The energetic cost of bipedal hopping in small mammals

Understanding Australia’s unique hopping species: a comparative review of the musculoskeletal system and locomotor biomechanics in Macropodoidea

Kangaroos and other macropodoids stand out among mammals for their unusual hopping locomotion and body shape. This review examines the scaling of hind- and forelimb bones, and the primary ankle extensor muscles and tendons. We find that the scaling of the musculoskeletal system is sensitive to the phylogenetic context. Tibia length increases with positive allometry among most macropodoids, but negative allometry in eastern grey kangaroos and isometry in red kangaroos. Femur length decreases with stronger negative allometry in eastern grey and red kangaroos than among other macropodoids. Muscle masses scale with negative allometry in western grey kangaroos and with isometry in red kangaroos, compared to positive allometry in other macropodoids. We further summarise the work on the hopping gait, energetics in macropodoids, and stresses in the musculoskeletal system in an evolutionary context, to determine what trade-offs may limit locomotor performance in macropodoids. When large kangaroos hop, they do not increase oxygen consumption with speed, unlike most mammals, including small hopping species. We conclude that there is not enough information to isolate the biomechanical factors that make large kangaroos so energy efficient. We identify key areas for further research to fill these gaps.

Elastic energy storage across speeds during steady-state hopping of desert kangaroo rats (Dipodomys deserti)

Small bipedal hoppers, including kangaroo rats, are thought to not benefit from substantial elastic energy storage and return during hopping. However, recent species-specific material properties research suggests that, despite relative thickness, the ankle extensor tendons of these small hoppers are considerably more compliant than had been assumed. With faster locomotor speeds demanding higher forces, a lower tendon stiffness suggests greater tendon deformation and thus a greater potential for elastic energy storage and return with increasing speed. Using the elastic modulus values specific to kangaroo rat tendons, we sought to determine how much elastic energy is stored and returned during hopping across a range of speeds. In vivo techniques were used to record tendon force in the ankle extensors during steady-speed hopping. Our data support the hypothesis that the ankle extensor tendons of kangaroo rats store and return elastic energy in relation to hopping speed, storing more at faster speeds. Despite storing comparatively less elastic energy than larger hoppers, this relationship between speed and energy storage offer novel evidence of a functionally similar energy storage mechanism, operating irrespective of body size or tendon thickness, across the distal muscle-tendon units of both small and large bipedal hoppers.

Plantar flexor muscles of kangaroo rats (Dipodomys deserti) shorten at a velocity to produce optimal power during jumping

The musculotendon work contributions across all joints during jumping by kangaroo rats are not well understood. Namely, measures of external joint work do not provide information on the contributions from individual muscles or in-series elastic structures. In this study, we examined the functional roles of a major ankle extensor muscle, the lateral gastrocnemius (LG), and a major knee extensor muscle, the vastus lateralis (VL), through in vivo sonomicrometry and electromyography techniques, during vertical jumping by kangaroo rats. Our data showed that both muscles increased shortening and activity with higher jumps. We found that knee angular velocity and VL muscle shortening velocity were coupled in time. In contrast, the ankle angular velocity and LG muscle shortening velocity were decoupled, and rapid joint extension near the end of the jump produced high power outputs at the ankle joint. Further, the decoupling of muscle and joint kinematics allowed the LG muscle to prolong the period of shortening velocity near optimal velocity, which likely enabled the muscle to sustain maximal power generation. These observations were consistent with an LG tendon that is much more compliant than that of the VL.

The energy allocation trade-offs underlying life history traits in hypometabolic strepsirhines and other primates

Life history, brain size and energy expenditure scale with body mass in mammals but there is little conclusive evidence for a correlated evolution between life history and energy expenditure (either basal/resting or daily) independent of body mass. We addressed this question by examining the relationship between primate free-living daily energy expenditure (DEE) measured by doubly labeled water method (n = 18 species), life history variables (maximum lifespan, gestation and lactation duration, interbirth interval, litter mass, age at first reproduction), resting metabolic rate (RMR) and brain size. We also analyzed whether the hypometabolic primates of Madagascar (lemurs) make distinct energy allocation tradeoffs compared to other primates (monkeys and apes) with different life history traits and ecological constraints. None of the life-history traits correlated with DEE after controlling for body mass and phylogeny. In contrast, a regression model showed that DEE increased with increasing RMR and decreasing reproductive output (i.e., litter mass/interbirth interval) independent of body mass. Despite their low RMR and smaller brains, lemurs had an average DEE remarkably similar to that of haplorhines. The data suggest that lemurs have evolved energy strategies that maximize energy investment to survive in the unusually harsh and unpredictable environments of Madagascar at the expense of reproduction.

