Locomotor kinematics on sand versus vinyl flooring in the sidewinder rattlesnake Crotalus cerastes

For terrestrial locomotion of animals and machines, physical characteristics of the substrate can strongly impact kinematics and performance. Snakes are an especially interesting system for studying substrate effects because their gait depends more on the environment than on their speed. We tested sidewinder rattlesnakes (Crotalus cerastes) on two surfaces: sand collected from their natural environment and vinyl tile flooring, an artificial surface often used to elicit sidewinding in laboratory settings. Of ten kinematic variables examined, two differed significantly between the substrates: the body's waveform had an average of ∼17% longer wavelength on vinyl flooring (measured in body lengths), and snakes lifted their bodies an average of ∼40% higher on sand (measured in body lengths). Sidewinding may also differ among substrates in ways we did not measure (e.g. ground reaction forces and energetics), leaving open clear directions for future study.

Effects of particle size and thickness of quartz sand on the webbed foot kinematics of mallard (Anas platyrhynchos)

The webbed foot structure of mallards (Anas platyrhynchos) exhibits effective anti-subsidence properties when walking on soft ground. To investigate the effects of quartz sand particle size and thickness on joint angles and the movement patterns of webbed feet, we created a testing substrate with quartz sand and utilized high-speed cameras and kinematic analysis tools for data acquisition. Mallards mainly adjusted the tarsometatarso-phalangeal joint (TMTPJ) during touch-down and lift-off stages in response to increasing particle size or enhanced ground roughness. Conversely, adjustments to the intertarsal joint (ITJ) predominantly took place during mid-stance. Conversely, mallards predominantly adjusted the ITJ during touch-down and lift-off when coping with increased quartz sand thickness, with TMTPJ adjustments mainly occurring at touch-down. As quartz sand particle size increased, the TMTPJ angle increased, the ITJ angle decreased, toe closure advanced, and the duty factor decreased throughout the entire stride cycle. In contrast, increasing quartz sand thickness led to more delayed TMTPJ adjustments, slower webbed foot closure, and an increased duty factor throughout the stride cycle. Mallards modify their leg posture to notably decrease the touch-down foot angle upon encountering sandy terrain. This action subsequently forms a depression beneath their feet, contributing to sand consolidation and limiting flow. During the stance phase, the mallard's weight is distributed across the webbed foot, generating minimal pressure and preventing significant subsidence while walking on sandy ground.

On the variability and dependence of human leg stiffness across strides during running and some consequences for the analysis of locomotion data

Typically, animal locomotion studies involve consecutive strides, which are frequently assumed to be independent with parameters that do not vary across strides. This assumption is often not tested. However, failing in particular to account for dependence across strides may cause an incorrect estimate of the uncertainty of the measurements and thereby lead to either missing (overestimating variance) or over-evaluating (underestimating variance) biological signals. In turn, this impacts replicability of the results because variability is accounted for differently across experiments. In this paper, we analyse the changes of a couple of measures of human leg stiffness across strides during running experiments, using a publicly available dataset. A major finding of this analysis is that the time series of these measurements of stiffness show autocorrelation even at large lags and so there is dependence between individual strides, even when separated by many intervening strides. Our results question the practice in biomechanics research of using each stride as an independent observation or of sub-selecting strides at small lags. Following the outcome of our analysis, we strongly recommend caution in doing so without first confirming the independence of the measurements across strides and without confirming that sub-selection does not produce spurious results.

Learning quadrupedal locomotion on deformable terrain

Simulation-based reinforcement learning approaches are leading the next innovations in legged robot control. However, the resulting control policies are still not applicable on soft and deformable terrains, especially at high speed. The primary reason is that reinforcement learning approaches, in general, are not effective beyond the data distribution: The agent cannot perform well in environments that it has not experienced. To this end, we introduce a versatile and computationally efficient granular media model for reinforcement learning. Our model can be parameterized to represent diverse types of terrain from very soft beach sand to hard asphalt. In addition, we introduce an adaptive control architecture that can implicitly identify the terrain properties as the robot feels the terrain. The identified parameters are then used to boost the locomotion performance of the legged robot. We applied our techniques to the Raibo robot, a dynamic quadrupedal robot developed in-house. The trained networks demonstrated high-speed locomotion capabilities on deformable terrains: The robot was able to run on soft beach sand at 3.03 meters per second although the feet were completely buried in the sand during the stance phase. We also demonstrate its ability to generalize to different terrains by presenting running experiments on vinyl tile flooring, athletic track, grass, and a soft air mattress.

