Decoupled form and function in disparate herbivorous dinosaur clades

Convergent evolution, the acquisition of morphologically similar traits in unrelated taxa due to similar functional demands or environmental factors, is a common phenomenon in the animal kingdom. Consequently, the occurrence of similar form is used routinely to address fundamental questions in morphofunctional research and to infer function in fossils. However, such qualitative assessments can be misleading and it is essential to test form/function relationships quantitatively. The parallel occurrence of a suite of morphologically convergent craniodental characteristics in three herbivorous, phylogenetically disparate dinosaur clades (Sauropodomorpha, Ornithischia, Theropoda) provides an ideal test case. A combination of computational biomechanical models (Finite Element Analysis, Multibody Dynamics Analysis) demonstrate that despite a high degree of morphological similarity between representative taxa (Plateosaurus engelhardti, Stegosaurus stenops, Erlikosaurus andrewsi) from these clades, their biomechanical behaviours are notably different and difficult to predict on the basis of form alone. These functional differences likely reflect dietary specialisations, demonstrating the value of quantitative biomechanical approaches when evaluating form/function relationships in extinct taxa.


Stegosaurus stenops
The skull of Stegosaurus stenops (NHMUK PV R36730) was CT scanned at the Natural History Museum, London, U.K., using a Metris (now Nikon Metrology) HMX ST 225 CT scanner. The skull consisted of disarticulated isolated elements which were scanned separately. Scan parameters therefore ranged from 180-220 kV at 160 mA, using copper filters of 0.25-2.5 mm in thickness.

Erlikosaurus andrewsi
The skull of Erlikosaurus andrewsi (IGM 100/111; Geological Institute of the Mongolian Academy of Sciences, Ulaan Bataar, Mongolia) was CT scanned at XTek Systems Ltd. (now Nikon Metrology), Tring, Hertfordshire, U.K., using a XT-H-225ST CT scanner. Scan parameters were set at 180 kV and 145 mA for the complete skull. Additional scans were performed for the braincase region at 180 kV and 135 mA. The resulting rotational projections were processed with custom-built software provided by X-Tek Systems Ltd. Creating a VGI and a VOL file, containing 1998 slices with a slice thickness of 145 μm for the complete skull and 1000 slices with a slice thickness of 108 μm for the braincase region.

Plateosaurus engelhardti
Scan data of MB.R.1937 were imported into Avizo (versions 6.3.1 and 7, FEI Visualization Science Group). Individual cranial elements were segmented utilising the Avizo segmentation editor, with manual removal of cracks and small breaks. MB.R.1937 has suffered lateromedial compression and shearing, with the right side in particular being displaced dorsally and medially. Cranial reconstruction was hence based primarily on elements from the left side of the skull, apart from the descending process of the postorbital, ascending process of the jugal and paraoccipital process of which the right-side element was considered better preserved. Each element, post repair, was mirrored across the bilaterally symmetrical long axis of the skull to produce their antimere. The proportions of each element and of the completed skull and mandible models were compared throughout to those of other Plateosaurus specimens and pre-existing reconstructions S1-S6 to ensure consistency.
Reconstruction and rearticulation was performed in systematic order with the least deformed bones-the left frontal, parietal, squamosal, quadrate and maxilla-restored first.
Restoration of the skull roof allowed rearticulation of the displaced braincase. The maxillae allowed rearticulation of the premaxillae after repair of the damaged ascending process and repair of warpage to provide a flat midline surface for articulation with the opposing premaxilla. These completed skull roof and snout regions then provided greater constraint on the remaining facial and palatal bones. The pterygoids of MB.R.1937 have been lateromedially crushed and buckled; these were restored last so that surrounding bones of the skull could be used to aid in reconstruction of their original proportions. The epipterygoids of MB.R.1937 are heavily fragmented; these were hence reconstructed after those of AMNH FARB 6810 (American Museum of Natural History, New York) S6] . Additionally, the orbitosphenoids of MB.R.1937 are entirely absent and so were manually reconstructed after those of other sauropodomorphs. The mandibles of MB.R.1937 required less reconstruction although the dentaries have suffered some lateromedially flattening and cracking, these were repaired using the curvature of the upper toothrow as a guide.

