio ofthe cost of transport for bipedalism versus quadrupedal-ism, the change in CG position, and the absolute cost oftransport.

ACKNOWLEDGMENTS

The authors wish to thank the Dr. M. Myers and tworeviewers for helpful comments and critiques.

LITERATURE CITED

Alexander RMcN. 2004. Bipedal animals, and their differencesfrom humans. J Anat 204:321–330.

Carey TS, Crompton RH. 2005. The metabolic costs of ‘bent hip,bent knee’ walking in humans. J Hum Evol 48:25–44.

D’Aout K, Aerts P, De Clercq D, De Meester K, Van Elsacker L.2002. Segment and joint angles of hind limb during bipedaland quadrupedal walking of the bonobo (Pan paniscus). Am JPhys Anthropol 119:37–51.

Dart RA. 1925. Australopithecus africanus: the Ape Man ofSouth Africa. Nature 145:195–199.

Foley RA. 1992. Evolutionary ecology of fossil hominids. In:Smith EA, Winterhalder B, editors. Evolutionary ecology andhuman behavior. New York: Aldine de Guyter. p 131–164.

Lovejoy CO. 1981. The origin of man. Science 211:341–350.Heglund NC, Cavagna GA. 1985. Efficiency of vertebrate loco-

motory muscles. J Exp Bio 115:283–292.Heglund NC, Fedak MA, Taylor CR, Cavagna GA. 1982. Ener-

getics and mechanics of terrestrial locomotion. IV. Total me-chanical energy changes as a function of speed and body sizein birds and mammasl. J Exp Bio 97:57–66.

Herreid CF, Full RJ, Prawel DA. 1981. Energetics of cockroachlocomotion. J Exp Bio 94:189–202.

Hewes GW. 1961. Food transport and the origin of hominidbipedalism. Am Anthropol 63:687–710.

Hunt KD. 1994. The evolution of human bipedality: ecology andfunctional morphology. J Hum Evol 26:183–202.

Hunt KD. 1998. Ecological morphology of Australopithecusafarensis: traveling terrestrially, eating arboreally. In: Stras-ser E, Fleagle JG, McHenry HM, Rosenberger A, editors. Pri-mate locomotion: recent advances. New York: Plenum. p 397–418.

Ishida H. 1991. A strategy for long distance walking in the ear-liest hominids: effect of posture on energy expenditure duringbipedal walking. In: Coppens Y, Senut B, editors. Origin(s)de la Bipedie Chez les Hominides. Paris: Editions du CNRS.p 9–15.

Jabonski NG, Chaplin G. 1993. Origin of habitual terrestrialbipedalism in the ancestor of the Hominidae. J Hum Evol24:259–280.

Kramer PA, Eck GG. 2000. Locomotor energetics and leg lengthin hominid bipedality. J Hum Evol 38:651–666.

Marchant LF. 1996. The Great apes revisited. Curr Anthropol37:142–147.

Nakatsukasa M, Hirasaki E, Ogihara N. 2006. Energy expendi-ture of bipedal walking is higher than that of quadrupedalwalking in Japanese macaques. Am J Phys Anthropol 131:33–37.

Nakatsukasa M, Ogihara N, Hamada Y, Goto Y, Yamada M,Hirakawa T, Hirasaki E. 2004. Energetic costs of bipedal andquadrupedal walking in Japanese macaques. Am J PhysAnthropol 124:248–256.

Pontzer H, Wrangham RW. 2004. Climbing and the daily energycost of locomotion in wild chimpanzees: implication for homi-noid locomotor evolution. J Hum Evol 46:315–333.

Rodman PS, McHenry HM. 1980. Bioenergetics and the originof hominid bipedalism. Am J Phys Anthropol 52:103–106.

Rose MD. 1991. The process of bipedaliztion in hominids. In:Coppens Y, Senut B, editors. Origine(s) de la Bipedie chez lesHominides (Cahier de Paleoanthropologie) Paris: Editions duCNRS. p 37–48.

Saibene F, Minetti AE. 2003. Biomechanical and physiologicalaspects of legged locomotion in humans. Eur J Appl Physiol88:297–316.

Sockol MD, Raichlen DA, Pontzer H. 2007. Chimpanzee locomo-tor energetics and the origin of human bipedalism. Proc NatAcad Sci USA 104:12265–12269.

Steudel-Numbers K. 2003. The energetic cost of locomotion:humans and primates compared to generalized endotherms. JHum Evol 44:255–262.

Steudel-Numbers K, Tilkens M. 2004. The effect of lower limblength on the energetic cost of locomotion: implications for fos-sil hominids. J Hum Evol 47:95–109.

Sylvester AD. 2004. Geometric modeling of the center of gravityin Pan troglodytes. Am J Phys Anthropol S 38:192 (abstract).

Sylvester AD. 2006. Locomotor decoupling and the origin ofhominin bipedalism. J Theor Biol 242:581–590.

Tanner NM. 1981. On becoming human cambridge. Cambridge:University Press Cambridge.

Taylor CR, Heglund NC, Maloiy GMO. 1982. Energetics andmechanics of terrestrial locomotion. I. Metabolic energy con-sumption as a function of speed and body size in birds andmammals. J Exp Biol 97:1–21.

Taylor CR, Rowntree VJ. 1973. Running on two or four legs:which consumes more energy? Science 179:186–187.

Wang WJ, Crompton RH, Li Y, Gunther MM. 2003. Energytransformation during erect and ‘bent-hip, bent-knee’ walkingby humans with implications for the evolution of bipedalism.J Hum Evol 44:563–579.

Wheeler PE. 1991. The thermoregulatory advantages of hominidbipedalism in open equatorial environments: the contributionof increased convective heat loss and cutaneous evaporativecooling. J Hum Evol 21:107–115.

Wrangham RW. 1980. Bipedal locomotion as a feeding adapta-tion in gelada baboons, and its implications for hominid evolu-tion. J Hum Evol 9:329–331.

488 A.D. SYLVESTER AND P.A. KRAMER

American Journal of Physical Anthropology