Modelling the locomotor energetics of extinct hominids

Bipedality is the defining characteristic of Hominidae and, consequently, the energetics of human bipedal locomotion has been of interest to anthropological researchers for many years. Scenarios of hominid evolution have been created to explain the rise of bipedality as predicated on such diverse factors as selection for energy efficiency (Foley, 1992), maximal thermal energy transfer (Wheeler, 1991a,b) and the use of display to maintain group cohesion (Jablonski and Chaplin, 1993). Without regard for which selective forces were at work, bipedality has been seen as a unitary adaptation, rather than as a general one with a variety of possible styles. Just as there are myriad forms of obligate and facultative quadrupedality, however, so too can there be different forms of bipedality. The style of bipedality that served the early hominids of the late Miocene was almost surely different from that of late Pliocene Homo.

The fossil record has begun to reveal that hominids can possess at least two body configurations (Jungers, 1991): relatively short-legged and long-legged versions. The former is characteristic of the early hominids, the australopithecines, while the latter is limited to Homo. Australopithecines are frequently seen as a transitional group, not fully modern in their form of bipedality and, consequently, energetically inefficient. Despite warnings from a few biomechanists (Witte et al., 1991), anthropologists have often equated short legs with inefficiency [an inherent bias of Steudel (1994), Webb (1996), Jungers (1982, 1991) and McHenry (1991b), to name a few]. The implicit logic is that short legs imply short stride lengths and that short strides require a higher cadence to maintain a particular velocity (Jungers, 1991). Unfortunately for anthropological analyses that rely on this logic, energetic expenditure is not solely a matter of the number of strides taken, but also of the energy required to take a single stride. This latter variable is dependent on the configuration of the locomotor anatomy, and shorter limb length implies, among other things, a smaller mass moment of inertia, which decreases energy expenditure. Consequently, it is reasonable to question the assumption that the short-legged australopithecines were inefficient simply because they possessed short lower limbs.

The second method calculates Ẇ_tot directly from basic anatomical variables and quantified movement data. Over a given temporal interval, Ẇ_tot can be divided into two components, internal work (v_int) and external work (Ẇ_ext). W_int is the mechanical energy required to move the body elements relative to the center of mass of the whole body (Cavagna and Kaneko, 1977). Anatomical variables such as body segment lengths and mass moments of inertia are combined with movement data obtained from cinegraphic analysis and used to solve for internal energy. Ẇ_ext is the mechanical energy required to move the center of mass of the whole body relative to the ground and can be directly determined from force-plate analysis (Cavagna et al., 1976). One important problem with the second method is determining the percentage energy transfer among the elements of a limb and between the limbs and the torso (Cavagna and Kaneko, 1977). Willems et al. (1995) provide specific guidance for solving this problem. In addition, this method is limited in that it can only calculate the mechanical power required by a system (Ẇ_tot) and not its metabolic rate or mechanical efficiency.

To understand the energetics of locomotion in modern humans, either or both methods are appropriate. To evaluate the energetics of extinct bipeds, however, the use of the first method is fraught with many problems. Obviously, the extinct hominid is not available to provide direct evidence, so a comparative approach is often used (see, for example, Rodman and McHenry, 1980). Predictive equations developed from the TMR of modern humans, chimpanzees (Pan troglodytes) and other non-human primates are used to predict the TMR of extinct hominids. This approach is flawed in that early hominids are neither habitual quadrupeds, as most other non-human primates are, nor do they exhibit the same body configuration as modern humans. The first method is, then, inappropriate for use in predicting the rate of locomotor energy expenditure of extinct hominids.

The second method holds much more promise. Since anatomical variables can be ascertained from the fossil record and the bipedal motion of australopithecines can be assumed to be similar to that of modern humans, the method of Willems et al. (1995) can be profitably used to develop a model that predicts the mechanical power requirements of extinct hominids. A corresponding model can also be developed of a modern human configuration and a comparison made between the two. This report details such an exercise.

