Where Have All the Giants Gone? How Animals Deal with the Problem of Size

Footfall patterns and stride parameters of Common hippopotamus (Hippopotamus amphibius) on land

Common hippopotamuses (hippos) are among the largest extant land mammals. They thus offer potential further insight into how giant body size on land influences locomotor patterns and abilities. Furthermore, as they have semi-aquatic habits and unusual morphology, they prompt important questions about how locomotion evolved in Hippopotamidae. However, basic information about how hippos move is limited and sometimes contradictory. We aimed to test if hippos trot at all speeds and if they ever use an aerial (suspended) phase, and to quantify how their locomotor patterns (footfalls and stride parameters) change with approximate speed. We surveyed videos available online and collected new video data from two zoo hippos in order to calculate the data needed to achieve our aims; gathering a sample of 169 strides from 32 hippos. No hippos studied used other than trotting (or near-trotting) footfall patterns, but at the fastest relative speeds hippos used brief aerial phases, apparently a new discovery. Hippos exhibit relatively greater athletic capacity than elephants in several ways, but perhaps not greater than rhinoceroses. Our data help form a baseline for assessing if other hippos use normal locomotion; relevant to clinical veterinary assessments of lameness; and for reconstructing the evolutionary biomechanics of hippo lineages.

Why animals can outrun robots

Animals are much better at running than robots. The difference in performance arises in the important dimensions of agility, range, and robustness. To understand the underlying causes for this performance gap, we compare natural and artificial technologies in the five subsystems critical for running: power, frame, actuation, sensing, and control. With few exceptions, engineering technologies meet or exceed the performance of their biological counterparts. We conclude that biology's advantage over engineering arises from better integration of subsystems, and we identify four fundamental obstacles that roboticists must overcome. Toward this goal, we highlight promising research directions that have outsized potential to help future running robots achieve animal-level performance.

Dynamic similarity and the peculiar allometry of maximum running speed

Animal performance fundamentally influences behaviour, ecology, and evolution. It typically varies monotonously with size. A notable exception is maximum running speed; the fastest animals are of intermediate size. Here we show that this peculiar allometry results from the competition between two musculoskeletal constraints: the kinetic energy capacity, which dominates in small animals, and the work capacity, which reigns supreme in large animals. The ratio of both capacities defines the physiological similarity index Γ, a dimensionless number akin to the Reynolds number in fluid mechanics. The scaling of Γ indicates a transition from a dominance of muscle forces to a dominance of inertial forces as animals grow in size; its magnitude defines conditions of "dynamic similarity" that enable comparison and estimates of locomotor performance across extant and extinct animals; and the physical parameters that define it highlight opportunities for adaptations in musculoskeletal "design" that depart from the eternal null hypothesis of geometric similarity. The physiological similarity index challenges the Froude number as prevailing dynamic similarity condition, reveals that the differential growth of muscle and weight forces central to classic scaling theory is of secondary importance for the majority of terrestrial animals, and suggests avenues for comparative analyses of locomotor systems.

Locomotion and the early Mesozoic success of Archosauromorpha

The Triassic was a time of ecological upheaval as life recovered from the Permian-Triassic mass extinction. Archosauromorphs were a key component of the recovery, diversifying substantially during the Triassic and encompassing the origins of dinosaurs, pterosaurs and crocodylomorphs. Here, we explore the evolution of locomotion in Archosauromorpha to test whether dinosaurs show any distinctive locomotory features that might explain their success. We implement geometric morphometrics on limb bone shapes and use limb ratios to calculate bipedality and cursoriality metrics. We find that the Avemetatarsalia (dinosaurs, pterosaurs and relatives) exhibit more variable limb form and limb ratios than any other group, indicating a wider range of locomotory modes. The earliest avemetatarsalians were bipedal and cursorial, and their range of form increased through the Triassic with notable diversification shifts following extinction events. This is especially true of dinosaurs, even though these changes cannot be discriminated from a stochastic process. By contrast, the Pseudosuchia (crocodilians and relatives) were more restricted in limb form and locomotor mode with disparity decreasing through time, suggesting more limited locomotor adaptation and vulnerability to extinction. Perhaps the greater locomotor plasticity of dinosaurs gave them a competitive advantage in the changing climates of the Late Triassic.

