Models in palaeontological functional analysis

Farewell to the requirement for character independence: phylogenetic methods to incorporate different types of dependence between characters

This paper discusses methods to take into account interactions between characters, in the context of parsimony analysis. These interactions can be in the form of some characters becoming inapplicable given certain states of other, primary characters; in the form of only certain states being allowed in some characters when a given state or set of states occurs for other characters; or in the form of transformation costs in some character being higher or lower when other characters have certain states or transformations between states. Character-state reconstructions and evaluation of trees under the assumption of independence may easily lead to ancestral assignments that violate elementary rules of biomechanics, well-established theories relating form and function or ideas about character co-variation. An obvious example is reconstructing an ancestral bird as wingless and flying at the same time; another is reconstructing a protein-coding gene as having a stop codon in some ancestors. If the characters are optimized independently, such chimeric ancestral reconstructions can occur even when no terminal displays the impossible combination of states. A set of conventions (implemented via new TNT commands and options) allows the definition of complex rules of interaction. By recoding groups of characters with proper step-matrix costs (and excluding impossible combinations from the set of permissible states), it is possible to find the ancestral reconstructions that maximize homology (and thus the degree to which similarities can be explained by common ancestry), within the constraints imposed by the rules specified by the user. We expect that considerations of biomechanics, functional morphology and natural history will be a source of many theories on possible character dependences, and that the present implementation will encourage users to take the possibility of character dependences into account in their phylogenetic analyses.

Biomechanics illuminates form-function relationships in bird bills

The field of comparative biomechanics examines how form, mechanical properties and environmental interactions shape the function of biological structures. Biomechanics has advanced by leaps and bounds as rapid technological progress opens up new research horizons. In this Review, I describe how our understanding of the avian bill, a morphologically diverse multifunctional appendage, has been transformed by employing a biomechanical perspective. Across functions from feeding to excavating hollows in trees and as a vocal apparatus, the study of the bill spans both solid and fluid biomechanics, rendering it useful to understand general principles across disciplines. The different shapes of the bill across bird species result in functional and mechanical trade-offs, thus representing a microcosm of many broader form-function questions. Using examples from diverse studies, I discuss how research into bird bills has been shaped over recent decades, and its influence on our understanding of avian ecology and evolution. Next, I examine how bill material properties and geometry influence performance in dietary and non-dietary contexts, simultaneously imposing trade-offs on other functions. Following an examination of the interactions of bills with fluids and their role as part of the vocal apparatus, I end with a discussion of the sensory biomechanics of the bill, focusing specifically on the bill-tip mechanosensory organ. With these case studies, I highlight how this burgeoning and consequential field represents a roadmap for our understanding of the function and evolution of biological structures.

One step further in biomechanical models in palaeontology: a nonlinear finite element analysis review

Finite element analysis (FEA) is no longer a new technique in the fields of palaeontology, anthropology, and evolutionary biology. It is nowadays a well-established technique within the virtual functional-morphology toolkit. However, almost all the works published in these fields have only applied the most basic FEA tools i.e., linear materials in static structural problems. Linear and static approximations are commonly used because they are computationally less expensive, and the error associated with these assumptions can be accepted. Nonetheless, nonlinearities are natural to be used in biomechanical models especially when modelling soft tissues, establish contacts between separated bones or the inclusion of buckling results. The aim of this review is to, firstly, highlight the usefulness of non-linearities and secondly, showcase these FEA tool to researchers that work in functional morphology and biomechanics, as non-linearities can improve their FEA models by widening the possible applications and topics that currently are not used in palaeontology and anthropology.

