Review Article 
Corresponding author: Anna Krahl ( anna.krahl@unituebingen.de ) Academic editor: Irina Ruf
© 2022 Holger Preuschoft, Anna Krahl, Ingmar Werneburg.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Preuschoft H, Krahl A, Werneburg I (2022) From sprawling to parasagittal locomotion in Therapsida: A preliminary study of historically collected museum specimens. Vertebrate Zoology 72: 907936. https://doi.org/10.3897/vz.72.e85989

Therapsids covered the entire spectrum of terrestrial locomotion from sprawling to parasagittal. Switching between sprawling and more erect locomotion may have been possible in earlier taxa. First, the axial skeleton shows little regionalization and allows lateral undulation, evolving then increasingly towards regionalization enabling dorsoventral swinging. During terrestrial locomotion, every step invokes a ground reaction force and functional loadings which the musculoskeletal system needs to accomodate. First insights into the functional loading regime of the fore and hindlimb skeleton and the body stem of therapsids presented herein are based on the assessment and preliminary measurements of the historical collection of therapsids exhibited in the Paleontological Collection of Eberhard Karls Universität Tübingen, Germany. The specimens included are the archosaur Hyperodapedon sanjuanensis, the early synapsid Dimetrodon limbatus for comparison, and the therapsids Keratocephalus moloch, Sauroctonus parringtoni, Tetragonias njalilus, and Belesodon magnificus. The vertebral columns and ribs of the mounts were carefully assessed for original fossil material and, when preserved, ribs, sacral, and anterior caudal vertebrae were measured. The body of a tetrapod is exposed to forces as well as bending and torsional moments. To resist these functional stresses, certain musculoskeletal specializations evolved. These include: 1) compression resistant platelike pectoral and pelvic girdle bones, 2) a vertebral column combined with tendinous and muscular structures to withstand compressive and tensile forces and moments, and 3) ribs and intercostal muscles to resist the transverse forces and torsional moments. The legs are compressive stressresistant, carry the body weight, and support the body against gravity. Tail reduction leads to restructuring of the musculoskeletal system of the pelvic girdle.
Bending, compressive stress, functional loading, ribs, synapsids, tensile stress, transverse forces, vertebrae
Therapsid locomotion and its evolution has been subject of various studies (e.g.,
We intend to establish a first overview on certain morphological and myological patterns of the body stem across Tetrapoda. The functional loading regimes of these locomotory systems will be discussed with the intend to improve our understanding of the sprawling to parasagittal locomotion in Tetrapoda in general and Therapsida in particular. Our approach is not a phylogenetic one because we first tried to establish a basic biomechanical understanding of certain locomotory systems. Nevertheless, in the future, studies on how these, often convergent, biomechanical patterns evolved in specific tetrapod and therapsid lineages will require a strict evolutionary framework to evaluate shifts in locomotory styles and posture in detail for specific taxa.
In contrast to terrestrial vertebrates (Fig.
Phylogenetic overview. Diapsida, represented by the archosaur Hyperodapedon sanjuanensis in our study, are the sistergroup to Synapsida. Synapids include the pelycosaurgrade Dimetrodon limbatus and Therapsida. From Therapsida, the dinocephalian Keratocephalus moloch, the anomodonts Stahleckeria potens and Tetragonias njalilus, the gorgonopsian Sauroctonus parringtoni, and the cynodont Belesodon magnificus were included in this study.