The body is modeled as a series of rigid links representing the main components of the locomotor anatomy: foot, calf, thigh and pelvis. Segment masses are lumped at the centroid of each link, while the mass representing the head, arms and trunk (HAT) is lumped at the centerline of the pelvis. Fig. 1 is a sketch of the model. The left side is a mirror image of the right. Similar to equation 6 in Willems et al. (1995, p. 380), the total instantaneous energy of the whole body is defined as the sum of the kinetic and potential energies of the HAT and lower limbs:

Two configurations of the model are established, one to represent a composite modern human female and the other to represent an extinct hominid, namely a member of Australopithecus afarensis. The modern configuration is developed from anthropometric data derived from Euro-American women (NASA, 1978). AL 288-1, also known popularly as ‘Lucy’, is chosen as the extinct hominid because she is the most complete hominid known from more than 2 million years ago. Over 40 % of her skeleton is known, including her pelvis, femur and tibia (Johanson et al., 1982). In addition, much debate in the anthropological literature has centered on her energetic efficiency at bipedality or lack thereof.

Three anatomical variables are necessary to calculate the energy used in motion: segment lengths, segment masses and segment mass moments of inertia. The lengths that represent body segments in the australopithecine configuration are derived from AL 288-1, while those for the composite woman are an average of the adult female data presented in NASA (1978). The long bone lengths are combined with factors given in NASA (1978; Table 3) to determine the length of thigh and calf segments. These factors convert bone lengths into biomechanical lengths, taking into consideration the thickness of cartilage as well as the potential offset between anatomical landmarks and joint centerlines. The total pelvic width is determined by adding the femoral neck length of each side to the interacetabular distance. The length of segment bc/cf (see Fig. 1) is half the pelvic width. The length of the foot is the distance from the ball of the foot to the intersection of the tibia with the foot. Table 1 summarizes the segment (biomechanical) lengths.

Segment masses are determined for modern humans from the literature (NASA, 1978; Zihlman, 1984) and are derived mainly from cadaver dissections. Segment masses are much more problematic to develop for AL 288-1. Since average segment masses do exist for modern humans, I develop segment masses for AL 288-1 by factoring the modern segment mass by the ratio of total body masses. In other words, I assume that the same percentage of body mass is contained in each segment for both configurations. This assumption allows the comparison of the two configurations to be based solely on differences in segment length. Future analysis will address the effect of varying relative segment mass on the comparison. The mass of each limb segment is lumped at its centroid, while the mass of the head, arms and trunk (HAT) is lumped at the center of the pelvis (point c in Fig. 1). Table 1 shows the masses used for each segment and the percentage of body mass that each represents.

The final segment variables that are needed are the mass moments of inertia (I) of the segments. I for each of the limb segments is calculated using the regression formulae in NASA (1978; section IV, methods 2 and 3) that use total body mass and segment mass to approximate segment mass moment of inertia. Using this approach to develop I for the limb segments of AL 288-1 assumes that, although her limb length is different, the distribution of her musculature and other tissues is similar to that of modern humans. Table 1 gives the relevant values for both configurations.

Fig. 2 shows an idealized view looking down on the HAT. Fig. 2A shows the distance of each block from the x axis, while Fig. 2B shows the distance from the z axis. The distances shown in Fig. 2A,B are relative, or unfactored, to allow the same values to be used for any configuration. The mass of each block is shown in Fig. 2C,D for the composite woman and AL 288-1, respectively. AL 288-1 has smaller values because, although she was approximately the same width (in the frontal plane) as a modern woman, she was shorter and narrower and, consequently, weighed less.

The contribution to the HAT mass moment of inertia represented by each differential element is obtained by adding the square of the distances shown in Fig. 2A,B and multiplying by the differential mass shown in Fig. 2C,D. The result of this calculation is shown in Fig. 2E,F for the composite woman and AL 288-1, respectively. The total mass moment of inertia is the sum of the individual blocks. This technique is used to develop the other two moments of inertia (I_bcxx and I_bcxy). All mass moments of inertia are shown in Table 1.