Estimating bite force in extinct dinosaurs using phylogenetically predicted physiological cross-sectional areas of jaw adductor muscles

I present a Bayesian phylogenetic predictive modelling (PPM) framework that allows the prediction of muscle parameters (physiological cross-sectional area, A _Phys) in extinct archosaurs from skull width (W _Sk) and phylogeny. This approach is robust to phylogenetic uncertainty and highly versatile given its ability to base predictions on simple, readily available predictor variables. The PPM presented here has high prediction accuracy (up to 95%), with downstream biomechanical modelling yielding bite force estimates that are in line with previous estimates based on muscle parameters from reconstructed muscles. This approach does not replace muscle reconstructions but one that provides a powerful means to predict A _Phys from skull geometry and phylogeny to the same level of accuracy as that measured from reconstructed muscles in species for which soft tissue data are unavailable or difficult to obtain.

Detecting Mismatch in Functional Narratives of Animal Morphology: a Test Case With Fossils

A boom in technological advancements over the last two decades has driven a surge in both the diversity and power of analytical tools available to biomechanical and functional morphology research. However, in order to adequately investigate each of these dense datasets, one must often consider only one functional narrative at a time. There is more to each organism than any one of these form-function relationships. Joint performance landscapes determined by maximum likelihood are a valuable tool that can be used to synthesize our understanding of these multiple functional hypotheses to further explore an organism's ecology. We present an example framework for applying these tools to such a problem using the morphological transition of ammonoids from the Middle Triassic to the Early Jurassic. Across this time interval, morphospace occupation shifts from a broad occupation across Westermann Morphospace to a dense occupation of a region emphasizing an exposed umbilicus and modest frontal profile. The hydrodynamic capacities and limitations of the shell have seen intense scrutiny as a likely explanation of this transition. However, conflicting interpretations of hydrodynamic performance remain despite this scrutiny, with scant offerings of alternative explanations. Our analysis finds that hydrodynamic measures of performance do little to explain the shift in morphological occupation, highlighting a need for a more robust investigation of alternative functional hypotheses that are often intellectually set aside. With this we show a framework for consolidating the current understanding of the form-function relationships in an organism, and assess when they are insufficiently characterizing the dynamics those data are being used to explain. We aim to encourage the broader adoption of this framework and these ideas as a foundation to bring the field close to comprehensive synthesis and reconstruction of organisms.

Cranial functional morphology of the pseudosuchian Effigia and implications for its ecological role in the Triassic

Pseudosuchians, archosaurian reptiles more closely related to crocodylians than to birds, exhibited high morphological diversity during the Triassic with numerous examples of morphological convergence described between Triassic pseudosuchians and post-Triassic dinosaurs. One example is the shuvosaurid Effigia okeeffeae which exhibits an "ostrich-like" bauplan comprising a gracile skeleton with edentulous jaws and large orbits, similar to ornithomimid dinosaurs and extant palaeognaths. This bauplan is regarded as an adaptation for herbivory, but this hypothesis assumes morphological convergence confers functional convergence, and has received little explicit testing. Here, we restore the skull morphology of Effigia, perform myological reconstructions, and apply finite element analysis to quantitatively investigate skull function. We also perform finite element analysis on the crania of the ornithomimid dinosaur Ornithomimus edmontonicus, the extant palaeognath Struthio camelus and the extant pseudosuchian Alligator mississippiensis to assess the degree of functional convergence with a taxon that exhibit "ostrich-like" bauplans and its closest extant relatives. We find that Effigia possesses a mosaic of mechanically strong and weak features, including a weak mandible that likely restricted feeding to the anterior portion of the jaws. We find limited functional convergence with Ornithomimus and Struthio and limited evidence of phylogenetic constraints with extant pseudosuchians. We infer that Effigia was a specialist herbivore that likely fed on softer plant material, a niche unique among the study taxa and potentially among contemporaneous Triassic herbivores. This study increases the known functional diversity of pseudosuchians and highlights that superficial morphological similarity between unrelated taxa does not always imply functional and ecological convergence.

