Comparative cranial myology and biomechanics of Plateosaurus and Camarasaurus and evolution of the sauropod feeding apparatus

Sauropodomorpha represents an important group of Mesozoic megaherbivores, and includes the largest terrestrial animals ever known. It was the first dinosaur group to become abundant and widespread, and its members formed a significant component of terrestrial ecosystems from the Late Triassic until the end of the Cretaceous. Both of these factors have been explained by their adoption of herbivory, but understanding the evolution of sauropodomorph feeding has been hampered by the scarcity of biomechanical studies. To address this, the jaw adductor musculature of the basal sauropodomorph Plateosaurus and the sauropod Camarasaurus have been reconstructed. These reconstructions provide boundary conditions for finite element models to assess differences in structural performance between the two taxa. Results demonstrate that Camarasaurus was capable of much greater bite forces than Plateosaurus, due to greater relative adductor muscle mass and shape changes to the mandible. The skull and mandible of Camarasaurus are also ‘stronger’ under static biting. The Plateosaurus mandible appears to compromise structural efficiency and force transmission in order to maintain relatively high jaw closure speed. This supports suggestions of facultative omnivory in basal sauropodomorph taxa. The expanded mandibular symphysis and ‘lateral plates’ of sauropods each lead to greater overall craniomandibular robustness, and may have been especially important in accommodating forces related to asymmetric loading. The functional roles of these characters, and observed general shape changes in increasing skull robustness, are consistent with hypotheses linking bulk‐herbivory with the origin of Sauropoda and the evolution of gigantism.

S A U R O P O D O M O R P H A represents one of the most important Mesozoic terrestrial herbivore groups, numbering more than 200 genera and occupying all continents (Galton & Upchurch 2004;Upchurch et al. 2004;Weishampel et al. 2004;Mannion et al. 2011;Sander 2013). This clade includes the sauropods, the largest terrestrial animals known, with taxa commonly exceeding 20 tonnes in body mass (Klein et al. 2011;Benson et al. 2014) and the largest reaching in the region of 60-70 tonnes (Mazzetta et al. 2004;Lacovara et al. 2014; but see Bates et al. 2015). The extreme nature of sauropodomorph biology makes exploration of their functional anatomy and evolution imperative for understanding the constraints acting upon terrestrial life (Clauss 2011;Sander et al. 2011;Sander 2013).
The ability to eat plants has been implicated in the early diversification of Sauropodomorpha (Galton 1985a;Barrett & Upchurch 2007;Barrett et al. 2011) and the evolution of the sauropod feeding apparatus (Barrett & Upchurch 2007;Upchurch et al. 2007;Sander & Clauss 2008;Sander et al. 2011;Sander 2013). Adoption of obligate high-fibre herbivory and bulk-feeding are seen as integral drivers of sauropod gigantism (Barrett & Upchurch 2007;Upchurch et al. 2007;Yates et al. 2010;Sander et al. 2011;Sander 2013;Barrett 2014;Benson et al. 2014). Whereas basally branching 'prosauropod' taxa appear to have remained relatively morphologically conservative (Barrett & Upchurch 2007;Young & Larvan 2010) the base of Sauropoda is associated with the appearance of numerous cranial traits hypothesized to have led to greater bite force, jaw processing power and increased robustness of the skull and mandible. These include the dorsoventral expansion of the mandibular symphysis, broadening of the snout, the development of 'lateral plates' of bone inferred to have braced the teeth, and gross changes to cranial shape (Upchurch & Barrett 2000;Barrett & Upchurch 2007;Upchurch et al. 2007). However, this hypothesized functional shift has not been tested quantitatively using biomechanical methods. Button et al. (2014) employed finite element analysis (FEA) of the crania of Diplodocus and Camarasaurus to investigate ecological phenomena, and Lautenschlager et al. (2016) used similar methods to compare the mechanical performance of Plateosaurus with that of other herbivorous dinosaurs. Here, this methodology is extended to the mandible of Camarasaurus. In addition, the jaw adductor musculature of Plateosaurus and Camarasaurus, restored digitally from CT scan data, are described in a detailed, comparative context for the first time. Plateosaurus is similar in craniodental morphology to other 'prosauropods' whereas Camarasaurus exhibits the 'broad-crowned' craniodental morphology considered plesiomorphic for sauropods (e.g. Chure et al. 2010), so that comparison of these taxa provides an opportunity to test functional hypotheses associated with the purported functional and ecological shift at the base of Sauropoda. Two main hypotheses are tested here. Firstly, that calculated bite forces of Camarasaurus will exceed those of Plateosaurus as a result of the changes in craniomandibular shape and adductor chamber morphology seen in sauropods. Secondly, that the skull and mandible of Camarasaurus will mechanically outperform Plateosaurus when loaded to replicate a static bite, as measured by lower levels of both functionally-induced stress and total strain energy.
Institutional abbreviations. AMNH, American Museum of Natural History, New York City, USA; CMNH, Carnegie Museum of Natural History, Pittsburgh, USA; DINO, Dinosaur National Monument, Vernal, USA; MB.R, Museum f€ ur Naturkunde, Berlin, Germany.

MATERIAL AND METHOD
Virtual osteological reconstruction CT scans of MB.R.1937, an adult individual of Plateosaurus engelhardti and CMNH 11338, a juvenile specimen of Camarasaurus lentus, were provided by Lawrence M. Witmer, with permission to use the Plateosaurus data from R. Goessling on behalf of the Humboldt Museum f€ ur Naturkunde. These scan data were imported into Avizo (v6.3.1, v7 and v8.0; Visualization Sciences Group; http://www.vsg3d.com). Complete reconstructions were made of Camarasaurus and Plateosaurus by assigning each cranial element of CMNH 11338 and MB.R.1937 to a separate label within the Avizo segmentation editor. Each specimen has suffered taphonomic deformation, with missing and warped elements. Retrodeformation was performed using translation, transformation and mirroring tools within Avizo (see Lautenschlager et al. 2014;Cuff & Rayfield 2015) to produce undistorted and complete 3D osteological reconstructions of Camarasaurus and Plateosaurus. See Button et al. (2016) for more information.

