Morphological conservation of limb natural pendular period in the domestic dog (Canis familiaris): implications for locomotor energetics

Natural Frequency Method: estimating the preferred walking speed of Tyrannosaurus rex based on tail natural frequency

Locomotor energetics are an important determinant of an animal's ecological niche. It is commonly assumed that animals minimize locomotor energy expenditure by selecting gait kinematics tuned to the natural frequencies of relevant body parts. We demonstrate that this allows estimation of the preferred step frequency and walking speed of Tyrannosaurus rex, using an approach we introduce as the Natural Frequency Method. Although the tail of bipedal dinosaurs was actively involved in walking, it was suspended passively by the caudal interspinous ligaments. These allowed for elastic energy storage, thereby reducing the metabolic cost of transport. In order for elastic energy storage to be high, step and natural frequencies would have to be matched. Using a 3D morphological reconstruction and a spring-suspended biomechanical model, we determined the tail natural frequency of T. rex (0.66 s^-1, range 0.41-0.84), and the corresponding walking speed (1.28 m s^-1, range 0.80-1.64), which we argue to be a good indicator of preferred walking speed (PWS). The walking speeds found here are lower than earlier estimations for large theropods, but agree quite closely with PWS of a diverse group of extant animals. The results are most sensitive to uncertainties regarding ligament moment arms, vertebral kinematics and ligament composition. However, our model formulation and method for estimation of walking speed are unaffected by assumptions regarding muscularity, and therefore offer an independent line of evidence within the field of dinosaur locomotion.

An inelastic quadrupedal model discovers four-beat walking, two-beat running, and pseudo-elastic actuation as energetically optimal

It is widely held that quadrupeds choose steady gaits that minimize their energetic cost of transport, but it is difficult to explore the entire range of possible footfall sequences empirically. We present a simple model of a quadruped that can spontaneously produce any of the thousands of planar footfall sequences available to quadrupeds. The inelastic, planar model consists of two point masses connected with a rigid trunk on massless legs. It requires only center of mass position, hind and forelimb proportions and a stride-length to speed relationship as input. Through trajectory optimization of a work and force-rate cost, and a large sample of random initial guesses, we provide evidence for the global optimality of symmetrical four-beat walking at low speeds and two beat running (trotting) at intermediate speeds. Using input parameters based on measurements in dogs (Canis lupus familiaris), the model predicts the correct phase offset in walking and a realistic walk-trot transition speed. It also spontaneously reproduces the double-hump ground reaction force profile observed in walking, and the smooth single-hump profile observed in trotting. Actuation appears elastic, despite the model’s lack of springs, suggesting that spring-like locomotory behaviour emerges as an optimal tradeoff between work minimization and force-rate penalties.

Why do quadrupedal mammals move in such consistent ways, when so many options are available? We tackled this problem by determining energetically-optimal gaits using a simple computational model of a four-legged animal. The model can use virtually any pattern of movement (physics-permitting!) but selects movement strategies observed in nature as energetically optimal. The similarities between the computer-based predictions and natural animal movement are striking, and suggest mammals utilize movement strategies that optimize energy use when they move.

A quantitative evaluation of physical and digital approaches to centre of mass estimation

Centre of mass is a fundamental anatomical and biomechanical parameter. Knowledge of centre of mass is essential to inform studies investigating locomotion and other behaviours, through its implications for segment movements, and on whole body factors such as posture. Previous studies have estimated centre of mass position for a range of organisms, using various methodologies. However, few studies assess the accuracy of the methods that they employ, and often provide only brief details on their methodologies. As such, no rigorous, detailed comparisons of accuracy and repeatability within and between methods currently exist. This paper therefore seeks to apply three methods common in the literature (suspension, scales and digital modelling) to three 'calibration objects' in the form of bricks, as well as three birds to determine centre of mass position. Application to bricks enables conclusions to be drawn on the absolute accuracy of each method, in addition to comparing these results to assess the relative value of these methodologies. Application to birds provided insights into the logistical challenges of applying these methods to biological specimens. For bricks, we found that, provided appropriate repeats were conducted, the scales method yielded the most accurate predictions of centre of mass (within 1.49 mm), closely followed by digital modelling (within 2.39 mm), with results from suspension being the most distant (within 38.5 mm). Scales and digital methods both also displayed low variability between centre of mass estimates, suggesting they can accurately and consistently predict centre of mass position. Our suspension method resulted not only in high margins of error, but also substantial variability, highlighting problems with this method.