Functional morphology of the ankle extensor muscle-tendon units in the springhare Pedetes capensis shows convergent evolution with macropods for bipedal hopping locomotion

This study assesses the functional morphology of the ankle extensor muscle-tendon units of the springhare Pedetes capensis, an African bipedal hopping rodent, to test for convergent evolution with the Australian bipedal hopping macropods. We dissect and measure the gastrocnemius, soleus, plantaris, and flexor digitorum longus in 10 adult springhares and compare them against similar-sized macropods using phylogenetically informed scaling analyses. We show that springhares align reasonably well with macropod predictions, being statistically indistinguishable with respect to the ankle extensor mean weighted muscle moment arm (1.63 vs. 1.65 cm, respectively), total muscle mass (41.1 vs. 29.2 g), total muscle physiological cross-sectional area (22.9 vs. 19.3 cm² ), mean peak tendon stress (26.2 vs. 35.2 MPa), mean tendon safety factor (4.7 vs. 3.6), and total tendon strain energy return capacity (1.81 vs. 1.82 J). However, total tendon cross-sectional area is significantly larger in springhares than predicted for a similar-sized macropod (0.26 vs. 0.17 cm² , respectively), primarily due to a greater plantaris tendon thickness (0.084 vs. 0.048 cm² ), and secondarily because the soleus muscle-tendon unit is present in springhares but is vestigial in macropods. The overall similarities between springhares and macropods indicate that evolution has favored comparable lower hindlimb body plans for bipedal hopping locomotion in the two groups of mammals that last shared a common ancestor ~160 million years ago. The springhare's relatively thick plantaris tendon may facilitate rapid transfer of force from muscle to skeleton, enabling fast and accelerative hopping, which could help to outpace and outmaneuver predators.

The Spine: A Strong, Stable, and Flexible Structure with Biomimetics Potential

From its first appearance in early vertebrates, the spine evolved the function of protecting the spinal cord, avoiding excessive straining during body motion. Its stiffness and strength provided the basis for the development of the axial skeleton as the mechanical support of later animals, especially those which moved to the terrestrial environment where gravity loads are not alleviated by the buoyant force of water. In tetrapods, the functions of the spine can be summarized as follows: protecting the spinal cord; supporting the weight of the body, transmitting it to the ground through the limbs; allowing the motion of the trunk, through to its flexibility; providing robust origins and insertions to the muscles of trunk and limbs. This narrative review provides a brief perspective on the development of the spine in vertebrates, first from an evolutionary, and then from an embryological point of view. The paper describes functions and the shape of the spine throughout the whole evolution of vertebrates and vertebrate embryos, from primordial jawless fish to extant animals such as birds and humans, highlighting its fundamental features such as strength, stability, and flexibility, which gives it huge potential as a basis for bio-inspired technologies.

Terrestrial locomotion energy costs vary considerably between species: no evidence that this is explained by rate of leg force production or ecology

Inter-specifically, relative energy costs of terrestrial transport vary several-fold. Many pair-wise differences of locomotor costs between similarly-sized species are considerable, and are yet to be explained by morphology or gait kinematics. Foot contact time, a proxy for rate of force production, is a strong predictor of locomotor energy costs across species of different size and might predict variability between similarly sized species. We tested for a relationship between foot contact time and metabolic rate during locomotion from published data. We investigated the phylogenetic correlation between energy expenditure rate and foot contact time, conditioned on fixed effects of mass and speed. Foot contact time does not explain variance in rate of energy expenditure during locomotion, once speed and body size are accounted for. Thus, perhaps surprisingly, inter-specific differences in the mass-independent net cost of terrestrial transport (NCOT) are not explained by rates of force production. We also tested for relationships between locomotor energy costs and eco-physiological variables. NCOT did not relate to any of the tested eco-physiological variables; we thus conclude either that interspecific differences in transport cost have no influence on macroecological and macrophysiological patterns, or that NCOT is a poor indicator of animal energy expenditure beyond the treadmill.