Stegosaurus stenops
For the restoration process of NHMUK PV R36730, surface models of the individual elements obtained from CT scanning were imported as .ply files into Avizo. Small cracks and fractures were removed manually by using the paintbrush tool in Avizo's segmentation editor. Retrodeformation of selected elements, such as the articulated braincase, was performed using the geometric morphometrics software Landmark (version 1.6, www.idav.ucdavis.edu/research/EvoMorph S7 ).
Missing elements (left jugal, left supraorbital2, right supraorbital1, right angular, right articular) on one side of the skull were reflected along the bilateral symmetry plane. Elements, which had not been preserved (palatines, vomer, predentary)

Erlikosaurus andrewsi
For the restoration of the skull of Erlikosaurus andrewsi the individual skull elements were segmented as separate materials in Avizo. Small crack, breaks and holes were removed by interpolating over the affected region. As with the digital models of Plateosaurus engelhardti and Stegosaurus stenops, the bilateral symmetry was exploited to restore incomplete (both lacrimals, right frontal) or partially missing elements (left nasal). Finally, the individual elements were articulated, following the information provided by undeformed regions of the skull or as indicated by sutures and articulation facets on each element S10 .

MUSCLE RECONSTRUTION
The jaw adductor musculature for the three studied taxa were reconstructed following the protocol laid out by Lautenschlager S11 . Digital models of each muscle group were reconstructed on the basis of osteological correlates for muscle origin and insertion sites S12 . Muscle dimensions and volumes were modelled according to spatial constraints within the adductor chamber and topological criteria.
As a full account of the adductor muscle reconstruction for Erlikosaurus andrewsi has previously been published the reader is referred to the respective publication S11 .

m. adductor externus superficialis (m. AMES)
The attachment site of the m. AMES on the temporal bar is consistent across sauropsids, although it rarely leaves a specific osteological correlate beyond a generally smooth surface on the postorbital and squamosal borders of the supratemporal fenestra S12,S13 . In Plateosaurus engelhardti the medial surfaces of the postorbital and squamosal along the edge of the bar are generally smooth, allowing the reconstruction of the m. AMES attachment here as a level I inference. Rostrally, this attachment area is constrained by the position of the m. PSTs. Caudally, the attachment site extends into the caudal corner of the supratemporal fenestra, on the main body of the squamosal. The mediolateral width of the m. AMES is constrained by the other muscles of the adductor externus group, rather than osteological features.
The insertion of the m. AMES on the surangular is likewise highly conserved across sauropsids, where it occupies the dorsolateral edge of the surangular S12,S13 . In Plateosaurus engelhardti this insertion site is marked by a smooth, dorsomedially bevelled region. This also makes the insertion site of the m. AMES a level I inference.

m. adductor externus medialis (m. AMEM)
The m. AMEM is somewhat problematic as it is generally difficult (or impossible) to discern from the m. AMEP and m. AMES in sauropsids S12,S13 . As a result, identification of its attachment sites depends heavily on the topology of other reconstructed muscles, especially for its insertion site on the mandible S11,S12 .
The m. AMEM originates along the caudal wall of the supratemporal fenestra in archosaurs S12,S13 , attaching along the rostral face of the parietal wing and medial process of the squamosal. This attachment is marked by a large, smooth region. The rostromedial boundary of the m. AMEM is defined by the relative position of the m. AMEP; a slight scar marks the distinction between the two muscle groups S12 . These correlates make the insertion area of the m. AMEM a level I inference for both taxa.
The m. AMEM inserts onto the dorsomedial edge of the surangular in sauropodomorphs S12 .
This area is narrow, smooth and slightly concave. This area is continuous with the insertion site of the m. AMEP, which extends from the dorsomedial edge of the surangular onto the coronoid area in both taxa. Distinguishing between the two is difficult; two smooth, slightly concave areas are observed with a weak break between them. This break is taken here as the distinction between the insertion sites of these two muscles, with the m. AMEM attachment site running from here until the dorsomedial edge of the surangular pinches out caudally. Nevertheless, the ambiguous nature of this distinction, and the lack of a specific correlate observed for this attachment in extant crocodilians and birds S12 , renders this reconstruction a level I' inference.