A–H Sprawling and parasagittal position of limbs. On the left side: anterior view; on the right side: lateral view. A, B Rayfins, attached to the middle of the body have no lever arm in relation to the body midline and therefore generate no moment. C, D Lobefins attached to the ventral half of the body. Note the lever arm h multiplied with the force exerted by the lobefin, it leads to the moment h*F which rotates the animal about its long body axis. E, F For terrestrial sprawling locomotion, two additional joints (elbow/knee, wrist/ankle) are advantageous. If the shoulder and pelvic joints are near the ventral margin of the trunk, the latter is lifted higher off the ground than if the joints were more dorsally. The autopodia can be directed medially (as in froglike anurans) or laterally (as often in crocodiles and lizards). The elbows are directed posteriorly and the knee anteriorly. For both, the lever arms (h) of the ground reaction forces are relatively long. This leads to great torques about the proximal joints, which must be counterbalanced by contractions of the m. pectoralis in the fore and the m. caudofemoralis in the hindlimb (Gatesy, 1999). G, H In parasagittal digitigrade limbs two further additional limb segments have been added by a mobile scapula and elongated metacarpals and tarsals. On the right side, the limb segments are above each other, so that no or only small moments occur in anterior view. On the left side, a common position is illustrated: a joint in the middle of the freely moving limb is approaching the midline, like in the famous valgusposition of the human knee, and the typical, though less observed carpal joints of cattle, other bovids, cervids. In the hindlimb, the hock joints are in many forms approached, while the fetlocks are directed laterally. In side view (H), the upper arm as well as the lower leg pass in each step from vertical (lever arm being zero) to horizontal (lever arm reaching cosine of joint angle, that is the length of the segment. Note in E, F the centre of mass is above the supporting limbs, while in G, H it is at the level and between the scapulae/iliac blades. I, J As long as segment lengths and angles between segments are not changed, stride length does not change with either a sprawling or parasagittal posture of the limbs, and the joint moments are not bigger in sprawling limbs. sin α, excursion angle of the forelimb; sin β, excursion angle of the hindlimb; sin γ, excursion angle of the forelimb; sin δ, excursion angle of the hindlimb. Progress made is proportional to the sine of the angles. I The excursion range of the fore and hindlimb depend on rotation of the humerus and femur. J Flexion and extension of elbow and knee joint permit greater excursion angles. F_{a}, inertial force against being accelerated; F_{i}, inertial force against being retarded/braking; F_{w}, weight force. K In many small mammals, the upper arms and lower legs are nearly held vertically during early phases of the limb cycle, while during later phases they are swung into a nearly horizontal position (Witte et al. 1999). The lever arms (h) of the vertical ground reaction forces (GRFs) are parallel to the horizontal and their length follows the cosine of the angle between the horizontal and the upper arm/leg or the lower arm/leg. The phases in which the lever arms have their shortest or greatest lengths, and in which the moments are the smallest and biggest are shown. These moments are opposed by muscle activity. L–O Wavelike trunk movements. L An early tetrapod seen from dorsally while walking. The stylopodia are swung laterally and forward during sprawling locomotion. During the stance phase, the stylopodia compel the trunk to give way laterally and the body moves approximately in a standing wave. l, length of the stance phase. M The schematic cross section at the level of the shoulder and hip joint show the lateral displacement of the trunk. N Extension of the limb joints lift the body up and down again in a wavelike curve because parasagittal locomotion can be described by inverse pendulum mechanics (
Terrestrial tetrapods (Fig.
Recent reptiles and salamanders keep their upper arms and thighs held laterally in an approximately horizontal position (=abducted or sprawling) (Fig.
In each stance phase of a lepidosaur or crocodilian (Fig.
The scapular blade of mammals swings (
Larger qadrupedal mammals walk on adducted extremities and their limbs are moved in a parasagittal plane (Fig.
Speed of walking is v = stride length (l) * frequency (F), whereby the frequency depends on the pendulum period (T): F = T = 2 * π * square root from l/G (
According to e.g.,
Synapsids show a variety of limb postures and associated changes of the locomotor system. Therapsids such as the dicynodont Stahleckeria potens (Fig.
The humeral heads of the here studied therapsids seem to have been expanded in dorsoventral direction and strongly compressed anteroposteriorly. The proximal articulation surfaces are relatively rough and the joint congruency in the glenoid is relatively low, suggesting elaborate cartilaginous caps. There is little doubt that extensive humeral abduction and adduction were possible. The flattened shape of the humeral head inhibits long axis rotation, which is necessary for excursions of the anterior zeugopodium. In all synapsids, radius and ulna are well developed. The humerus is held in a sprawling position, the zeugopodium can be pronated so that the digits point forward (e.g.,
The femoral heads of the studied therapsids have a somewhat oval shape with a longer diameter in approximately anteroposterior direction than in dorsoventral direction. A moderate abduction of the thigh is possible, similar but to a lesser extend than the humerus. Femur abductors (e.g., m. iliofemoralis) are muscles, which insert into the proximal femur, while the femoral head is angled from the shaft. This means that the femoral head is proximal and medial to the trochanter major. The knee joint of synapsids is directed forward. Therefore, the zeugopodium of the hindlimb does not need to be pronated, the bony elements maintain their position during the entire walking cycle (e.g.,
Yet, studies on functional loading of skeletal elements are rare for Therapsida:
During therapsid evolution, their tails became lighter and shortened (
To our knowledge, studies focussing on the functional loading of the fore and hindlimbs in combination with the axial skeleton, combining functional morphology with more technical observations, have not been conducted on therapsids. For our review, here we present first insights into the available data based on the historical collection of Friedrich von Huene (1875–1969) at the Paleontological Collection, Eberhard Karls Universität Tübingen (
Fore and hindlimb. In all tetrapods, the connection between the extremities and the trunk varies between the anterior and the posterior girdles (e.g.,
An acceleration (in e.g., rapid flight, jumping etc.) imposes a higher functional loading onto the hindlimbs than onto the forelimbs. Therefore, a direct force transmission from the hindlimb onto the axial skeleton via a rather rigid sacral region is advantageous over a hypothetical rigid connection between the pectoral girdle and the axial skeleton. In slowing down or stopping, a tetrapod can afford minor delays in the transmission of force between the trunk and the anterior extremity. The reasons for this are a physical principle (illustrated in Fig.