A Step Forward: Functional Diversity and Emerging Themes of Slow-Speed Locomotion in Vertebrates

Walking can be defined broadly as a slow-speed movement produced when appendages interact with the ground to generate forward propulsion. Until recently, most studies of walking have focused on humans and a handful of domesticated vertebrates moving at a steady rate over highly simplified, static surfaces, which may bias our understanding of the unifying principles that underlie vertebrate locomotion. In the last few decades, studies have expanded to include a range of environmental contexts (e.g., uneven terrain, perturbations, deformable substrates) and greater phylogenetic breadth (e.g., non-domesticated species, small and/or ectothermic tetrapods and fishes); these studies have revealed that even a gait as superficially simple as walking is far more complex than previously thought. In addition, technological advances and accessibility of imaging systems and computational power have recently expanded our capabilities to test hypotheses about the locomotor movements of extant and extinct organisms in silico. In this symposium, scientists showcased diverse taxa (from extant fishes to extinct dinosaurs) moving through a range of variable conditions (speed perturbations, inclines, and deformable substrates) to address the causes and consequences of functional diversity in locomotor systems and discuss nascent research areas and techniques. From the symposium contributions, several themes emerged: (1) slow-speed, appendage-based movements in fishes are best described as walking-like movements rather than true walking gaits, (2) environmental variation (e.g., deformable substrates) and dynamic stimuli (e.g., perturbations) trigger kinematic and neuromuscular changes in animals that make defining a single gait or the transition between gaits more complicated than originally thought, and (3) computational advances have increased the ability to process large data sets, emulate the 3D motions of extant and extinct taxa, and even model species interactions in ancient ecosystems. Although this symposium allowed us to make great strides forward in our understanding of vertebrate walking, much ground remains to be covered. First, there is a much greater range of vertebrate appendage-based locomotor behaviors than has been previously recognized and existing terminology fails to accurately capture and describe this diversity. Second, despite recent efforts, the mechanisms that vertebrates use modify locomotor behaviors in response to predictable and unpredictable locomotor challenges are still poorly understood. Third, while computer-based models and simulations facilitate a greater understanding of the kinetics and kinematics of movement in both extant and extinct animals, a universal, one-size-fits-all, predictive model of appendage-based movement in vertebrates remains elusive.

Mudskippers modulate their locomotor kinematics when moving on deformable and inclined substrates

Many ecological factors influence animal movement, including properties of the media that they move on or through. Animals moving in terrestrial environments encounter conditions that can be challenging for generating propulsion and maintaining stability, such as inclines and deformable substrates that can cause slipping and sinking. In response, tetrapods tend to adopt a more crouched posture and lower their center of mass on inclines and increase the surface area of contact on deformable substrates, such as sand. Many amphibious fishes encounter the same challenges when moving on land, but how these finned animals modulate their locomotion with respect to different environmental conditions and how these modifications compare with those seen within tetrapods is relatively understudied. Mudskippers (Gobiidae: Oxudercinae) are a particularly noteworthy group of amphibious fishes in this context given that they navigate a wide range of environmental conditions, from flat mud to inclined mangrove trees. They use a unique form of terrestrial locomotion called 'crutching', where their pectoral fins synchronously lift and vault the front half of the body forward before landing on their pelvic fins while the lower half of the body and tail are kept straight. However, recent work has shown that mudskippers modify some aspects of their locomotion when crutching on deformable surfaces, particularly those at an incline. For example, on inclined dry sand, mudskippers bent their bodies laterally and curled and extended their tails to potentially act as a secondary propulsor and/or anti-slip device. In order to gain a more comprehensive understanding of the functional diversity and context-dependency of mudskipper crutching, we compared their kinematics on different combinations of substrate types (solid, mud, dry sand) and inclines (0°, 10°, 20°). In addition to increasing lateral bending on deformable and inclined substrates, we found that mudskippers increased the relative contact time and contact area of their paired fins while becoming more crouched, responses comparable to those seen in tetrapods and other amphibious fishes. Mudskippers on these substrates also exhibited previously undocumented behaviors, such as extending and adpressing the distal portions of their pectoral fins more anteriorly, dorsoventrally bending their trunk, "belly-flopping" on sand, and "gripping" the mud substrate with their pectoral fin rays. Our study highlights potential compensatory mechanisms shared among vertebrates in terrestrial environments while also illustrating that locomotor flexibility and even novelty can emerge when animals are challenged with environmental variation.