Virtual muscle reconstruction
Jaw adductor muscles were reconstructed from a combination of first-hand observations and examination of CT scans of MB.R.1937 and CMNH 11338. Muscle origination and insertion sites were identified on the basis of phylogenetic bracketing (Witmer 1995) and osteological correlates (see Holliday 2009), with topological constraints provided by other tissues and comparison to more distant outgroups (Lepidosauria (Fairman 1999;Holliday & Witmer 2007)) where appropriate. Additionally, comparisons were made with two earlier jaw muscle reconstructions of Plateosaurus (Galton 1985b;Fairman 1999). Virtual muscles were then constructed following the protocol of Lautenschlager (2013), with muscle size constrained by osteological and soft-tissue topological constraints.
Forces were calculated using the 'dry skull method' (Thomason 1991). Physiological cross-sectional area (PCSA) for each muscle was calculated by dividing the total volume of each muscle, measured using the Avizo material statistics module, by its estimated fibre length. As muscle pennation cannot be measured for extinct taxa, total muscle length, as measured from the midpoint of the origination site to the midpoint of the attachment site, was taken as an approximation for fibre length, also measured in Avizo. In the absence of physiological data on sauropodomorph muscles this is necessary in order to minimize ad hoc assumptions; however, it should be noted that as muscle length represents the maximum possible fibre length it will produce a minimum estimate of muscle force. PCSA values were multiplied by the upper and lower values of the specific tension of muscle as reported by Thomason et al. (1990) (147-392 kPa) to produce upper and lower bounds of contractile muscle force.
CMNH 11338 represents a juvenile Camarasaurus lentus. The adductor musculature was first reconstructed on the juvenile-sized skull. Then, in order to provide an estimate of adult bite force, this juvenile skull model (with the reconstructed adductor muscles) was scaled up to reach the dimensions of adult C. lentus skulls. Differences in skull proportions between CMNH 11338 and adult C. lentus fall within the range of variation observed between adult specimens (Ikejiri et al. 2005). Indeed, no significant ontogenetic changes in skull morphology, beyond a general size increase, are currently recognized for C. lentus (Ikejiri et al. 2005). In this case, the digital model, with reconstructed muscle volumes, was scaled by 180% in all axes to match the linear dimensions of the adult individual DINO 28 (Madsen et al. 1995) as in Button et al. (2014). The force provided by each of these adult-scaled adductor muscles was then calculated following the same protocol as described above. It should be noted, however, that the low sample size of relatively complete skulls of Camarasaurus means that the relative influences of ontogenetic and individual variation are unknown. This is further complicated by the absence of species-level apomorphies in the crania of Camarasaurus spp. (Madsen et al. 1995;Ikejiri et al. 2005); a comprehensive review of referred cranial material is necessary to elucidate any other potential ontogenetic trends. As a result, the estimates of adult bite force presented herein should be treated with caution.

Bite force calculation
Resultant bite force will depend not only on muscle mass, but also on the line of muscle action and the mechanical efficiency of the mandible. To quantify these factors, the angle of each muscle line of action to the vertical was measured in both the sagittal (a) and coronal (b) planes. Additionally, the mechanical advantage (MA musc ; see Westneat 1994) was calculated for each muscle as the ratio between the inlever and outlever, measured at a gape angle of 12°. The inlever was measured as the length of a perpendicular line drawn between the line of muscle action and the jaw joint. The outlever was then measured as the distance from the jaw joint to the biting tooth. MA musc was calculated for bites at both the anteriormost and posteriormost dentary teeth, representing the minimum and maximum bite forces along the dentary tooth row, respectively. These measurements and the contractile force of each muscle (F musc ) permit the calculation of the force (F out ) supplied by each muscle at these bite positions through simple lever mechanics (e.g. Reichel 2010; Sakamoto 2010; Lautenschlager 2013): Total bilateral bite force was then calculated as the sum of these forces from each side of the skull for Plateosaurus and both the juvenile and adult-scaled models of Camarasaurus.