The morphology of the girdles and the associated myology differ between crocodilians, lepidosaurs, birds, and mammals (Fig.
A–C Bodystem simplified as a beam, resting on two pairs of supports at equal distances. Sketches based on finite element structure analysismodels. The trunk is assumed to have two times the weight of the head and neck and the tail. If the beam consists of soft material, gravity deforms it as shown in A. A Head and tail bend downwards and the trunk sags in the middle imposing tensile and compressive stresses onto the model. Compressive stress, vertically hatched; tensile stress, hatched horizontally. B The tail is reduced like in some therapsids. Only the compressive stresses are shown because the compressionresistant skeleton is the only preserved material we have. The highest values are indicated by darker hatching. The highest forces occur along an arch reaching from the anterior support along the back to the posterior support. That means the shoulder blade should be inclined posterodorsally and the ilium should be inclined anterodorsally. C Head and neck are elongated (which has the same effect as a heavier head in combination with a shorter neck) and the tail is completely reduced. The posterior support is connected to the trunk by a joint, which must be balanced by a muscular tie (double line). The pulling force causes very high stress in the beam behind the joint. D–F Transverse forces of the same beam. D Shows an equal amount of functional loading distributed onto the fore and hindlimbs, and the long tail. E The combination of a short tail and a heavy head results in high loads on the fore limbs like in many therapsids. F A high load on the hindlimbs results from a forward inclination of the latter, like in the majority of mammals. The inclined limb is kept in balance by a muscular tie which connects the limb with the trunk. This leads to high transverse forces in the posterior cantilever. G–I Bending moments in the beam shown above in A, B, C The bending moments are the products of the transverse force at a certain length multiplied by distance to the nearest support. Therefore, their arrangement along the length of a body shows curvilinear outlines. Above the supports, positive values are high, between the supports, the sign changes, and reaches its lowest point where the transverse forces cross the zero line. G Long tail, stress peaks are about equally high, the highest negative values reached a maximum near the middle of the trunk. H Short tail and heavy skull result in a higher stress peak above the fore limb than in the hindlimb. I The hindlimb is inclined and balanced in the joint by a muscular tie. This results in very high transverse forces caudally to the joint, which create a very marked stress peak and reduce the negative values between the supports. J, K Torsional moments. J During locomotion between anterior and posterior extremities in the trunks of quadrupedal tetrapods. Torsional stresses concentrate near the external body wall and create a space free of functional loadings, i.e., the body cavity. K Torsion also occurs in the neck of therapsids, e.g., during feeding. The weight of the head combines with the horizontal force component to a resultant, in line with the sprawling legs, which reaches the ground within the area of support, otherwise the animal would fall over. L–O Different patterns of loading the extremity girdles. In M reptiles, N birds, O mammals, and L Therapsida. Skeletal elements black, active muscles red. Ground reaction force (GRFs) indicated by upward directed arrows, the length of which is roughly proportional to the size of the respective force. In M crocodilians and lepidosaurs, the retraction of the femur is performed by m. caudofemoralis. In N Aves, O Mammalia, and L Therapsida, femoral retraction is performed mostly by pelvifemoral muscles originating from the pelvis caudally to the acetabular joint (ilium in Therapsida, ischium in Mammalia, synsacrum in Aves). Reptiles, synapsids, and birds have in common that the shoulder joint is balanced mainly by a very strong m. pectoralis. In mammals, the scapula is suspended by e.g., the m. supraspinatus. P, Q Suspension of the body stem from the pectoral girdle in cross section. P In reptiles, Q in cursorial mammals. P Please note that the most anterior ribs of reptiles primarily provide the insertion area for the m. serratus (which carries the body stem). Q In mammals the anterior ribs close the circle of forces via their rigid connection to the sternum. The m. pectoralis of mammals suspends the body and aids in keeping the glenoid joint in balance (changed after Hohn, 2011). Abbreviations: GRF, ground reaction force.
In the pelvic girdle of reptiles, associated with a posterodorsally expanding ilium (Fig.
The pectoral and pelvic girdles are very similarly functionally loaded: On a transverse section, weight is approximately evenly distributed on all four limbs while standing (Fig.