Performance and Kinematic Differences Between Terrestrial and Aquatic Running in Anolis Sagrei

Many animals frequently transition between different media while navigating their heterogeneous environments. These media vary in compliance, moisture content, and other characteristics that affect their physical properties. As a result, animals may need to alter their kinematics to adapt to potential changes in media while maintaining performance during predator escape and foraging. Due to its fluid nature, water is highly compliant, and although usually associated with swimming, water running has evolved in a variety of animals ranging from insects to mammals. While the best studied large water runners are the bipedal basilisk lizards (Basiliscus spp.), other lizards have also been observed to run across the surface of water, namely Hemidactylus platyurus, a house gecko, and in this study, Anolis sagrei, the brown anole. Unlike the basilisk lizard, the primarily arboreal Anolis sagrei is not adapted for water running. Moreover, water running in A. sagrei, similar to that of the house gecko, was primarily quadrupedal. Here, we tested for performance and kinematic differences between aquatic and terrestrial running and if the variance in performance and kinematic variables differed between the two media. We found no difference in average and maximum velocity between running on land and water. We also found that Anolis sagrei had higher hindlimb stride frequencies, decreased duty factor, and shorter stride lengths on water, as well as more erect postures. Finally, we found that most kinematics did not differ in variance between the two media, but of those that were different, almost all were more variable during terrestrial running. Our findings show that animals may be capable of specialized modes of locomotion, even if they are not obviously adapted for them, and that they may do this by modulating their kinematics to facilitate locomotion through novel environments.

Comparison between the kinematics for kangaroo rat hopping on a solid versus sand surface

In their natural habitats, animals move on a variety of substrates, ranging from solid surfaces to those that yield and flow (e.g. sand). These substrates impose different mechanical demands on the musculoskeletal system and may therefore elicit different locomotion patterns. The goal of this study is to compare bipedal hopping by desert kangaroo rats (Dipodomys deserti) on a solid versus granular substrate under speed-controlled conditions. To accomplish this goal, we developed a rotary treadmill, which is able to have different substrates or uneven surfaces. We video recorded six kangaroo rats hopping on a solid surface versus sand at the same speed (1.8 m s^-1) and quantified the differences in the hopping kinematics between the two substrates. We found no significant differences in the hop period, hop length or duty cycle, showing that the gross kinematics on the two substrates were similar. This similarity was surprising given that sand is a substrate that absorbs mechanical energy. Measurements of the penetration resistance of the sand showed that the combination of the sand properties, toe-print area and kangaroo rat weight was probably the reason for the similarity.

Camouflage versus running performance as strategies against predation in a lizard inhabiting different habitats

Running speed and camouflage are associated with the foraging and anti-predator abilities of animals. The toad-headed lizard, Phrynocephalus versicolor, has evolved a darker dorsal color in melanistic habitats and maintained a lighter color in adjacent, non-melanistic habitats. We test the hypothesis that lizards have weaker running speed on well-matching backgrounds than on less matching backgrounds. We used lizard models to compare the predation pressure, while the running speed of dark and light lizards were compared in field tunnels using a video recording method. Our results indicated that both the dark lizards in melanistic Heishankou (HSK) and the light lizards in non-melanistic Guazhou (GZ) face lower predation pressure than potential color-background unmatched lizards. The light lizards have a potentially higher running speed than darker lizards in melanistic habitats, which implies that substrate color matching populations with benefits of camouflage might have lower anti-predation pressure, and the costs of investment in melanin production may reduce running capacity.