I performed a check of this technique by calculating the HAT mass moments of inertia of the six male subjects shown in Chandler et al. (1975). Chandler et al. (1975) provide the mass and centroid location of each body segment (head, torso, right and left upper arm, lower arm and hand) included in the HAT. I was able, therefore, to transfer the axis of rotation from the center of mass of each segment to the center of the pelvis through the application of the parallel axis theorem (Meriam, 1978). Although the data of Chandler et al. (1975) cannot be used to estimate population parameters, they are sufficient to give a general guideline because my composite woman is of similar body mass (60 kg versus 50.62–89.15 kg, respectively) and stature (160.4 cm versus 164.5–181.7 cm, respectively) to Chandler’s subjects. I calculate I_bcxx for Chandler’s subjects to be 7–14 kg m² and I_bcyy to be 0.4–1 kg m². The method I present above yields similar values (see Table 1). I did not use the data presented in Chandler et al. (1975) to calculate the mass moments of inertia used in this analysis because they are inappropriate for use in developing the HAT mass moments of inertia for AL 288-1, whose mass and stature are well outside the range of Chandler’s subjects.

In addition to the three segment variables described above, movement profiles are needed to solve the energy equations. By ‘movement profile’, I mean the variation in the angles between the links (θ_ad, θ_db, etc.) with the percentage of the stride cycle. These angular excursions, in combination with segment lengths, are used to determine translational (v) and rotational (ω) velocity. Angular excursions are available in the literature (Perry, 1992; Winter, 1987; Inman et al., 1981) for modern humans walking at various velocities. I construct an ‘average’ woman from these. Because no movement profiles are known for australopithecines, I use the same profiles for both configurations.

To develop the joint angular excursions, I used the average hip, knee and ankle angles given by Winter (1987) for slow, natural and fast cadences and combined them with the angles for pelvic swing (θ_bcxz) and pelvic tilt (θ_bcyz) from Inman et al. (1981). Winter defines a ‘slow’ cadence as approximately 1m s⁻¹, while a ‘natural’ cadence is 1.36 m s⁻¹ and a ‘fast’ cadence is 2 m s⁻¹. Modern humans tend to change from a walk to a run between 2 and 2.4 m s⁻¹ (Waters et al., 1988). Winter’s ‘fast cadence’ is, therefore, close to the fastest (normal) walk exhibited by modern adults. One cautionary note should be added here: this definition of cadence assumes an average leg length that might be found in someone 1.65–1.85 m tall. Shorter people with shorter legs might feel that 1.36 m s⁻¹ was a ‘fast’ rather than a ‘natural’ walk. The concept of equivalent velocity, as discussed below, attempts to compensate for the effect of leg length on locomotor effort.

I use the angular excursions found in Winter (1987) rather than other published sources because Winter’s data are clearly detailed. Unfortunately, other researchers, including Inman et al. (1991), present data that, although more elaborate, are not as easily understood. In addition, Inman et al. (1991) presents curves for individuals without providing any estimates of basic anthropometrics or a method to create an average person from the individuals. Winter (1987; Table 32) provides joint angles at 2 ° increments of the percentage of the stride cycle and standard deviations.

The angular excursions of the lower limb (θ_ae, θ_ad and θ_db) are created from the angles presented in Winter (1987). These angular excursions are shown in Fig. 3A,B,C, respectively. Pelvic swing (θ_bcxz) (Fig. 3D) and pelvic tilt (θ_bcyz) (Fig. 3E) are developed from Inman et al. (1991).

Once the angular excursions are defined, then the angular velocities can be calculated. Because the angular excursions form a continuous curve, the derivative is the instantaneous slope, i.e. the tangent, of the curve at any point in time. If you allow the temporal increment to get larger, then the derivative is simply the slope of a line between two successive angles divided by the difference in time between the two. I calculate angular velocity in this way. In addition, I average angular velocity over three successive temporal increments to produce a smooth angular velocity curve. This procedure is similar to that of Willems et al. (1995). Fig. 4 shows the final angular velocity profiles for each angle and equivalent velocity.

When the movement profiles have been developed, the displacement of each joint in the model can be calculated. The displacement of each point is determined by idealizing the model as an open kinematic loop. From 0 to 40 % of the stride cycle, point a (see Fig. 1) is in contact with the ground and the displacement of all other points can be determined sequentially with reference to point a. From 40 to 50 % of the stride cycle, point e is the point of contact and reference.

