Theoretical considerations on maximum running speeds for large and small animals

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.

Body size, shape and ecology in tetrapods

Body size and shape play fundamental roles in organismal function and it is expected that animals may possess body proportions that are well-suited to their ecological niche. Tetrapods exhibit a diverse array of body shapes, but to date this diversity in body proportions and its relationship to ecology have not been systematically quantified. Using whole-body skeletal models of 410 extinct and extant tetrapods, we show that allometric relationships vary across individual body segments thereby yielding changes in overall body shape as size increases. However, we also find statistical support for quadratic relationships indicative of differential scaling in small-medium versus large animals. Comparisons of locomotor and dietary groups highlight key differences in body proportions that may mechanistically underlie occupation of major ecological niches. Our results emphasise the pivotal role of body proportions in the broad-scale ecological diversity of tetrapods.

Here, the authors examine how body size, shape, and segment proportions correspond to ecology in models of 410 tetrapods. They find variable allometric relationships, differential scaling in small and large animals, and body proportions as a potential niche occupation mechanism.

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.

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.

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.

Why are the fastest runners of intermediate size? Contrasting scaling of mechanical demands and muscle supply of work and power

The fastest land animals are of intermediate size. Cheetah, antelope, greyhounds and racehorses have been measured running much faster than reported for elephants or elephant shrews. Can this be attributed to scaling of physical demands and explicit physiological constraints to supply? Here, we describe the scaling of mechanical work demand each stride, and the mechanical power demand each stance. Unlike muscle stress, strain and strain rate, these mechanical demands cannot be circumvented by changing the muscle gearing with minor adaptations in bone geometry or trivial adjustments to limb posture. Constraints to the capacity of muscle to supply work and power impose fundamental limitations to maximum speed. Given an upper limit to muscle work capacity each contraction, maximum speeds in big animals are constrained by the mechanical work demand each step. With an upper limit to instantaneous muscle power production, maximal speeds in small animals are limited by the high power demands during brief stance periods. The high maximum speed of the cheetah may therefore be attributed as much to its size as to its other anatomical and physiological adaptations.

The fast and the frugal: Divergent locomotory strategies drive limb lengthening in theropod dinosaurs

Limb length, cursoriality and speed have long been areas of significant interest in theropod paleobiology, since locomotory capacity, especially running ability, is critical in the pursuit of prey and to avoid becoming prey. The impact of allometry on running ability, and the limiting effect of large body size, are aspects that are traditionally overlooked. Since several different non-avian theropod lineages have each independently evolved body sizes greater than any known terrestrial carnivorous mammal, ~1000kg or more, the effect that such large mass has on movement ability and energetics is an area with significant implications for Mesozoic paleoecology. Here, using expansive datasets that incorporate several different metrics to estimate body size, limb length and running speed, we calculate the effects of allometry on running ability. We test traditional metrics used to evaluate cursoriality in non-avian theropods such as distal limb length, relative hindlimb length, and compare the energetic cost savings of relative hindlimb elongation between members of the Tyrannosauridae and more basal megacarnivores such as Allosauroidea or Ceratosauridae. We find that once the limiting effects of body size increase is incorporated there is no significant correlation to top speed between any of the commonly used metrics, including the newly suggested distal limb index (Tibia + Metatarsus/ Femur length). The data also shows a significant split between large and small bodied theropods in terms of maximizing running potential suggesting two distinct strategies for promoting limb elongation based on the organisms’ size. For small and medium sized theropods increased leg length seems to correlate with a desire to increase top speed while amongst larger taxa it corresponds more closely to energetic efficiency and reducing foraging costs. We also find, using 3D volumetric mass estimates, that the Tyrannosauridae show significant cost of transport savings compared to more basal clades, indicating reduced energy expenditures during foraging and likely reduced need for hunting forays. This suggests that amongst theropods, hindlimb evolution was not dictated by one particular strategy. Amongst smaller bodied taxa the competing pressures of being both a predator and a prey item dominant while larger ones, freed from predation pressure, seek to maximize foraging ability. We also discuss the implications both for interactions amongst specific clades and Mesozoic paleobiology and paleoecological reconstructions as a whole.

Mammals repel mosquitoes with their tails

The swinging of a mammal's tail has long been thought to deter biting insects, which, in cows, can drain up to 0.3 liters of blood per day. How effective is a mammal's tail at repelling insects? In this combined experimental and theoretical study, we filmed horses, zebras, elephants, giraffes and dogs swinging their tails. The tail swings at triple the frequency of a gravity-driven pendulum, and requires 27 times more power input. Tails can also be used like a whip to directly strike at insects. This whip-like effect requires substantial torques from the base of the tail on the order of 101–102 N m, comparable to the torque of a sedan, but still within the physical limits of the mammal. Based on our findings, we designed and built a mammal tail simulator to simulate the swinging of the tail. The simulator generates mild breezes of 1 m s–1, comparable to a mosquito's flight speed, and sufficient to deter up to 50% of mosquitoes from landing. This study may help us determine new mosquito-repelling strategies that do not depend on chemicals.