Segmental morphometrics of the olive baboon (Papio anubis): a longitudinal study from birth to adulthood

The linear dimensions and inertial characteristics of the body are important in locomotion and they change considerably during the ontogeny of animals, including humans. This longitudinal and ontogenetic study has produced the largest dataset to date of segmental morphometrics in a Catarrhini species, the olive baboon. The objectives of the study were to quantify the changes in body linear and inertial dimensions and to explore their (theoretical) mechanical significance for locomotion. We took full-body measurements of captive individuals at regular intervals. Altogether, 14 females and 16 males were followed over a 7-year period, i.e. from infancy to adulthood. Our results show that individual patterns of growth are very consistent and follow the general growth pattern previously described in olive baboons. Furthermore, we obtained similar growth curve structures for segment lengths and masses, although the respective time scales were slightly different. The most significant changes in body morphometrics occurred during the first 2 years of life and concerned the distal parts of the body. Females and males were similar in size and shape at birth. The rate and duration of growth produced substantial size-related differences throughout ontogeny, while body shapes remained very similar between the sexes. We also observed significant age-related variations in limb composition, with a proximal shift of the centre of mass within the limbs, mainly due to changes in mass distribution and in the length of distal segments. Finally, we observed what we hypothesize to be 'early biomechanical optimization' of the limbs for quadrupedal walking. This is due to a high degree of convergence between the limbs' natural pendular periods in infants, which may facilitate the onset of quadrupedal walking. Furthermore, the mechanical significance of the morphological changes observed in growing baboons may be related to changing functional demands with the onset of autonomous (quadrupedal) locomotion. From a wider perspective, these data provide unique insights into questions surrounding both the processes of locomotor development in primates and how these processes might evolve.

Bipedality from locomotor autonomy to adulthood in captive olive baboon (Papio anubis): Cross-sectional follow-up and first insight into the impact of body mass distribution

OBJECTIVE

Despite that the biomechanics of standing and walking bipedally has been extensively studied in nonhuman primates, the morphological features that may constrain, or facilitate, the control of balance and thus of the spontaneous occurrence of bipedal behavior are poorly known. We aim to test the relationship between body mass distribution and bipedal behavior using a nonhuman primate species, the olive baboon, Papio anubis, raised in captivity.

MATERIALS AND METHODS

We collected quantitative data on the frequency and duration of bipedalism together with morphometrics on a sample of 22 individuals. We used ontogenetic changes as a natural experiment that provides insights into the impact of morphology. Specifically we focus on 1) quantifying how body mass distribution changes from infancy to adulthood in baboons; and 2) whether the different patterns of mass distribution influence the behavioral variables, i.e., a) the frequency and b) the duration of bouts of bipedal behavior realized in different activity contexts.

RESULTS

With regard to assisted bipedal behaviors, the duration and frequency of bouts of standing, contrary to walking, are significantly related to age. With regard to unassisted bipedal behaviors, no correlation to age is observed; the bout duration of walking is strongly correlated to body mass and mass distribution, contrary to the frequency of walking as well as the bout duration and frequency of bipedal standing.

DISCUSSION

Our results suggest a close relationship between the pattern of mass distribution and the mechanism of balance control in the spontaneous bipedal walking of baboons. The mechanical effects of the pattern of mass distribution on the ability to perform bipedally in extant nonhuman primates are discussed in the context of the evolution toward habitual bipedalism.

Energetic benefits and adaptations in mammalian limbs: Scale effects and selective pressures

Differences in limb size and shape are fundamental to mammalian morphological diversity; however, their relevance to locomotor costs has long been subject to debate. In particular, it remains unknown if scale effects in whole limb morphology could partially underlie decreasing mass-specific locomotor costs with increasing limb length. Whole fore- and hindlimb inertial properties reflecting limb size and shape-moment of inertia (MOI), mass, mass distribution, and natural frequency-were regressed against limb length for 44 species of quadrupedal mammals. Limb mass, MOI, and center of mass position are negatively allometric, having a strong potential for lowering mass-specific locomotor costs in large terrestrial mammals. Negative allometry of limb MOI results in a 40% reduction in MOI relative to isometry's prediction for our largest sampled taxa. However, fitting regression residuals to adaptive diversification models reveals that codiversification of limb mass, limb length, and body mass likely results from selection for differing locomotor modes of running, climbing, digging, and swimming. The observed allometric scaling does not result from selection for energetically beneficial whole limb morphology with increasing size. Instead, our data suggest that it is a consequence of differing morphological adaptations and body size distributions among quadrupedal mammals, highlighting the role of differing limb functions in mammalian evolution.