The displacements are used to calculate the translational velocity of each point for each temporal increment. Total time to complete a step can be calculated from the total distance moved during a step and the average velocity of the HAT. Total distance moved is simply the difference in x axis displacement of point c from t=0 % of the stride cycle to t=50 % of the stride cycle. Instantaneous velocity is calculated as the difference in the position of a point between two temporal increments divided by the duration of the increment.

To be valid, the model should demonstrate several important features of walking, including: (1) no negative vertical displacements, i.e. below ground level, of the swing foot; (2) heel strike of the stance foot at t=0 % of the stride cycle and of the swing foot at t=50 % of the stride cycle; (3) heel-off for the stance leg before t=50 % of the stride cycle with the toe in contact with the ground; and (4) double stance (swing and stance feet in contact with the ground) from approximately t=0 % to t=10 % of the stride cycle. As shown in Table 2 and Fig. 5, the stance leg fulfills the expectations derived from empirical observations of human walking patterns. The swing leg also has remarkable success in meeting these expectations. Because the displaced location of the swing heel and toe is the sum of the displacements of the other segments and positional errors accumulate, it is expected that the swing foot would have more difficulty in attaining the correct position. For instance, in the australopithecine model, the maximum foot drag (negative vertical displacement) is caused by the heel and is −0.005 m. This represents an out-of-position error of less than 1 %. Both a visual inspection of the patterns and a quantitative evaluation indicate that the model predicts positions in space that are in fundamental agreement with empirical observations.

Stride length can be calculated for a modern human from sex, velocity and stature (Grieve and Gear, 1966) and from the model as twice the horizontal displacement of the HAT (point c) from t=0 % to t=50 % of the stride cycle. Table 2 shows predictions from both methods of calculation of stride lengths for both configurations. The model predicts stride lengths for the modern configuration that are less than 7 % smaller than predicted. The calculated stride length for AL 288-1 of 0.77–1.03 m differs by as much as 11 % from the predictions. The short legs and consequent short stature of the australopithecine configuration, however, potentially place it beyond the valid range of the predictive equations. Stride lengths for AL 288-1 derived from the model are reasonable when compared with those seen in the Laetoli hominid footprint trail (Leakey, 1987; White, 1977, 1980), whose stride lengths range from 0.62 to 0.944 m (Alexander, 1984; Robbins, 1987; Tuttle, 1987).

The horizontal (x direction) velocity can be calculated from the variation in x displacement. The average velocity of the center of the pelvis (point c) over 50 % of the stride cycle should equal the velocity of forward progression of the body because point c will move half the stride length in 50 % of the stride cycle time. Other points in the model will not average to the forward progression velocity over 50 % of the stride cycle because they do not move half the stride length in half the stride cycle time. For instance, while the swing foot moves a distance equal to the stride length, the stance foot remains stationary. The average velocity of point c for both configurations and all equivalent velocities is equal to the input forward velocity (data not shown).

To determine whether the rate of energy consumption calculated by the model is similar to empirical observations of modern humans, I compare the model-generated data with empirical data from Cavagna and Kaneko (1977) and Cavagna et al. (1976). Cavagn. a and Kaneko (1977) calculate internal mechanical power, Ẇ_int, as the sum of the changes in kinetic energy of both the arms and legs and p.resent it as a funct.ion of forward velocity. Fig. 6 shows that Ẇ_int is lower than Ė_sumcalculated in the present study. At slow and natural equivalent velocity, the values of Cavagna and Kaneko (1977) are similar to those from the model, while at the fast equivalent velocity, the model produces values higher than Cavagna and Kaneko observed. Possible causes for this discrepancy are as follows: (1) their values do not include the effect of changes in potential energy; and (2) their model does not include an element for the foot.

Cavagna et al. (1976) describe the total mechanical power changes of the center. of mass of the body,. Ẇ_ext. Fig. 6 shows that their values of Ẇ_ext are smaller than Ė_sum,pe calculated in the present study.One possible explanation for this discrepancy is that Ė_sum,pe is calculated from the translational and rotational velocities of the center of the pelvis and not from the actual center of mass of the body. Waters et al. (1973) suggest that the variation in forward velocity of the torso increases from head to pelvis, and the difference in forward velocity between the center of mass of the HAT and the center of the pelvis may vary substantially. If the forward velocity of the pelvis varies through the stride cycle more than that of the center of. mass of the body, then Ė_sum,pe should substantially exceed W_ext..