Modeling Sprawling Locomotion of the Stem Amniote Orobates: An Examination of Hindlimb Muscle Strains and Validation Using Extant Caiman

The stem amniote Orobates pabsti has been reconstructed to be capable of relatively erect, balanced, and mechanically power-saving terrestrial locomotion. This suggested that the evolution of such advanced locomotor capabilities preceded the origin of crown-group amniotes. We here further investigate plausible body postures and locomotion of Orobates by taking soft tissues into account. Freely available animation software BLENDER is used to first reconstruct the lines of action of hindlimb adductors and retractors for Orobates and then estimate the muscle strain of these muscles. We experimentally varied different body heights in modeled hindlimb stride cycles of Orobates to find the posture that maximizes optimal strains over the course of a stride cycle. To validate our method, we used Caiman crocodilus. We replicated the identical workflow used for the analysis of Orobates and compared the locomotor posture predicted for Caiman based on muscle strain analysis with this species’ actual postural data known from a previously published X-ray motion analysis. Since this validation experiment demonstrated a close match between the modeled posture that maximizes optimal adductor and retractor muscle strain and the in vivo posture employed by Caiman, using the same method for Orobates was justified. Generally, the use of muscle strain analysis for the reconstruction of posture in quadrupedal vertebrate fossils thus appears a promising approach. Nevertheless, results for Orobates remained inconclusive as several postures resulted in similar muscle strains and none of the postures could be entirely excluded. These results are not in conflict with the previously inferred moderately erect locomotor posture of Orobates and suggest considerable variability of posture during locomotion.

"Simple" Biomechanical Model for Ants Reveals How Correlated Evolution among Body Segments Minimizes Variation in Center of Mass as Heads Get Larger

The field of comparative biomechanics strives to understand the diversity of the biological world through the lens of physics. To accomplish this, researchers apply a variety of modeling approaches to explore the evolution of form and function ranging from basic lever models to intricate computer simulations. While advances in technology have allowed for increasing model complexity, insight can still be gained through the use of low-parameter "simple" models. All models, regardless of complexity, are simplifications of reality and must make assumptions; "simple" models just make more assumptions than complex ones. However, "simple" models have several advantages. They allow individual parameters to be isolated and tested systematically, can be made applicable to a wide range of organisms and make good starting points for comparative studies, allowing for complexity to be added as needed. To illustrate these ideas, we perform a case study on body form and center of mass stability in ants. Ants show a wide diversity of body forms, particularly in terms of the relative size of the head, petiole(s), and gaster (the latter two make-up the segments of the abdomen not fused to thorax in hymenopterans). We use a "simple" model to explore whether balance issues pertaining to the center of mass influence patterns of segment expansion across major ant clades. Results from phylogenetic comparative methods imply that the location of the center of mass in an ant's body is under stabilizing selection, constraining the center of mass to the middle segment (thorax) over the legs. This is potentially maintained by correlated rates of evolution between the head and gaster on either end. While these patterns arise from a model that makes several assumptions/simplifications relating to shape and materials, they still offer intriguing insights into the body plan of ants across ∼68% of their diversity. The results from our case study illustrate how "simple," low-parameter models both highlight fundamental biomechanical trends and aid in crystalizing specific questions and hypotheses for more complex models to address.

Cranial suture biomechanics in Metoposaurus krasiejowensis (Temnospondyli, Stereospondyli) from the upper Triassic of Poland

Cranial sutures connect adjacent bones of the skull and play an important role in the absorption of stresses that may occur during different activities. The Late Triassic temnospondyl amphibian Metoposaurus krasiejowensis has been extensively studied over the years in terms of skull biomechanics, but without a detailed description of the function of cranial sutures. In the present study, 34 thin sections of cranial sutures were examined in order to determine their histovariability and interpret their biomechanical role in the skull. The histological model was compared with three-dimensional-finite element analysis (FEA) simulations of the skull under bilateral and lateral biting as well as skull-raising loads for maximum and minimum principal stress. Histologically, only two sutural morphologies were recognised in the skull of Metoposaurus: interdigitated sutures (commonly associated with compressive stresses) are dominant along the entire length of the skull roof and palate; tongue-and-groove sutures (commonly associated with tensile stresses) are present across the maxilla. FEA shows a much more complex picture of stress type and distribution than predicted by sutures. Common to both methods is a predominance of compressive stresses which act on the skull during biting. The methods predict different stress regimes during biting in the posterior part of the skull: where histological analysis suggests compression, FEA predicts tension. For lateral biting and skull raising, histological and digital reconstructions show similar general patterns but with some variations.