Functional capacity of kangaroo rat hindlimbs: adaptations for locomotor performance

Many cursorial and large hopping species are extremely efficient locomotors with various morphological adaptations believed to reduce mechanical demand and improve movement efficiency, including elongated distal limb segments. However, despite having elongated limbs, small hoppers such as desert kangaroo rats (Dipodomys deserti) are less efficient locomotors than their larger counterparts, which may be in part due to avoiding predators through explosive jumping movements. Despite potentially conflicting mechanical demands between the two movements, kangaroo rats are both excellent jumpers and attain high hopping speeds, likely due to a specialized hindlimb musculoskeletal morphology. This study combined experimental dissection data with a static analysis of muscle moment generating capacities using a newly developed musculoskeletal model to characterize kangaroo rat hindlimb musculoskeletal architecture and investigate how morphology has evolved to meet hopping and jumping mechanical demands. Hindlimb morphology appears biased towards generating constant moment arms over large joint ranges of motion in this species, which may balance competing requirements by reducing the need for posture and movement specific excitation patterns. The ankle extensors are a major exception to the strong positive relationship exhibited by most muscles between muscle architecture parameters (e.g. Lfibre) and joint moment arms. These muscles appear suited to meeting the high moments required for jumping: the biarticular nature of the ankle extensors is leveraged to reduce MTU strain and create a four-bar linkage that facilitates proximal force transfer. The kangaroo rat hindlimb provides an interesting case study for understanding how morphology balances the sometimes competing demands of hopping and jumping.

Why do mammals hop? Understanding the ecology, biomechanics and evolution of bipedal hopping

Bipedal hopping is a specialized mode of locomotion that has arisen independently in at least five groups of mammals. We review the evolutionary origins of these groups, examine three of the most prominent hypotheses for why bipedal hopping may have arisen, and discuss how this unique mode of locomotion influences the behavior and ecology of modern species. While all bipedal hoppers share generally similar body plans, differences in underlying musculoskeletal anatomy influence what performance benefits each group may derive from this mode of locomotion. Based on a review of the literature, we conclude that the most likely reason that bipedal hopping evolved is associated with predator avoidance by relatively small species in forested environments. Yet, the morphological specializations associated with this mode of locomotion have facilitated the secondary acquisition of performance characteristics that enable these species to be highly successful in ecologically demanding environments such as deserts. We refute many long-held misunderstandings about the origins of bipedal hopping and identify potential areas of research that would advance the understanding of this mode of locomotion.

Comparative Physiology of Fatigue

This review attempts to provide insights into factors associated with fatigue in human and nonhuman animals by using the two fundamental approaches of comparative physiology: determining common principles that govern structure and function in animals that are relatively invariant between animals and evaluating animals that have been highly adapted by natural selection to demonstrate extreme performance. In this review, I approach the topic of fatigue by considering factors that are associated with its reciprocal or inverse or duration of sustained performance before fatigue sets in to end the performance. The two general factors that I consider that affect endurance time more than any other are body temperature and body mass. The former affects endurance time because of thermodynamic effects on chemical reaction rates and metabolism; the latter acts through the mechanism of allometry or scaling. The examples of extreme animal performance that I discuss are two examples of bird migration, the diving performance of marine mammals, and the unique relationship that governs energy cost of locomotion in hopping kangaroos.