New genicular joint angle criteria for flexor muscle (Musculus Semimembranosus) during the terrestrial mammals walking

Background

The genicular or knee joint angles of terrestrial mammals remain constant during the stance phase of walking; however, the angles differ among taxa. The knee joint angle is known to correlate with taxa and body mass among extant mammals, yet several extinct mammals, such as desmostylians, do not have closely related descendants. Furthermore, fossils lose their soft tissues by the time they are unearthed, making body mass estimates difficult. These factors cause significant problems when reconstructing the proper postures of extinct mammals. Terrestrial mammals use potential and kinetic energy for locomotion; particularly, an inverted pendulum mechanism is used for walking. This mechanism requires maintaining the rod length constant, therefore, terrestrial mammals maintain their joint angle in a small range. A muscle reaction referred to as co-contraction is known to increase joint stiffness; both the agonist and antagonist muscles work simultaneously on the same joint at the same time. The musculus semimembranosus flexes the knee joint and acts as an antagonist to muscles that extend it.

Methods

Twenty-one species of terrestrial mammals were examined to identify the elements that constitute the angle between the m. semimembranosus and the tibia based on the period between the hindlimb touching down and taking off from the ground. Measurements were captured from videos in high-speed mode (420 fps), selecting 13 pictures from the first 75% of each video while the animals were walking. The angles between the main force line of the m. semimembranosus and the tibia, which were defined as θ_sm-t, were measured.

Results

The maximum and minimum angles between the m. semimembranosus and the tibia (θ_sm-t) of the stance instance (SI) were successfully determined for more than 80% of the target animals (17 out of 21 species) during SI-1 to SI-13 within ±10° from the mean. The difference between each successive SI was small and, therefore, the θ_sm-t transition was smooth. According to the results of the total stance differences among the target animals, θ_sm-t was relatively constant during a stance and, therefore, average θ_sm-t (θ_ave) can represent each animal. Only Carnivora had a significant difference in the correlation between body mass and θ_ave. In addition, there were significant differences in θ_ave between plantigrade and unguligrade locomotion.

Conclusion

Our measurements show that θ_ave was 100 ± 10° regardless taxon, body mass, and locomotor mode. Thus, only three points on skeletons need to be measured to determine θ_ave. This offers a new approximation approach for understanding hindlimb posture that could be applied to the study of the hindlimbs of extinct mammals with no closely related extant descendants.

Necrobotics: Biotic Materials as Ready-to-Use Actuators

Designs perfected through evolution have informed bioinspired animal-like robots that mimic the locomotion of cheetahs and the compliance of jellyfish; biohybrid robots go a step further by incorporating living materials directly into engineered systems. Bioinspiration and biohybridization have led to new, exciting research, but humans have relied on biotic materials-non-living materials derived from living organisms-since their early ancestors wore animal hides as clothing and used bones for tools. In this work, an inanimate spider is repurposed as a ready-to-use actuator requiring only a single facile fabrication step, initiating the area of "necrobotics" in which biotic materials are used as robotic components. The unique walking mechanism of spiders-relying on hydraulic pressure rather than antagonistic muscle pairs to extend their legs-results in a necrobotic gripper that naturally resides in its closed state and can be opened by applying pressure. The necrobotic gripper is capable of grasping objects with irregular geometries and up to 130% of its own mass. Furthermore, the gripper can serve as a handheld device and innately camouflages in outdoor environments. Necrobotics can be further extended to incorporate biotic materials derived from other creatures with similar hydraulic mechanisms for locomotion and articulation.

Low effective mechanical advantage of giraffes' limbs during walking reveals trade-off between limb length and locomotor performance

Giraffes (Giraffa camelopardalis) possess specialized locomotor morphology, namely elongate and gracile distal limbs. While this contributes to their overall height and enhances feeding behavior, we propose that the combination of long limb segments and modest muscle lever arms results in low effective mechanical advantage (EMA, the ratio of in-lever to out-lever moment arms), when compared with other cursorial mammals. To test this, we used a combination of experimentally measured kinematics and ground reaction forces (GRFs), musculoskeletal modeling, and inverse dynamics to calculate giraffe forelimb EMA during walking. Giraffes walk with an EMA of 0.34 (±0.05 SD), with no evident association with speed within their walking gait. Giraffe EMA was about four times lower than expectations extrapolated from other mammals, ranging from 0.03 to 297 kg, and this provides further evidence that EMA plateaus or even diminishes in mammals exceeding horse size. We further tested the idea that limb segment length is a factor which determines EMA, by modeling the GRF and muscle moment arms in the extinct giraffid Sivatherium giganteum and the other extant giraffid, Okapia johnstoni. Giraffa and Okapia shared similar EMA, despite a four to sixfold difference in body mass (Okapia EMA = 0.38). In contrast, Sivatherium, sharing a similar body mass with Giraffa, had greater EMA (0.59), which we propose reflects behavioral differences, such as a somewhat increased capability for athletic performance. Our modeling approach suggests that limb length is a determinant of GRF moment arm magnitude and that unless muscle moment arms scale isometrically with limb length, tall mammals are prone to low EMA.

