Variation in Center of Mass Estimates for Extant Sauropsids and its Importance for Reconstructing Inertial Properties of Extinct Archosaurs

Ontogenetic and interelemental study of appendicular bones of Caiman latirostris Daudin, 1802 sheds light on osteohistological variability in crocodylians

The osteohistology of vertebrates provides a reliable source to deduce biological information, particularly regarding growth and development. Although osteohistological studies in Neosuchia (Crocodyliformes, Mesoeucrocodylia) are relatively numerous, the number of species studied within the group is still small. Extant crocodilians are known to exhibit intraspecific variability linked to environmental conditions, habitat, feeding, and other intrapopulation factors. Here, we analyzed the osteohistology of the living South American Caiman latirostris throughout posthatching ontogeny. The histology of several appendicular bones of 13 different-sized captive and wild individuals were examined. Although some thin sections revealed the classic lamellar, parallel-fibered, or woven bone matrices, others showed a variation and a mix between the organization of the bone tissue. These histological differences are likely related to variability in the growth dynamics of caimans. In some bones of the juveniles studied, remnants of embryonic bone were observed. Osteohistological variation related to prevailing environmental conditions is documented. Furthermore, our results show ontogenetic variation in the type of bone tissues deposited throughout the development of C. latirostris. This study offers a broad framework for life history interpretations for C. latirostris and provides insight into the evolutionary history and ontogenetic growth of extinct crocodylian lineages.

Influence of posture during gliding flight in the flying lizardDraco volans

The agamid lizards of the genusDracoare undoubtedly the most renown reptilian gliders, using their rib-supported patagial wings as lifting surfaces while airborne. Recent investigations into these reptiles highlighted the role of body posture during gliding, however, the aerodynamics of postural changes inDracoremain unclear. Here, we examine the aerodynamics and gliding performances ofDraco volansusing a numerical approach focusing on three postural changes: wing expansion, body camber, and limb positioning. To this aim, we conducted 70 three-dimensional steady-state computational fluid dynamics simulations of gliding flight and 240 two-dimensional glide trajectory calculations. Our results demonstrate that while airborne,D. volansgenerates a separated turbulent boundary layer over its wings characterized by a large recirculation cell that is kept attached to the wing surface by interaction with wing-tip vortices, increasing lift generation. This lift generating mechanism may be controlled by changing wing expansion and shape to modulate the generation of aerodynamic force. Furthermore, our trajectory simulations highlight the influence of body camber and orientation on glide range. This sheds light on howD. volanscontrols its gliding performance, and conforms to the observation that these animals plan their glide paths prior to take off. Lastly,D. volansis mostly neutral in pitch and highly maneuverable, similar to other vertebrate gliders. The numerical study presented here thus provides a better understanding of the lift generating mechanism and the influence of postural changes in flight in this emblematic animal and will facilitate the study of gliding flight in analogous gliding reptiles for which direct observations are unavailable.

Decoupling body shape and mass distribution in birds and their dinosaurian ancestors

It is accepted that non-avian theropod dinosaurs, with their long muscular tails and small forelimbs, had a centre-of-mass close to the hip, while extant birds, with their reduced tails and enlarged wings have their mass centred more cranially. Transition between these states is considered crucial to two key innovations in the avian locomotor system: crouched bipedalism and powered flight. Here we use image-based models to challenge this dichotomy. Rather than a phylogenetic distinction between 'dinosaurian' and 'avian' conditions, we find terrestrial versus volant taxa occupy distinct regions of centre-of-mass morphospace consistent with the disparate demands of terrestrial bipedalism and flight. We track this decoupled evolution of body shape and mass distribution through bird evolution, including the origin of centre-of-mass positions more advantageous for flight and major reversions coincident with terrestriality. We recover modularity in the evolution of limb proportions and centre-of-mass that suggests fully crouched bipedalism evolved after powered flight.

Quantitative biomechanical assessment of locomotor capabilities of the stem archosaur Euparkeria capensis

Birds and crocodylians are the only remaining members of Archosauria (ruling reptiles) and they exhibit major differences in posture and gait, which are polar opposites in terms of locomotor strategies. Their broader lineages (Avemetatarsalia and Pseudosuchia) evolved a multitude of locomotor modes in the Triassic and Jurassic periods, including several occurrences of bipedalism. The exact timings and frequencies of bipedal origins within archosaurs, and thus their ancestral capabilities, are contentious. It is often suggested that archosaurs ancestrally exhibited some form of bipedalism. Euparkeria capensis is a central taxon for the investigation of locomotion in archosaurs due to its phylogenetic position and intermediate skeletal morphology, and is argued to be representative of facultative bipedalism in this group. However, no studies to date have biomechanically tested if bipedality was feasible in Eupakeria. Here, we use musculoskeletal models and static simulations in its hindlimb to test the influences of body posture and muscle parameter estimation methods on locomotor potential. Our analyses show that the resulting negative pitching moments around the centre of mass were prohibitive to sustainable bipedality. We conclude that it is unlikely that Euparkeria was facultatively bipedal, and was probably quadrupedal, rendering the inference of ancestral bipedal abilities in Archosauria unlikely.

The extinct shark Otodus megalodon was a transoceanic superpredator: Inferences from 3D modeling

Although shark teeth are abundant in the fossil record, their bodies are rarely preserved. Thus, our understanding of the anatomy of the extinct Otodus megalodon remains rudimentary. We used an exceptionally well-preserved fossil to create the first three-dimensional model of the body of this giant shark and used it to infer its movement and feeding ecology. We estimate that an adult O. megalodon could cruise at faster absolute speeds than any shark species today and fully consume prey the size of modern apex predators. A dietary preference for large prey potentially enabled O. megalodon to minimize competition and provided a constant source of energy to fuel prolonged migrations without further feeding. Together, our results suggest that O. megalodon played an important ecological role as a transoceanic superpredator. Hence, its extinction likely had large impacts on global nutrient transfer and trophic food webs.

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

Giraffes are the tallest living animals, using their height to access food unavailable to their competitors. It is not clear how their specialized anatomy impacts their athletic ability. We made musculoskeletal models of the forelimbs from a giraffe and two close relatives and used motion-capture and force data to measure how efficient they are when walking in a straight line. A horse, for example, uses just 1 unit of muscle force to oppose 1 unit of force on the ground. Giraffe limbs are comparatively disadvantaged—their muscles must develop 3 units of force to oppose 1 unit of force on the ground. This explains why giraffes walk and run at modest speeds.

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.

Birds can transition between stable and unstable states via wing morphing

Birds morph their wing shape to accomplish extraordinary manoeuvres^1–4, which are governed by avian-specific equations of motion. Solving these equations requires information about a bird’s aerodynamic and inertial characteristics⁵. Avian flight research to date has focused on resolving aerodynamic features, whereas inertial properties including centre of gravity and moment of inertia are seldom addressed. Here we use an analytical method to determine the inertial characteristics of 22 species across the full range of elbow and wrist flexion and extension. We find that wing morphing allows birds to substantially change their roll and yaw inertia but has a minimal effect on the position of the centre of gravity. With the addition of inertial characteristics, we derived a novel metric of pitch agility and estimated the static pitch stability, revealing that the agility and static margin ranges are reduced as body mass increases. These results provide quantitative evidence that evolution selects for both stable and unstable flight, in contrast to the prevailing narrative that birds are evolving away from stability⁶. This comprehensive analysis of avian inertial characteristics provides the key features required to establish a theoretical model of avian manoeuvrability.

Analysis of inertial characteristics across 22 bird species shows that evolution has selected for avian manoeuvrability using both stable and unstable flight dynamics.