A comparative study of trabecular bone mass distribution in cursorial and non-cursorial limb joints

Skeletal design among cursorial animals is a compromise between a stable body that can withstand locomotor stress and a light design that is energetically inexpensive to grow, maintain, and move. Cursors have been hypothesized to reduce distal musculoskeletal mass to maintain a balance between safety and energetic cost due to an exponential increase in energetic demand observed during the oscillation of the distal limb. Additionally, experimental research shows that the cortical bone in distal limbs experiences higher strains and remodeling rates, apparently maintaining lower mass at the expense of a smaller safety factor. This study tests the hypothesis that the trabecular bone mass in the distal limb epiphyses of cursors is relatively lower than that in the proximal limb epiphyses to minimize the energetic cost of moving the limb. This study utilized peripheral quantitative computed tomography scanning to measure the trabecular mass in the lower and upper limb epiphyses of hominids, cercopithecines, and felids that are considered cursorial and non-cursorial. One-way ANOVA with Tukey post hoc corrections was used to test for significant differences in trabecular mass across limb epiphyses. The results indicate that overall, both cursors and non-cursors exhibit varied trabecular mass in limb epiphyses and, in certain instances, conform to a proximal-distal decrease in mass irrespective of cursoriality. Specifically, hominid and cercopithecine hind limb epiphyses exhibit a proximal-distal decrease in mass irrespective of cursorial adaptations. These results suggest that cursorial mammals employ other energy saving mechanisms to minimize energy costs during running.

Ground reaction force adaptations to tripedal locomotion in dogs

To gain insight into the adaptive mechanisms to tripedal locomotion and increase understanding of the biomechanical consequences of limb amputation, this study investigated kinetic and temporal gait parameters in dogs before and after the loss of a hindlimb was simulated. Nine clinically sound Beagle dogs trotted on an instrumented treadmill and the ground reaction forces as well as the footfall patterns were compared between quadrupedal and tripedal locomotion. Stride and stance durations decreased significantly in all limbs when the dogs ambulated tripedally, while relative stance duration increased. Both vertical and craniocaudal forces were significantly different in the remaining hindlimb. In the forelimbs, propulsive force increased in the contralateral and decreased in the ipsilateral limb, while the vertical forces were unchanged (except for mean force in the contralateral limb). Bodyweight was shifted to the contralateral and cranial body side so that each limb bore ~33% of the dog's bodyweight. The observed changes in the craniocaudal forces and the vertical impulse ratio between the fore- and hindlimbs suggest that a nose-up pitching moment occurs during the affected limb pair's functional step. To regain pitch balance for a given stride cycle, a nose-down pitching moment is exerted when the intact limb pair supports the body. These kinetic changes indicate a compensatory mechanism in which the unaffected diagonal limb pair is involved. Therefore, the intact support pair of limbs should be monitored closely in canine hindlimb amputees.

Scale effects between body size and limb design in quadrupedal mammals

Recently the metabolic cost of swinging the limbs has been found to be much greater than previously thought, raising the possibility that limb rotational inertia influences the energetics of locomotion. Larger mammals have a lower mass-specific cost of transport than smaller mammals. The scaling of the mass-specific cost of transport is partly explained by decreasing stride frequency with increasing body size; however, it is unknown if limb rotational inertia also influences the mass-specific cost of transport. Limb length and inertial properties--limb mass, center of mass (COM) position, moment of inertia, radius of gyration, and natural frequency--were measured in 44 species of terrestrial mammals, spanning eight taxonomic orders. Limb length increases disproportionately with body mass via positive allometry (length ∝ body mass(0.40)); the positive allometry of limb length may help explain the scaling of the metabolic cost of transport. When scaled against body mass, forelimb inertial properties, apart from mass, scale with positive allometry. Fore- and hindlimb mass scale according to geometric similarity (limb mass ∝ body mass(1.0)), as do the remaining hindlimb inertial properties. The positive allometry of limb length is largely the result of absolute differences in limb inertial properties between mammalian subgroups. Though likely detrimental to locomotor costs in large mammals, scale effects in limb inertial properties appear to be concomitant with scale effects in sensorimotor control and locomotor ability in terrestrial mammals. Across mammals, the forelimb's potential for angular acceleration scales according to geometric similarity, whereas the hindlimb's potential for angular acceleration scales with positive allometry.