Multi-joint analysis of pose viability supports the possibility of salamander-like hindlimb configurations in the Permian tetrapod Eryops megacephalus

Salamanders are often used as analogs for early tetrapods in paleontological reconstructions of locomotion. However, concerns have been raised about whether this comparison is justifiable, necessitating comparisons of a broader range of early tetrapods with salamanders. Here, we test whether the osteological morphology of the hindlimb in the early tetrapod (temnospondyl amphibian) Eryops megacephalus could have facilitated the sequence of limb configurations used by salamanders during terrestrial locomotion. To do so, we present a new method that enables the examination of full limb configurations rather than isolated joint poses. Based on this analysis, we conclude that E. megacephalus may indeed have been capable of salamander-like hindlimb kinematics. Our method facilitates the holistic visual comparison of limb configurations between taxa without reliance on the homology of coordinate system definitions, and can thus be applied to facilitate various comparisons between extinct and extant taxa, spanning the diversity of locomotion both past and present.

Walking-and Running and Jumping-with Dinosaurs and Their Cousins, Viewed Through the Lens of Evolutionary Biomechanics

Archosauria diversified throughout the Triassic Period before experiencing two mass extinctions near its end ∼201 Mya, leaving only the crocodile-lineage (Crocodylomorpha) and bird-lineage (Dinosauria) as survivors; along with the pterosaurian flying reptiles. About 50 years ago, the "locomotor superiority hypothesis" (LSH) proposed that dinosaurs ultimately dominated by the Early Jurassic Period because their locomotion was superior to other archosaurs'. This idea has been debated continuously since, with taxonomic and morphological analyses suggesting dinosaurs were "lucky" rather than surviving due to being biologically superior. However, the LSH has never been tested biomechanically. Here we present integration of experimental data from locomotion in extant archosaurs with inverse and predictive simulations of the same behaviours using musculoskeletal models, showing that we can reliably predict how extant archosaurs walk, run and jump. These simulations have been guiding predictive simulations of extinct archosaurs to estimate how they moved, and we show our progress in that endeavour. The musculoskeletal models used in these simulations can also be used for simpler analyses of form and function such as muscle moment arms, which inform us about more basic biomechanical similarities and differences between archosaurs. Placing all these data into an evolutionary and biomechanical context, we take a fresh look at the LSH as part of a critical review of competing hypotheses for why dinosaurs (and a few other archosaur clades) survived the Late Triassic extinctions. Early dinosaurs had some quantifiable differences in locomotor function and performance vs. some other archosaurs, but other derived dinosaurian features (e.g., metabolic or growth rates, ventilatory abilities) are not necessarily mutually exclusive from the LSH; or maybe even an opportunistic replacement hypothesis; in explaining dinosaurs' success.

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.

Inertial biometry from commercial 3D body meshes

Body segments inertial parameters (or, more generally encompassing humans and animal species, inertial biometry), often necessary in kinetics calculations, have been obtained in the past from cadavers, medical 3D imaging, 3D scanning, or geometric approximations. This restricted the inertial archives to a few species. The methodology presented here uses commercial 3D meshes of human and animal bodies, which can be further re-shaped and 'posed', according to an underlying skeletal structure, before processing. The sequence of steps from virtually chopping the mesh to the estimation of inertial parameters of body segments is described. The accuracy of the method is tested by comparing the estimated results to real data published for humans (male and female), horses, and domestic cats. The proposed procedure opens the possibility of remarkably expanding biomechanics research when body size and shape change, or when external tools, such as prosthesis and sport material, take part in biological movement.

Scaling of fibre area and fibre glycogen concentration in the hindlimb musculature of monitor lizards: implications for locomotor performance with increasing body size

A considerable biomechanical challenge faces larger terrestrial animals as the demands of body support scale with body mass (Mb), while muscle force capacity is proportional to muscle cross-sectional area, which scales with Mb2/3. How muscles adjust to this challenge might be best understood by examining varanids, which vary by five orders of magnitude in size without substantial changes in posture or body proportions. Muscle mass, fascicle length and physiological cross-sectional area all scale with positive allometry, but it remains unclear, however, how muscles become larger in this clade. Do larger varanids have more muscle fibres, or does individual fibre cross-sectional area (fCSA) increase? It is also unknown if larger animals compensate by increasing the proportion of fast-twitch (higher glycogen concentration) fibres, which can produce higher force per unit area than slow-twitch fibres. We investigated muscle fibre area and glycogen concentration in hindlimb muscles from varanids ranging from 105 g to 40,000 g. We found that fCSA increased with modest positive scaling against body mass (Mb0.197) among all our samples, and ∝Mb0.278 among a subset of our data consisting of never-frozen samples only. The proportion of low-glycogen fibres decreased significantly in some muscles but not others. We compared our results with the scaling of fCSA in different groups. Considering species means, fCSA scaled more steeply in invertebrates (∝Mb0.575), fish (∝Mb0.347) and other reptiles (∝Mb0.308) compared with varanids (∝Mb0.267), which had a slightly higher scaling exponent than birds (∝Mb0.134) and mammals (∝Mb0.122). This suggests that, while fCSA generally increases with body size, the extent of this scaling is taxon specific, and may relate to broad differences in locomotor function, metabolism and habitat between different clades.