Three-dimensional polygonal muscle modelling and line of action estimation in living and extinct taxa

Biomechanical models and simulations of musculoskeletal function rely on accurate muscle parameters, such as muscle masses and lines of action, to estimate force production potential and moment arms. These parameters are often obtained through destructive techniques (i.e., dissection) in living taxa, frequently hindering the measurement of other relevant parameters from a single individual, thus making it necessary to combine multiple specimens and/or sources. Estimating these parameters in extinct taxa is even more challenging as soft tissues are rarely preserved in fossil taxa and the skeletal remains contain relatively little information about the size or exact path of a muscle. Here we describe a new protocol that facilitates the estimation of missing muscle parameters (i.e., muscle volume and path) for extant and extinct taxa. We created three-dimensional volumetric reconstructions for the hindlimb muscles of the extant Nile crocodile and extinct stem-archosaur Euparkeria, and the shoulder muscles of an extant gorilla to demonstrate the broad applicability of this methodology across living and extinct animal clades. Additionally, our method can be combined with surface geometry data digitally captured during dissection, thus facilitating downstream analyses. We evaluated the estimated muscle masses against physical measurements to test their accuracy in estimating missing parameters. Our estimated muscle masses generally compare favourably with segmented iodine-stained muscles and almost all fall within or close to the range of observed muscle masses, thus indicating that our estimates are reliable and the resulting lines of action calculated sufficiently accurately. This method has potential for diverse applications in evolutionary morphology and biomechanics.

Quantifying avian inertial properties using calibrated computed tomography

Estimating centre of mass and mass moments of inertia is an important aspect of many studies in biomechanics. Characterising these parameters accurately in three dimensions is challenging with traditional methods requiring dissection or suspension of cadavers. Here, we present a method to quantify the three-dimensional centre of mass and inertia tensor of birds of prey using calibrated computed tomography (CT) scans. The technique was validated using several independent methods, providing body segment mass estimates within approximately 1% of physical dissection measurements and moment of inertia measurements with a 0.993 R2 correlation with conventional trifilar pendulum measurements. Calibrated CT offers a relatively straightforward, non-destructive approach that yields highly detailed mass distribution data that can be used for three-dimensional dynamics modelling in biomechanics. Although demonstrated here with birds, this approach should work equally well with any animal or appendage capable of being CT scanned.

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.

Predictive simulations of running gait reveal a critical dynamic role for the tail in bipedal dinosaur locomotion

Locomotion has influenced the ecology, evolution, and extinction of species throughout history, yet studying locomotion in the fossil record is challenging. Computational biomechanics can provide novel insight by mechanistically relating observed anatomy to whole-animal function and behavior. Here, we leverage optimal control methods to generate the first fully predictive, three-dimensional, muscle-driven simulations of locomotion in an extinct terrestrial vertebrate, the bipedal non-avian theropod dinosaur Coelophysis. Unexpectedly, our simulations involved pronounced lateroflexion movements of the tail. Rather than just being a static counterbalance, simulations indicate that the tail played a crucial dynamic role, with lateroflexion acting as a passive, physics-based mechanism for regulating angular momentum and improving locomotor economy, analogous to the swinging arms of humans. We infer this mechanism to have existed in many other bipedal non-avian dinosaurs as well, and our methodology provides new avenues for exploring the functional diversity of dinosaur tails in the future.

Convex hull estimation of mammalian body segment parameters

Obtaining accurate values for body segment parameters (BSPs) is fundamental in many biomechanical studies, particularly for gait analysis. Convex hulling, where the smallest-possible convex object that surrounds a set of points is calculated, has been suggested as an effective and time-efficient method to estimate these parameters in extinct animals, where soft tissues are rarely preserved. We investigated the effectiveness of convex hull BSP estimation in a range of extant mammals, to inform the potential future usage of this technique with extinct taxa. Computed tomography scans of both the skeleton and skin of every species investigated were virtually segmented. BSPs (the mass, position of the centre of mass and inertial tensors of each segment) were calculated from the resultant soft tissue segments, while the bone segments were used as the basis for convex hull reconstructions. We performed phylogenetic generalized least squares and ordinary least squares regressions to compare the BSPs calculated from soft tissue segments with those estimated using convex hulls, finding consistent predictive relationships for each body segment. The resultant regression equations can, therefore, be used with confidence in future volumetric reconstruction and biomechanical analyses of mammals, in both extinct and extant species where such data may not be available.

Computational modelling of muscle fibre operating ranges in the hindlimb of a small ground bird (Eudromia elegans), with implications for modelling locomotion in extinct species

The arrangement and physiology of muscle fibres can strongly influence musculoskeletal function and whole-organismal performance. However, experimental investigation of muscle function during in vivo activity is typically limited to relatively few muscles in a given system. Computational models and simulations of the musculoskeletal system can partly overcome these limitations, by exploring the dynamics of muscles, tendons and other tissues in a robust and quantitative fashion. Here, a high-fidelity, 26-degree-of-freedom musculoskeletal model was developed of the hindlimb of a small ground bird, the elegant-crested tinamou (Eudromia elegans, ~550 g), including all the major muscles of the limb (36 actuators per leg). The model was integrated with biplanar fluoroscopy (XROMM) and forceplate data for walking and running, where dynamic optimization was used to estimate muscle excitations and fibre length changes throughout both gaits. Following this, a series of static simulations over the total range of physiological limb postures were performed, to circumscribe the bounds of possible variation in fibre length. During gait, fibre lengths for all muscles remained between 0.5 to 1.21 times optimal fibre length, but operated mostly on the ascending limb and plateau of the active force-length curve, a result that parallels previous experimental findings for birds, humans and other species. However, the ranges of fibre length varied considerably among individual muscles, especially when considered across the total possible range of joint excursion. Net length change of muscle-tendon units was mostly less than optimal fibre length, sometimes markedly so, suggesting that approaches that use muscle-tendon length change to estimate optimal fibre length in extinct species are likely underestimating this important parameter for many muscles. The results of this study clarify and broaden understanding of muscle function in extant animals, and can help refine approaches used to study extinct species.

New data on tail lengths and variation along the caudal series in the non-avialan dinosaurs

The tails of non-avialan dinosaurs varied considerably in terms of overall length, total number of vertebrae, and gross form and function. A new dataset confirms that there is little or no consistent relationship between tail length and snout-sacrum length. Consequently, attempts to estimate one from the other are likely to be very error-prone. Patterns of changes in centra lengths across the caudal series vary among non-avian dinosaurs. However, some overarching patterns do emerge. A number of taxa show (anterior to posterior) a series of short centra, followed by a series of longer centra, with the remainder of the tail consisting of a long series of centra tapering in length. This pattern is consistent with functional constraints, and the anterior series of longer centra are coincident with the major attachments of femoral musculature. This pattern is not present in many basal taxa and may have evolved independently in different dinosaurian groups, further suggesting functional importance.

A Whole-Body Musculoskeletal Model of the Mouse

Neural control of movement cannot be fully understood without careful consideration of interactions between the neural and biomechanical components. Recent advancements in mouse molecular genetics allow for the identification and manipulation of constituent elements underlying the neural control of movement. To complement experimental studies and investigate the mechanisms by which the neural circuitry interacts with the body and the environment, computational studies modeling motor behaviors in mice need to incorporate a model of the mouse musculoskeletal system. Here, we present the first fully articulated musculoskeletal model of the mouse. The mouse skeletal system has been developed from anatomical references and includes the sets of bones in all body compartments, including four limbs, spine, head and tail. Joints between all bones allow for simulation of full 3D mouse kinematics and kinetics. Hindlimb and forelimb musculature has been implemented using Hill-type muscle models. We analyzed the mouse whole-body model and described the moment-arms for different hindlimb and forelimb muscles, the moments applied by these muscles on the joints, and their involvement in limb movements at different limb/body configurations. The model represents a necessary step for the subsequent development of a comprehensive neuro-biomechanical model of freely behaving mice; this will close the loop between the neural control and the physical interactions between the body and the environment.