A new look at the Dynamic Similarity Hypothesis: the importance of swing phase

The Dynamic Similarity Hypothesis (DSH) suggests that when animals of different size walk at similar Froude numbers (equal ratios of inertial and gravitational forces) they will use similar size-corrected gaits. This application of similarity theory to animal biomechanics has contributed to fundamental insights in the mechanics and evolution of a diverse set of locomotor systems. However, despite its popularity, many mammals fail to walk with dynamically similar stride lengths, a key element of gait that determines spontaneous speed and energy costs. Here, we show that the applicability of the DSH is dependent on the inertial forces examined. In general, the inertial forces are thought to be the centripetal force of the inverted pendulum model of stance phase, determined by the length of the limb. If instead we model inertial forces as the centripetal force of the limb acting as a suspended pendulum during swing phase (determined by limb center of mass position), the DSH for stride length variation is fully supported. Thus, the DSH shows that inter-specific differences in spatial kinematics are tied to the evolution of limb mass distribution patterns. Selection may act on morphology to produce a given stride length, or alternatively, stride length may be a "spandrel" of selection acting on limb mass distribution.

Morphometrics and inertial properties in the body segments of chimpanzees (Pan troglodytes)

Inertial characteristics and dimensions of the body and body segments form an integral part of a biomechanical analysis of motion. In primate studies, however, segment inertial parameters of non-human hominoids are scarce and often obtained using varying techniques. Therefore, the principal aim of this study was to expand the existing chimpanzee inertial property data set using a non-invasive measuring technique. We also considered age- and sex-related differences within our sample. By means of a geometric model based on Crompton et al. (1996; Am J Phys Anthropol 99, 547-570) we generated inertial properties using external segment length and diameter measurements of 53 anaesthetized chimpanzees (Pan troglodytes). We report absolute inertial parameters for immature and mature subjects and for males and females separately. Proportional data were computed to allow the comparison between age classes and sex classes. In addition, we calculated whole limb inertial properties and we discuss their potential biomechanical consequences. We found no significant differences between the age classes in the proportional data except for hand and foot measures where juveniles exhibit relatively longer and heavier distal segments than adults. Furthermore, most sex-related differences can be directly attributed to the higher absolute segment masses in male chimpanzees resulting in higher moments of inertia. Additionally, males tend to have longer upper limbs than females. However, regarding proportional data we discuss the general inertial properties of the chimpanzee. The described segment inertial parameters of males and females, and of the two age classes, represent a valuable data set ready for use in a range of biomechanical locomotor models. These models offer great potential for improving our understanding of early hominin locomotor patterns.

The application to bipeds of a geometric model of lower-limb-segment inertial properties

Drawing inferences about locomotor energetics from limb morphology, especially in regard to small differences between individuals, depends critically on valid estimates of lower-limb inertial properties. While there are numerous options for such estimations in the literature, geometric models that involve simple measures and straightforward mathematics combined with the ability to capture individual variation are rare. In this research, we apply a method, originally developed for quadrupeds, that models limb segments as elliptical columns. When the elliptical model is applied to bipeds, it provides a means of estimating limb-segment inertial properties accurately enough to test differences between individuals of similar stature and mass, but with variation in mass distribution and limb length. We test the method against commonly used equations and are able to show the validity of the method for thigh and shank segments.