Finite element analysis
Finite element models. Osteological reconstructions of the skull and mandible were imported into HyperMesh (v11; Altair; http://www.altairhyperworks.co.uk/product/Hyper-Mesh) for meshing. Standard element clean-up procedures were conducted within HyperMesh yielding models with the following numbers of tetrahedral elements: Plateosaurus skull, 1 919 342; Plateosaurus mandible, 264 283; Camarasaurus skull, 877 796; and Camarasaurus mandible, 198 154. Bites were simulated at the anteriormost and posteriormost teeth of the cranium and the mandible and at a midpoint bite position. A summary of the models solved is given in Table 1.
Material properties. The material properties and anisotropy of tissues cannot be measured directly in extinct taxa, but have to be estimated from extant analogues. However, validation studies have demonstrated that FEA can accurately replicate patterns of stress and strain, if not the absolute magnitudes of these forces, even when approximated, isotropic properties are applied (Strait et al. 2005;Bright & Rayfield 2011;Bright 2014). Hence, meaningful comparisons can still be made between different models, provided that the material properties are consistent between them. Bovine Haversian bone was chosen as an analogue for sauropod cranial bone due to the histological similarity between it and sauropod long bones (Curry 1999;Sander et al. 2011); unfortunately, histological sections from sauropodomorph crania are currently lacking.
Bone properties assigned to the models were identical to those of bovine Haversian bone (Young's Modulus = 23.1 GPa, Poisson's ratio = 0.29; see Reilly & Burstein 1975). These measurements were reported from cattle femora, and so are likely to be overestimated with respect to the properties of cranial bone; as a result, the lowest value for the Poisson's ratio was chosen, as in previous analyses of sauropodomorph crania (Young et al. 2012;Button et al. 2014 In addition to the tooth constraints detailed here, all models were also constrained at the quadrates. Two sets of Plateosaurus cranium models were created: those scaled as per the life reconstruction and those scaled so that the ratio between cranium surface area and applied muscle force matched that reconstructed for Camarasaurus (the 'structural comparison'). Similarly, two mandible models were also created: those scaled as per the life reconstruction and a 'structural comparison' where those the ratio between mandible surface area and applied muscle force was scaled to match that of Camarasaurus. Bite forces were calculated for the minimum and maximum muscle forces as calculated for each taxon.
comparisons between models where teeth were assigned properties of pure dentine or enamel show little difference between models using different values (see Button et al. 2016). In the absence of data on dinosaur cranial bone anisotropy, all materials were assumed to be isotropic to minimize ad hoc assumptions.
Model constraints. Artificially inflated stresses can be associated with point constraints (Bright 2014). To mitigate this, constraints were modelled as a series of rigid links (a 'diffuse coupling constraint' or DCC), spreading the constraint over a series of nodes (Young et al. 2012;Button et al. 2014). All skull models were constrained against translation in the x (anteroposterior), y (dorsoventral) and z (mediolateral) planes at the quadrates. Mandible models were constrained against translation in all three of these axes at the articular glenoid. Each model was then constrained against translation in the y plane (the axis of biting) at the four biting teeth. The location of the biting teeth was varied in order to simulate bilateral bites at three different locations along the tooth row, as detailed in Table 1.
The mandibular symphysis is particularly important in the transferral of forces during asymmetric biting (Porro et al. 2011). To test the importance of the expansion of the symphysis in sauropods more thoroughly, unilateral anterior, midpoint and posterior bites were also modelled for the mandible with only the teeth on the right-hand side constrained (Table 1).
Model loading. Models were loaded with maximum adductor muscle forces as calculated above. Loads were applied across multiple nodes on the muscle origination/insertion sites of the skull and mandible, respectively. This was performed using a custom-built macro supplied by Altair, which simultaneously loads multiple nodes, projected towards a node resulting in a vector equivalent to the line of action of each muscle. Muscle forces applied to the adult Camarasaurus model were scaled up from those of the juvenile so that total applied force remained in the same proportion to surface area. As a consequence, results from finite element modelling of an adult skull are redundant with respect to the results derived from the juvenile model (Dumont et al. 2009) and so are not reported below.
Two separate load cases were applied to the Plateosaurus skull and mandible models. The first load case applied the estimated muscle forces for Plateosaurus, as calculated above. A second set of 'structural' analyses was performed in an effort to disentangle the effects of size and shape in the relative performance of crania. For these analyses the muscle forces applied to the Plateosaurus skull and mandible models were scaled so that the ratio between overall force and skull/mandible surface area, as measured in Avizo, was constant in both taxa. This accounts for the differences in size and relative adductor muscle mass between them (Dumont et al. 2009), so that the resulting comparisons of stress and strain values primarily highlights differences in induced stress and strain due to cranial or mandibular shape.
Analyses. Models were exported to Abaqus (v6.10.2; Dassault Syst emes Simulia; http://www.3ds.com/productsservices/simulia/products/abaqus/) for solving. Relative performance of each skull was gauged through comparison of functionally incurred von Mises stresses. Von Mises stress represents a single value of 'overall stress', approximating the proximity to failure of a tissue and so provides a measure of the strength of a structure under loading (Rayfield 2007;Dumont et al. 2009). Additionally, comparisons were made between the contour plots representing principal stresses and strains.
The mechanical efficiency of the skull and mandible of both taxa was compared by computing the total strain energy of each model under replicated bilateral biting. This metric represents the external energy spent deforming a body under loading; lower values hence describe structures which are more efficient at transmitting applied forces (Dumont et al. 2009).
The total strain energy was computed for the Camarasaurus, Plateosaurus and scaled Plateosaurus (see above) cranium and mandible models when performing a bilateral bite at the anterior, midpoint and posterior biting points. However, whereas stress varies with surface area, the total strain energy is proportional to the square of the total applied force and the cube of the volume of each model (Dumont et al. 2009). In order to correct for the differences in volume between the cranium and mandible of each taxon, the strain energy values obtained from the scaled Plateosaurus models were multiplied by (Volume Plateosaurus model / Volume Camarasaurus model ) 1/3 , following Dumont et al. (2011). Comparison of the resulting strain energy value with those obtained from the Camarasaurus models allowed the relative efficiency of each structure to be judged in the context of the shape differences between them.