Pterosaur dietary hypotheses: a review of ideas and approaches

Pterosaurs are an extinct group of Mesozoic flying reptiles, whose fossil record extends from approximately 210 to 66 million years ago. They were integral components of continental and marginal marine ecosystems, yet their diets remain poorly constrained. Numerous dietary hypotheses have been proposed for different pterosaur groups, including insectivory, piscivory, carnivory, durophagy, herbivory/frugivory, filter-feeding and generalism. These hypotheses, and subsequent interpretations of pterosaur diet, are supported by qualitative (content fossils, associations, ichnology, comparative anatomy) and/or quantitative (functional morphology, stable isotope analysis) evidence. Pterosaur dietary interpretations are scattered throughout the literature with little attention paid to the supporting evidence. Reaching a robustly supported consensus on pterosaur diets is important for understanding their dietary evolution, and their roles in Mesozoic ecosystems. A comprehensive examination of the pterosaur literature identified 314 dietary interpretations (dietary statement plus supporting evidence) from 126 published studies. Multiple alternative diets have been hypothesised for most principal taxonomic pterosaur groups. Some groups exhibit a high degree of consensus, supported by multiple lines of evidence, while others exhibit less consensus. Qualitative evidence supports 87.3% of dietary interpretations, with comparative anatomy most common (62.1% of total). More speciose groups of pterosaur tend to have a greater range of hypothesised diets. Consideration of dietary interpretations within alternative phylogenetic contexts reveals high levels of consensus between equivalent monofenestratan groups, and lower levels of consensus between equivalent non-monofenestratan groups. Evaluating the possible non-biological controls on apparent patterns of dietary diversity reveals that numbers of dietary interpretations through time exhibit no correlation with patterns of publication (number of peer-reviewed publications through time). 73.8% of dietary interpretations were published in the 21st century. Overall, consensus interpretations of pterosaur diets are better accounted for by non-biological signals, such as the impact of the respective quality of the fossil record of different pterosaur groups on research levels. That many interpretations are based on qualitative, often untestable lines of evidence adds significant noise to the data. More experiment-led pterosaur dietary research, with greater consideration of pterosaurs as organisms with independent evolutionary histories, will lead to more robust conclusions drawn from repeatable results. This will allow greater understanding of pterosaur dietary diversity, disparity and evolution and facilitate reconstructions of Mesozoic ecosystems.

Merging cranial histology and 3D-computational biomechanics: a review of the feeding ecology of a Late Triassic temnospondyl amphibian

Finite Element Analysis (FEA) is a useful method for understanding form and function. However, modelling of fossil taxa invariably involves assumptions as a result of preservation-induced loss of information in the fossil record. To test the validity of predictions from FEA, given such assumptions, these results could be compared to independent lines of evidence for cranial mechanics. In the present study a new concept of using bone microstructure to predict stress distribution in the skull during feeding is put forward and a correlation between bone microstructure and results of computational biomechanics (FEA) is carried out. The bony framework is a product of biological optimisation; bone structure is created to meet local mechanical conditions. To test how well results from FEA correlate to cranial mechanics predicted from bone structure, the well-known temnospondyl Metoposaurus krasiejowensis was used as a model. A crucial issue to Temnospondyli is their feeding mode: did they suction feed or employ direct biting, or both? Metoposaurids have previously been characterised either as active hunters or passive bottom dwellers. In order to test the correlation between results from FEA and bone microstructure, two skulls of Metoposaurus were used, one modelled under FE analyses, while for the second one 17 dermal bone microstructure were analysed. Thus, for the first time, results predicting cranial mechanical behaviour using both methods are merged to understand the feeding strategy of Metoposaurus. Metoposaurus appears to have been an aquatic animal that exhibited a generalist feeding behaviour. This taxon may have used two foraging techniques in hunting; mainly bilateral biting and, to a lesser extent, lateral strikes. However, bone microstructure suggests that lateral biting was more frequent than suggested by Finite Element Analysis (FEA). One of the potential factors that determined its mode of life may have been water levels. During optimum water conditions, metoposaurids may have been more active ambush predators that were capable of lateral strikes of the head. The dry season required a less active mode of life when bilateral biting is particularly efficient. This, combined with their characteristically anteriorly positioned orbits, was optimal for ambush strategy. This ability to use alternative modes of food acquisition, independent of environmental conditions, might hold the key in explaining the very common occurrence of metoposaurids during the Late Triassic.