A–D Sternum and rib angle in ventral view. Sternum, curvature of cartilaginous ribs, and rib angle in ventral view. D Morphology of the region in a crocodile as example. The black arrows indicate the direction of acting forces, not their sizes (changed and redrawn after
In the skull, mass inertia and weight combine to form a resultant running in lateroventral direction, which is in line with the sprawled position of the forelimbs (Fig.
Axial skeleton. All tetrapods need to maintain their body off the ground against gravity. A theoretical model, a beam on two supportive structures, shows that the skull and neck and the tail bend downward, as well as the back sags between the two supportive structures (Fig.
Multiplication of a transverse force at a given place by its lever arm results in the bending moment, which, if plotted along the trunk, unites to form a curvilinear function (Fig.
During walking and trotting, body weight is supported in phases by only one limb of a pair, while the other swings foreward. In addition to the transverse forces and the bending moment, the trunk has to resist a torsional moment as well (Fig.
Fore and hindlimb. In contrast to most diapsids, therapsids have a less long and heavy, in many cases a markedly reduced tail. However, at least anomodont heads were relatively large and heavy because of their large chewing apparatus and its associated muscles (e.g.,
The skeleton of the pelvic girdle is expanded at its ventral side in anteroposterior direction as well as in lateromedial direction. This corresponds with the pattern of compressive forces in lateral (Fig.
Axial skeleton. Since the m. pectoralis profundus originates from the sternum in mammals, the connection between this element and the anterior often straight ribs is strong. In crocodiles and in lizards, the m. serratus acts on the short, very strong ribs which do not reach the sternum. In early synapsids, this muscle may have extended cranially onto the cervical vertebrae, e.g., in the sphenacodontid Dimetrodon limbatus five and in the gorgonopsian Sauroctonus parringtoni two cervical ribs are found. In line with this observation is that the innervation of the forelimb through the plexus brachialis comes from the lower neck segments and only one root comes from the first thoracic (e.g.,
The ribs of early therapsids differ from those of mammals and are similar to those of diapsid reptiles: proximally, they have two articular surfaces, the head and the tuberculum. This vlike shape provides stability and inhibits that the ribs are bend outward or inward. The force that induces outward or inward bending of the ribs is given in sprawling tetrapods when the stylopodia are abducted. In contrast, cranial or caudal bending of the ribs about an axis which connects both joints is easily taking place. Torsional moments are greater in reptiles than in mammals, because their ground reaction forces have longer lever arms. As a consequence, the trunk in extant reptiles is more rounded, or tubelike than in mammals that have a more laterally compressed trunk at the level of the pectoral and the pelvic girdles. Doubleheaded ribs are suited to sustain various loads (Fig.
A–C Functional loading of ribs on cross sections. Skeletal elements drawn thicker than musculature. A The weight of the intestines pushes downward and is represented by six arrows. On the right side, the parts of weight combine with the pulling force of the muscles to resultants, which agree with the local direction of the muscles. The ventral tips of the ribs are pulled downward, and can be sustained because of the long, bifurcated collum and tuberculum. B Torsional moments compress the ribs on one side, while extending them on the other. In the first case, ribs tend to vault laterally, in the second, the curvature becomes flatter. C In contrast to the trunk carried freely above the ground (left side, also in A), a bellydragging posture (right side) leads to compression of the ribs, not to tension. Ribs in side view. D, E Sketch of a synapsid, with sprawling forelimbs and parasagittally moving hindlimbs. D Lateral, E top view. Segment length is the same in both sketches, the excursion of the hip and shoulder joint are identical, as well as the step length sl. The excursion range of the zeugopodium is enabled by a rotation about the long axis of the stylopodium. F Direct transfer of body weight on the ground (bold arrows) leads to a more inclined position of the rib (after
1. The compressive components of torsion, which lead to bending of the rib outward (Fig.
2. The force of the pulling and weightcarrying m. serratus (Fig.
3. Downward directed pull of the ventral body wall by gravity: The tension of the body wall leads to more vertically oriented ribs in the most posterior part of the dorsal vertebral column again.
4. Carrying the body weight in resting or sprawling bellydragging (sensu
It can be expected that the ribs are inclined to average angles mediating between the various functional loadings, which may vary dependending on the lifestyle. The independance from the most ventral part of the ribs, close to the sternum is secured by the not ossified and therefore mobile (see above) cartilaginous parts (Fig.
Therapsida evolved a relatively heavy head with a short neck and a short, or at least not heavy tail. These characteristics shifted the center of mass of the body forward, towards the forelimbs (
Most recent mammals walk with both limb pairs moved in a parasagittal plane. The swinging scapula provides an additional leg segment that adds to stride length. The necessity for strong leg adductors to maintain the sprawling posture becomes superfluous. Instead, recent mammals have a slender sternum which is craniocaudally oriented (Fig.