A review and reappraisal of the specific gravities of present and past multicellular organisms, with an emphasis on tetrapods

The density, or specific gravity (SG), of organisms has numerous important implications for their form, function, ecology, and other facets of beings living and dead, and it is especially necessary to apply SG values that are as accurate as practical when estimating their masses which is itself a critical aspect of living things. Yet a comprehensive review and analysis of this notable subject of anatomy has never been conducted and published. This is such an effort, being as extensive as possible with the data on hand, bolstered by some additional observations, and new work focusing on extinct animals who densities are least unknown: pterosaurs and dinosaurs with extensive pneumatic complexes, including the most sophisticated effort to date for a sauropod. Often difficult to determine even via direct observation, techniques for obtaining the best possible SG data are explained and utilized, including observations of floating animals. Neutral specific gravity (NSG) is proposed as the most important value for tetrapods with respiratory tracts of fluctuating volume. SGs of organisms range from 0.08 to 2.6, plant tissues from 0.08 to 1.39, and vertebrates from about 0.75 (some giant pterosaurs) to 1.2 (those with heavy armor and/or skeletons). Tetrapod NSGs tend to be somewhat higher than widely thought, especially those theropod and sauropod dinosaurs and pterosaurs with air-sacs because respiratory system volume is usually measured at maximum inhalation in birds. Also discussed is evidence that the ratio of the mass of skeletons relative to total body mass has not been properly assayed in the past.

The accuracy and precision of body mass estimation in non-avian dinosaurs

Inferring the body mass of fossil taxa, such as non-avian dinosaurs, provides a powerful tool for interpreting physiological and ecological properties, as well as the ability to study these traits through deep time and within a macroevolutionary context. As a result, over the past 100 years a number of studies advanced methods for estimating mass in dinosaurs and other extinct taxa. These methods can be categorized into two major approaches: volumetric-density (VD) and extant-scaling (ES). The former receives the most attention in non-avian dinosaurs and advanced appreciably over the last century: from initial physical scale models to three-dimensional (3D) virtual techniques that utilize scanned data obtained from entire skeletons. The ES approach is most commonly applied to extinct members of crown clades but some equations are proposed and utilized in non-avian dinosaurs. Because both approaches share a common goal, they are often viewed in opposition to one another. However, current palaeobiological research problems are often approach specific and, therefore, the decision to utilize a VD or ES approach is largely question dependent. In general, biomechanical and physiological studies benefit from the full-body reconstruction provided through a VD approach, whereas large-scale evolutionary and ecological studies require the extensive data sets afforded by an ES approach. This study summarizes both approaches to body mass estimation in stem-group taxa, specifically non-avian dinosaurs, and provides a comparative quantitative framework to reciprocally illuminate and corroborate VD and ES approaches. The results indicate that mass estimates are largely consistent between approaches: 73% of VD reconstructions occur within the expected 95% prediction intervals of the ES relationship. However, almost three quarters of outliers occur below the lower 95% prediction interval, indicating that VD mass estimates are, on average, lower than would be expected given their stylopodial circumferences. Inconsistencies (high residual and per cent prediction deviation values) are recovered to a varying degree among all major dinosaurian clades along with an overall tendency for larger deviations between approaches among small-bodied taxa. Nonetheless, our results indicate a strong corroboration between recent iterations of the VD approach based on 3D specimen scans suggesting that our current understanding of size in dinosaurs, and hence its biological correlates, has improved over time. We advance that VD and ES approaches have fundamentally (metrically) different advantages and, hence, the comparative framework used and advocated here combines the accuracy afforded by ES with the precision provided by VD and permits the rapid identification of discrepancies with the potential to open new areas of discussion.

More than one way to be a giant: Convergence and disparity in the hip joints of saurischian dinosaurs

Saurischian dinosaurs evolved seven orders of magnitude in body mass, as well as a wide diversity of hip joint morphology and locomotor postures. The very largest saurischians possess incongruent bony hip joints, suggesting that large volumes of soft tissues mediated hip articulation. To understand the evolutionary trends and functional relationships between body size and hip anatomy of saurischians, we tested the relationships among discrete and continuous morphological characters using phylogenetically corrected regression. Giant theropods and sauropods convergently evolved highly cartilaginous hip joints by reducing supraacetabular ossifications, a condition unlike that in early dinosauromorphs. However, transitions in femoral and acetabular soft tissues indicate that large sauropods and theropods built their hip joints in fundamentally different ways. In sauropods, the femoral head possesses irregularly rugose subchondral surfaces for thick hyaline cartilage. Hip articulation was achieved primarily using the highly cartilaginous femoral head and the supraacetabular labrum on the acetabular ceiling. In contrast, theropods covered their femoral head and neck with thinner hyaline cartilage and maintained extensive articulation between the fibrocartilaginous femoral neck and the antitrochanter. These findings suggest that the hip joints of giant sauropods were built to sustain large compressive loads, whereas those of giant theropods experienced compression and shear forces.

Can skeletal surface area predict in vivo foot surface area?

The surface area of feet in contact with the ground is a key morphological feature that influences animal locomotion. Underfoot pressures (and consequently stresses experienced by the foot), as well as stability of an animal during locomotion, depend on the size and shape of this area. Here we tested whether the area of a skeletal foot could predict in vivo soft tissue foot surface area. Computed tomography scans of 29 extant tetrapods (covering mammals, reptiles, birds and amphibians) were used to produce models of both the soft tissues and the bones of their feet. Soft tissue models were oriented to a horizontal plane, and their outlines projected onto a surface to produce two-dimensional silhouettes. Silhouettes of skeletal models were generated either from bones in CT pose or with all autopodial bones aligned to the horizontal plane. Areas of these projections were calculated using alpha shapes (mathematical tight-fitting outline). Underfoot area of soft tissue was approximately 1.67 times that of skeletal tissue area (~ 2 times for manus, ~ 1.6 times for pes, if analysed separately). This relationship between skeletal foot area and soft tissue area, while variable in some of our study taxa, could provide information about the size of the organisms responsible for fossil trackways, suggest what size of tracks might be expected from potential trackmakers known only from skeletal remains, and aid in soft tissue reconstruction of skeletal remains for biomechanical modelling.

Ontogenetic changes in the body plan of the sauropodomorph dinosaur Mussaurus patagonicus reveal shifts of locomotor stance during growth

Ontogenetic information is crucial to understand life histories and represents a true challenge in dinosaurs due to the scarcity of growth series available. Mussaurus patagonicus was a sauropodomorph dinosaur close to the origin of Sauropoda known from hatchling, juvenile and mature specimens, providing a sufficiently complete ontogenetic series to reconstruct general patterns of ontogeny. Here, in order to quantify how body shape and its relationship with locomotor stance (quadruped/biped) changed in ontogeny, hatchling, juvenile (~1 year old) and adult (8+ years old) individuals were studied using digital models. Our results show that Mussaurus rapidly grew from about 60 g at hatching to ~7 kg at one year old, reaching >1000 kg at adulthood. During this time, the body's centre of mass moved from a position in the mid-thorax to a more caudal position nearer to the pelvis. We infer that these changes of body shape and centre of mass reflect a shift from quadrupedalism to bipedalism occurred early in ontogeny in Mussaurus. Our study indicates that relative development of the tail and neck was more influential in determining the locomotor stance in Sauropodomorpha during ontogeny, challenging previous studies, which have emphasized the influence of hindlimb vs. forelimb lengths on sauropodomorph stance.