m. adductor mandibulae externus profundus (m. AMEP)
This muscle occupies the rostromedial area of the supratemporal fenestra in sauropsids S12,S13 . It originates on the parietal rostral to the attachment of the m. AMEM. In Plateosaurus engelhardti, it chiefly occupies the lateral surface of the main body of the parietal. It is bounded laterally by the m. 9 PSTs, which occupies the rostroolateral wing of the parietal. The prominent smooth regions on the parietal marking the attachment of this muscle make this origination site a level I inference for both taxa.
In extant sauropsids the m. AMEP attaches in the region of the coronoid eminence, rostral to the attachment of the m. AMEM (in those cases where it can be distinguished from the latter muscle) S12,S13 , making such an attachment a level I inference in sauropodomorphs. Hence, here it is reconstructed as attaching to the dorsomedial surface of the rostralmost surangular and caudal coronoid in Plateosaurus engelhardti. Further rostral expansion of the m. AMEP is prevented by the ectopterygoid, which tightly constrains both the size and attitude of this muscle.

m. pseudotemporalis superficialis (m. PSTs)
The m. PSTs is the deepest and most rostral of the temporal muscles, originating from the rostral wall of the supratemporal fenestra in archosaurs S12,S13 . Reconstructed it as originating here is a class I inference, although the generally smooth surface of the supratemporal fossa makes its attachment site hard to distinguish from those of the m. AMEP and m. AMES. It is here reconstructed as occupying the majority of the rostrolateral parietal wing, the caudal wall of the laterosphenoid and the frontal. The frontal portion of the supratemporal fossa in Plateosaurus engelhardti is deep; this is not a taphonomic artefact as it is preserved on both sides and is also seen in other Plateosaurus specimens (e.g. AMNH FARB 6810; S6]). Similar deep fossae are present on the frontals of some other 'prosauropods' and theropods, where it has also been reconstructed as representing the extent of m. PSTs attachment S14,S15 , although Holliday S12 considered such an attachment in these theropods unlikely, partially due to the strong horizontal orientation of the fossa. However, due to its close association with the supratemporal fossa and caudodorsal orientation in Plateosaurus engelhardti, this fossa is reconstructed here as being occupied by the m. PSTs, as in previous reconstructions of Plateosaurus S2,S16 . 10 The mandibular insertion of the m. PSTs is somewhat problematic in dinosaurs S12 , Galton S2 and Fairman S16] reconstructed an insertion onto the medial region of the coronoid in Plateosaurus, through comparison with lepidosaurs. However, phylogenetic bracketing S12 , the large-size of the adductor fossa and the small size of the coronoid eminence instead suggest insertion within the rostral mandibular adductor fossa, similar to the condition seen in crocodiles and most ratites S12,S13 . Still, the variability of this attachment site in birds, and the lack of a specific osteological correlate for m. PSTs attachment, render this a level II' inference. An attachment in the region of the coronoid eminence would also lead to problems regarding spatial relationships with the other adductor muscles as the adductor chamber is very narrow.
In Plateosaurus engelhardti the mandibular adductor fossa is strongly laterally compressed.
This spatial constraint suggests a tendinous, rather than fleshy, attachment of this muscle S11 , as in extant crocodilians S12,S13,S17,S18 . Additionally, the enlarged and well-developed pterygoid flange of Plateosaurus engelhardti tightly compresses the pathway for the m. PSTs. This is similar to the morphology seen in extant crocodilians where the compressive environment is associated with the development of a sesamoid (the 'cartilago transilisens') within the m. PSTs S17 . The development of similar fibrocartilaginous structure within the m. PSTs in Plateosaurus engelhardti is therefore tenable.