Inertial properties of hominoid limb segments

Quantitative, accurate data regarding the inertial properties of body segments are of paramount importance when developing musculo-skeletal locomotor models of living animals and, by inference, their ancestors. The limited number of available primate cadavers, and the destructive nature of the post-mortem, result in such data being very rare for primates. This study builds on the work of Crompton et al. (Am. J. Phys. Anthropol. 1996, 99, 547-570) and reports inertial properties of the body segments of gorillas, chimpanzees, orangutans and gibbons. Segment mass, centre of mass and the radius of gyration of five ape cadavers were measured using a complex-pendulum technique and compared with the results derived from external measurements of segment lengths and diameters on the same animals. With additional data from external measurements of eight more hominoid cadavers, and published data, intergeneric differences between the inertial properties and the distribution of mass between limb segments are analysed and related to the locomotor habits of the species. We found that segment inertial properties show extensive overlap between ape genera as a result of large interindividual variation. Segment mass distribution also overlaps between apes and humans, with the exception of the shank segment. However, owing to a different distribution of mass between the limb segments, the centre of mass of both the arms and the legs is located more distally in apes than in humans, and the natural pendular period of ape forelimbs is larger than that of the hindlimbs. This suggests that, in contrast to the limbs of cursorial mammals and cercopithecoid primates, hominoid limbs are not optimized for efficiency in quadrupedal walking, but rather reflect a compromise between various locomotor modes. Common chimpanzees may have secondarily evolved a more efficient quadrupedal gait.

Morphological analysis of the hindlimb in apes and humans. I. Muscle architecture

We present quantitative data on the hindlimb musculature of Pan paniscus, Gorilla gorilla gorilla, Gorilla gorilla graueri, Pongo pygmaeus abelii and Hylobates lar and discuss the findings in relation to the locomotor habits of each. Muscle mass and fascicle length data were obtained for all major hindlimb muscles. Physiological cross-sectional area (PCSA) was estimated. Data were normalized assuming geometric similarity to allow for comparison of animals of different size/species. Muscle mass scaled closely to (body mass)(1.0) and fascicle length scaled closely to (body mass)(0.3) in most species. However, human hindlimb muscles were heavy and had short fascicles per unit body mass when compared with non-human apes. Gibbon hindlimb anatomy shared some features with human hindlimbs that were not observed in the non-human great apes: limb circumferences tapered from proximal-to-distal, fascicle lengths were short per unit body mass and tendons were relatively long. Non-human great ape hindlimb muscles were, by contrast, characterized by long fascicles arranged in parallel, with little/no tendon of insertion. Such an arrangement of muscle architecture would be useful for locomotion in a three dimensionally complex arboreal environment.

Locomotor versatility in the white-handed gibbon (Hylobates lar): A spatiotemporal analysis of the bipedal, tripedal, and quadrupedal gaits

This study gives a qualitative and quantitative description of the different terrestrial locomotor modes of a group of white-handed gibbons (Hylobates lar) from the Wild Animal Park Planckendael, Belgium. The gibbons were filmed during voluntary locomotion on a grassy and smooth substrate and on a pole. These video images allowed us to define seven different gait types, based on spatial and temporal footfall patterns. Consequent digitization of the video images (n = 254) yielded duty factors, stride lengths, and stride frequencies of the fore- and hind limbs during locomotion at a wide range of speeds. These spatiotemporal gait characteristics were regressed against velocity, and the regression lines of the different gait types were compared. In addition, gibbon bipedalism was compared with bonobo (Pan paniscus) and human bipedalism. Gibbons appear to be very versatile animals, using a bipedal, tripedal, or quadrupedal gait during terrestrial travel with an overlapping speed range. The spatiotemporal characteristics of these gaits are largely similar, although they have clearly distinct footfall patterns. Bipedal walking on the pole is slightly different from terrestrial bipedalism, but differences between substrate types (grass vs. catwalk) are subtle. During bipedalism, gibbons increase both stride length and frequency to increase speed, just as humans and bonobos do, but at a given speed, gibbons take relatively larger strides at lower rates. Bipedal walking in gibbons also appears to be relatively fast-gibbons could keep on walking at speeds where humans have to start running. Apparently, adaptations for arboreal locomotion have not constrained the terrestrial locomotor abilities of gibbons. This may indicate that the step from an arboreal ancestral ape to a terrestrial, upright bipedal hominin might not be difficult and that structural specializations are not a prerequisite for adopting a (non-habitual) bipedal gait.