Lower rotational inertia and larger leg muscles indicate more rapid turns in tyrannosaurids than in other large theropods

Synopsis

Tyrannosaurid dinosaurs had large preserved leg muscle attachments and low rotational inertia relative to their body mass, indicating that they could turn more quickly than other large theropods.

Methods

To compare turning capability in theropods, we regressed agility estimates against body mass, incorporating superellipse-based modeled mass, centers of mass, and rotational inertia (mass moment of inertia). Muscle force relative to body mass is a direct correlate of agility in humans, and torque gives potential angular acceleration. Agility scores therefore include rotational inertia values divided by proxies for (1) muscle force (ilium area and estimates of m. caudofemoralis longus cross-section), and (2) musculoskeletal torque. Phylogenetic ANCOVA (phylANCOVA) allow assessment of differences in agility between tyrannosaurids and non-tyrannosaurid theropods (accounting for both ontogeny and phylogeny). We applied conditional error probabilities a(p) to stringently test the null hypothesis of equal agility.

Results

Tyrannosaurids consistently have agility index magnitudes twice those of allosauroids and some other theropods of equivalent mass, turning the body with both legs planted or pivoting over a stance leg. PhylANCOVA demonstrates definitively greater agilities in tyrannosaurids, and phylogeny explains nearly all covariance. Mass property results are consistent with those of other studies based on skeletal mounts, and between different figure-based methods (our main mathematical slicing procedures, lofted 3D computer models, and simplified graphical double integration).

Implications

The capacity for relatively rapid turns in tyrannosaurids is ecologically intriguing in light of their monopolization of large (>400 kg), toothed dinosaurian predator niches in their habitats.

The importance of muscle architecture in biomechanical reconstructions of extinct animals: a case study using Tyrannosaurus rex

Functional reconstructions of extinct animals represent a crucial step towards understanding palaeocological interactions, selective pressures and macroevolutionary patterns in the fossil record. In recent years, computational approaches have revolutionised the field of 'evolutionary biomechanics' and have, in general, resulted in convergence of quantitative estimates of performance on increasingly narrow ranges for well studied taxa. Studies of body mass and locomotor performance of Tyrannosaurus rex - arguably the most intensively studied extinct animal - typify this pattern, with numerous independent studies predicting similar body masses and maximum locomotor speeds for this animal. In stark contrast to this trend, recent estimates of maximum bite force in T. rex vary considerably (> 50%) despite use of similar quantitative methodologies. Herein we demonstrate that the mechanistic causes of these disparate predictions are indicative of important and underappreciated limiting factors in biomechanical reconstructions of extinct organisms. Detailed comparison of previous models of T. rex bite force reveals that estimations of muscle fibre lengths and architecture are the principal source of disagreement between studies, and therefore that these parameters represents the greatest source of uncertainty in these reconstructions, and potentially therefore extinct animals generally. To address the issue of fibre length and architecture estimation in extinct animals we present data tabulated from the literature of muscle architecture from over 1100 muscles measured in extant terrestrial animals. Application of this dataset in a reanalysis of T. rex bite force emphasises the need for more data on jaw musculature from living carnivorous animals, alongside increased sophistication of modelling approaches. In the latter respect we predict that implementing limits on skeletal loading into musculoskeletal models will narrow predictions for T. rex bite force by excluding higher-end estimates.

Cancellous bone and theropod dinosaur locomotion. Part I-an examination of cancellous bone architecture in the hindlimb bones of theropods

This paper is the first of a three-part series that investigates the architecture of cancellous ('spongy') bone in the main hindlimb bones of theropod dinosaurs, and uses cancellous bone architectural patterns to infer locomotor biomechanics in extinct non-avian species. Cancellous bone is widely known to be highly sensitive to its mechanical environment, and has previously been used to infer locomotor biomechanics in extinct tetrapod vertebrates, especially primates. Despite great promise, cancellous bone architecture has remained little utilized for investigating locomotion in many other extinct vertebrate groups, such as dinosaurs. Documentation and quantification of architectural patterns across a whole bone, and across multiple bones, can provide much information on cancellous bone architectural patterns and variation across species. Additionally, this also lends itself to analysis of the musculoskeletal biomechanical factors involved in a direct, mechanistic fashion. On this premise, computed tomographic and image analysis techniques were used to describe and analyse the three-dimensional architecture of cancellous bone in the main hindlimb bones of theropod dinosaurs for the first time. A comprehensive survey across many extant and extinct species is produced, identifying several patterns of similarity and contrast between groups. For instance, more stemward non-avian theropods (e.g. ceratosaurs and tyrannosaurids) exhibit cancellous bone architectures more comparable to that present in humans, whereas species more closely related to birds (e.g. paravians) exhibit architectural patterns bearing greater similarity to those of extant birds. Many of the observed patterns may be linked to particular aspects of locomotor biomechanics, such as the degree of hip or knee flexion during stance and gait. A further important observation is the abundance of markedly oblique trabeculae in the diaphyses of the femur and tibia of birds, which in large species produces spiralling patterns along the endosteal surface. Not only do these observations provide new insight into theropod anatomy and behaviour, they also provide the foundation for mechanistic testing of locomotor hypotheses via musculoskeletal biomechanical modelling.

Cancellous bone and theropod dinosaur locomotion. Part III-Inferring posture and locomotor biomechanics in extinct theropods, and its evolution on the line to birds

This paper is the last of a three-part series that investigates the architecture of cancellous bone in the main hindlimb bones of theropod dinosaurs, and uses cancellous bone architectural patterns to infer locomotor biomechanics in extinct non-avian species. Cancellous bone is highly sensitive to its prevailing mechanical environment, and may therefore help further understanding of locomotor biomechanics in extinct tetrapod vertebrates such as dinosaurs. Here in Part III, the biomechanical modelling approach derived previously was applied to two species of extinct, non-avian theropods, Daspletosaurus torosus and Troodon formosus. Observed cancellous bone architectural patterns were linked with quasi-static, three-dimensional musculoskeletal and finite element models of the hindlimb of both species, and used to derive characteristic postures that best aligned continuum-level principal stresses with cancellous bone fabric. The posture identified for Daspletosaurus was largely upright, with a subvertical femoral orientation, whilst that identified for Troodon was more crouched, but not to the degree observed in extant birds. In addition to providing new insight on posture and limb articulation, this study also tested previous hypotheses of limb bone loading mechanics and muscular control strategies in non-avian theropods, and how these aspects evolved on the line to birds. The results support the hypothesis that an upright femoral posture is correlated with bending-dominant bone loading and abduction-based muscular support of the hip, whereas a crouched femoral posture is correlated with torsion-dominant bone loading and long-axis rotation-based muscular support. Moreover, the results of this study also support the inference that hindlimb posture, bone loading mechanics and muscular support strategies evolved in a gradual fashion along the line to extant birds.