m. pseudotemporalis profundus (m. PSTp)
Phylogenetic bracketing suggests that m. PSTp would have originated from the lateral wall of the epipterygoid in those dinosaurs that possessed the bone S12 even though distinct osteological correlates are rare. The more basally branching Plateosaurus engelhardti retained an epipterygoid; the m. PSTp is here reconstructed as originating on the expanded rostrolateral surface of the epipterygoid, dorsal to the midshaft.

11
The mandibular attachment of the m. PSTp is also difficult to discern due to the ambiguous nature of osteological correlates for this muscle and its typically vestigial development in extant archosaurs S12 . Topological relationships with other muscles, in particular the m. PSTs, and the small area of attachment on the mediodorsal edge of the surangular, make an rostroventral attachment within the mandibular adductor fossa adjacent to that of the m. PSTs seem more likely than attachment on the medial surface of the coronoid region S16 , as in squamates and most birdsS12,S13.
Although the m. PSTs is herein considered to be similar to that of extant crocodilians, in these taxa the m. PSTp merges into the m. PTd rather than inserting onto the mandible itself S13,S18 .

m. adductor mandibulae posterior (m. AMP)
The attachment sites for the m. AMP are highly conserved across all sauropsids S12,S13 . This conservatism permits robust reconstruction of the origination and insertion sites of this muscle in all dinosaurs as level I inferences. Plateosaurus engelhardti exhibits a wide surface on the pterygoid wing of the quadrate for the origination of the m. AMP, as in other dinosaurs including Diplodocus and Camarasaurus S12,S19,S20 . The muscle would then have inserted into the mandibular adductor fossa. Galton S2 and Fairman S16 reconstructed the m. AMP as filling the entire mandibular fossa in Plateosaurus; however the reconstructed insertion sites of the m.PST group herein means that the m. AMP is restricted to the caudal two-thirds of the attachment site.

m. pterygoideus dorsalis (m. PTd)
Origination and insertion sites of the m. PTd are highly conserved across sauropsids, allowing robust level I inferences of attachment sites in dinosaurs S12,S13 . In Plateosaurus engelhardti the m.
PTd would have originated from the lateral surface of the pterygoid flange S2 , extending dorsally onto the dorsal surface of the pterygoid, leaving a generally smooth surface. It extended at least as far rostrally 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 S11 .
The mandibular insertion site, along the medial border of the prearticular and articular, is also a type I inference in dinosaurs S12 . In Plateosaurus engelhardti the muscle appears to have attached to the medioventral surface of the prearticular where it borders the articular fossa, extending caudally into a slight depression on the medial surface of the retroarticular process. insertion sites for this muscle are well-constrained, the muscle thickness is less so as there are no osteological or reconstructed topological constraints upon how far the muscle could have bulged medially towards the oral cavity. As a result, to make a conservative estimate, the muscle was projected to maintain a similar thickness to that reconstructed from the more well-constrained insertion site for the majority of its length.

Stegosaurus stenops m. adductor mandibulae superficialis (m. AMES)
The m. AMES originates from the ventromedial surface of the postorbital/squamosal (supratemporal bar) in Stegosaurus stenops. A prominent ridge separates the ventral surface of the supratemporal bar into a medial and a lateral part. The medial part is deeply excavated and the m.