Muscle origination and insertion site reconstruction
The abbreviations for the jaw adductor muscles used herein are given in Table 2. Identified muscle origination and insertion sites are shown in Figure 1 and summarized in Table 3. The level of inference (sensu Witmer 1995, 1997) of each attachment site is indicated. Holliday 2009). These origination and insertion sites can be identified by the smooth scars they leave on the temporal bar and the surangular, respectively, even if more specific osteological correlates are rare (Holliday 2009). As a result, both of the attachment areas of the m.AMES can be reconstructed as robust level I inferences.
In both Plateosaurus and Camarasaurus the m.AMES is reconstructed as originating from the smooth dorsomedial and medial surfaces of the postorbital posterior process and the medial surface of the squamosal anterolateral process. This smooth surface extends posteriorly onto the main body of the squamosal in both taxa, indicating that the m.AMES extended into the posterior corner of the supratemporal fenestra. Anteriorly, the origination area of the m.AMES is bounded by that of the m.PSTs.
The m.AMES is then reconstructed as inserting onto an elongate smooth region on the dorsolateral edge of the surangular. This surface is strongly bevelled in Plateosaurus and more modestly so in Camarasaurus. The mediolateral thickness of the m.AMES is well constrained by its topological relationships with the other muscles of the m.AME group. The origination and insertion sites of the muscle as reconstructed here are identical to those of Galton (1985b) andFairman (1999). is hence a level I inference in sauropodomorphs (Holliday 2009). It is here reconstructed as attaching to the dorsomedial surface of posterior end of the coronoid and the anterior end of the surangular in both taxa. The attachment region on the dorsomedial surface of the surangular is narrow (especially so in Plateosaurus), smooth and slightly concave. The posterior extent of the m.AMEP is difficult to constrain as it is continuous with the m.AMEM. In Plateosaurus a weak break is observed between the two elongate, slightly concave scars observed on the dorsomedial edge of the surangular. In Camarasaurus this break is more pronounced, separating a circular, slightly dorsoventrally expanded scar at the anterior end of the surangular from a more elongate one running posteriorly. This break is here taken as indicating the boundary between the insertion sites of the m.AMEP and   Table 2. the m.AMEM, with the m.AMEP inserting anterior to it in both taxa. The anterior extent of the m.AMEP, as well as its size and orientation, is further constrained in Plateosaurus by the position of the ectopterygoid. The ectopterygoid of Camarasaurus is positioned more anteriorly, relieving these constraints. The origination and insertion sites of the muscle as reconstructed here are identical to those of Fairman (1999) and Galton (1985b). The m.AME inserts onto a narrow, slightly concave, region along the dorsomedial edge of the surangular, posterior to the m.AMEP, in sauropodomorphs (Holliday 2009). Distinguishing the insertions of these two muscles can be problematic; the m.AMEM is here considered to occupy the posterior of the two partially distinct scars in this region, as described above. This attachment runs posteriorly to the point where the dorsomedial edge of the surangular pinches out. Nevertheless, the distinction made between the insertion sites of these muscles here is somewhat ambiguous, particularly as the insertion of the F I G . 2 . Reconstructed jaw adductor musculature for Plateosaurus (left) and Camarasaurus (right), in right lateral view. Reconstructions are shown at multiple depths, with the removal of successively superficial muscles groups. From top to bottom: all muscles; removal of the m.AMES, removal of the m.AME group, removal of the m.AME, m.PST and m.AMP groups. Scale bars represent 100 mm. m.AMEM lacks a specific, distinct correlate in extant crocodilians and birds (Holliday 2009). As a result, the insertion of the m.AMEM reconstructed here represents a level I 0 inference. The origination and insertion sites of the muscle as reconstructed here are identical to those of Fairman (1999) and Galton (1985b).  The mediolateral thickness of the m.PSTs is well constrained by the other adductor muscles and the palatal bones. This is particularly obvious in Plateosaurus, whose strongly developed pterygoid flange tightly constricts the thickness of the m.PSTs. The mandibular adductor fossa of Plateosaurus is also strongly laterally compressed, suggesting a tendinous (rather than fleshy) attachment of this muscle (Lautenschlager 2013)  m. pseudotemporalis profundus (m.PSTp). Osteological correlates of m.PSTp attachment are rare, but phylogenetic bracketing indicates that origination on the anterolateral surface of the epipterygoid would have been plesiomorphic for dinosaurs (Holliday 2009). The m.PSTp is hence reconstructed as originating from the expanded anterolateral surface of the epipterygoid, dorsal to the midshaft in Plateosaurus, as a level I inference. By contrast, the epipterygoid was lost in neosauropods and it is possible that neosauropods lost the m.PSTp as a corollary (Holliday 2009). Consequently, this muscle was not reconstructed for Camarasaurus.
Reconstructing the mandibular insertion of the m.PSTp is highly problematic in sauropodomorphs as the muscle is typically vestigial in extant archosaurs and does not leave unambiguous osteological correlates (Holliday 2009). Fairman (1999) reconstructed the m.PSTp of Plateosaurus as attaching to the medial surface of the coronoid region, as in lepidosaurs and most birds (Holliday & Witmer, 2007;Holliday, 2009). However, the small area available for attachment on the mediodorsal edge of the surangular, and topological constraints provided by other muscles (particularly the m.PSTs), suggest that such an insertion is unlikely in Plateosaurus. Instead, the m.PSTp is reconstructed as attaching within the mandibular adductor fossa adjacent to the m.PSTs, similar to the condition observed in crocodilians (Holliday & Witmer 2007;Holliday 2009) and as reconstructed for the theropod Erlikosaurus (Lautenschlager 2013). Still, it should be noted that in extant crocodilians the m.PSTp merges into the m.PTd rather than directly inserting onto the mandible itself (Holliday & Witmer 2007;Holliday et al. 2013). The absence of a specific osteological correlate and variation within the extant phylogenetic bracket for this character render its reconstruction a level III 0 inference; the lowest confidence associated with any of the reconstructed attachment sites discussed herein. The m.AMP would have inserted into the mandibular fossa in both taxa, as in other dinosaurs (Holliday 2009). Galton (1985b) and Fairman (1999) reconstructed the m.AMP as filling the entire mandibular fossa in Plateosaurus. However, the insertions of the m.PSTs and m.PSTp in the mandibular fossa, as reconstructed here, restricts that of the m.AMP to the posterior two-thirds of the fossa in both taxa. In Camarasaurus, the generally smooth surface of the fossa extends from the surangular onto the medial surface of the prearticular, suggesting that the m.AMP insertion extended ventrally to cover some of the prearticular also. Fairman 1999). However, the anterior extent of this attachment is difficult to constrain, as its osteological correlates are poorly differentiated from those for the nasal passages and paranasal sinuses (Witmer 1997;Holliday 2009;Lautenschlager 2013). It extended at least as far anteriorly as the suture with the ectopterygoid, occupying a trough-like depression in the dorsolateral surface of the pterygoid, similar to the extent reconstructed for Erlikosaurus (Lautenschlager 2013), but no other features clarify whether (or how far) it extended further anteriorly. To quantify the impact of uncertainty in the anterior extent of this attachment on reconstructed muscle mass, a maximum estimate of the origination area was made in addition to this minimum estimate. In the maximum estimate, the m.PTd occupies the entire dorsolateral surface of the pterygoid ramus as far anteriorly as the suture with the palatine, as reconstructed for some theropods (e.g. Holliday 2009); the generally smooth and slightly concave morphology of this region offers some support for this reconstruction. Nevertheless, the extent of this attachment area has little impact on the cross-sectional area of the muscle, which is constrained by the surrounding soft and hard tissues within the adductor chamber, so the effect of this uncertainty on calculated muscle forces is minimal (Table 4).
The mandibular insertion site of the m.PTd is also a type I inference in sauropdomorphs (Holliday 2009). In both taxa the m.PTd attached to the medioventral surface of the prearticular, extending posteriorly to occupy a slight depression in the medial surface of the articular.
m. pterygoideus ventralis (m.PTv). The origination of the m.PTv, from the ventrolateral surface of the pterygoid, is highly conserved across sauropsids and can be reconstructed as a type I inference in sauropodomorphs (Holliday 2009), even if unambiguous correlates for the extent of this attachment are rare. The m.PTv is reconstructed in both taxa as originating from a smooth edge on the ventrolateral surface of the pterygoid, extending onto the ventral aspect of the pterygoid flange (Galton 1985b;Fairman 1999).
The insertion site of the m.PTv is also a class I inference in sauropodomorphs (Holliday 2009). It inserted onto the ventral edge of the angular and articular, wrapping around the ventral surface of the mandible to extend into an excavated area on its lateral surface (which is shallow in Plateosaurus, but prominent in Camarasaurus).
The thickness of the m.PTv is less well constrained. There are no osteological or reconstructed topological constraints on how far the main body of the muscle could have bulged medially towards the oral cavity. However, the lateromedial thickness of the dorsal end of the m.PTv is indicated by the scar on the ventral surface of the pterygoid. As a result, to provide a conservative estimate, the muscle was then projected to maintain this thickness for the majority of its length.