If the tail is reduced, it cannot provide a sufficiently stable insertion for the retractors of the femur. Instead postcoxal processes of the pelvis (synsacrum and ischium in birds, ischia and pubis in mammals) offer areas into which the retractors may insert (Fig.
An array of ribs, in especially the anterior part of the trunk is a characteristic of all Tetrapoda. In landliving vertebrates, ribs are part of the respiratory system (e.g.,
In the most cranial ribs the m. serratus pulls dorsally and in the more posterior ribs the muscular body wall (m. rectus abdominis, m. obliquus abdominis externus, m. obliquus abdominis internus, m. transversus abdominis) pulls ventrally. The m. serratus suspends the ribs and carries the body (
Belesodon magnificus (
Keratocephalus moloch (
Parasagittal locomotion evolved convergently in Aves, Meta, and Eutheria. In therapsids, this posture was attained in the hindlimbs earlier than in the forelimbs (
Limb segments of the more extended parasagittal position can become longer without an increase of energy consumption. Many synapsids were of medium size [(e.g., Dimetrodon limbatus (Fig.
Stahleckeria potens (
Tetragonias njalilus (
Possible evolutionary scenarios for the development of parasagittal locomotion are:
1. Small mammals hold their legs horizontally only during part of the locomotory cycle (roughly during one third) and save some energy this way (e.g.,
2. The horizontal components of the ground reaction forces perpendicular to locomotion (F_{y} in Fig.
3. For a digitigrade limb posture, an additional limb segment is formed by the tarsus and metapodium. This additional limb segment elongates the free limb and therefore step length (e.g.,
4. During sprawling locomotion of synapsids, humeral long axis rotation may be limited, based on the oval humeral head surface observable in limbs (Dimetrodon limbatus, Stahleckeria potens, Sauroctonus parringtoni, Tetragonias njalilus, Belesodon magnificus). The digits are continuously pointing forward and the forearms are crossed during the entire limb cycle. This leads in many forms to a division of labor in which the ulna is loaded more in the proximal and the radius more in the distal part. In parasagittal locomotion, the manus is placed forward and extension and flexion of the elbow and knee joint increase the stride length (
5. A swinging scapula and an accordingly restructured thorax add to stride length by basically adding another additional limb segment to the leg (
Therapsid heads have been rather large and presumably heavy. Lateral movements of the heavy head require a broad support from the forelimbs, especially when performed rapidly. Hindlimbs are not subject to this condition, especially, if the tail is never exposed to statical loading or lateral accelerations. A reason for a more parasagittal posture of the hindlimb in therapsids earlier in evolution than in the forelimbs may be that the reduced, lighter, and/or shortened tail did not constrain the hindlimb to a sprawling position earlier in locomotion than the forelimb was subjected to.
Belesodon magnificus (
Measurement 1 (cm)  Measurement 2 (cm)  Measurement 3 (cm) (anteroposterior)  Measurement 4 (cm) (lateralmedial)  Measurement 5 (cm) (anteroposterior)  Measurement 6 (cm) (lateralmedial)  Measurement 7 (cm)  Measurement 8 (cm)  Measurement 9 (cm)  Measurement 10 (cm)  
rib 9 (left)  n.m.  n.m.  0.6  1.0  0.3  1.1  2.6  1.7  1.5  n.m. 
rib 11 (left and right)  n.m.  n.m.  0.6 and 0.6  1.0 and 1.1  0.4 and 0.5  1.0 and 1.0  Broken and 3.7  1.6 and 2.7  Broken and 2.1  n.m. 
rib 16 (left)  n.m.  n.m.  0.7  1.1  0.7  1.0  2.3  1.6  1.8  n.m. 
rib 19 (left)  n.m.  n.m.  0.5  0.8  2.3  1.4  1.8  n.m. 