The influence of speed and size on avian terrestrial locomotor biomechanics: Predicting locomotion in extinct theropod dinosaurs

How extinct, non-avian theropod dinosaurs moved is a subject of considerable interest and controversy. A better understanding of non-avian theropod locomotion can be achieved by better understanding terrestrial locomotor biomechanics in their modern descendants, birds. Despite much research on the subject, avian terrestrial locomotion remains little explored in regards to how kinematic and kinetic factors vary together with speed and body size. Here, terrestrial locomotion was investigated in twelve species of ground-dwelling bird, spanning a 1,780-fold range in body mass, across almost their entire speed range. Particular attention was devoted to the ground reaction force (GRF), the force that the feet exert upon the ground. Comparable data for the only other extant obligate, striding biped, humans, were also collected and studied. In birds, all kinematic and kinetic parameters examined changed continuously with increasing speed, while in humans all but one of those same parameters changed abruptly at the walk-run transition. This result supports previous studies that show birds to have a highly continuous locomotor repertoire compared to humans, where discrete 'walking' and 'running' gaits are not easily distinguished based on kinematic patterns alone. The influences of speed and body size on kinematic and kinetic factors in birds are developed into a set of predictive relationships that may be applied to extinct, non-avian theropods. The resulting predictive model is able to explain 79-93% of the observed variation in kinematics and 69-83% of the observed variation in GRFs, and also performs well in extrapolation tests. However, this study also found that the location of the whole-body centre of mass may exert an important influence on the nature of the GRF, and hence some caution is warranted, in lieu of further investigation.

Whole-body 3D kinematics of bird take-off: key role of the legs to propel the trunk

Previous studies showed that birds primarily use their hindlimbs to propel themselves into the air in order to take-off. Yet, it remains unclear how the different parts of their musculoskeletal system move to produce the necessary acceleration. To quantify the relative motions of the bones during the terrestrial phase of take-off, we used biplanar fluoroscopy in two species of birds, diamond dove (Geopelia cuneata) and zebra finch (Taeniopygia guttata). We obtained a detailed 3D kinematics analysis of the head, the trunk and the three long bones of the left leg. We found that the entire body assisted the production of the needed forces to take-off, during two distinct but complementary phases. The first one, a relatively slow preparatory phase, started with a movement of the head and an alignment of the different groups of bones with the future take-off direction. It was associated with a pitch down of the trunk and a flexion of the ankle, of the hip and, to a lesser extent, of the knee. This crouching movement could contribute to the loading of the leg muscles and store elastic energy that could be released in the propulsive phase of take-off, during the extension of the leg joints. Combined with the fact that the head, together with the trunk, produced a forward momentum, the entire body assisted the production of the needed forces to take-off. The second phase was faster with mostly horizontal forward and vertical upward translation motions, synchronous to an extension of the entire lower articulated musculoskeletal system. It led to the propulsion of the bird in the air with a fundamental role of the hip and ankle joints to move the trunk upward and forward. Take-off kinematics were similar in both studied species, with a more pronounced crouching movement in diamond dove, which can be related to a large body mass compared to zebra finch.

Forelimb muscle and joint actions in Archosauria: insights from Crocodylus johnstoni (Pseudosuchia) and Mussaurus patagonicus (Sauropodomorpha)

Many of the major locomotor transitions during the evolution of Archosauria, the lineage including crocodiles and birds as well as extinct Dinosauria, were shifts from quadrupedalism to bipedalism (and vice versa). Those occurred within a continuum between more sprawling and erect modes of locomotion and involved drastic changes of limb anatomy and function in several lineages, including sauropodomorph dinosaurs. We present biomechanical computer models of two locomotor extremes within Archosauria in an analysis of joint ranges of motion and the moment arms of the major forelimb muscles in order to quantify biomechanical differences between more sprawling, pseudosuchian (represented the crocodile Crocodylus johnstoni) and more erect, dinosaurian (represented by the sauropodomorph Mussaurus patagonicus) modes of forelimb function. We compare these two locomotor extremes in terms of the reconstructed musculoskeletal anatomy, ranges of motion of the forelimb joints and the moment arm patterns of muscles across those ranges of joint motion. We reconstructed the three-dimensional paths of 30 muscles acting around the shoulder, elbow and wrist joints. We explicitly evaluate how forelimb joint mobility and muscle actions may have changed with postural and anatomical alterations from basal archosaurs to early sauropodomorphs. We thus evaluate in which ways forelimb posture was correlated with muscle leverage, and how such differences fit into a broader evolutionary context (i.e. transition from sprawling quadrupedalism to erect bipedalism and then shifting to graviportal quadrupedalism). Our analysis reveals major differences of muscle actions between the more sprawling and erect models at the shoulder joint. These differences are related not only to the articular surfaces but also to the orientation of the scapula, in which extension/flexion movements in Crocodylus (e.g. protraction of the humerus) correspond to elevation/depression in Mussaurus. Muscle action is highly influenced by limb posture, more so than morphology. Habitual quadrupedalism in Mussaurus is not supported by our analysis of joint range of motion, which indicates that glenohumeral protraction was severely restricted. Additionally, some active pronation of the manus may have been possible in Mussaurus, allowing semi-pronation by a rearranging of the whole antebrachium (not the radius against the ulna, as previously thought) via long-axis rotation at the elbow joint. However, the muscles acting around this joint to actively pronate it may have been too weak to drive or maintain such orientations as opposed to a neutral position in between pronation and supination. Regardless, the origin of quadrupedalism in Sauropoda is not only linked to manus pronation but also to multiple shifts of forelimb morphology, allowing greater flexion movements of the glenohumeral joint and a more columnar forelimb posture.

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

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

Downsizing a giant: re-evaluating Dreadnoughtus body mass

Estimates of body mass often represent the founding assumption on which biomechanical and macroevolutionary hypotheses are based. Recently, a scaling equation was applied to a newly discovered titanosaurian sauropod dinosaur (Dreadnoughtus), yielding a 59 300 kg body mass estimate for this animal. Herein, we use a modelling approach to examine the plausibility of this mass estimate for Dreadnoughtus. We find that 59 300 kg for Dreadnoughtus is highly implausible and demonstrate that masses above 40 000 kg require high body densities and expansions of soft tissue volume outside the skeleton several times greater than found in living quadrupedal mammals. Similar results from a small sample of other archosaurs suggests that lower-end mass estimates derived from scaling equations are most plausible for Dreadnoughtus, based on existing volumetric and density data from extant animals. Although volumetric models appear to more tightly constrain dinosaur body mass, there remains a clear need to further support these models with more exhaustive data from living animals. The relative and absolute discrepancies in mass predictions between volumetric models and scaling equations also indicate a need to systematically compare predictions across a wide size and taxonomic range to better inform studies of dinosaur body size.

Temporal and phylogenetic evolution of the sauropod dinosaur body plan

The colossal size and body plan of sauropod dinosaurs are unparalleled in terrestrial vertebrates. However, to date, there have been only limited attempts to examine temporal and phylogenetic patterns in the sauropod bauplan. Here, we combine three-dimensional computational models with phylogenetic reconstructions to quantify the evolution of whole-body shape and body segment properties across the sauropod radiation. Limitations associated with the absence of soft tissue preservation in fossils result in large error bars about mean absolute body shape predictions. However, applying any consistent skeleton : body volume ratio to all taxa does yield changes in body shape that appear concurrent with major macroevolutionary events in sauropod history. A caudad shift in centre-of-mass (CoM) in Middle Triassic Saurischia, associated with the evolution of bipedalism in various dinosaur lineages, was reversed in Late Triassic sauropodomorphs. A craniad CoM shift coincided with the evolution of quadrupedalism in the Late Triassic, followed by a more striking craniad shift in Late Jurassic-Cretaceous titanosauriforms, which included the largest sauropods. These craniad CoM shifts are strongly correlated with neck enlargement, a key innovation in sauropod evolution and pivotal to their gigantism. By creating a much larger feeding envelope, neck elongation is thought to have increased feeding efficiency and opened up trophic niches that were inaccessible to other herbivores. However, we find that relative neck size and CoM position are not strongly correlated with inferred feeding habits. Instead the craniad CoM positions of titanosauriforms appear closely linked with locomotion and environmental distributions, potentially contributing to the continued success of this group until the end-Cretaceous, with all other sauropods having gone extinct by the early Late Cretaceous.