Effects of limb mass distribution on mechanical power outputs during quadrupedalism

Many researchers have suggested that cursorial mammals concentrate limb muscle mass proximally to reduce energy costs during locomotion. Although supported by experiments where mass is added to an individual's limbs, mammals with naturally occurring distally heavy limbs such as primates have similar energy costs compared with other mammals. This study presents a new hypothesis to explain how animals with distally heavy limbs maintain low energy costs. Since distal mass should increase energy costs due to higher amounts of muscular power outputs, this hypothesis is based on the divergent effects of stride frequency on internal and external power outputs (the power output to move the limbs and the body center of mass, respectively). The use of low stride frequencies reduces limb velocities and therefore decreases internal power, while associated long strides increase the vertical displacement of the body center of mass and therefore increase external power. Total power (the sum of internal and external power) may therefore not differ among mammals with different limb mass distributions. To test this hypothesis, I examined a sample of infant baboons (Papio cynocephalus) during ontogeny and compared them with more cursorial mammals. Limb mass distribution changes with age (from distal to more proximally concentrated) in baboons, and the infants used shorter strides and higher stride frequencies when limb mass was most proximally concentrated. Compared with non-primates who have more proximally concentrated limb mass, the infants used longer strides and lower stride frequencies. Relatively low internal power was associated with low stride frequencies in both the intra- and inter-specific samples. However, only in the inter-specific comparison were relatively long strides associated with high external power outputs. In both the intra-specific and the inter-specific samples, total power did not differ between groups who differed in limb mass distribution. The results of this study suggest that a trade-off mechanism is available to quadrupeds with distally heavy limbs allowing them to maintain similar total power outputs (and likely similar energy costs) compared with mammals with more proximally concentrated limb mass.

Effects of limb mass distribution on the ontogeny of quadrupedalism in infant baboons (Papio cynocephalus) and implications for the evolution of primate quadrupedalism

Primate quadrupedal kinematics differ from those of other mammals. Several researchers have suggested that primate kinematics are adaptive for safe travel in an arboreal, small-branch niche. This study tests a compatible hypothesis that primate kinematics are related to their limb mass distribution patterns. Primates have more distally concentrated limb mass than most other mammals due to their grasping hands and feet. Experimental studies have shown that increasing distal limb mass by adding weights to the limbs of humans and dogs influences kinematics. Adding weights to distal limb elements increases the natural period of a limb's oscillation, leading to relatively long swing and stride durations. It is therefore possible that primates' distal limb mass is responsible for some of their unique kinematics. This hypothesis was tested using a longitudinal ontogenetic sample of infant baboons (Papio cynocephalus). Because limb mass distribution changes with age in infant primates, this project examined how these changes influence locomotor kinematics within individuals. The baboons in this sample showed a shift in their kinematics as their limb mass distributions changed during ontogeny. When their limb mass was most distally concentrated (at young ages), stride frequencies were relatively low, stride lengths were relatively long, and stance durations were relatively long compared to older ages when limb mass was more proximally concentrated. These results suggest that the evolution of primate quadrupedal kinematics was tied to the evolution of grasping hands and feet.

Froude number corrections in anthropological studies

The Froude number has been widely used in anthropology to adjust for size differences when comparing gait parameters or other nonmorphological locomotor variables (such as optimal walking speed or speed at gait transitions) among humans, nonhuman primates, and fossil hominins. However, the dynamic similarity hypothesis, which is the theoretical basis for Froude number corrections, was originally developed and tested at much higher taxonomic levels, for which the ranges of variation are much greater than in the intraspecific or intrageneric comparisons typical of anthropological studies. Here we present new experimental data on optimal walking speed and the mass-specific cost of transport at that speed from 19 adult humans walking on a treadmill, and evaluate the predictive power of the dynamic similarity hypothesis in this sample. Contrary to the predictions of the dynamic similarity hypothesis, we found that the mass-specific cost of transport at experimentally measured optimal walking speed and Froude number were not equal across individuals, but retained a significant correlation with body mass. Overall, the effect of lower limb length on optimal walking speed was weak. These results suggest that the Froude number may not be an effective way for anthropologists to correct for size differences across individuals, but more studies are needed. We suggest that researchers first determine whether geometric similarity characterizes their data before making inferences based on the dynamic similarity hypothesis, and then check the consistency of their results with and without Froude number corrections before drawing any firm conclusions.