Divergent locomotor evolution in "giant" kangaroos: Evidence from foot bone bending resistances and microanatomy

The extinct sthenurine (giant, short-faced) kangaroos have been proposed to have a different type of locomotor behavior to extant (macropodine) kangaroos, based both on physical limitations (the size of many exceeds the proposed limit for hopping) and anatomical features (features of the hind limb anatomy suggestive of weight-bearing on one leg at a time). Here, we use micro computerised tomography (micro-CT) scans of the pedal bones of six kangaroos, three sthenurine, and three macropodine, ranging from ~50 to 150 kg, to investigate possible differences in bone resistances to bending and cortical bone distribution that might relate to differences in locomotion. Using second moment of area analysis, we show differences in resistance to bending between the two subfamilies. Distribution of cortical bone shows that sthenurines had less resistant calcaneal tubers, implying a different foot posture during locomotion, and the long foot bones were more resistant to the medial bending stresses. These differences were the most pronounced between Pleistocene monodactyl sthenurines (Sthenurus stirlingi and Procoptodon browneorum) and the two species of Macropus (the extant M. giganteus and the extinct M. cf. M. titan) and support the hypothesis that these derived sthenurines employed bipedal striding. The Miocene sthenurine Hadronomas retains some more macropodine-like features of bone resistance to bending, perhaps reflecting its retention of the fifth pedal digit. The Pleistocene macropodine Protemnodon has a number of unique features, possibly indicative of a type of locomotion unlike the other kangaroos.

Whole-limb scaling of muscle mass and force-generating capacity in amniotes

Skeletal muscle mass, architecture and force-generating capacity are well known to scale with body size in animals, both throughout ontogeny and across species. Investigations of limb muscle scaling in terrestrial amniotes typically focus on individual muscles within select clades, but here this question was examined at the level of the whole limb across amniotes generally. In particular, the present study explored how muscle mass, force-generating capacity (measured by physiological cross-sectional area) and internal architecture (fascicle length) scales in the fore- and hindlimbs of extant mammals, non-avian saurians (‘reptiles’) and bipeds (birds and humans). Sixty species spanning almost five orders of magnitude in body mass were investigated, comprising previously published architectural data and new data obtained via dissections of the opossum Didelphis virginiana and the tegu lizard Salvator merianae. Phylogenetic generalized least squares was used to determine allometric scaling slopes (exponents) and intercepts, to assess whether patterns previously reported for individual muscles or functional groups were retained at the level of the whole limb, and to test whether mammals, reptiles and bipeds followed different allometric trajectories. In general, patterns of scaling observed in individual muscles were also observed in the whole limb. Reptiles generally have proportionately lower muscle mass and force-generating capacity compared to mammals, especially at larger body size, and bipeds exhibit strong to extreme positive allometry in the distal hindlimb. Remarkably, when muscle mass was accounted for in analyses of muscle force-generating capacity, reptiles, mammals and bipeds almost ubiquitously followed a single common scaling pattern, implying that differences in whole-limb force-generating capacity are principally driven by differences in muscle mass, not internal architecture. In addition to providing a novel perspective on skeletal muscle allometry in animals, the new dataset assembled was used to generate pan-amniote statistical relationships that can be used to predict muscle mass or force-generating capacity in extinct amniotes, helping to inform future reconstructions of musculoskeletal function in the fossil record.