Muscle volumetric reconstructions and forces
Calculated volumes, physiological cross-sectional areas and contractile forces are given in Table 4. The reconstructed volumes for each muscle are illustrated in Figure 2. Calculated muscle volumes and forces are lower in Plateosaurus than Camarasaurus, even after accounting for skull size (Table 4). These taxa also differ in the relative contributions provided by the different muscle groups to total bite force; a greater proportion of total bite force is provided by the palatal musculature (in particular the m.PTd) in Camarasaurus.
Uncertainty in the anterior extent of the m.PTd origin results in only a minor (c. 2.4%) difference in contractile muscle force, as the cross-sectional area of the main body of the m.PTd is tightly constrained by surrounding hard and soft tissues (Figs 1-2). Although the reconstruction of a more expansive origination of the m.PTd (Fig. 1A, B, D) does lead to an increase in overall muscle mass, the resulting increase in muscle length, used as a proxy for fibre length herein, leads to a lower calculated estimate of contractile force (Table 4). This discrepancy results from the way in which muscle forces were calculated. The relationship between muscle fibre and total length is not constant (e.g. van Eijden et al. 1997); total length only provides a maximum possible estimate of fibre length. Consequently, using total length as a proxy tends to underestimate contractile force; this effect may be particularly notable for more elongate muscles.

Calculated bite forces
Measured muscle angles, mechanical advantage for each muscle belly for both anterior and posterior bites and calculated bite forces are given in Table 5. Calculated bite forces for adult Camarasaurus greatly exceed those of both Plateosaurus and juvenile Camarasaurus. Reconstructed bite forces for the juvenile Camarasaurus also exceed those of Plateosaurus, even though their skulls are of similar length. Calculated anterior and posterior bite forces for the juvenile Camarasaurus are 329% and 325% those of Plateosaurus, respectively. Bite force as a proportion of total applied force is also greater for Camarasaurus than Plateosaurus, especially for anterior bites.
Although there is uncertainty involved in the reconstruction of some muscles, a threefold difference in total muscle volume in either taxon is not tenable. The lower mechanical advantage means that the m.PTv, whose volume is poorly constrained, would need to be increased by over seven times its current size to provide the same output on bite force as that of Camarasaurus; such an enlargement cannot be accommodated. The relative biting performance of these taxa is hence robust to uncertainty in reconstructed adductor muscle volume.

Finite element analysis results
Von Mises stress values are given in Table 6, contour plots are given in Figures 3 and 4, and additional results, including principal stress and strain plots, are provided in Button et al. (2016). Both taxa exhibit broadly similar overall patterns and magnitudes of induced von Mises stress in the skull for all biting positions (cf. Fig. 3A, C), although observed stresses are slightly lower for Camarasaurus (Table 6). When corrected for differences in size Values given are those calculated for each individual muscle on each side of the skull, so that total PCSA and applied force across both sides of the skull are double the sum of the individual values given here. For Plateosaurus values for both potential reconstructions of the m.PTd (one with the insertion area on the pterygoid being limited anteriorly and the other being more expansive; see text) are given. The ratio of total PCSA of all muscles (from both sides): the total cranium surface area is given to provide a value for total contractile muscle force corrected for differences in the size of the skull for each taxon. *Upper and lower values of specific tension of muscle from Thomason et al. (1990). and applied force (the 'structural comparison') differences in stress and strain accommodation are more apparent. Greater stress magnitudes are recorded for Plateosaurus in all biting positions (cf. Fig. 3B, C), with mean elemental stresses being 25-336% those of Camarasaurus, although the distribution of peak stresses and strains remain similar between the two taxa. In both taxa localized stress peaks are present in the subtemporal and postorbital bars, the quadrate, and in the ventral surface of the pterygoid in all biting positions. Elevated stresses are also observed as a result of bending in the arched nasal region during anterior and, to a lesser extent, midpoint bites in both taxa (Fig. 3). This is particularly apparent in Plateosaurus, where a strong peak in compressive stress is observed at the anterior edge of the base of the premaxillary ascending process ( Fig. 3; see also Button et al. 2016). In posterior biting elevated stress and some sharp peaks are observed in the suborbital bar, postorbital bar and lacrimal in both taxa, although peak stresses are lower in Camarasaurus. Stress and strain distributions within the mandible differ less between biting positions in both taxa (Fig. 4). In each taxon elevated stress and strain is more widespread in more anterior bites due to the longer moment arm for bending forces resulting from loading of the biting teeth. This is particularly pronounced in Plateosaurus, where large stresses and strains are observed along the dorsal and ventral edges of the relatively gracile dentary.  Table 4. a, angle of the muscle line of action from the vertical as measured in the sagittal plane; b, angle from the vertical in the coronal plane; aMA, mechanical advantage of each muscle for an anterior biting position; pMA, mechanical advantage for a posterior bite. Calculated contributions of each muscle and the total bilateral bite force are given.
A greater discrepancy is observed between the mandibles of each taxon when loaded under a unilateral bite. High stress peaks are observed in the articular region of Plateosaurus (Fig. 5A, B), as compared to Camarasaurus (Fig. 5C). After size correction, functionally induced stresses are notably greater in the mandible of Plateosaurus, with relatively high stresses along the ventral edges of both the working and balancing sides of the mandible (Fig. 5B, C).
After correcting for differences in size, the total strain energy is also notably lower for both the skull and mandible of Camarasaurus than those of Plateosaurus at all biting positions (Table 6), particularly so in the mandible during anterior and midpoint bites. An exception to this is in the mandible during a posterior bite, however, where the total strain energy exhibited by both the Camarasaurus and Plateosaurus models is very similar (Table 6).

Myological comparison of Plateosaurus and Camarasaurus
One minor rearrangement in jaw musculature occurs between the basally branching sauropodomorph Plateosaurus and the neosauropod Camarasaurus, in the insertion site of the m.PSTp. The absence of the epipterygoid in neosauropods (Upchurch et al. 2004) indicates that, at the very least, the insertion site of this muscle must have shifted, but the absence of any other osteological correlates T A B L E 6 . Results of the analyses replicating bilateral anterior, midpoint and posterior bites in the skull and mandible of Plateosaurus and Camarasaurus. Maximum, minimum and mean element von Mises stresses and the total strain energy is given for each analysis. The 'structural comparison' Plateosaurus models were scaled so that the ratio between total applied muscle force and the cranium/mandible skull surface area equalled that of the Camarasaurus model, so that differences in von Mises stress results between the two will be a result of variance in shape, rather than size or applied muscle force. Strain energy results (*) were further corrected to account for differences in volume between the two taxa, again allowing comparison of performance in terms of shape, rather than size or applied muscle force. See text and Table 1 for more details.