Convex-hull mass estimates of the dodo (Raphus cucullatus): application of a CT-based mass estimation technique

The external appearance of the dodo (Raphus cucullatus, Linnaeus, 1758) has been a source of considerable intrigue, as contemporaneous accounts or depictions are rare. The body mass of the dodo has been particularly contentious, with the flightless pigeon alternatively reconstructed as slim or fat depending upon the skeletal metric used as the basis for mass prediction. Resolving this dichotomy and obtaining a reliable estimate for mass is essential before future analyses regarding dodo life history, physiology or biomechanics can be conducted. Previous mass estimates of the dodo have relied upon predictive equations based upon hind limb dimensions of extant pigeons. Yet the hind limb proportions of dodo have been found to differ considerably from those of their modern relatives, particularly with regards to midshaft diameter. Therefore, application of predictive equations to unusually robust fossil skeletal elements may bias mass estimates. We present a whole-body computed tomography (CT) -based mass estimation technique for application to the dodo. We generate 3D volumetric renders of the articulated skeletons of 20 species of extant pigeons, and wrap minimum-fit ‘convex hulls’ around their bony extremities. Convex hull volume is subsequently regressed against mass to generate predictive models based upon whole skeletons. Our best-performing predictive model is characterized by high correlation coefficients and low mean squared error (a = − 2.31, b = 0.90, r² = 0.97, MSE = 0.0046). When applied to articulated composite skeletons of the dodo (National Museums Scotland, NMS.Z.1993.13; Natural History Museum, NHMUK A.9040 and S/1988.50.1), we estimate eviscerated body masses of 8–10.8 kg. When accounting for missing soft tissues, this may equate to live masses of 10.6–14.3 kg. Mass predictions presented here overlap at the lower end of those previously published, and support recent suggestions of a relatively slim dodo. CT-based reconstructions provide a means of objectively estimating mass and body segment properties of extinct species using whole articulated skeletons.

A Three-Dimensional Skeletal Reconstruction of the Stem Amniote Orobates pabsti (Diadectidae): Analyses of Body Mass, Centre of Mass Position, and Joint Mobility

Orobates pabsti, a basal diadectid from the lower Permian, is a key fossil for the understanding of early amniote evolution. Quantitative analysis of anatomical information suffers from fragmentation of fossil bones, plastic deformation due to diagenetic processes and fragile preservation within surrounding rock matrix, preventing further biomechanical investigation. Here we describe the steps taken to digitally reconstruct MNG 10181, the holotype specimen of Orobates pabsti, and subsequently use the digital reconstruction to assess body mass, position of the centre of mass in individual segments as well as the whole animal, and study joint mobility in the shoulder and hip joints. The shape of most fossil bone fragments could be recovered from micro-focus computed tomography scans. This also revealed structures that were hitherto hidden within the rock matrix. However, parts of the axial skeleton had to be modelled using relevant isolated bones from the same locality as templates. Based on the digital fossil, mass of MNG 10181 was estimated using a model of body shape that was varied within a plausible range to account for uncertainties of the dimension. In the mean estimate model the specimen had an estimated mass of circa 4 kg. Varying of the mass distribution amongst body segments further revealed that Orobates carried most of its weight on the hind limbs. Mostly unrestricted joint morphology further suggested that MNG 10181 was able to effectively generate propulsion with the pelvic limbs. The digital reconstruction is made available for future biomechanical studies.

An advanced shape-fitting algorithm applied to quadrupedal mammals: improving volumetric mass estimates

Body mass is a fundamental physical property of an individual and has enormous bearing upon ecology and physiology. Generating reliable estimates for body mass is therefore a necessary step in many palaeontological studies. Whilst early reconstructions of mass in extinct species relied upon isolated skeletal elements, volumetric techniques are increasingly applied to fossils when skeletal completeness allows. We apply a new 'alpha shapes' (α-shapes) algorithm to volumetric mass estimation in quadrupedal mammals. α-shapes are defined by: (i) the underlying skeletal structure to which they are fitted; and (ii) the value α, determining the refinement of fit. For a given skeleton, a range of α-shapes may be fitted around the individual, spanning from very coarse to very fine. We fit α-shapes to three-dimensional models of extant mammals and calculate volumes, which are regressed against mass to generate predictive equations. Our optimal model is characterized by a high correlation coefficient and mean square error (r (2)=0.975, m.s.e.=0.025). When applied to the woolly mammoth (Mammuthus primigenius) and giant ground sloth (Megatherium americanum), we reconstruct masses of 3635 and 3706 kg, respectively. We consider α-shapes an improvement upon previous techniques as resulting volumes are less sensitive to uncertainties in skeletal reconstructions, and do not require manual separation of body segments from skeletons.

A temnospondyl trackway from the early Mesozoic of western Gondwana and its implications for basal tetrapod locomotion

BACKGROUND

Temnospondyls are one of the earliest radiations of limbed vertebrates. Skeletal remains of more than 190 genera have been identified from late Paleozoic and early Mesozoic rocks. Paleozoic temnospondyls comprise mainly small to medium sized forms of diverse habits ranging from fully aquatic to fully terrestrial. Accordingly, their ichnological record includes tracks described from many Laurasian localities. Mesozoic temnospondyls, in contrast, include mostly medium to large aquatic or semi-aquatic forms. Exceedingly few fossil tracks or trackways have been attributed to Mesozoic temnospondyls, and as a consequence very little is known of their locomotor capabilities on land.

METHODOLOGY/PRINCIPAL FINDINGS

We report a ca. 200 Ma trackway, Episcopopus ventrosus, from Lesotho, southern Africa that was made by a 3.5 m-long animal. This relatively long trackway records the trackmaker dragging its body along a wet substrate using only the tips of its digits, which in the manus left characteristic drag marks. Based on detailed mapping, casting, and laser scanning of the best-preserved part of the trackway, we identified synapomorphies (e.g., tetradactyl manus, pentadactyl pes) and symplesiomorphies (e.g., absence of claws) in the Episcopopus trackway that indicate a temnospondyl trackmaker.

CONCLUSIONS/SIGNIFICANCE

Our analysis shows that the Episcopopus trackmaker progressed with a sprawling posture, using a lateral-sequence walk. Its forelimbs were the major propulsive elements and there was little lateral bending of the trunk. We suggest this locomotor style, which differs dramatically from the hindlimb-driven locomotion of salamanders and other extant terrestrial tetrapods can be explained by the forwardly shifted center of mass resulting from the relatively large heads and heavily pectoral girdles of temnospondyls.

Anatomical and biomechanical traits of broiler chickens across ontogeny. Part II. Body segment inertial properties and muscle architecture of the pelvic limb

In broiler chickens, genetic success for desired production traits is often shadowed by welfare concerns related to musculoskeletal health. Whilst these concerns are clear, a viable solution is still elusive. Part of the solution lies in knowing how anatomical changes in afflicted body systems that occur across ontogeny influence standing and moving. Here, to demonstrate these changes we quantify the segment inertial properties of the whole body, trunk (legs removed) and the right pelvic limb segments of five broilers at three different age groups across development. We also consider how muscle architecture (mass, fascicle length and other properties related to mechanics) changes for selected muscles of the pelvic limb. All broilers used had no observed lameness, but we document the limb pathologies identified post mortem, since these two factors do not always correlate, as shown here. The most common leg disorders, including bacterial chondronecrosis with osteomyelitis and rotational and angular deformities of the lower limb, were observed in chickens at all developmental stages. Whole limb morphology is not uniform relative to body size, with broilers obtaining large thighs and feet between four and six weeks of age. This implies that the energetic cost of swinging the limbs is markedly increased across this growth period, perhaps contributing to reduced activity levels. Hindlimb bone length does not change during this period, which may be advantageous for increased stability despite the increased energetic costs. Increased pectoral muscle growth appears to move the centre of mass cranio-dorsally in the last two weeks of growth. This has direct consequences for locomotion (potentially greater limb muscle stresses during standing and moving). Our study is the first to measure these changes in the musculoskeletal system across growth in chickens, and reveals how artificially selected changes of the morphology of the pectoral apparatus may cause deficits in locomotion.