As a final test of the model, I compare Ė_tot with a prediction of treadmill m.etabolic rate (TMR, from Pandolf et al., 1977) minus BMR+ Ẇ_std, which is a measure of standing metabolic rate (SMR). SMR is calculated from resting metabolic rate (established for Anthropoidea by Leonard and Robertson, 1992) and the metabolic cost of resting and standing for women (FAO/UNU/WHO, 1985; Annex 5). At all velocities, Ė_tot is less than the empirically determined values (Fig. 7). As equation 1 indicates, physiologically derived energy expenditures are influenced by both balance and control requirements and by the efficiency of the power delivery system, and neither. of these parameters is known for the whole body at this time. Ẇ_tot must, therefore, be less than TMR−SMR, but exactly how much smaller is unknown. In addition, because of the differences b.etween Ė_sum,pe and Ẇ_ext cited above, Ė_totwill be larger than W_tot.

The mass-specific mechanical power required to move the lower limbs (Ė_sum,rl) is shown in Fig. 8. The configuration that represents AL 288-1 requires less energy to move its limbs than does that of the composite woman when the two are compared over the same temporal increment and for the same mass. This finding holds true for all three equivalent velocities. The cost of transport (CoT_rl) is shown in Fig. 9. Interestingly, the configuration of AL 288-1 requires essentially the same energy (within 2 %) to move 1 kg of mass over 1 m as does that of the modern woman.

On a mass-specific basis, the configuration developed from the fossil remains of AL 288-1 uses less energy to move than, and has the same cost of transport as, the modern human configuration. This deceptively simple finding has important ramifications for the understanding of AL 288-1 and her congeners. The idea that the individuals that composed Australopithecus in general, or A. afarensis specifically, were transitional bipeds – encumbered with short legs because of continued reliance on arboreal resources, but energetically compromised because of their shortness – appears no longer to be tenable. Short legs do not by themselves make a biped inefficient, as an understanding of the basic principles of dynamics indicates. Rather, ‘designing’ an efficient biped is a matter of balancing the conflicting effects of increasing equivalent velocity (and therefore energy expenditure) against decreasing internal and external work. While short legs can force an individual to take more steps, which does require more energy expenditure in one part of the system, short legs can also decrease the energy used per step.

Of course, the locomotor anatomy of Al 288-1 may have contained elements that would have decreased her efficiency at locomotion. She may have had a larger proportion of fast-twitch muscles, a less optimal arrangement of stabilization musculature or a host of other trade-offs that may have limited her proficiency. Unfortunately, the fossilized remains of osteological elements provide little insight into the soft tissue anatomy of extinct creatures. We will, therefore, probably never fully understand the mechanism by which australopithecines moved in their environment. Nonetheless, the central issue discussed here is that short legs are not sufficient evidence to claim that the form of bipedality exhibited by AL 288-1 was inefficient or transitional.

One important question that has not been addressed is whether it is appropriate to use movement profiles developed from modern humans for AL 288-1. An extensive, and often acrimonious, debate has flourished in the anthropological literature over whether the locomotor anatomy of AL 288-1 is ‘modern’ (Lovejoy et al., 1973; McHenry, 1975; White, 1980; Latimer et al., 1987; Lovejoy, 1988; Latimer and Lovejoy, E. 1989) or not (Robinson, 1972; Zihlman, 1978; Zihlman and Brunker, 1979; Jungers, 1982; Stern and Susman, 1983). With no general agreement in sight, I find no character in the locomotor anatomy of AL 288-1 that prohibits the motions that modern humans undergo and, instead, find many characters that indicate that AL 288-1 could move as modern humans do (Kramer, 1998). In addition, the Laetoli hominid footprint trail is remarkably human-like (Robbins, 1987; Tuttle, 1987) and, with a date of greater than 3.6 million years ago (Drake and Curtis, 1987), attributable to Australopithecus. While it seems almost certainly true that the motion of AL 288-1 was somewhat different from that of modern humans, it is equally likely that the motion of her limbs was fundamentally similar to that of modern humans. AL 288-1 could flex and extend her thighs, straighten her knees, swing and tilt her pelvis and push off with her feet just as modern humans do. Because of this, the use of the movement profiles developed from modern humans is justified (Kramer, 1998).