Minimum
suggests that it was lost altogether (Holliday 2009). Insertion and origination sites for all other adductor muscles remain consistent between the two taxa, but muscle lines of action differ due to changes in overall skull proportions and architecture. Lines of muscle action in Camarasaurus are generally more vertical (and so more efficient at driving vertical jaw adduction) than those of Plateosaurus, especially with respect to the pterygoideus group (Table 5). Jaw adductor muscle size also differs markedly between the two taxa, in terms of overall and relative muscle volume, and cross-sectional area (Table 4). After scaling to minimize the influence of skull size, the summed physiological cross-sectional area (proportional to contractile force) of the adductor musculature of Plateosaurus is c. 57% of that of Camarasaurus. Although Plateosaurus possesses relatively large origination areas in the supratemporal fossa (Fig. 1A, D) and expansive insertion areas on the mandible (Fig. 1E, F) osteological constraints result in a relatively small, and particularly narrow, adductor chamber (Figs 2, 6). Within sauropods such as Camarasaurus these constraints are relaxed by the increase in the relative size of the postorbital region, and the strong transverse expansion of the skull (cf. Figs 1C, I; 7). The size of the sauropod adductor chamber is further increased due to rearrangement of the palate. In the plesiomorphic sauropodomorph condition, as in Plateosaurus, the ectopterygoid sutures to the medial surface of the jugal (Fig. 6A), which tightly constrains the anterior extent of the adductor chamber (Fig. 6B, C). In neosauropods, such as Camarasaurus, the ectopterygoid is shifted anteriorly, suturing to the medial surface of the maxilla (Upchurch et al. 2004; Fig. 6D), releasing this anterior constraint on the adductor musculature (Fig. 7E, F). In Plateosaurus the narrow shape of the skull and the presence of a large pterygoid flange also limit the extent of the adductor musculature (Fig. 1B).
The relative contributions of the different muscle groups to overall muscle volume, and thus bite force, varies between the two taxa, with the pterygoideus group muscles being more important in Camarasaurus than Plateosaurus (Table 5). This difference is even more striking in the diplodocoid neosauropod Diplodocus, where the palatal musculature accounts for >68% of the total jaw adductor force (Button et al. 2014). Along with the morphology of the expanded craniomandibular joint, the relative importance of the pterygoideus group muscles in

Bite force comparison
Calculated bite forces for Camarasaurus greatly exceed those of Plateosaurus (Table 5). This reflects both the absolutely and relatively greater adductor muscle mass of Camarasaurus (Table 4) and its greater biting efficiency (in terms of the proportion of input muscle force converted to bite force) in comparison to that of Plateosaurus (Table 5). Increased bite efficiency is a consequence of changes in jaw shape that result in greater mechanical advantage for most of the adductor muscles in Camarasaurus, in particular the expansion of the coronoid eminence, which increases the inlever for the m.AME group. The longer tooth row of Plateosaurus results in greater variance in muscle outlevers, and so in bite force and closing speed across the jaw. Within a third-order lever, such as a vertebrate jaw, the mechanical advantage is the inverse of jaw closure speed (Sakamoto 2010). Anterior bites of Plateosaurus would have been weak, but relatively fast, whereas posterior bites and bites across the entire tooth row of Camarasaurus would have been relatively powerful but slow.