Dimetrodon limbatus (
Measurement 1 (cm)  Measurement 2 (cm)  Measurement 3 (cm) (anteroposterior)  Measurement 4 (cm) (lateralmedial)  Measurement 5 (cm) (anteroposterior)  Measurement 6 (cm) (lateralmedial)  Measurement 7 (cm)  Measurement 8 (cm)  Measurement 9 (cm)  Measurement 10 (cm)  
rib 1  n.m.  n.m.  0.6  1.1  0.5  0.6  1.9  1.7  1.0  0.3 
rib 2  n.m.  n.m.  0.7  1.2  n.m.  n.m.  n.m.  2.1  n.m.  n.m. 
rib 3  n.m.  n.m.  0.9  1.1  0.7  0.8  n.m.  n.m.  n.m.  n.m. 
rib 8  n.m.  n.m.  1.2  1.8  0.8  0.7  n.m.  n.m.  n.m.  n.m. 
rib 9  n.m.  n.m.  1.2  1.8  0.9  0.7  n.m.  n.m.  n.m.  n.m. 
rib 12  n.m.  n.m.  n.m.  n.m.  0.8  0.9  3.5  2.5  2.8  2.3 
rib 13  n.m.  n.m.  0.9  0.8  0.9  0.8  2.9  3.3  2.8  2.2 
rib 16  n.m.  n.m.  0.8  1.3  n.m.  n.m.  n.m.  n.m.  n.m.  n.m. 
Dimetrodon limbatus (
centrum width (cm)  centrum height (cm)  centrum length (cm)  
second last presacral  3.6  3.0  3.8 
last presacral  3.5  3.2  3.7 
1. sacral  3.5  3.2  2.8 
2. sacral  3.2  3.2  2.9 
3. sacral  2.6  2.5  2.8 
1. caudal  3.0  2.5  3.0 
2. caudal  2.4  2.7  3.0 
3. caudal  2.7  3.0  2.5 
4. caudal  2.6  2.7  2.6 
5. caudal  2.8  2.4  2.6 
6. caudal  2.7  2.7  2.4 
7. caudal  2.5  2.7  2.6 
8. caudal  2.7  3.0  2.2 
9. caudal  2.1  1.8  2.4 
10. caudal  2.0  1.8  2.0 
11. caudal  1.6  1.6  2.1 
12. caudal  1.6  1.4  1.8 
13. caudal  1.4  1.3  1.8 
14. caudal  1.4  1.4  1.8 
Hyperodapedon sanjuanensis (
Measurement 1 (cm)  Measurement 2 (cm)  Measurement 3 (cm) (anteroposterior)  Measurement 4 (cm) (lateralmedial)  Measurement 5 (cm) (anteroposterior)  Measurement 6 (cm) (lateralmedial)  Measurement 7 (cm)  Measurement 8 (cm)  Measurement 9 (cm)  Measurement 10 (cm)  
rib 1 (left)  n.m.  5.5  0.4  1.2  0.4  0.9  2.0  n.m.  n.m.  n.m. 
rib 2 (right)  n.m.  5.5  0.5  0.6  0.4  0.5  2.0  1.5  1.6  0.9 
rib 3 (right)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  2.4  2.1  1.2  1.0 
rib 4 (left)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  3.1  2.5  1.6  1.1 
rib 7 (right)  15.0  15.5  0.5  1.3  0.5  1.0  3.2  2.5  3.4  0.4 
rib 9 (right)  20.0  16.0  0.8  1.6  0.7  1.3  3.2  2.9  2.4  0.5 
rib 10 (right)  20.6  17.0  0.7  1.1  0.8  1.1  2.9  2.4  1.7  n.m. 
rib 11 (right)  20.9  16.0  1.0  1.5  1.0  1.0  n.m.  n.m.  n.m.  n.m. 
rib 12 (left)  17.0  16.6  0.6  1.2  0.7  1.2  2.9  n.m.  n.m.  n.m. 
rib 13 (right)  20.7  18.3  0.8  0.9  0.6  1.3  n.m.  n.m.  n.m.  n.m. 
rib 14 (left)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  n.m. 
rib 18 (right)  21.5  20.4  0.7  0.8  0.5  0.9  n.m.  n.m.  n.m.  n.m. 
rib 19 (right)  17.7  15.8  0.5  0.8  0.5  1.1  n.m.  n.m.  n.m.  n.m. 
rib 20 (left)  23.0  16.4  0.6  0.8  0.4  0.8  n.m.  n.m.  n.m.  n.m. 
Hyperodapedon sanjuanensis (
centrum width (cm)  centrum height (cm)  centrum length (cm)  
second last presacral  3.0  2.4  3.3 
last presacral  2.5  2.8  2.5 
1. sacral  2.8  2.3  3.5 
2. sacral  2.9  2.5  3.4 
1. caudal  2.0  2.4  2.6 
2. caudal  2.3  2.3  2.4 
3. caudal  2.0  2.2  2.3 
4. caudal  1.8  2.4  2.1 
5. caudal  2.0  2.2  2.0 
6. caudal  1.5  2.0  1.8 
7. caudal  1.2  1.8  1.8 
8. caudal  1.0  1.6  2.0 
9. caudal  1.1  2.0  1.7 
Keratocephalus moloch (
Measurement 1 (cm)  Measurement 2 (cm)  Measurement 3 (cm) (anteroposterior)  Measurement 4 (cm) (lateralmedial)  Measurement 5 (cm) (anteroposterior)  Measurement 6 (cm) (lateralmedial)  Measurement 7 (cm)  Measurement 8 (cm)  Measurement 9 (cm)  Measurement 10 (cm)  
rib 12 (left and right)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  13 and 16  7 and 7  12 and 13  n.m. 
rib 13 (left and right)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  15 and 15  6 and 7  12 and 13  n.m. 
rib 14 (right)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  15  7  12  n.m. 
rib 15 (right)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  13  5.5  12  n.m. 