Scaling of convex hull volume to body mass in modern primates, non-primate mammals and birds

The volumetric method of ‘convex hulling’ has recently been put forward as a mass prediction technique for fossil vertebrates. Convex hulling involves the calculation of minimum convex hull volumes (vol_CH) from the complete mounted skeletons of modern museum specimens, which are subsequently regressed against body mass (M_b) to derive predictive equations for extinct species. The convex hulling technique has recently been applied to estimate body mass in giant sauropods and fossil ratites, however the biomechanical signal contained within vol_CH has remained unclear. Specifically, when vol_CH scaling departs from isometry in a group of vertebrates, how might this be interpreted? Here we derive predictive equations for primates, non-primate mammals and birds and compare the scaling behaviour of M_b to vol_CH between groups. We find predictive equations to be characterised by extremely high correlation coefficients (r² = 0.97–0.99) and low mean percentage prediction error (11–20%). Results suggest non-primate mammals scale body mass to vol_CH isometrically (b = 0.92, 95%CI = 0.85–1.00, p = 0.08). Birds scale body mass to vol_CH with negative allometry (b = 0.81, 95%CI = 0.70–0.91, p = 0.011) and apparent density (vol_CH/M_b) therefore decreases with mass (r² = 0.36, p<0.05). In contrast, primates scale body mass to vol_CH with positive allometry (b = 1.07, 95%CI = 1.01–1.12, p = 0.05) and apparent density therefore increases with size (r² = 0.46, p = 0.025). We interpret such departures from isometry in the context of the ‘missing mass’ of soft tissues that are excluded from the convex hulling process. We conclude that the convex hulling technique can be justifiably applied to the fossil record when a large proportion of the skeleton is preserved. However we emphasise the need for future studies to quantify interspecific variation in the distribution of soft tissues such as muscle, integument and body fat.

More than one way of being a moa: differences in leg bone robustness map divergent evolutionary trajectories in Dinornithidae and Emeidae (Dinornithiformes)

The extinct moa of New Zealand included three families (Megalapterygidae; Dinornithidae; Emeidae) of flightless palaeognath bird, ranging in mass from <15 kg to >200 kg. They are perceived to have evolved extremely robust leg bones, yet current estimates of body mass have very wide confidence intervals. Without reliable estimators of mass, the extent to which dinornithid and emeid hindlimbs were more robust than modern species remains unclear. Using the convex hull volumetric-based method on CT-scanned skeletons, we estimate the mass of a female Dinornis robustus (Dinornithidae) at 196 kg (range 155–245 kg) and of a female Pachyornis australis (Emeidae) as 50 kg (range 33–68 kg). Finite element analysis of CT-scanned femora and tibiotarsi of two moa and six species of modern palaeognath showed that P. australis experienced the lowest values for stress under all loading conditions, confirming it to be highly robust. In contrast, stress values in the femur of D. robustus were similar to those of modern flightless birds, whereas the tibiotarsus experienced the highest level of stress of any palaeognath. We consider that these two families of Dinornithiformes diverged in their biomechanical responses to selection for robustness and mobility, and exaggerated hindlimb strength was not the only successful evolutionary pathway.

Shake a tail feather: the evolution of the theropod tail into a stiff aerodynamic surface

Theropod dinosaurs show striking morphological and functional tail variation; e.g., a long, robust, basal theropod tail used for counterbalance, or a short, modern avian tail used as an aerodynamic surface. We used a quantitative morphological and functional analysis to reconstruct intervertebral joint stiffness in the tail along the theropod lineage to extant birds. This provides new details of the tail's morphological transformation, and for the first time quantitatively evaluates its biomechanical consequences. We observe that both dorsoventral and lateral joint stiffness decreased along the non-avian theropod lineage (between nodes Theropoda and Paraves). Our results show how the tail structure of non-avian theropods was mechanically appropriate for holding itself up against gravity and maintaining passive balance. However, as dorsoventral and lateral joint stiffness decreased, the tail may have become more effective for dynamically maintaining balance. This supports our hypothesis of a reduction of dorsoventral and lateral joint stiffness in shorter tails. Along the avian theropod lineage (Avialae to crown group birds), dorsoventral and lateral joint stiffness increased overall, which appears to contradict our null expectation. We infer that this departure in joint stiffness is specific to the tail's aerodynamic role and the functional constraints imposed by it. Increased dorsoventral and lateral joint stiffness may have facilitated a gradually improved capacity to lift, depress, and swing the tail. The associated morphological changes should have resulted in a tail capable of producing larger muscular forces to utilise larger lift forces in flight. Improved joint mobility in neornithine birds potentially permitted an increase in the range of lift force vector orientations, which might have improved flight proficiency and manoeuvrability. The tail morphology of modern birds with tail fanning capabilities originated in early ornithuromorph birds. Hence, these capabilities should have been present in the early Cretaceous, with incipient tail-fanning capacity in the earliest pygostylian birds.

Homology and architecture of the caudal basket of Pachycephalosauria (Dinosauria: Ornithischia): the first occurrence of myorhabdoi in Tetrapoda

Background

Associated postcranial skeletons of pachycephalosaurids, most notably those of Stegoceras and Homalocephale, reveal enigmatic osseous structures not present in other tetrapod clades. The homology and functional significance of these structures have remained elusive as they were originally interpreted to be abdominal ribs or gastralia, and more recently have been interpreted as de novo structures in the tail.

Principal Findings

Analysis of these structures in nearly all pachycephalosaurid skeletons has facilitated a complete description of their architecture, and the establishment of patterns consistent with those of myorhabdoid ossifications — ossifications of the myoseptal tendons associated with myomeres. The presence and structure of myorhabdoid ossifications are well established for teleost fish, but this marks their first recognition within Tetrapoda. These elements are both structurally and histologically distinct from the deep, paraxial ossified tendon bundles of other ornithischian clades, although they may have performed a similar function in the stiffening of the tail.

Conclusions/Significance

These myorhabdoi are not de novo structures, but are instead ossifications (and therefore more amenable to fossilization) of the normally unossified plesiomorphic caudal myosepta of vertebrates. The ubiquitous ossification of these structures in pachycephalosaurids (all specimens preserving the tail also exhibit myorhabdoid ossifications) suggests it is a likely synapomorphic condition for Pachycephalosauria.