Biomechanical modelling comparison
Finite element modelling demonstrates that functionally induced stresses and strains are greater in both the cranium and mandible of Plateosaurus at all tested biting positions, after correcting for size and applied force (Figs 3B, C; 4B, C). As a result, if loading were increased, the skull of Plateosaurus would fail first; the cranium and mandible of Camarasaurus can hence be considered 'stronger' under static biting. Interestingly, stress magnitudes between Camarasaurus and the unscaled Plateosaurus are similar, suggesting conservation of similar safety factors when realistic loads are applied. Additionally, the distributions of elevated stress and strain patterns are broadly similar for the two taxa.
Premaxillary and anterior maxillary bites result in elevated stresses in the ascending processes of the premaxillae in both taxa. However, the magnitude of this induced stress is much greater in Plateosaurus, which also exhibits elevated stresses in the region surrounding the premaxilla-maxilla suture. Barrett & Upchurch (2007) suggested that slight movements of the premaxilla during biting may have been possible in 'prosauropods' by virtue of a flexible joint at the premaxilla-maxilla suture and that this 'passive kinesis' might have dampened these stresses in a 'shock-absorbing' function, similar to the role of patent sutures in the skull of Tyrannosaurus rex (Rayfield 2004). However, more significant movements of the premaxilla are rendered impossible by its immobile contact with the nasals (Barrett & Upchurch 2007;contra Gow et al. 1990); even if appreciable dorsal rotation was possible in response to loading this would only increase bending stresses in the delicate premaxillary ascending processes.
Anterior and posterior maxillary bites also result in elevated stresses in the premaxillary ascending processes in Camarasaurus, but magnitudes are markedly lower. The retraction of the external naris within Sauropoda leads to the posterodorsal displacement of the relatively fragile ascending processes and expansion of the robust main body of the premaxilla. Elevated stresses are also observed in the very thin sheet of the maxilla forming the wall of the antorbital fossa and the bordering nasals in Plateosaurus. However, in Camarasaurus, where the antorbital fossa excavates only a small portion of the maxilla and the fenestra is much reduced, these elevated stresses are not observed.
For posterior bites, elevated stresses are observed in the suborbital regions proximate to the biting teeth in both taxa. However, stresses are lower in Camarasaurus than Plateosaurus due to the shorter tooth row and to the dorsoventral expansion of the cheek region of sauropods relative to the condition in basal sauropodomorph taxa; consequently, the skull of Camarasaurus is more robust proximate to the posteriormost biting teeth. Similarly, although elevated stresses are observed in the palates of both taxa, stress magnitudes are much greater in Plateosaurus. This results from its more gracile build, as the elongate ectopterygoid shaft accumulates high stresses.
Similarly, although anterior and midpoint bites result in elevated stresses and strains in the dentary due to cantilever bending in the mandibles of both taxa, magnitudes are notably lower in the strongly dorsoventrally expanded dentary of Camarasaurus. Total induced stress varies more markedly with changes in bite position in Plateosaurus than Camarasaurus. This is due both to the more gracile dentary and longer tooth row of Plateosaurus. A longer tooth row will result in a greater difference in the moment arm for bending forces, and so induced stresses, resulting from biting at the anteriormost versus the posteriormost teeth.
During anterior and midpoint bites, particularly within the cranium, stresses within the biting teeth are greater in Plateosaurus than Camarasaurus (Figs 3B, C; 4B-F; 5E-F; 7A-F), with peaks occurring along the lateral surfaces of the tooth crowns. Internal stresses are concentrated within the tooth roots of Plateosaurus, with those in the surrounding bone much lower (Fig. 7A, B). In Camarasaurus stress is spread more diffusely in the surrounding lateral plate (Fig. 7C-I). This lends support to the hypothesized function of these plates as bracing the teeth (Upchurch & Barrett 2000; see also Young et al. 2012), which may have been even more important in lateral tugging or stripping behaviours. However, caution must be applied to interpretations of stress patterns in this region given the simplistic manner in which the tooth attachments were modelled. The models lack a periodontal ligament, which may influence localized patterns of stress and strain at the base of the teeth (Gr€ oning et al. 2011;Wood et al. 2011;Fitton et al. 2015). Previous sensitivity analyses suggest that inclusion of the periodontal ligament would have resulted in lower stresses in the alveolar bone proximate to the biting tooth (Gr€ oning et al. 2011). Finer-scale modelling, including that of hypothetical morphologies, could be used to further investigate the biomechanical significance of this character.
The mandibular symphysis remains relatively unstressed during all tested bilateral biting scenarios (Fig. 5D-F). This is expected given that the constraints on the biting teeth are symmetrical and posterior to the symphysis. In contrast, during unilateral anterior and midpoint bites, stresses are higher in the symphyseal region for both taxa (Fig. 5D-F) as forces are transmitted through it from the working to the balancing side. After correction for size, stresses within the mandibular symphysis of Plateosaurus are greater than those of Camarasaurus (Fig. 5E, F). This suggests that the expanded mandibular symphysis of sauropods might have been important in accommodating high stresses resulting from asymmetric loading, which is consistent with its previously hypothesized role in strengthening the mandible against feeding-related forces (Barrett & Upchurch 1994;Upchurch & Barrett 2000;Barrett et al. 2007;Upchurch et al. 2007). It should be noted, however, that the mandibular symphysis was modelled in a relatively simplistic manner here, and lacked distinct material properties for sutures. Some validation studies have shown that inclusion of sutures within FE models has minimal impact on overall patterns of stress and strain (Bright & Gr€ oning 2011), suggesting that comparisons between models will yield some valid signal. However, it should be noted that work on extant archosaurs has demonstrated that sutures exert a greater impact on the mechanical behaviour of the mandible (Porro et al. 2011(Porro et al. , 2013Reed et al. 2011;Rayfield 2011). Future work, incorporating sutures, is required to test the behaviour of the mandible in more detail; however, the material properties of archosaur cranial sutures remain poorly known (Porro et al. 2013;Cuff et al. 2015).
Total strain energy values for the skull of Camarasaurus are lower than those for Plateosaurus under all tested biting scenarios, and lower in the mandible for anterior and posterior bites. This indicates that the skull of Camarasaurus was stiffer than that of Plateosaurus and so would have been more efficient at transmitting the force supplied by the adductor musculature (Dumont et al. 2009(Dumont et al. , 2011. This compounds the signal observed in the comparative myology and lever-arm mechanics of these taxa, indicating that Camarasaurus was capable of F I G . 6 . The constraints upon the jaw adductor musculature provided by the palate in Plateosaurus (A-C) and Camarasaurus (D-F). A, ventral views of Plateosaurus with the right half of the cranium coloured by individual element, and the left half with the jaw adductor muscle bodies depicted as cut along a transect level with the alveolar margin of the skull. B, C, renders of the cranium of Plateosaurus with the jugal and postorbital removed; the jaw adductor musculature is indicated in pink and the ectopterygoid in purplej B, right lateral view; C, anterodorsolateral view. D, cranium of Camarasaurus, with skull elements and adductor muscles indicated as in A. E, F, cranium of Camarasaurus with the jugal and postorbital removed, the maxilla rendered semi-transparent and coloured as in B and C; E, right lateral view; F, anterodorsolateral view. Abbreviations: ect, ectopterygoid; j, jugal; mx, maxilla; pal, palate; pt, pterygoid. All scale bars represent 100 mm. exerting relatively more powerful bites than Plateosaurus due to the greater efficiency of the skull and the arrangement and volume of the adductor musculature. Interestingly, however, whereas the mandible of Plateosaurus is observed to be inefficient for anterior and midpoint bites, under posterior biting it performs comparably with that of Camarasaurus (Table 6). This corroborates the results of lever-arm analysis indicating that the mechanical properties of the jaw of Plateosaurus varied considerably across the tooth row, further suggesting some division in role between the anteriormost and posteriormost teeth.