Ontogenetic changes in limb posture, kinematics, forces and joint moments in American alligators (Alligator mississippiensis)

As animals increase in size, common patterns of morphological and physiological scaling may require them to perform behaviors such as locomotion while experiencing a reduced capacity to generate muscle force and an increased risk of tissue failure. Large mammals are known to manage increased mechanical demands by using more upright limb posture. However, the presence of such size-dependent changes in limb posture has rarely been tested in animals that use non-parasagittal limb kinematics. Here, we used juvenile to subadult American alligators (total length 0.46-1.27 m, body mass 0.3-5.6 kg) and examined their limb kinematics, forces, joint moments and center of mass (CoM) to test for ontogenetic shifts in posture and limb mechanics. Larger alligators typically walked with a more adducted humerus and femur and a more extended knee. Normalized peak joint moments reflected these postural patterns, with shoulder and hip moments imposed by the ground reaction force showing relatively greater magnitudes in the smallest individuals. Thus, as larger alligators use more upright posture, they incur relatively smaller joint moments than smaller alligators, which could reduce the forces that the shoulder and hip adductors of larger alligators must generate. The CoM shifted nonlinearly from juveniles through subadults. The more anteriorly positioned CoM in small alligators, together with their compliant hindlimbs, contributes to their higher forelimb and lower hindlimb normalized peak vertical forces in comparison to larger alligators. Future studies of alligators that approach maximal adult sizes could give further insight into how animals with non-parasagittal limb posture modulate locomotor patterns as they increase in mass and experience changes in the CoM.

Allometry in desert ant locomotion (Cataglyphis albicans and Cataglyphis bicolor) - does body size matter?

Desert ants show a large range of adaptations to their habitats. They can reach extremely high running speeds, for example, to shorten heat stress during foraging trips. It has recently been examined how fast walking speeds are achieved in different desert ant species. It is intriguing in this context that some species exhibit distinct intraspecific size differences. We therefore performed a complete locomotion analysis over the entire size spectrum of the species Cataglyphis bicolor, and we compared this intraspecific dataset with that of the allometrically similar species Cataglyphis albicans. Emphasis was on the allometry of locomotion: we considered the body size of each animal and analysed the data in terms of relative walking speed. Body size was observed to affect walking parameters, gait patterns and phase relationships in terms of absolute walking speed. Unexpectedly, on a relative scale, all ants tended to show the same overall locomotion strategy at low walking speeds, and significant differences occurred only between C. albicans and C. bicolor at high walking speeds. Our analysis revealed that C. bicolor ants use the same overall strategy across all body sizes, with small ants reaching the highest walking speeds (up to 80 body lengths s-1) by increasing their stride length and incorporating aerial phases. By comparison, C. albicans reached high walking speeds mainly by a high synchrony of leg movement, lower swing phase duration and higher stride frequency ranging up to 40 Hz.

Influence of captivity and selection on limb long bone cross-sectional morphology of reindeer

The emergence of pastoralism and animal husbandry has been a critical point in the history of human evolution. Beyond profound behavioural changes in domesticated animals compared to wild ones, characterising the morphological changes associated with domestication process remains challenging. Because reindeer (Rangifer tarandus) can be considered to still be in the early phases of the domestication process, the study of modern populations provides a unique opportunity to examine the impact of captivity and selective breeding on skeletal changes. In this work, we investigated the morphological changes in long limb bone cross-sections using 137 wild and domestic reindeer individuals bred in free-range, in captivity or used for racing and pulling. The shape and shaft cortical thickness of the six long limb bones (i.e., humerus, radioulna, metacarpal, femur, tibia and metatarsal) were measured using a 2D-geometric morphometrics approach taking into account subspecies, sex, body mass and lifestyle differences. These bones are important to understanding functional morphological changes because they can provide information on feeding and locomotor behaviours, as well as on body propulsion and weight bearing. Apart from the effects of taxonomy, etho-ecology and sex, we have found that captivity and selection induced important variations in the size and body mass of modern reindeer. Our results also showed that patterns of variation in cortical bone thickness of long limb bone cross-sections were strongly impacted by body mass and human-imposed restrictions in roaming. This demonstrates that bone cross-sections can provide information on changes in locomotor, reproductive and feeding behaviours induced by the domestication process. These results are valuable not only for (paleo) biologists studying the impact of captivity and selection in ungulates but also for archaeologists exploring the origins of domestication and early herding strategies.