Keratocephalus moloch (
centrum width (cm)  centrum height (cm)  centrum length (cm)  
second last presacral  9.0  7.2  4.5 
last presacral  10.0  8.7  4.6 
1. sacral  10.0  10.2  5.5 
2. sacral  7.5  11.5  5.5 
3. sacral  8.3  9.3  6.0 
1. caudal  8.5  8.8  5.5 
Sauroctonus parringtoni (
Measurement 1 (mm)  Measurement 2 (mm)  Measurement 3 (mm) (anteroposterior)  Measurement 4 (mm) (lateralmedial)  Measurement 5 (mm) (anteroposterior)  Measurement 6 (mm) (lateralmedial)  Measurement 7 (mm)  Measurement 8 (mm)  Measurement 9 (mm)  Measurement 10 (mm)  
rib 1  65 cm  65  6.82  9.75  5.8  7.61  21.27  14.8  11.4  3.1 
rib 2  85  85  6.9  7.68  5.3  6.15  24.85  12.96  17.87  3.55 
rib 3  115  110  7.07  8.67  7.2  7.38  23,2  15.28  11.54  3.34 
rib 4  135  130  5.8  8.4  4.66  7.5  27.2  13.7  22.1  3.18 
rib 5  150  135  7.32  11  7.3  8.45  32.12  13,5  18.3  3.55 
rib 6  140  130  5.33  9  4.45  6.87  n.m.  n.m.  n.m.  n.m. 
rib 7  155  135  6.3  9.6  7.36  7.76  n.m.  n.m.  n.m.  3 
rib 8  180  135  6.84  7  5.75  7.09  21.7  14.3  17.34  2.8 
rib 9  170  145  5.67  8.81  5,97  7.48  n.m.  n.m.  n.m.  n.m. 
rib 10  190  165  4.22  10.4  5.42  5.5  n.m.  n.m.  n.m.  n.m. 
rib 11  210  185  6.2  7.58  6.25  6.35  21.89  16.22  16.2  
rib 12  190  170  7.12  7.52  6.82  6.41  33.41  14.56  26  3.5 
rib 13  180  145  5.87  8.54  6.01  7.61  34  17.5  25  1.2 
rib 14  175  140  7.47  7.95  6.91  6.14  36.02  15.61  25.11  2.9 
rib 15  170  135  9.42  7.64  7.63  4.55  32.53  14.34  25.11  4.3 
rib 16  160  130  5.69  6.68  4.94  7.1  28.6  13.73  22.9  3.43 
rib 17  130  110  8.33  9.12  6.43  8.48  n.m.  12.7  n.m.  4 
rib 18  110  100  5.43  8.56  5.69  6.26  29.8  12.23  28.05  6 
rib 19  100  80  5.73  7.2  4.42  4.75  20.4  13.43  19.7  1.85 
rib 20  85  65  5.68  9.84  5.21  7.55  19.92  11  14.3  1 
rib 21  90  70  5.86  8.25  5.62  9.11  18.2  10.2  17.4  1 
Sauroctonus parringtoni (
centrum width(cm)  centrum height(cm)  centrum length (cm)  
second last presacral  20.4  19  25 
last presacral  18.7  18  15 
1. sacral  36  20  18 
2. sacral  23.7  18  19 
3. sacral  21.4  16  17 
1. caudal  25,4  22  22 
2. caudal  23.3  12  19 
3. caudal  24.2  14  22 
4. caudal  22  12  14 
5. caudal  16.2  14  14 
6. caudal  19.20  12  10 
7. caudal  18.2  14  16 
Stahleckeria potens (
Measurement 1 (cm)  Measurement 2 (cm)  Measurement 3 (cm) (anteroposterior)  Measurement 4 (cm) (lateralmedial)  Measurement 5 (cm) (anteroposterior)  Measurement 6 (cm) (lateralmedial)  Measurement 7 (cm)  Measurement 8 (cm)  Measurement 9 (cm)  Measurement 10 (cm)  
rib 8 (left complete)  55  47.5  2.7  2.6  1.8  2.4  13.6  10.9  5.6  1.3 
rib 9 (left)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  14.0  10.7  6.6  1.4 
rib 12 (right)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  10.6  7.6  7.0  n. m. 