How head shape and substrate particle size affect fossorial locomotion in lizards

Granular substrates ranging from silt to gravel cover much of the Earth's land area, providing an important habitat for fossorial animals. Many of these animals use their heads to penetrate the substrate. Although there is considerable variation in head shape, how head shape affects fossorial locomotor performance in different granular substrates is poorly understood. Here, head shape variation for 152 species of fossorial lizards was quantified for head diameter, slope and pointiness of the snout. The force needed to penetrate different substrates was measured using 28 physical models spanning this evolved variation. Ten substrates were considered, ranging in particle size from 0.025 to 4 mm in diameter and consisting of spherical or angular particles. Head shape evolved in a weakly correlated manner, with snouts that were gently sloped being blunter. There were also significant clade differences in head shape among fossorial lizards. Experiments with physical models showed that as head diameter increased, absolute penetration force increased but force normalized by cross-sectional area decreased. Penetration force decreased for snouts that tapered more gradually and were pointier. Larger and angular particles required higher penetration forces, although intermediate size spherical particles, consistent with coarse sand, required the lowest force. Particle size and head diameter effect were largest, indicating that fossorial burrowers should evolve narrow heads and bodies, and select relatively fine particles. However, variation in evolved head shapes and recorded penetration forces suggests that kinematics of fossorial movement are likely an important factor in explaining evolved diversity.

Morphological function of toe fringe in the sand lizard Phrynocephalus mystaceus

Toe fringe is the most typical morphological feature of lizards adapted to sandy environments, and it is simple in shape, can evolve repeatedly, and has a high degree of repetition; therefore, this feature is suitable for testing the adaptive convergence suggested by form-environment correlations. Phrynocephalus mystaceus mainly lives in dune habitats, has a developed bilateral toe fringe, and exhibits fast sand-burying behavior for predator avoidance. We tested the effects of resecting the medial and bilateral toe fringes on the locomotor performance and sand-burying performance of P. mystaceus. The results showed that the maximum sprint speed and acceleration on sand substrate did not significantly differ under different conditions (P > 0.05). Sand-burying performance scores of the unresected individuals were significantly greater than those of the resected individuals (P < 0.05). A partial least squares (PLS) regression analysis showed that the relative area of toe fringe was the main factor affecting the sand-burying performance of unresected P. mystaceus. For lizards without fringe, the PLS regression showed that the swinging index of the hind-limb was the main factor affecting the sand-burying performance of the lizard. A comparison of the swinging indexes of the hind-limb of the lizard under three states revealed that under the unresected states, the frequency of the swinging of the hind-limb was significantly higher than those of lizards with resected bilateral fringes, further indicating that the lizards compensated for the loss of fringe by increasing the time and frequency of swinging of the hind-limb. A path analysis also showed that the fringe affected the sand-burying performance of P. mystaceus not only directly but also indirectly by affecting the frequency of the swinging of the hind-limb. After the bilateral toe fringe was removed, a significant negative correlation between locomotor and sand-burying performance was observed (P < 0.05). Taken together, these results provide experimental evidence that toe fringe is positively associated with the sand-burying performance of P. mystaceus.

Locomotion and palaeoclimate explain the re-evolution of quadrupedal body form in Brachymeles lizards

Evolutionary reversals, including re-evolution of lost structures, are commonly found in phylogenetic studies. However, we lack an understanding of how these reversals happen mechanistically. A snake-like body form has evolved many times in vertebrates, and occasionally a quadrupedal form has re-evolved, including in Brachymeles lizards. We use body form and locomotion data for species ranging from snake-like to quadrupedal to address how a quadrupedal form could re-evolve. We show that large, quadrupedal species are faster at burying and surface locomotion than snake-like species, indicating a lack of expected performance trade-off between these modes of locomotion. Species with limbs use them while burying, suggesting that limbs are useful for burying in wet, packed substrates. Palaeoclimatological data suggest that Brachymeles originally evolved a snake-like form under a drier climate probably with looser soil in which it was easier to dig. The quadrupedal clade evolved as the climate became humid, where limbs and large size facilitated fossorial locomotion in packed soils.