The evolutionary biomechanics of locomotor function in giant land animals

Giant land vertebrates have evolved more than 30 times, notably in dinosaurs and mammals. The evolutionary and biomechanical perspectives considered here unify data from extant and extinct species, assessing current theory regarding how the locomotor biomechanics of giants has evolved. In terrestrial tetrapods, isometric and allometric scaling patterns of bones are evident throughout evolutionary history, reflecting general trends and lineage-specific divergences as animals evolve giant size. Added to data on the scaling of other supportive tissues and neuromuscular control, these patterns illuminate how lineages of giant tetrapods each evolved into robust forms adapted to the constraints of gigantism, but with some morphological variation. Insights from scaling of the leverage of limbs and trends in maximal speed reinforce the idea that, beyond 100-300 kg of body mass, tetrapods reduce their locomotor abilities, and eventually may lose entire behaviours such as galloping or even running. Compared with prehistory, extant megafaunas are depauperate in diversity and morphological disparity; therefore, turning to the fossil record can tell us more about the evolutionary biomechanics of giant tetrapods. Interspecific variation and uncertainty about unknown aspects of form and function in living and extinct taxa still render it impossible to use first principles of theoretical biomechanics to tightly bound the limits of gigantism. Yet sauropod dinosaurs demonstrate that >50 tonne masses repeatedly evolved, with body plans quite different from those of mammalian giants. Considering the largest bipedal dinosaurs, and the disparity in locomotor function of modern megafauna, this shows that even in terrestrial giants there is flexibility allowing divergent locomotor specialisations.

The allometry of locomotion

Organismal locomotion mediates ecological interactions and shapes community dynamics. Locomotion is constrained by intrinsic and environmental factors and integrating these factors should clarify how locomotion affects ecology across scales. We extended general theory based on metabolic scaling and biomechanics to predict the scaling of five locomotor performance traits: routine speed, maximum speed, maximum acceleration, minimum powered turn radius, and angular speed. To test these predictions, we used phylogenetically informed analyses of a new database with 884 species and found support for our quantitative predictions. Larger organisms were faster but less maneuverable than smaller organisms. Routine and maximum speeds scaled with body mass to 0.20 and 0.17 powers, respectively, and plateaued at higher body masses, especially for maximum speed. Acceleration was unaffected by body mass. Minimum turn radius scaled to a 0.19 power, and the 95% CI included our theoretical prediction, as we predicted. Maximum angular speed scaled higher than predicted but in the same direction. We observed universal scaling among locomotor modes for routine and maximum speeds but the intercepts varied; flying organisms were faster than those that swam or ran. Acceleration was independent of size in flying and aquatic taxa but decreased with body mass in land animals, possibly due to the risk of injury large, terrestrial organisms face at high speeds and accelerations. Terrestrial mammals inhabiting structurally simple habitats tended to be faster than those in complex habitats. Despite effects of body size, locomotor mode, and habitat complexity, universal scaling of locomotory performance reveals the general ways organisms move across Earth's complex environments.

Rules of nature's Formula Run: Muscle mechanics during late stance is the key to explaining maximum running speed

The maximum running speed of legged animals is one evident factor for evolutionary selection-for predators and prey. Therefore, it has been studied across the entire size range of animals, from the smallest mites to the largest elephants, and even beyond to extinct dinosaurs. A recent analysis of the relation between animal mass (size) and maximum running speed showed that there seems to be an optimal range of body masses in which the highest terrestrial running speeds occur. However, the conclusion drawn from that analysis-namely, that maximum speed is limited by the fatigue of white muscle fibres in the acceleration of the body mass to some theoretically possible maximum speed-was based on coarse reasoning on metabolic grounds, which neglected important biomechanical factors and basic muscle-metabolic parameters. Here, we propose a generic biomechanical model to investigate the allometry of the maximum speed of legged running. The model incorporates biomechanically important concepts: the ground reaction force being counteracted by air drag, the leg with its gearing of both a muscle into a leg length change and the muscle into the ground reaction force, as well as the maximum muscle contraction velocity, which includes muscle-tendon dynamics, and the muscle inertia-with all of them scaling with body mass. Put together, these concepts' characteristics and their interactions provide a mechanistic explanation for the allometry of maximum legged running speed. This accompanies the offering of an explanation for the empirically found, overall maximum in speed: In animals bigger than a cheetah or pronghorn, the time that any leg-extending muscle needs to settle, starting from being isometric at about midstance, at the concentric contraction speed required for running at highest speeds becomes too long to be attainable within the time period of a leg moving from midstance to lift-off. Based on our biomechanical model, we, thus, suggest considering the overall speed maximum to indicate muscle inertia being functionally significant in animal locomotion. Furthermore, the model renders possible insights into biological design principles such as differences in the leg concept between cats and spiders, and the relevance of multi-leg (mammals: four, insects: six, spiders: eight) body designs and emerging gaits. Moreover, we expose a completely new consideration regarding the muscles' metabolic energy consumption, both during acceleration to maximum speed and in steady-state locomotion.