Ecological and evolutionary significance of sizes of giant extinct kangaroos

A method, based on femoral circumference, allowed us to develop body mass estimates for 11 extinct Pleistocene megafaunal species of macropodids (Protemnodon anak, P. brehus, P. hopei, P. roechus, Procoptodon goliah, ‘P.’ gilli, Simosthenurus maddocki, S. occidentalis, Sthenurus andersoni, S. stirlingi and S. tindalei) and three fossil populations of the extant eastern grey kangaroo (Macropus giganteus). With the possible exception of P. goliah, the extinct taxa were browsers, among which sympatric, congeneric species sort into size classes separated by body mass increments of 20–75%. None show evidence of size variation through time, and only the smallest (‘P.’ gilli) exhibits evidence suggestive of marked sexual dimorphism. The largest surviving macropodids (five species of Macropus) are grazers which, although sympatric, do not differ greatly in body mass today, but at least one species (M. giganteus) fluctuated markedly in body size over the course of the Pleistocene. Sexual dimorphism in these species is marked, and may have varied through time. There is some mass overlap between the extinct and surviving macropodid taxa. With a mean estimated body mass of 232 kg, Procoptodon goliah was the largest hopping mammal ever to exist.

Effects of size, sex, and voluntary running speeds on costs of locomotion in lines of laboratory mice selectively bred for high wheel-running activity

Selective breeding for over 35 generations has led to four replicate (S) lines of laboratory house mice (Mus domesticus) that run voluntarily on wheels about 170% more than four random-bred control (C) lines. We tested whether S lines have evolved higher running performance by increasing running economy (i.e., decreasing energy spent per unit of distance) as a correlated response to selection, using a recently developed method that allows for nearly continuous measurements of oxygen consumption (VO2) and running speed in freely behaving animals. We estimated slope (incremental cost of transport [COT]) and intercept for regressions of power (the dependent variable, VO2/min) on speed for 49 males and 47 females, as well as their maximum VO2 and speeds during wheel running, under conditions mimicking those that these lines face during the selection protocol. For comparison, we also measured COT and maximum aerobic capacity (VO2max) during forced exercise on a motorized treadmill. As in previous studies, the increased wheel running of S lines was mainly attributable to increased average speed, with males also showing a tendency for increased time spent running. On a whole-animal basis, combined analysis of males and females indicated that COT during voluntary wheel running was significantly lower in the S lines (one-tailed P=0.015). However, mice from S lines are significantly smaller and attain higher maximum speeds on the wheels; with either body mass or maximum speed (or both) entered as a covariate, the statistical significance of the difference in COT is lost (one-tailed P> or =0.2). Thus, both body size and behavior are key components of the reduction in COT. Several statistically significant sex differences were observed, including lower COT and higher resting metabolic rate in females. In addition, maximum voluntary running speeds were negatively correlated with COT in females but not in males. Moreover, males (but not females) from the S lines exhibited significantly higher treadmill VO2max as compared to those from C lines. The sex-specific responses to selection may in part be consequences of sex differences in body mass and running style. Our results highlight how differences in size and running speed can account for lower COT in S lines and suggest that lower COT may have coadapted in response to selection for higher running distances in these lines.

Locomotion energetics and gait characteristics of a rat-kangaroo, Bettongia penicillata, have some kangaroo-like features

The locomotory characteristics of kangaroos and wallabies are unusual, with both energetic costs and gait parameters differing from those of quadrupedal running mammals. The kangaroos and wallabies have an evolutionary history of only around 5 million years; their closest relatives, the rat-kangaroos, have a fossil record of more than 26 million years. We examined the locomotory characteristics of a rat-kangaroo, Bettongia penicillata. Locomotory energetics and gait parameters were obtained from animals exercising on a motorised treadmill at speeds from 0.6 m s(-1) to 6.2 m s(-1). Aerobic metabolic costs increased as hopping speed increased, but were significantly different from the costs for a running quadruped; at the fastest speed, the cost of hopping was 50% of the cost of running. Therefore B. penicillata can travel much faster than quadrupedal runners at similar levels of aerobic output. The maximum aerobic output of B. penicillata was 17 times its basal metabolism. Increases in speed during hopping were achieved through increases in stride length, with stride frequency remaining constant. We suggest that these unusual locomotory characteristics are a conservative feature among the hopping marsupials, with an evolutionary history of 20-30 million years.

Unifying principles in terrestrial locomotion: do hopping Australian marsupials fit in?