rib 14 (left)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  8.1  4.8  5.4  n. m. 
rib 15 (left and right)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  6.5 and 6.6  3.9 and 4.8  5.1 and 5.2  n. m. and 0.3 
rib 16 (left and right complete)  110.5  76.5  3.8  4.5  3.7  4.4  7.5 and 7.2  4.7 and 4.3  4.4 and 4.6  n. m. and 0.2 
rib 17 (right)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  6.2  4.2  3.7  n. m. 
rib 18 (right)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  6.7  4.5  5.3  n. m. 
rib 19 (right)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  5.8  4.1  3.6  n. m. 
rib 20 (left and right)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  6.1 and 6.2  4.0 and 4.2  3.7 and 4.6  n. m. 
rib 23 (left)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  8.7  5.1  3.9  n. m. 
rib 24 (left)  n.m.  n.m.  n.m.  n.m.  n.m.  n.m.  8.5  6.0  4.5  n. m. 
Stahleckeria potens (
centrum width(cm)  centrum height(cm)  centrum length (cm)  
second last presacral  —  —   
last presacral  9.2  8.9  5.4 
1. sacral  9.4  11.6  42.4 
2. sacral  n.m.  n.m.  n.m. 
3. sacral  n.m.  n.m.  n.m. 
4. sacral  n.m.  n.m.  n.m. 
5. sacral  n.m.  n.m.  n.m. 
6. sacral  n.m.  n.m.  n.m. 
7. sacral  n.m.  n.m.  n.m. 
8. sacral  6.2  5.6  n.m. 
1. caudal  n.m.  n.m.  n.m. 
2. caudal  7.5  8.6  4.0 
3. caudal  8.4  8.0  4.1 
4. caudal  7.8  6.5  4.5 
5. caudal  7.0  6.4  4.8 
6. caudal  7.1  8.2  4.2 
7. caudal  7.3  4  3.4 
Segments of body stem. The remains of the vertebral columns of Stahleckeria potens, Belesodon magnificus, Keratocephalus moloch, and Tetragonias njalilus are too fragmentary to determine the number of vertebrae, their regionalization, and which are ribbearing or carrying wide transverse processes.
Taxon  no. of cervical vertebrae  no. of dorsal vertebrae  no. of sacral vertebrae  no. of caudal vertebrae  cervical vertebrae with ribs  dorsal vertebrae without ribs  tail vertebrae with transverse processes  citation 
Sauroctonus parringtoni ( 
7  21  3  33–34  2  0  7 

Hyperodapedon sanjuanensis ( 
6  19  2  35–40  6  0  Impossible to determine  von Huene (1939–42) 
Dimetrodon limbatus ( 
unknown  27 presacrals ( 
3 ( 
> 20 in e.g. the specimen described by 
all  0  Impossible to determine 
DFGgrant WE 5440/61 to Ingmar Werneburg.
The authors have declared no competing interests.
HP wishes to express that this article is based to a large extent on the work done by former colleagues of him in alphabetical order: Wolfgang Maier, Carsten Niemitz, Adolf Seilacher, Frank Westphal, Ulrich Witzel, and coworkers in alphabetical order: Andreas Christian, Norman Creel, Brigitte Demes, Martin Fritz, Michael Günther, Stephan Recknagel, Hartmut Witte. Although some do not show up in the reference list, all of them helped to solve problems, often with the aid of mathematics, often with FEtechniques. They also kept a watchful eye on my tendency to consider things as selfevident and insisted on stepbystep thinking. The same kind of influence was exerted from many graduate and PhD students who were working at times in Functional Morphology. HP owes many thanks to all of them! Further, the authors would like to thank the reviewers, Jörg Fröbisch and one anonymous reviewer, for there many helpful comments that led to an improved manuscript.
The material we examined includes the skeletons of the archosaur Hyperodapedon sanjuanensis (
1. Hyperodapedon sanjuanensis (Rhynchosauria, Archosauromorpha,
2. The mounted skeleton of Dimetrodon limbatus (
3. Sauroctonus parringtoni (Gorgonopsia) (
4. Stahleckeria potens (
No cervical ribs have been preserved. Only two ribs, ribs 8 (left side) and 16 (right side), are complete (von Huene 1935–
5. Belesodon magnificus (
6. Tetragonias njalilus (
7. Keratocephalus moloch (tapinocephalid dinocephalian; Synapsida: Therapsida) (