The method of Willems et al. (1995) is a useful technique for exploring the locomotor energetics of extinct hominids. Their method provides a procedure for predicting energetic expenditure in animals on whom experimentation is impossible. The model described herein, which was developed from their approach, accurately describes the motion of modern human bipeds and can be used profitably to evaluate the locomotor energetics of AL 288-1.

When the rates of energy expenditure of the two configurations are compared, several pivotal issues in paleoanthroplogy become clearer. The long legs of Homo are not the inevitable outcome of selection for efficient bipedality. Instead, the important anthropological questions of ‘why bipedality?’ and ‘why long legs?’ need to be as clearly separated in the minds of researchers as the origin of bipedality and the development of long legs were in geological time. The locomotor anatomy of AL 288-1 has often been misunderstood as a complex compromise between efficient ape arboreality and efficient (modern) bipedality. While her pelvis has been seen by most anthropologists as strong evidence of terrestrial bipedality, many have decried her short legs as explicable as useful only to a creature dependent on climbing as a fundamental adaptation. This analysis clearly indicates that AL 288-1 was not fundamentally compromised by her short legs and that short legs can be appropriate for a terrestrial biped. AL 288-1 may well have been an effective biped at walking speeds, not despite her short legs, but rather because of them.

 
• BMR

  basal metabolic rate (W kg⁻¹)

 
• CoT

  cost of transport (J kg⁻¹ m⁻¹)

 
• dE

  difference in energy between two consecutive temporal increments (J)

 
• dm

  pseudo-differential mass of a block (kg)

 
• dx x

  axis displacement of a point (m)

 
• dy y

  axis displacement of a point (m)

 
• Ė

  energy (J)

 
• Ė

  energy expenditure per unit of time (power) calculated in the present study (W kg⁻¹)

 
• f

  function

 
• g

  acceleration due to gravity (9.8 m s⁻²)

 
• h

  segment length (m)

 
• I

  mass moment of inertia (kg m²)

 
• l

  leg length (m)

 
• m

  mass (kg)

 
• SL

  stride length (m)

 
• SMR

  standing metabolic rate (W kg⁻¹)

 
• ST

  stature (m)

 
• t

  time (s or percentage of the stride cycle)

 
• TMR

  treadmill metabolic rate (W kg⁻¹)

 
• u

  horizontal translational velocity (m s⁻¹)

 
• v

  translational velocity (m s⁻¹)

 
• 

  volumetric rate of oxygen consumption

 
• W

  work (W kg⁻¹)

 
• W

  experimentally determined mechanical power from the literature (W kg⁻¹)

 
• x

  distance along the x axis (m)

 
• y

  distance along the y axis (m)

 
• z

  distance along the z axis (m)

 
• η

  mechanical efficiency

 
• θ

  angular excursion (degrees)

 
• ω

  angular velocity (rad %⁻¹ stride cycle or rad s⁻¹)

List of subscripts
 
• ad

  right calf

 
• ae

  right foot

 
• bc

  right half of pelvis

 
• c

  center of pelvis

 
• cf

  left half of pelvis

 
• db

  right thigh

 
• ext

  external

 
• fg

  left thigh

 
• f

  forward

 
• gh

  left calf

 
• hi

  left foot

 
• i

  current temporal increment

 
• int

  internal

 
• i–1

  previous temporal increment

 
• k

  kinetic

 
• l

  left leg

 
• max

  for a step

 
• mod

  modern human p potential

 
• pe

  pelvis

 
• r

  right leg

 
• rl

  right and left legs

 
• std

  standing plus control and balance sum summed value

 
• tot

  total

 
• xx

  about the x axis

 
• xy

  in the xy plane

 
• xz

  in the xz plane

 
• yy

  about the y axis

 
• yz

  in the yz plane

I wish to thank Dr Gerald G. Eck for his invaluable assistance with and support for this research. I am also greatly indebted to two anonymous reviewers for many helpful suggestions and criticisms of earlier versions of this work. In addition, I wish to thank Mr Brian J. Kramer for many hours of discussion of the dynamic principles upon which this effort is based.