The Effects of Mechanical Scale on Neural Control and the Regulation of Joint Stability

Recent work has demonstrated how the size of an animal can affect neural control strategies, showing that passive viscoelastic limb properties have a significant role in determining limb movements in small animals but are less important in large animals. We extend that work to consider effects of mechanical scaling on the maintenance of joint integrity; i.e., the prevention of aberrant contact forces within joints that might lead to joint dislocation or cartilage degradation. We first performed a literature review to evaluate how properties of ligaments responsible for joint integrity scale with animal size. Although we found that the cross-sectional area of the anterior cruciate ligament generally scaled with animal size, as expected, the effects of scale on the ligament’s mechanical properties were less clear, suggesting potential adaptations in passive contributions to the maintenance of joint integrity across species. We then analyzed how the neural control of joint stability is altered by body scale. We show how neural control strategies change across mechanical scales, how this scaling is affected by passive muscle properties and the cost function used to specify muscle activations, and the consequences of scaling on internal joint contact forces. This work provides insights into how scale affects the regulation of joint integrity by both passive and active processes and provides directions for studies examining how this regulation might be accomplished by neural systems.

The scaling of ground reaction forces and duty factor in monitor lizards: implications for locomotion in sprawling tetrapods

Geometric scaling predicts a major challenge for legged, terrestrial locomotion. Locomotor support requirements scale identically with body mass (α M¹), while force-generation capacity should scale α M^2/3 as it depends on muscle cross-sectional area. Mammals compensate with more upright limb postures at larger sizes, but it remains unknown how sprawling tetrapods deal with this challenge. Varanid lizards are an ideal group to address this question because they cover an enormous body size range while maintaining a similar bent-limb posture and body proportions. This study reports the scaling of ground reaction forces and duty factor for varanid lizards ranging from 7 g to 37 kg. Impulses (force×time) (α M^0.99-1.34) and peak forces (α M^0.73-1.00) scaled higher than expected. Duty factor scaled α M^0.04 and was higher for the hindlimb than the forelimb. The proportion of vertical impulse to total impulse increased with body size, and impulses decreased while peak forces increased with speed.

Monitoring muscle over three orders of magnitude: Widespread positive allometry among locomotor and body support musculature in the pectoral girdle of varanid lizards (Varanidae)

There is a functional trade-off in the design of skeletal muscle. Muscle strength depends on the number of muscle fibers in parallel, while shortening velocity and operational distance depend on fascicle length, leading to a trade-off between the maximum force a muscle can produce and its ability to change length and contract rapidly. This trade-off becomes even more pronounced as animals increase in size because muscle strength scales with area (length² ) while body mass scales with volume (length³ ). In order to understand this muscle trade-off and how animals deal with the biomechanical consequences of size, we investigated muscle properties in the pectoral girdle of varanid lizards. Varanids are an ideal group to study the scaling of muscle properties because they retain similar body proportions and posture across five orders of magnitude in body mass and are highly active, terrestrially adapted reptiles. We measured muscle mass, physiological cross-sectional area, fascicle length, proximal and distal tendon lengths, and proximal and distal moment arms for 27 pectoral girdle muscles in 13 individuals across 8 species ranging from 64 g to 40 kg. Standard and phylogenetically informed reduced major axis regression was used to investigate how muscle architecture properties scale with body size. Allometric growth was widespread for muscle mass (scaling exponent >1), physiological cross-sectional area (scaling exponent >0.66), but not tendon length (scaling exponent >0.33). Positive allometry for muscle mass was universal among muscles responsible for translating the trunk forward and flexing the elbow, and nearly universal among humeral protractors and wrist flexors. Positive allometry for PCSA was also common among trunk translators and humeral protractors, though less so than muscle mass. Positive scaling for fascicle length was not widespread, but common among humeral protractors. A higher proportion of pectoral girdle muscles scaled with positive allometry than our previous work showed for the pelvic girdle, suggesting that the center of mass may move cranially with body size in varanids, or that the pectoral girdle may assume a more dominant role in locomotion in larger species. Scaling exponents for physiological cross-sectional area among muscles primarily associated with propulsion or with a dual role were generally higher than those associated primarily with support against gravity, suggesting that locomotor demands have at least an equal influence on muscle architecture as body support. Overall, these results suggest that larger varanids compensate for the increased biomechanical demands of locomotion and body support at higher body sizes by developing larger pectoral muscles with higher physiological cross-sectional areas. The isometric scaling rates for fascicle length among locomotion-oriented pectoral girdle muscles suggest that larger varanids may be forced to use shorter stride lengths, but this problem may be circumvented by increases in limb excursion afforded by the sliding coracosternal joint.

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.