Ontogeny of limb mass distribution in infant baboons (Papio cynocephalus)

Primates have more distally distributed limb muscle mass compared to most nonprimate mammals. The heavy distal limbs of primates are likely related to their strong manual and pedal grasping abilities, and interspecific differences in limb mass distributions among primates are correlated with the amount of time spent on arboreal supports. Within primate species, individuals at different developmental stages appear to differ in limb mass distribution patterns. For example infant macaques have more distally distributed limb mass at young ages. A shift from distal to proximal limb mass concentrations coincides with a shift from dependent travel (grasping their mother's hair) to independent locomotion. Because the functional demands placed on limbs may differ between taxa, understanding the ontogeny of limb mass distribution patterns is likely an essential element in interpreting the diversity of limb mass distribution patterns present in adult primates. This study examines changes in limb inertial properties during ontogeny in a longitudinal sample of infant baboons (Papio cynocephalus). The results of this study show that infant baboons undergo a transition from distal to proximal limb mass distribution patterns. This transition in limb mass distribution coincides with the transition from dependent to independent locomotion during infant development. Compared to more arboreal macaques, infant baboons undergo a faster transition to more proximal limb mass distribution patterns. These results suggest that functional demands placed on the limbs during ontogeny have a strong impact on the development of limb mass distribution patterns.

Convergence of forelimb and hindlimb Natural Pendular Period in baboons (Papio cynocephalus) and its implication for the evolution of primate quadrupedalism

The patterns of muscle mass distribution along the lengths of limbs may have important effects on the mechanics and energetics of quadrupedalism. Specifically, Myers and Steudel (J. Morphol. 234 (1997) 183) have shown that fore- and hindlimb Natural Pendular Periods (NPPs) may affect quadrupedal kinematics and must converge to reduce locomotor energetic costs. This study quantifies patterns of limb mass distribution in a live sample of Papio cynocephalus using limb inertial properties (mass, center of mass, mass moment of inertia, and radius of gyration). These inertial properties are calculated using a geometric modeling technique similar to that of Crompton et al. (Am. J. phys. Anthrop. 99 (1996) 547). The inertial properties in Papio are compared to those of Canis from Myers and Steudel (J. Morphol. 234 (1997) 183). The Papio sample has convergent fore- and hindlimb NPPs. Additionally, these limb NPPs are relatively large compared to those of Canis due to the relatively distally distributed limb mass in the Papio sample (relatively large limb masses, relatively distal centers of mass and radii of gyration, and relatively large limb mass moments of inertia). This relatively distal limb mass appears related to the grasping abilities of their hands and feet. Causal links are explored between limb shape adaptations for grasping hands and feet and the kinematics of primate quadrupedalism. In particular, if primates in general follow Papio's limb mass distribution pattern, then relatively large limb NPPs may lead to the relatively low stride frequencies already documented for primates. The kinematics of primate quadrupedalism appears to have been strongly influenced by both selection for grasping hands and feet and selection for reduced locomotor energetic costs.

Energy cost of wheel running in house mice: implications for coadaptation of locomotion and energy budgets

Laboratory house mice (Mus domesticus) that had experienced 10 generations of artificial selection for high levels of voluntary wheel running ran about 70% more total revolutions per day than did mice from random-bred control lines. The difference resulted primarily from increased average velocities rather than from increased time spent running. Within all eight lines (four selected, four control), females ran more than males. Average daily running distances ranged from 4.4 km in control males to 11.6 km in selected females. Whole-animal food consumption was statistically indistinguishable in the selected and control lines. However, mice from selected lines averaged approximately 10% smaller in body mass, and mass-adjusted food consumption was 4% higher in selected lines than in controls. The incremental cost of locomotion (grams food/revolution), computed as the partial regression slope of food consumption on revolutions run per day, did not differ between selected and control mice. On a 24-h basis, the total incremental cost of running (covering a distance) amounted to only 4.4% of food consumption in the control lines and 7.5% in the selected ones. However, the daily incremental cost of time active is higher (15.4% and 13.1% of total food consumption in selected and control lines, respectively). If wheel running in the selected lines continues to increase mainly by increases in velocity, then constraints related to energy acquisition are unlikely to be an important factor limiting further selective gain. More generally, our results suggest that, in small mammals, a substantial evolutionary increase in daily movement distances can be achieved by increasing running speed, without remarkable increases in total energy expenditure.