Cranial biomechanics underpins high sauropod diversity in resource-poor environments

High megaherbivore species richness is documented in both fossil and contemporary ecosystems despite their high individual energy requirements. An extreme example of this is the Late Jurassic Morrison Formation, which was dominated by sauropod dinosaurs, the largest known terrestrial vertebrates. High sauropod diversity within the resource-limited Morrison is paradoxical, but might be explicable through sophisticated resource partitioning. This hypothesis was tested through finite-element analysis of the crania of the Morrison taxa Camarasaurus and Diplodocus. Results demonstrate divergent specialization, with Camarasaurus capable of exerting and accommodating greater bite forces than Diplodocus, permitting consumption of harder food items. Analysis of craniodental biomechanical characters taken from 35 sauropod taxa demonstrates a functional dichotomy in terms of bite force, cranial robustness and occlusal relationships yielding two polyphyletic functional ‘grades’. Morrison taxa are widely distributed within and between these two morphotypes, reflecting distinctive foraging specializations that formed a biomechanical basis for niche partitioning between them. This partitioning, coupled with benefits associated with large body size, would have enabled the high sauropod diversities present in the Morrison Formation. Further, this provides insight into the mechanisms responsible for supporting the high diversities of large megaherbivores observed in other Mesozoic and Cenozoic communities, particularly those occurring in resource-limited environments.


Taxon choice
The mandible can be modelled as a beam, where its flexural stiffness will be proportional to 193 the second moment of area (I), a measure of the distribution of material around the centroid of the cross-sectional of a beam [23,24]. It has been used as a proxy for resistance to bending 195 of the mandible in multiple groups [e.g. 25, 26], including archosaurs [8,27]. However, 196 calculation of the second moment of area requires knowledge of the cross-section of the jaw, 197 and as many of the specimens used in this study have only been figured in lateral view this 198 was not possible.

199
In calculation of I it is the cross section dimension along the axis of the load that is most    The average height of the mandible was calculated by measuring its area (minus the 224 dentition) in lateral view, and dividing it by the length of the mandible. This value was cubed The total length of the muscle insertion area on the mandible (adductor fossa length) was 248 divided by the total mandible length to give a proxy for the relative total area of muscle 249 attachment ( figure S8). This serves as a proxy for the size and, as muscle output force is 250 proportional to cross sectional area, strength of the jaw musculature.    The angle from the vertical of this line of action was then measured (figure S10).
The aberrant taxon Nigersaurus is problematic in regards to this character as it has closed the 298 supratemporal fenestrae and a bend in the quadrate blocks the line from the insertion area on 299 the surangular to the temporal region [33]. Here we follow Sereno et al. [33] in assuming that 300 this muscle mass must have shifted onto the quadrate, and measured the line of action  Nigersaurus skull reconstruction modified from [33]. The shape of the snout is correlated with feeding ecology in extant herbivores, with the 325 general observation that nonselective grazers feeding on low, sward-like vegetation tend to 326 have broader snouts, as opposed to the narrower snouts of more selective browsers [34][35][36][37][38].  Diplodocus showing a highly procumbent dentition that no longer can be brought into 354 occlusion. Procumbent dentitions, especially highly procumbent ones, will be less effective at 355 static biting as the inclination of the long axis with respect to the biting direction will result in bending within the teeth; dentitions of varying procumbency probably represent 357 specializations towards various raking and branch stripping behaviours [11,45,46]. 358 The angle between the long axis and the tooth and a line at the level of the base of the  The slenderness index of sauropod teeth is the ratio of the height of the crown to the 370 maximum breadth of the crown. Initially developed as a phylogenetic character [47] it has since been used to classify sauropods into the 'broad' and 'narrow' crowned functional 372 groups and trace the comparative diversity of each through time [12,48]. 'Broad-crowned' 373 teeth are more robust, and tend to show the development of heavy mesiodistal wear facets 374 resulting from interdigitating occlusion. Narrow-crowned teeth in contrast are more gracile, 375 and generally associated with either more precise shearing or an absence of occlusion.  Within Eusauropoda, diplodocids secondarily lose occlusion [12,45]. Although the style of 385 occlusion varies between sauropods (see below), the presence of occlusion is still an 386 important functional similarity between those taxa that do exhibit occlusion in comparison to 387 those that do not, hence the inclusion of this character as well as C19 and C20. be less suited to oral processing than the more plesiomorphic interdigitating-bite condition.

402
Interestingly, many taxa bearing these dentitions specialized for slicing, but not processing,   Table S1 presents summary statistics for the first 10 PC axes.     Figure S15: Biomechanical morphospace plot of PC axes 2 and 3.

448
In order to test for the presence of functional convergence between 'narrow-crowned' 449 diplodocoids and titanosaurs, and a functional distinction between a 'broad-' and 'narrow-        adult Camarasaurus skull (DINO28, anteroposterior skull length =528mm [78]). Adult muscle cross-sectional areas were then obtained by multiplying the cross-sectional areas 523 calculated for CMNH11338 by 3.24 (the square of the linear increase in dimensions).

524
As the specific tension of the muscles of extinct taxa cannot be measured directly, an entire 525 possible range was bracketed by using a range of specific tension measures (147 kPa -526 392kPa) for vertebrate muscle [79]. Higher specific muscle tensions would generate 527 increased muscle and bite forces, but the relative differences between the two models would 528 remain the same. Table S4          very similar between the two, except for higher peak forces in the biting teeth in the analyses 635 with constraint in all axes, considered here to be an artefact due to overconstraint.   to provide a null model against which purported stripping-specific adaptations of Diplodocus 657 could be tested.

658
The models were constrained at the anterior four biting teeth as above, and fully constrained 659 at the occipital condyle. A stripping force was applied at the teeth equal to the shear strength