Mammalian terrestrial locomotion has many unifying principles. However, the Macropodoidea are a particularly interesting group that exhibit a number of significant deviations from the principles that seem to apply to other mammals. While the properties of materials that comprise the musculoskeletal system of mammals are similar, evidence suggests that tendon properties in macropodoid marsupials may be size or function dependent, in contrast to the situation in placental mammals. Postural differences related to hopping versus running have a dramatic effect on the scaling of the pelvic limb musculoskeletal system. Ratios of muscle fibre to tendon cross-sectional areas for ankle extensors and digital flexors scale with positive allometry in all mammals, but exponents are significantly higher in macropods. Tendon safety factors decline with increasing body mass in mammals, with eutherians at risk of ankle extensor tendon rupture at a body mass of about 150 kg, whereas kangaroos encounter similar problems at a body mass of approximately 35 kg. Tendon strength appears to limit locomotor performance in these animals. Elastic strain energy storage in tendons is mass dependent in all mammals, but exponents are significantly larger in macropodid. Tibial stresses may scale with positive allometry in kangaroos, which result in lower bone safety factors in macropods compared to eutherian mammals.

Experimental alteration of limb posture in the chicken (Gallus gallus) and its bearing on the use of birds as analogs for dinosaur locomotion

Extant birds represent the only diverse living bipeds, and can be informative for investigations into the life-history parameters of their extinct dinosaurian relatives. However, morphological changes that occurred during early avian evolution, including the unique adoption of a nearly horizontal femoral orientation associated with a shift in center of mass (CM), suggest that caution is warranted in the use of birds as analogs for nonavian dinosaur locomotion. In this study, we fitted a group of white leghorn chickens (Gallus gallus) with a weight suspended posterior to the hip in order to examine the effects on loading and morphology. This caused a CM shift that necessitated a change in femoral posture (by 35 degrees towards the horizontal, P < 0.001), and resulted in reorientation of the ground reaction force (GRF) vector relative to the femur (from 41 degrees to 82 degrees, P < 0.001). Despite similar strain magnitudes, an overall increase in torsion relative to bending (from 1.70 to 1.95 times bending, P < 0.001) was observed, which was weakly associated with a tendency for increased femoral cross-sectional dimensions (P = 0.1). We suggest that a relative increase in torsion is consistent with a change in femoral posture towards the horizontal, since this change increases the degree to which the bone axis and the GRF vector produce mediolateral long-axis rotation of the bone. These results support the hypothesis that a postural change during early avian evolution could underlie the allometric differences seen between bird and nonavian dinosaur femora by requiring more robust femoral dimensions in birds due to an increase in torsion.

Muscle-tendon stresses and elastic energy storage during locomotion in the horse

The stresses acting in muscle-tendon units and ligaments of the forelimb and hindlimb of horses were determined over a range of speed and gait based on recordings of ground reaction forces and limb kinematics. Maximum stresses of 40-50 MPa were calculated to act in several of the principal forelimb (superficial digital flexor (SDF), deep digital flexor (DDF), ulnaris lateralis (UL) and flexor carpi ulnaris/radialis (FCU/R)) and hindlimb tendons (plantaris, DDF) at the fastest galloping speeds recorded (up to 7.4 m s-1). Smaller stresses were found for the gastrocnemius (GAST) tendon (30 MPa) and suspensory ligaments (S-Ligs) (18-25 MPa). Average peak muscle stresses reached 200-240 kPa during galloping. Tendon and muscle stresses increased more steeply with changes of gait and during galloping, than during trotting. Calculations of elastic strain energy storage based on tendon stress showed similar patterns of increase with change of speed and gait, with the greatest contribution to elastic savings by the DDF tendons of the forelimb and hindlimb. In general, the hindlimb contributed two-thirds and the forelimb one-third to overall energy storage. Comparison of tendon elastic energy savings with mechanical work showed a maximum 40% recovery of mechanical work by elastic savings when the horses changed gait from a walk to a slow trot. Percentage of recovery then decreased with increased trotting speed, but increased again with a change of gait to a gallop, reaching 36% recovery at the fastest measured galloping speed (7.4 m s-1). The long length of horse tendons in relation to extremely short pennate muscle fibers suggests a highly specialized design for economical muscle force generation and enhanced elastic energy savings. However, elastic energy savings in terms of percentage of recovery of mechanical work and metabolic energy is less than that observed in wallabies and kangaroos during hopping, but similar to that in humans during running, and greater than that for dogs during trotting and galloping.