Computational modelling of locomotor muscle moment arms in the basal dinosaur Lesothosaurus diagnosticus: assessing convergence between birds and basal ornithischians

Ornithischia (the 'bird-hipped' dinosaurs) encompasses bipedal, facultative quadrupedal and quadrupedal taxa. Primitive ornithischians were small bipeds, but large body size and obligate quadrupedality evolved independently in all major ornithischian lineages. Numerous pelvic and hind limb features distinguish ornithischians from the majority of other non-avian dinosaurs. However, some of these features, notably a retroverted pubis and elongate iliac preacetabular process, appeared convergently in maniraptoran theropods, and were inherited by their avian descendants. During maniraptoran/avian evolution these pelvic modifications led to significant changes in the functions of associated muscles, involving alterations to the moment arms and the activation patterns of pelvic musculature. However, the functions of these features in ornithischians and their influence on locomotion have not been tested and remain poorly understood. Here, we provide quantitative tests of bipedal ornithischian muscle function using computational modelling to estimate 3D hind limb moment arms for the most complete basal ornithischian, Lesothosaurus diagnosticus. This approach enables sensitivity analyses to be carried out to explore the effects of uncertainties in muscle reconstructions of extinct taxa, and allows direct comparisons to be made with similarly constructed models of other bipedal dinosaurs. This analysis supports some previously proposed qualitative inferences of muscle function in basal ornithischians. However, more importantly, this work highlights ambiguities in the roles of certain muscles, notably those inserting close to the hip joint. Comparative analysis reveals that moment arm polarities and magnitudes in Lesothosaurus, basal tetanuran theropods and the extant ostrich are generally similar. However, several key differences are identified, most significantly in comparisons between the moment arms of muscles associated with convergent osteological features in ornithischians and birds. Craniad migration of the iliofemoralis group muscles in birds correlates with increased leverage and use of medial femoral rotation to counter stance phase adduction moments at the hip. In Lesothosaurus the iliofemoralis group maintains significantly higher moment arms for abduction, consistent with the hip abduction mode of lateral limb support hypothesized for basal dinosaurs. Sensitivity analysis highlights ambiguity in the role of musculature associated with the retroverted pubis (puboischiofemoralis externus group) in ornithischians. However, it seems likely that this musculature may have predominantly functioned similarly to homologous muscles in extant birds, activating during the swing phase to adduct the lower limb through lateral rotation of the femur. Overall the results suggest that locomotor muscle leverage in Lesothosaurus (and by inference basal ornithischians in general) was more similar to that of other non-avian dinosaurs than the ostrich, representing what was probably the basal dinosaur condition. This work thereby contradicts previous hypotheses of ornithischian-bird functional convergence.

Dinosaur speed demon: the caudal musculature of Carnotaurus sastrei and implications for the evolution of South American abelisaurids

In the South American abelisaurids Carnotaurus sastrei, Aucasaurus garridoi, and, to a lesser extent Skorpiovenator bustingorryi, the anterior caudal ribs project at a high dorsolateral inclination and have interlocking lateral tips. This unique morphology facilitated the expansion of the caudal hypaxial musculature at the expense of the epaxial musculature. Distinct ridges on the ventrolateral surfaces of the caudal ribs of Aucasaurus garridoi are interpreted as attachment scars from the intra caudofemoralis/ilio-ischiocaudalis septa, and confirm that the M. caudofemoralis of advanced South American abelisaurids originated from a portion of the caudal ribs. Digital muscle models indicate that, relative to its overall body size, Carnotaurus sastrei had a substantially larger M. caudofemoralis than any other theropod yet studied. In most non-avian theropods, as in many extant sauropsids, the M. caudofemoralis served as the primary femoral retractor muscle during the locomotive power stroke. This large investment in the M. caudofemoralis suggests that Carnotaurus sastrei had the potential for great cursorial abilities, particularly short-burst sprinting. However, the tightly interlocking morphology of the anterior caudal vertebrae implies a reduced ability to make tight turns. Examination of these vertebral traits in evolutionary context reveals a progressive sequence of increasing caudofemoral mass and tail rigidity among the Abelisauridae of South America.

A computational analysis of limb and body dimensions in Tyrannosaurus rex with implications for locomotion, ontogeny, and growth

The large theropod dinosaur Tyrannosaurus rex underwent remarkable changes during its growth from <10 kg hatchlings to >6000 kg adults in <20 years. These changes raise fascinating questions about the morphological transformations involved, peak growth rates, and scaling of limb muscle sizes as well as the body's centre of mass that could have influenced ontogenetic changes of locomotion in T. rex. Here we address these questions using three-dimensionally scanned computer models of four large, well-preserved fossil specimens as well as a putative juvenile individual. Furthermore we quantify the variations of estimated body mass, centre of mass and segment dimensions, to characterize inaccuracies in our reconstructions. These inaccuracies include not only subjectivity but also incomplete preservation and inconsistent articulations of museum skeletons. Although those problems cause ambiguity, we conclude that adult T. rex had body masses around 6000-8000 kg, with the largest known specimen ("Sue") perhaps ∼9500 kg. Our results show that during T. rex ontogeny, the torso became longer and heavier whereas the limbs became proportionately shorter and lighter. Our estimates of peak growth rates are about twice as rapid as previous ones but generally support previous methods, despite biases caused by the usage of scale models and equations that underestimate body masses. We tentatively infer that the hindlimb extensor muscles masses, including the large tail muscle M. caudofemoralis longus, may have decreased in their relative size as the centre of mass shifted craniodorsally during T. rex ontogeny. Such ontogenetic changes would have worsened any relative or absolute decline of maximal locomotor performance. Regardless, T. rex probably had hip and thigh muscles relatively larger than any extant animal's. Overall, the limb "antigravity" muscles may have been as large as or even larger than those of ratite birds, which themselves have the most muscular limbs of any living animal.

Models in palaeontological functional analysis

Models are a principal tool of modern science. By definition, and in practice, models are not literal representations of reality but provide simplifications or substitutes of the events, scenarios or behaviours that are being studied or predicted. All models make assumptions, and palaeontological models in particular require additional assumptions to study unobservable events in deep time. In the case of functional analysis, the degree of missing data associated with reconstructing musculoskeletal anatomy and neuronal control in extinct organisms has, in the eyes of some scientists, rendered detailed functional analysis of fossils intractable. Such a prognosis may indeed be realized if palaeontologists attempt to recreate elaborate biomechanical models based on missing data and loosely justified assumptions. Yet multiple enabling methodologies and techniques now exist: tools for bracketing boundaries of reality; more rigorous consideration of soft tissues and missing data and methods drawing on physical principles that all organisms must adhere to. As with many aspects of science, the utility of such biomechanical models depends on the questions they seek to address, and the accuracy and validity of the models themselves.

On the inference of function from structure using biomechanical modelling and simulation of extinct organisms

Biomechanical modelling and simulation techniques offer some hope for unravelling the complex inter-relationships of structure and function perhaps even for extinct organisms, but have their limitations owing to this complexity and the many unknown parameters for fossil taxa. Validation and sensitivity analysis are two indispensable approaches for quantifying the accuracy and reliability of such models or simulations. But there are other subtleties in biomechanical modelling that include investigator judgements about the level of simplicity versus complexity in model design or how uncertainty and subjectivity are dealt with. Furthermore, investigator attitudes toward models encompass a broad spectrum between extreme credulity and nihilism, influencing how modelling is conducted and perceived. Fundamentally, more data and more testing of methodology are required for the field to mature and build confidence in its inferences.

Recovering missing data: estimating position and size of caudal vertebrae in Staurikosaurus pricei Colbert, 1970

Missing data is a common problem in paleontology. It makes it difficult to reconstruct extinct taxa accurately and restrains the inclusion of some taxa on comparative and biomechanical studies. Particularly, estimating the position of vertebrae on incomplete series is often non-empirical and does not allow precise estimation of missing parts. In this work we present a method for calculating the position of preserved middle sequences of caudal vertebrae in the saurischian dinosaur Staurikosaurus pricei, based on the length and height of preserved anterior and posterior caudal vertebral centra. Regression equations were used to estimate these dimensions for middle vertebrae and, consequently, to assess the position of the preserved middle sequences. It also allowed estimating these dimensions for non-preserved vertebrae. Results indicate that the preserved caudal vertebrae of Staurikosaurus may correspond to positions 1-3, 5, 7, 14-19/15-20, 24-25/25-26, and 29-47, and that at least 25 vertebrae had transverse processes. Total length of the tail was estimated in 134 cm and total body length was 220-225 cm.