APPLICATIONS OF THREE-DIMENSIONAL BOX MODELING TO PALEONTOLOGICAL FUNCTIONAL ANALYSIS

Functional analysis through computer modeling can inform on how extinct organisms moved and fed, allowing us to test long-standing paleobiological hypotheses. Many such studies are based on digital models derived from computed tomography or surface scanning, but these methods are not appropriate for all fossils. Here, we show that box modeling—3-D modeling of complex shapes based on simple objects—can be used to reconstruct the morphology of various fossil specimens. Moreover, the results of computational functional analyses utilizing such models are very similar to those for models derived from tomographic or surface-based techniques. Box modeling is more broadly applicable than alternative methods for digitizing specimens; hence, there is great potential for this approach in paleontological functional analysis. Possible applications include large-scale comparative studies, analyses of hypothetical morphologies, and virtually restoring incomplete/distorted specimens.

Common evolutionary trends underlie the four-bar linkage systems of sunfish and mantis shrimp

Comparative biomechanics offers an opportunity to explore the evolution of disparate biological systems that share common underlying mechanics. Four-bar linkage modeling has been applied to various biological systems such as fish jaws and crustacean appendages to explore the relationship between biomechanics and evolutionary diversification. Mechanical sensitivity states that the functional output of a mechanical system will show differential sensitivity to changes in specific morphological components. We document similar patterns of mechanical sensitivity in two disparate four-bar systems from different phyla: the opercular four-bar system in centrarchid fishes and the raptorial appendage of stomatopods. We built dynamic linkage models of 19 centrarchid and 36 stomatopod species and used phylogenetic generalized least squares regression (PGLS) to compare evolutionary shifts in linkage morphology and mechanical outputs derived from the models. In both systems, the kinematics of the four-bar mechanism show significant evolutionary correlation with the output link, while travel distance of the output arm is correlated with the coupler link. This common evolutionary pattern seen in both fish and crustacean taxa is a potential consequence of the mechanical principles underlying four-bar systems. Our results illustrate the potential influence of physical principles on morphological evolution across biological systems with different structures, behaviors, and ecologies.

Reconstructing the past: methods and techniques for the digital restoration of fossils

During fossilization, the remains of extinct organisms are subjected to taphonomic and diagenetic processes. As a result, fossils show a variety of preservational artefacts, which can range from small breaks and cracks, disarticulation and fragmentation, to the loss and deformation of skeletal structures and other hard parts. Such artefacts can present a considerable problem, as the preserved morphology of fossils often forms the basis for palaeontological research. Phylogenetic and taxonomic studies, inferences on appearance, ecology and behaviour and functional analyses of fossil organisms strongly rely on morphological information. As a consequence, the restoration of fossil morphology is often a necessary prerequisite for further analyses. Facilitated by recent computational advances, virtual reconstruction and restoration techniques offer versatile tools to restore the original morphology of fossils. Different methodological steps and approaches, as well as software are outlined and reviewed here, and advantages and disadvantages are discussed. Although the complexity of the restorative processes can introduce a degree of interpretation, digitally restored fossils can provide useful morphological information and can be used to obtain functional estimates. Additionally, the digital nature of the restored models can open up possibilities for education and outreach and further research.