Scaling of elastic strain energy in kangaroos and the benefits of being big

Large kangaroos are unique among mammals in their ability to uncouple aerobic metabolic energy costs from the speed of locomotion, making hopping an economical gait. During the first half of the ground-contact phase, kinetic energy lost from the body is stored as elastic strain energy, predominantly in the hind limbs. The subsequent recoil returns kinetic and potential energy to the body. Here we show that the allometry of structures in the legs and feet of Macropodoidea is different from that of quadrupedal eutherian mammals. The potential for elastic energy storage in hoppers is shown to scale with strong positive allometry. This is a function of the structural properties of muscle-tendon units in the distal hind limbs and the postures adopted by hopping kangaroos. Our findings demonstrate how the use of tissue elasticity is strongly mass dependent and help explain the observed energetic phenomena.

Energetic efficiency and ecology as selective factors in the saltatory adaptation of prosimian primates

We tend to assume that natural selection will bring about 'optimal' configurations in morphology and behaviour. Jumping locomotion involves large forces and energy costs which, in this non-cyclic activity, are generated anew with each jump. Jumping appears to be, therefore, a major target for optimization. It has been a standard assumption that jumpers will tend to adopt ballistic paths which will minimize the energy costs involved in jumping, and will act to minimize the loads applied to the body. Experimental studies, using kinematic analysis of digitized video recordings of the jump in five prosimian primates, with a 25-fold range in body mass, show that most do not adopt energy-efficient paths until the length of the jump is close to the maximum they can attain. Statistical analysis of quantified field observations suggests that, of three primate jumpers, only the largest, most unspecialized appears to take the forces applied to the musculoskeletal system into consideration when selecting supports used in locomotion. 'Ecological' factors, such as time pressure and habitat support density, may thus be the prime consideration for many species in determining the manner in which they jump.

Energetics of running: a new perspective

The amount of energy used to run a mile is nearly the same whether it is run at top speed or at a leisurely pace (although it is used more rapidly at the higher speed). This puzzling independence of energy cost and speed is found generally among running animals, although, on a per gram basis, cost is much higher for smaller animals. Running involves little work against the environment; work is done by muscles and tendons to lift and accelerate the body and limbs. Some of the work is recovered from muscle-tendon springs without metabolic cost and work rate does not parallel metabolic rate with either speed or size. Regardless of the amount of work muscles do, they must be activated and develop force to support the weight of the body. Load-carrying experiments have shown that the cost of supporting an extra newton of load is the same as the weight-specific cost of running. Size differences in cost are proportional to stride frequency at equivalent speeds, suggesting that the time available for developing force is important in determining cost. We report a simple inverse relationship between the rate of energy used for running and the time the foot applies force to the ground during each stride. These results support the hypothesis that it is primarily the cost of supporting the animal's weight and the time course of generating this force that determines the cost of running.

Running and breathing in mammals

Mechanical constraints appear to require that locomotion and breathing be synchronized in running mammals. Phase locking of limb and respiratory frequency has now been recorded during treadmill running in jackrabbits and during locomotion on solid ground in dogs, horses, and humans. Quadrupedal species normally synchronize the locomotor and respiratory cycles at a constant ratio of 1:1 (strides per breath) in both the trot and gallop. Human runners differ from quadrupeds in that while running they employ several phase-locked patterns (4:1, 3:1, 2:1, 1:1, 5:2, and 3:2), although a 2:1 coupling ratio appears to be favored. Even though the evolution of bipedal gait has reduced the mechanical constraints on respiration in man, thereby permitting greater flexibility in breathing pattern, it has seemingly not eliminated the need for the synchronization of respiration and body motion during sustained running. Flying birds have independently achieved phase-locked locomotor and respiratory cycles. This hints that strict locomotor-respiratory coupling may be a vital factor in the sustained aerobic exercise of endothermic vertebrates, especially those in which the stresses of locomotion tend to deform the thoracic complex.