Convergent Evolution of Elongate Forms in Craniates and of Locomotion in Elongate Squamate Reptiles

Synopsis Elongate, snake- or eel-like, body forms have evolved convergently many times in most major lineages of vertebrates. Despite studies of various clades with elongate species, we still lack an understanding of their evolutionary dynamics and distribution on the vertebrate tree of life. We also do not know whether this convergence in body form coincides with convergence at other biological levels. Here, we present the first craniate-wide analysis of how many times elongate body forms have evolved, as well as rates of its evolution and reversion to a non-elongate form. We then focus on five convergently elongate squamate species and test if they converged in vertebral number and shape, as well as their locomotor performance and kinematics. We compared each elongate species to closely related quadrupedal species and determined whether the direction of vertebral or locomotor change matched in each case. The five lineages examined are obscure species from remote locations, providing a valuable glimpse into their biology. They are the skink lizards Brachymeles lukbani, Lerista praepedita, and Isopachys anguinoides, the basal squamate Dibamus novaeguineae, and the basal snake Malayotyphlops cf. ruficaudus. Our results support convergence among these species in the number of trunk and caudal vertebrae, but not vertebral shape. We also find that the elongate species are relatively slower than their limbed counterparts and move with lower frequency and higher amplitude body undulations, with the exception of Isopachys. This is among the first evidence of locomotor convergence across distantly related, elongate species.

Evolution of fossorial locomotion in the transition from tetrapod to snake-like in lizards

Dramatic evolutionary transitions in morphology are often assumed to be adaptive in a new habitat. However, these assumptions are rarely tested because such tests require intermediate forms, which are often extinct. In vertebrates, the evolution of an elongate, limbless body is generally hypothesized to facilitate locomotion in fossorial and/or cluttered habitats. However, these hypotheses remain untested because few studies examine the locomotion of species ranging in body form from tetrapod to snake-like. Here, we address these functional hypotheses by testing whether trade-offs exist between locomotion in surface, fossorial and cluttered habitats in Australian Lerista lizards, which include multiple intermediate forms. We found that snake-like species penetrated sand substrates faster than more lizard-like species, representing the first direct support of the adaptation to fossoriality hypothesis. By contrast, body form did not affect surface locomotion or locomotion through cluttered leaf litter. Furthermore, all species with hindlimbs used them during both fossorial and surface locomotion. We found no evidence of a trade-off between fossorial and surface locomotion. This may be either because Lerista employed kinematic strategies that took advantage of both axial- and limb-based propulsion. This may have led to the differential occupation of their habitat, facilitating diversification of intermediate forms.

Effective drag of a rod in fluid-saturated granular beds

We measure the drag encountered by a vertically oriented rod moving across a sedimented granular bed immersed in a fluid under steady-state conditions. At low rod speeds, the presence of the fluid leads to a lower drag because of buoyancy, whereas a significantly higher drag is observed with increasing speeds. The drag as a function of the depth is observed to decrease from being quadratic at low speeds to appearing more linear at higher speeds. By scaling the drag with the average weight of the grains acting on the rod, we obtain the effective friction μ_{e} encountered over six orders of magnitude of speeds. While a constant μ_{e} is found when the grain size, rod depth, and fluid viscosity are varied at low speeds, a systematic increase is observed as the speed is increased. We analyze μ_{e} in terms of the inertial number I and viscous number J to understand the relative importance of inertia and viscous forces, respectively. For sufficiently high fluid viscosities, we find that the effect of varying the speed, depth, and viscosity can be described by the empirical function μ_{e}=μ_{o}+kJ^{n}, where μ_{o} is the effective friction measured in the quasistatic limit, and k and n are material constants. The drag is then analyzed in terms of the effective viscosity η_{e} and found to decrease systematically as a function of J. We further show that η_{e} as a function of J is directly proportional to the fluid viscosity and the μ_{e} encountered by the rod.