The evolution of herbivory in sauropodomorph dinosaurs
The diversification of sauropodomorph dinosaurs and the evolution of sauropod gigantism have been attributed to the adoption of obligate high-fibre herbivory, and specialization towards bulk-feeding, close to the base of Eusauropoda (Barrett & Upchurch 2007;Upchurch et al. 2007;Yates et al. 2010;Sander 2013;Barrett 2014). Interpretation of our results in a phylogenetic context (Fig. 8) allows evaluation of these hypotheses through testing of the biomechanical significance of feeding-related characters. However, it should be noted that resolving finerscale patterns is complicated by the paucity of cranial data from basal sauropodiform taxa and the homoplasy seen in many characters of the feeding apparatus (Barrett & Upchurch 2007;Yates et al. 2010). Nevertheless, these results provide perspective on broader functional trends in sauropodomorph cranial evolution.
The retention of an elongate snout and tooth row, despite the resulting compromises in force transmission and 'strength' during anterior bites, suggests that jaw closure speed remained relatively important in Plateosaurus and other 'prosauropod' grade taxa. Jaw closure speed is of little importance in herbivory, but is more critical with regards to prey capture. This therefore implies some degree of faunivory, corroborating the anatomical (Barrett 2000;Barrett & Upchurch 2007) and phylogenetic (Barrett et al. 2011)  Trends in adductor chamber architecture and size are difficult to evaluate in basal sauropodomorph taxa as detailed myological reconstructions are, currently, only available for Plateosaurus. Nevertheless, the gross morphology and size of the supratemporal region remains relatively consistent in 'prosauropod' grade taxa, differing primarily in the size of the supratemporal fossa that, although particularly well-developed in Plateosaurus, is also present in other taxa (Galton & Upchurch 2004). In all 'prosauropods' the adductor chamber remains relatively vertical and insertion areas on the mandible appear to have remained consistent. However, the size of the coronoid eminence, and so leverage of the m.AME group, is somewhat variable between taxa and may also reflect dietary variation (Barrett & Upchurch 2007).
Comparison of 'prosauropod' and proximate outgroup taxa from which sufficient regions of the palate have been preserved (e.g. Eoraptor ) allows inference of broad trends. Relative to 'prosauropod' taxa such as Plateosaurus, the lateral articulation of the ectopterygoid is shifted more anteriorly to contact the maxilla in sauropods and, possibly, the more basal sauropodiform Melanorosaurus (Yates 2007). This is taken further in neosauropods, such as Camarasaurus, where the ectopterygoid no longer contacts the jugal and the suborbital fenestra is nearly obliterated (Upchurch et al. 2004;Fig. 6). This anterior migration of the ectopterygoid results in anteroposterior expansion of the adductor chamber. This is accentuated further in sauropods by the transverse expansion of the skull and the relative decrease in the size of the preorbital region. This anteroposterior and mediolateral expansion of the adductor chamber permits the greater adductor muscle volume reconstructed in sauropods such as Camarasaurus relative to that in 'prosauropods' such as Plateosaurus. As well as this increase, the m.PSTp appears to have been lost within Sauropoda at some point along with the epipterygoid (Holliday 2009); an epipterygoid has been reported in Shunosaurus (Zheng 1991), Mamenchisaurus (Ouyang & He 2002 and Nebulasaurus (Xing et al. 2015), but appears to have been absent in neosauropods (Upchurch et al. 2004).
Immediate outgroups to Sauropoda show the stepwise acquisition of other craniodental characters that have been inferred as related to feeding behaviour (Barrett & Upchurch 2007;Upchurch et al. 2007;Fig. 8). These include characters that our finite element models identify as providing greater 'strength' to the skull and mandible with regard to feeding-related loads, including the presence of lateral plates, dorsoventral expansion of the tooth-bearing portion of the mandible and dorsoventral expansion of the mandibular symphysis (see above).
Additionally, general trends in cranial morphology occurring at the base of Eusauropoda (the increased breadth of the snout, the increased height of the premaxilla and accompanying posterodorsal deflection of the premaxilla ascending processes, reduction of the antorbital fossa, dorsoventral expansion of the cheek region, and generally more robust build of the skull and mandible) also lower the magnitudes of peak functionally-induced stresses.
The increase in bite force that characterizes the 'prosauropod'-sauropod transition results from an increase in coronoid eminence height, reduction in tooth row length and other changes in shape that result in greater mechanical advantages for the majority of the jaw adductor muscles. An increase in mechanical advantage, and thus bite force at the expense of speed, is typical of herbivorous lineages where jaw closure speed is no longer important (Stayton 2006). This increase in bite force is mirrored by the appearance of characters that facilitated cropping of tough, fibrous plant matter at the expense of oral processing efficiency. These include the development of spatulate tooth crowns, tooth-tooth occlusion, a reduced tooth row, broader snout and the inferred loss of cheeks, which would have allowed a wider gape (Barrett & Upchurch 2007;Upchurch et al. 2007). The abbreviation of the tooth row and development of a homodont dentition in sauropods like Camarasaurus results in bite mechanics that are more consistent over the length of the jaw, as would be expected in a non-chewing herbivore where the entire tooth row was used in cropping (Christiansen 1999).
These trends towards greater structural strength and increased cropping abilities are consistent with an ecological shift towards generalized bulk-feeding on tough, fibrous plant material (Barrett & Upchurch 2007;Upchurch et al. 2007;Yates et al. 2010;Sander et al. 2011;Sander 2013). Moreover, the functional interrelationships between sequentially acquired myological, osteological and biomechanical characters supports their development under a model of correlated progression (sensu Thomson 1966Thomson , 1988Kemp 2007), where functionally integrated characters evolve in a correlated fashion due to positive feedback loops between them (Barrett & Upchurch 2007;Barrett 2014). Under this scenario, the development of more sophisticated adaptations for herbivory (Barrett & Upchurch 2007) and increases in bite force would have allowed the consumption of coarser forage, and the associated increase in feeding-related forces would also support the evolution of structural characters of the skull and mandible.
Similarly, an ecological shift towards obligate herbivory and bulk feeding has been suggested to have driven the evolution of the sauropod bauplan through positive feedback loops between cranial and postcranial character complexes   Characters found to be primarily associated with cranial robustness in blue, those primarily associated with cropping ability (bite force, tooth form) in red; wrinkled tooth enamel is of uncertain functional significance. Trends in craniodental morphology found by the analyses presented herein to be functionally significant (the increase in adductor chamber size within Sauropodomorpha and numerous shape changes within Sauropodiformes) are indicated and colour-coded as appropriate.
The identification of myological and biomechanical trends within the craniodental apparatus that are consistent with this ecological shift provides support for those scenarios linking an ecological shift to gigantism. However, quantitative comparisons between trends in postcranial character complexes, body size and biomechanical data from a larger sample of sauropodomorph taxa within a rigorous phylogenetic context is still required in order to more thoroughly test these hypotheses.

CONCLUSIONS
Myological reconstructions of the jaw adductor musculature in the 'prosauropod' Plateosaurus and the neosauropod Camarasaurus indicate greater muscle masses in the latter, with modifications of the skull and palate that allow expansion of the adductor chamber. Calculated bite forces for Camarasaurus are also much greater, due both to increased muscle mass and greater mechanical advantage of the jaw adductor musculature. Finite element modelling demonstrates that the skull and mandible of Camarasaurus are both more mechanically efficient and 'stronger' under loading replicating static biting than Plateosaurus. This is primarily a consequence of the generally more robust build of cranial elements in Camarasaurus.
Modelling also demonstrates the biomechanical significance of some sauropod synapomorphies including shape changes in the snout and the lateral plates. These appear to dissipate stresses in the biting teeth and the expanded mandibular symphysis, which may have been particularly important under asymmetric loading. Further modelling studies involving theoretical morphologies and introducing more compliant cranial suture tissues could be used to more thoroughly test the significance of these characters.
Placing these results in a phylogenetic context indicates morphological trends that result in greater bite forces and increased cranial robustness close to the base of Sauropoda, coincident with the development of more 'herbivorous' adaptations of the teeth. These trends provide biomechanical evidence for the hypothesized shift towards bulk-feeding and obligate herbivory at the base of Sauropoda. The functional linkages present between these characters suggest that this ecological shift drove the evolution of these disparate characters through correlatedprogression, with positive feedback loops precipitating a functional complex adapted towards the exertion and accommodation of greater forces. The coincidence of this ecological shift with those in various aspects of sauropodomorph anatomy suggests that dietary evolution drove the evolution of postcranial characters and ultimately sauropod gigantism in a similar manner, although comparisons between the appearance of cranial characters with evolutionary trends in body mass and the postcranial skeleton are required to test this further.