13
AMES most likely has a fleshy attachment here S12 . Whether the muscle's origin extends to the lateral surface is not clear. The ridge separating the ventral surface of the supraorbital bar continues caudally onto the base of the squamosal and the quadrate contact, further separating the adductor chamber from the rostrolateral surface of the quadrate. As a result, the region near the squamosal/quadrate contact is deeply excavated and reminiscent of a muscle attachment site. An additional lateral attachment of the m. AMES is possible, although the muscle is sometimes reconstructed to be restricted to the medial surface of the supratemporal bar in dinosaurs S12 . A similar morphology is found, though, in Corythosaurus casuarius and Ostrom S21 suggested an origin of the m. AMES from the lateral surface of the squamosal, however, not without noting the unusual position. A corresponding fossa on the lateral surface of the quadrate-squamosal contact is further present in specimens of Psittacosaurus mongoliensis and P. gobiensis and an attachment has for the m. AMES has been reconstructed S22 . Fairman S16 suggested the presence of two muscles, m.
levator anguli oris (m. LAO) and m. retractor anguli oris (m. RAO), located laterally to m. AMES and originating from the ventral portions of the postorbital and squamosal, respectively, in a muscular reconstruction of Plateosaurus engelhardti. These muscles are found in many lepidosaurs S23 and have been hypothesised to be present in ankylosaurs S24 and hadrosaurids S21 .
However, as pointed out by Holliday S12 , the muscles are not present in any extant archosaurs, making their reconstruction in dinosaurs a weak (level III') inference. Therefore it seems plausible that slips of the m. AMES also attached to the lateral fossa in Stegosaurus stenops as it has been reconstructed herein.
The insertion of the m. AMES on the mandible is demarcated by an elongate, shallow fossa on the lateral surface of the surangular, just rostral to the articular contact. The fossa follows the dorsal margin of the surangular and is somewhat crescent-shaped. In shape and position the insertion of the m. AMES in Stegosaurus stenops is similar to that of Plateosaurus engelhardti S12 .

m. adductor mandibulae profundus (m. AMEP)
The origin of the m. AMEP is marked by a faint depression on the medial wall of the temporal fossa. The caudal extend of the attachment is indicated by a faint ridge, whereas the rostral extent might be demarcated by a shift in surface topology close to the parietal/postorbital suture. A distinct vertical crest indicative of the rostral extent, as found in theropod dinosaurs S11,S12 , is not present in Stegosaurus stenops.
The m. AMEP inserts on the dorsomedial surface of the surangular, although the exact position and extent is somewhat unclear. A shallow depression and slightly rugose area is present in on the surangular caudal to coronoid region suggesting an attachment. Holliday S12  As in most dinosaursS12 the, the m. pterygoideus ventralis originates from the caudoventral edge of the pterygoid. The pterygoid shows no clear osteological correlates as in some theropods S11,S12 , but this position is supported by inference of phylogenetically bracketing taxa and the arrangement of the surrounding muscles.
The m. PTv inserts on the medioventral surface of the angular and a portion of the muscle wraps around the bone to attach onto the lateral surface of the angular. The medial insertion is marked by a smooth fossa ventral to the jaw joint and the retroarticular process, whereas a rostrocaudally elongate depression indicates the lateral insertion. The latter is dorsoventrally narrow, suggesting only a moderate expansion of the muscle on the lateral side unlike the large, bulging muscle reconstructed for other dinosaurs S12 .      Erlikosaurus andrewsi subjected to different bite scenarios. From left to right, bilateral bite at the tip of the skull/dentary, the first maxillary tooth/occluding tooth on dentary, last occluding maxillary/dentary tooth (indicated by red arrows). All models in original size, but scaled to same peak stress.

ADDITIONAL DATA AND FIGURES FOR BIOMECHANICAL ANALYSES
32 Figure S5 Comparison of Von Mises stress distribution for models an antorbital fenestra. Models of (a-c) Plateosaurus engelhardti, (d-f) Stegosaurus stenops without and (g-i) with antorbital fenestra, (j-l) Erlikosaurus andrewsi subjected to different bite scenarios. From left to right, bilateral bite at the tip of the skull/dentary, the first maxillary tooth/occluding tooth on dentary, last occluding maxillary/dentary tooth (indicated by red arrows). All models scaled to same surface area and to same peak stress.