Biomechanical insights into the role of foot pads during locomotion in camelid species

From the camel’s toes to the horse’s hooves, the diversity in foot morphology among mammals is striking. One distinguishing feature is the presence of fat pads, which may play a role in reducing foot pressures, or may be related to habitat specialization. The camelid family provides a useful paradigm to explore this as within this phylogenetically constrained group we see prominent (camels) and greatly reduced (alpacas) fat pads. We found similar scaling of vertical ground reaction force with body mass, but camels had larger foot contact areas, which increased with velocity, unlike alpacas, meaning camels had relatively lower foot pressures. Further, variation between specific regions under the foot was greater in alpacas than camels. Together, these results provide strong evidence for the role of fat pads in reducing relative peak locomotor foot pressures, suggesting that the fat pad role in habitat specialization remains difficult to disentangle.

Transitions between foot postures are associated with elevated rates of body size evolution in mammals

Terrestrial mammals have evolved various foot postures: flat-footed (plantigrady), tiptoed (digitigrady), and hooved (unguligrady) postures. Although the importance of foot posture on ecology and body size of mammalian species has been widely recognized, its evolutionary trajectory and influence on body size evolution across mammalian phylogeny remain untested. Taking a Bayesian phylogenetic approach combined with a comprehensive dataset of foot postures in 880 extant mammalian species, we investigated the evolutionary history of foot postures and rates of body size evolution, within the same posture and at transitions between postures. Our results show that the common ancestor of mammals was plantigrade, and transitions predominantly occurred only between plantigrady and digitigrady and between digitigrady and unguligrady. At the transitions between plantigrady and digitigrady and between digitigrady and unguligrady, rates of body size evolution are significantly elevated leading to the larger body masses of digitigrade species (∼1 kg) and unguligrade species (∼78 kg) compared with their respective ancestral postures [plantigrady (∼0.75 kg) and digitigrady]. Our results demonstrate the importance of foot postures on mammalian body size evolution and have implications for mammalian body size increase through time. In addition, we highlight a way forward for future studies that seek to integrate morphofunctional and macroevolutionary approaches.

Flight energetics, caste dimorphism and scaling properties in the bumblebee, Bombus impatiens

Animal size affects the energetics of locomotion. Using female caste dimorphism in bumblebees, we assessed how body mass impacts morphological and physiological traits linked with flight. The allometric relationships obtained for wing surface area, wingbeat frequency, and flight and resting metabolic rates of workers could predict the trait values of queens that were more than fourfold larger. Flight success of queens decreased over time in part because of a large increase in body mass and a decrease in traits linked with flight, namely wingbeat frequency and metabolic rate, and the activity of metabolic enzymes tended to decrease. After taking into account temporal changes, body mass, flight wingbeat frequency and metabolic rate were repeatable. Finally, we found significant family resemblance for all traits measured, indicating that shared genes and/or environmental effects impact phenotypic variation. Together, our results show that the functional association between body morphology and flight physiology is robust, providing further insights into the mechanistic basis of metabolic rate scaling patterns during locomotion in animals.

Scaling of the ankle extensor muscle-tendon units and the biomechanical implications for bipedal hopping locomotion in the post-pouch kangaroo Macropus fuliginosus

Bipedal hopping is used by macropods, including rat-kangaroos, wallabies and kangaroos (superfamily Macropodoidea). Interspecific scaling of the ankle extensor muscle-tendon units in the lower hindlimbs of these hopping bipeds shows that peak tendon stress increases disproportionately with body size. Consequently, large kangaroos store and recover more strain energy in their tendons, making hopping more efficient, but their tendons are at greater risk of rupture. This is the first intraspecific scaling analysis on the functional morphology of the ankle extensor muscle-tendon units (gastrocnemius, plantaris and flexor digitorum longus) in one of the largest extant species of hopping mammal, the western grey kangaroo Macropus fuliginosus (5.8-70.5 kg post-pouch body mass). The effective mechanical advantage of the ankle extensors does not vary with post-pouch body mass, scaling with an exponent not significantly different from 0.0. Therefore, larger kangaroos balance rotational moments around the ankle by generating muscle forces proportional to weight-related gravitational forces. Maximum force is dependent upon the physiological cross-sectional area of the muscle, which we found scales geometrically with a mean exponent of only 0.67, rather than 1.0. Therefore, larger kangaroos are limited in their capacity to oppose large external forces around the ankle, potentially compromising fast or accelerative hopping. The strain energy return capacity of the ankle extensor tendons increases with a mean exponent of ~1.0, which is much shallower than the exponent derived from interspecific analyses of hopping mammals (~1.4-1.9). Tendon safety factor (ratio of rupture stress to estimated peak hopping stress) is lowest in the gastrocnemius (< 2), and it decreases with body mass with an exponent of -0.15, extrapolating to a predicted rupture at 160 kg. Extinct giant kangaroos weighing 250 kg could therefore not have engaged in fast hopping using 'scaled-up' lower hindlimb morphology of extant western grey kangaroos.