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  1. Abstract Locomotor evolution in synapsids involved numerous functional shifts associated with the transition from sprawled to erect limb postures on the line to therian mammals. Given that bone structure frequently reflects functional requirements, this study investigated evolutionary changes in synapsid humerus and femur proportions as a lens to evaluate functional shifts through time. A total of 936 bones were measured, representing 330 species across the full 320+ million years of synapsid history. This dataset was used to test whether transformations in stylopod proportions are consistent with inferred changes in bone loading mechanics, alignment of joint and muscle forces, muscular control of the shoulder and hip, and differential support of body weight by the fore‐ and hindlimbs. As variation in bone dimensions may also correlate with bone or body size, this study first developed a novel approach for calculating species‐specific, size‐corrected measures of bone proportions. By disentangling the effect of body size from functional signals recorded in bone geometry, this then enabled a node‐to‐node appraisal of how bone allometry itself evolved through time. Ancestral state reconstruction of size‐corrected stylopod proportions reveals trends that broadly support many hypothesized shifts in locomotor biomechanics along the therian stem lineage. However, patterns of transformation are frequently complex, suggesting functional mosaicism, and stylopod proportions that typify therians as a whole are often not achieved until crown Theria itself. Several instances of temporary trend reversal are also inferred, particularly within non‐mammalian cynodonts, indicating greater functional or ecological diversification in this group. 
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  2. Synopsis Size has an impact on various aspects of an animal's biology, including physiology, biomechanics, and ecology. Accurately and precisely estimating size, in particular body mass, is therefore a core objective of paleobiologists. Two approaches for estimating body mass are common: whole-body volumetric models and individual element-scaling (e.g., bones, teeth). The latter has been argued to be more accurate, while the former more precise. Here, we use minimum convex hulls (MCHs) to generate a predictive volumetric model for estimating body mass across a broad taxonomic and size range (127 g – 2735 kg). We compare our MCH model to stylopodial-scaling, incorporating data from the literature, and find that MCH body mass estimation is both more accurate and more precise than stylopodial estimation. An explanation for the difference between methods is that reptile and mammal stylopod circumference and length dimensions scale differentially (slope 1.179 ± 0.102 vs. 1.038 ± 0.031, respectively), such that reptiles have more robust bones for a given size. Consequently, a mammalian-weighted stylopodial-scaling sample overestimates the body mass of larger reptiles, and this error increases with size. We apply both estimation equations to a sample of 12 Permo-Triassic tetrapods and find that stylopodial-scaling consistently estimates a higher body mass than MCH estimation, due to even more robust bones in extinct species (slope = 1.319 ± 0.213). Finally, we take advantage of our MCH models to explore constraints regarding the position of the center of mass (CoM) and find that relative body proportions (i.e., skull:tail ratio) influence CoM position differently in mammals, crocodylians, and Permo-Triassic tetrapods. Further, we find that clade-specific body segment expansion factors do not affect group comparisons but may be important for individual specimens with rather disproportionate bodies (e.g., the small-headed and large-tailed Edaphosaurus). Our findings suggest that the whole-body volumetric approach is better suited for estimating body mass than element-scaling when anatomies are beyond the scope of the sample used to generate the scaling equations and provides added benefits such as the ability to measure inertial properties. 
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  3. Abstract This paper is the second in a two‐part series that charts the evolution of appendicular musculature along the mammalian stem lineage, drawing upon the exceptional fossil record of extinct synapsids. Here, attention is focused on muscles of the hindlimb. Although the hindlimb skeleton did not undergo as marked a transformation on the line to mammals as did the forelimb skeleton, the anatomy of extant tetrapods indicates that major changes to musculature have nonetheless occurred. To better understand these changes, this study surveyed the osteological evidence for muscular attachments in extinct mammalian and nonmammalian synapsids, two extinct amniote outgroups, and a large selection of extant mammals, saurians, and salamanders. Observations were integrated into an explicit phylogenetic framework, comprising 80 character–state complexes covering all muscles crossing the hip, knee, and ankle joints. These were coded for 33 operational taxonomic units spanning >330 Ma of tetrapod evolution, and ancestral state reconstruction was used to evaluate the sequence of muscular evolution along the stem lineage from Amniota to Theria. The evolutionary history of mammalian hindlimb musculature was complex, nonlinear, and protracted, with several instances of convergence and pulses of anatomical transformation that continued well into the crown group. Numerous traits typically regarded as characteristically “mammalian” have much greater antiquity than previously recognized, and for some traits, most synapsids are probably more reflective of the ancestral amniote condition than are extant saurians. More broadly, this study highlights the utility of the fossil record in interpreting the evolutionary appearance of distinctive anatomies. 
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  4. Abstract This paper is the first in a two‐part series that charts the evolution of appendicular musculature along the mammalian stem lineage, drawing upon the exceptional fossil record of extinct synapsids. Here, attention is focused on muscles of the forelimb. Understanding forelimb muscular anatomy in extinct synapsids, and how this changed on the line to mammals, can provide important perspective for interpreting skeletal and functional evolution in this lineage, and how the diversity of forelimb functions in extant mammals arose. This study surveyed the osteological evidence for muscular attachments in extinct mammalian and nonmammalian synapsids, two extinct amniote outgroups, and a large selection of extant mammals, saurians, and salamanders. Observations were integrated into an explicit phylogenetic framework, comprising 73 character–state complexes covering all muscles crossing the shoulder, elbow, and wrist joints. These were coded for 33 operational taxonomic units spanning >330 Ma of tetrapod evolution, and ancestral state reconstruction was used to evaluate the sequence of muscular evolution along the stem lineage from Amniota to Theria. In addition to producing a comprehensive documentation of osteological evidence for muscle attachments in extinct synapsids, this work has clarified homology hypotheses across disparate taxa and helped resolve competing hypotheses of muscular anatomy in extinct species. The evolutionary history of mammalian forelimb musculature was a complex and nonlinear narrative, punctuated by multiple instances of convergence and concentrated phases of anatomical transformation. More broadly, this study highlights the great insight that a fossil‐based perspective can provide for understanding the assembly of novel body plans. 
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  5. The evolutionary transition from early synapsids to therian mammals involved profound reorganization in locomotor anatomy and function, centered around a shift from “sprawled” to “erect” limb postures. When and how this functional shift was accomplished has remained difficult to decipher from the fossil record alone. Through biomechanical modeling of hindlimb force-generating performance in eight exemplar fossil synapsids, we demonstrate that the erect locomotor regime typifying modern therians did not evolve until just before crown Theria. Modeling also identifies a transient phase of increased performance in therapsids and early cynodonts, before crown mammals. Further, quantifying the global actions of major hip muscle groups indicates a protracted juxtaposition of functional redeployment and conservatism, highlighting the intricate interplay between anatomical reorganization and function across postural transitions. We infer a complex history of synapsid locomotor evolution and suggest that major evolutionary transitions between contrasting locomotor behaviors may follow highly nonlinear trajectories. 
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  6. Previously, the authors published a framework for phylogenetically informed reconstruction of appendicular musculature in extinct synapsids. In the present study, this framework is employed to rigorously infer the arrangement of muscles in the hindlimb of eight exemplar taxa that capture the evolutionary transformation from basal synapsids to crown therians. Muscle maps detailing origins and insertions are presented for each taxon. These will aid the interpretation of fossil material in the future, especially fragmentary remains of related species, and provide a foundation for functional analysis of the appendicular skeleton and its evolution. 
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