3D bite modeling and feeding mechanics of the largest living amphibian, the Chinese giant salamander Andrias davidianus (Amphibia:Urodela)

Biting is an integral feature of the feeding mechanism for aquatic and terrestrial salamanders to capture, fix or immobilize elusive or struggling prey. However, little information is available on how it works and the functional implications of this biting system in amphibians although such approaches might be essential to understand feeding systems performed by early tetrapods. Herein, the skull biomechanics of the Chinese giant salamander, Andrias davidianus is investigated using 3D finite element analysis. The results reveal that the prey contact position is crucial for the structural performance of the skull, which is probably related to the lack of a bony bridge between the posterior end of the maxilla and the anterior quadrato-squamosal region. Giant salamanders perform asymmetrical strikes. These strikes are unusual and specialized behavior but might indeed be beneficial in such sit-and-wait or ambush-predators to capture laterally approaching prey. However, once captured by an asymmetrical strike, large, elusive and struggling prey have to be brought to the anterior jaw region to be subdued by a strong bite. Given their basal position within extant salamanders and their "conservative" morphology, cryptobranchids may be useful models to reconstruct the feeding ecology and biomechanics of different members of early tetrapods and amphibians, with similar osteological and myological constraints.

Comparative finite-element analysis: a single computational modelling method can estimate the mechanical properties of porcine and human vertebrae

Significant advances in the functional analysis of musculoskeletal systems require the development of modelling techniques with improved focus, accuracy and validity. This need is particularly visible in the fields, such as palaeontology, where unobservable parameters may lie at the heart of the most interesting research questions, and where models and simulations may provide some of the most innovative solutions. Here, we report on the development of a computational modelling method to generate estimates of the mechanical properties of vertebral bone across two living species, using elderly human and juvenile porcine specimens as cases with very different levels of bone volume fraction and mineralization. This study is presented in two parts; part I presents the computational model development and validation, and part II the virtual loading regime and results. This work paves the way for the future estimation of mechanical properties in fossil mammalian bone.

Modelling the past: new generation approaches to understanding biological patterns in the fossil record

The history of life on this planet is gleaned from analysing how fossils are distributed through time and space. While these patterns are now rather securely known, at least for well-studied parts of the world, their interpretation remains far from simple. Fossils preserve only partial data from which to reconstruct their biology and the geological record is incomplete and biased, so that taxonomic ranges and palaeocommunity structure are imperfectly known. To better understand the often highly complex deep-time processes that gave rise to the empirical fossil record, palaeontologists have turned to modelling the past. Here, we summarize a series of 11 papers that showcase where modelling the past is being applied to advance our understanding across a wide spectrum of current palaeontological endeavours.

The importance of craniofacial sutures in biomechanical finite element models of the domestic pig

Craniofacial sutures are a ubiquitous feature of the vertebrate skull. Previous experimental work has shown that bone strain magnitudes and orientations often vary when moving from one bone to another, across a craniofacial suture. This has led to the hypothesis that craniofacial sutures act to modify the strain environment of the skull, possibly as a mode of dissipating high stresses generated during feeding or impact. This study tests the hypothesis that the introduction of craniofacial sutures into finite element (FE) models of a modern domestic pig skull would improve model accuracy compared to a model without sutures. This allowed the mechanical effects of sutures to be assessed in isolation from other confounding variables. These models were also validated against strain gauge data collected from the same specimen ex vivo. The experimental strain data showed notable strain differences between adjacent bones, but this effect was generally not observed in either model. It was found that the inclusion of sutures in finite element models affected strain magnitudes, ratios, orientations and contour patterns, yet contrary to expectations, this did not improve the fit of the model to the experimental data, but resulted in a model that was less accurate. It is demonstrated that the presence or absence of sutures alone is not responsible for the inaccuracies in model strain, and is suggested that variations in local bone material properties, which were not accounted for by the FE models, could instead be responsible for the pattern of results.