Bite forces

Bite force measurements for the three dinosaur taxa were calculated using MDA for both the original sized cranial models (Fig. 2a) and for all models scaled to the same surface area to allow size-independent comparability (Fig. 2b). The highest bite forces are recorded in Stegosaurus stenops, both in the original (231–410 N) and scaled models (166–321 N): these values lie within the range of bite forces found by a previous study25. As expected, bite forces increase as the bite point shifts caudally (i.e. closer to the jaw joint). Bite forces in Plateosaurus engelhardti and Erlikosaurus andrewsi are found to be very similar to each other (Plateosaurus, 69–138 N; Erlikosaurus, 50–121 N) regardless of scaling (Plateosaurus, 46–123 N; Erlikosaurus, 50–121 N) and are consistently 60–75 percent lower than those for Stegosaurus stenops (unscaled: 231–410 N; scaled: 166–321 N). Independently obtained bite force estimates derived from the respective FEA models, as well as lever mechanic calculations, show a good correspondence with those obtained from the MDAs for all taxa and bite positions (Fig. 2). The only exception to this concerns the first maxillary tooth position in the originally-sized model of Stegosaurus stenops. In this example, bite forces obtained from FEA and lever mechanic models are only around 50–60 percent of the value obtained from the MDA model. Repeated analyses resulted in the same values suggesting that this is not a methodological artefact, but the reason for this outlier is unclear.

Figure 2 Bite force measurements for studied taxa recorded with multibody dynamics analysis. (a) All models in original size, (b) models scaled to same surface area. Bold lines represent recorded values during bite cycle with shaded background showing maximum and minimum values obtained during multiple analyses. Filled bars denote calculated bite force values derived from lever mechanic relations, open bars denote values obtained from reaction forces at bite points of the FE models. Full size image

Cranial stress distribution

A comparison of the stress distributions over the skull and lower jaw models reveals considerable differences between the three taxa. The overall lowest stress magnitudes in the skull models are recorded for Plateosaurus engelhardti, which exhibits a largely uniform distribution of stresses for the different bite scenarios (Fig. 3a–c). Localised stress hotspots are restricted to the bite points, the premaxillary process in the two rostral bite scenarios and the muscle attachments (see Supplementary information for details on muscle origins and insertions). In contrast, the skull models of Stegosaurus stenops and, in particular, Erlikosaurus andrewsi are characterised by increased stress magnitudes. In Stegosaurus stenops stresses are centred on the rostral skull and the antorbital region (Fig. 3d–f), whereas in Erlikosaurus andrewsi large regions on the caudal part of the skull are relatively highly stressed (Fig. 3g–i), especially for the caudal bite scenario.

Figure 3 Comparison of Von Mises stress distribution for scaled models. Models of (a–c) Plateosaurus engelhardti, (d–f) Stegosaurus stenops and (g–i) 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. Full size image

The lower jaw models across all taxa generally show higher stress magnitudes and less uniform stress distributions than the skull models (Fig. 3). As with the skull, the jaw models of Plateosaurus engelhardti display the lowest stress magnitudes. Stress is highest in the postdentary region and at the muscle insertions (Fig. 3a–c). Localised hotspots are found on the dentary lateral to the tooth row, although not along the lateral dentary shelf, during the rostral biting scenarios and at the tip of the dentary for a bite at the caudal-most tooth position. In comparison, Stegosaurus stenops shows high stress magnitudes across the entire jaw, with a focus on the postdentary and articular regions (Fig. 3d–f). The highest stress magnitudes are recorded in Erlikosaurus andrewsi, in particular for a bite in the rostral region of the tooth row (Fig. 3h). In contrast, the bite at the caudal-most tooth position shows a distinct pattern of stress distribution with high magnitudes in the postdentary bones and a largely unstressed dentary region (Fig. 3i).

In addition to the osteological models, further models were analysed that incorporated a keratinous beak covering the rostral regions of the skull and dentary in Stegosaurus stenops and Erlikosaurus andrewsi (Supplementary Fig. S4). As demonstrated in previous analyses, the presence of a keratinous sheath has stress mitigating effects on the underlying bone26 and this observation was confirmed here. This effect is more pronounced in the skull models and for the two rostral biting regimes. The overall stress distribution remains largely unchanged, although individual stress magnitudes decrease.

Stegosaurus stenops differs notably from the other taxa examined in the absence of an antorbital fenestra22. To rule out the possibility that its absence obscures functional similarities, a hypothetical skull model was created to incorporate this feature (see Materials and Methods). However, analyses of the different bite scenarios display only negligible differences in terms of the stress distributions between the actual and hypothetical models of Stegosaurus stenops (Supplementary Fig. S5).

A geometric morphometric analysis of the results from all FEAs quantitatively confirms these observations (Fig. 4a). Deformation as a result of loading is most pronounced in the skull of Erlikosaurus andrewsi, whereas Stegosaurus stenops and Plateosaurus engelhardti show little variation from the undeformed/unloaded shape. For the lower jaw models, the differences between the taxa are more uniform with the highest variation found in Stegosaurus stenops. Calculation of Euclidean distances further demonstrates that the functional behaviour of the skull and the mandible are not consistent across the tested bite scenarios (Fig. 4b). While the skulls of Plateosaurus engelhardti and Stegosaurus stenops are most similar in their deformation pattern for a bite point at the tip of the skull, Stegosaurus stenops and Erlikosaurus andrewsi are more similar to each other in the other bite scenarios. In contrast, the deformation patterns of the mandibles indicate a closer functional similarity between Erlikosaurus andrewsi and Stegosaurus stenops, whereas Plateosaurus engelhardti and Stegosaurus stenops are the most dissimilar.

Figure 4 Quantitative assessment of biomechanical differences. (a) Principal component plot showing extent of deformation of models during biting simulations using FEA. Skull and lower jaw models plotted into the same coordinate system. Numbers indicate bite position (corresponding to Fig. 3): 1, bite at the tip of the skull/dentary, 2, the first maxillary tooth/occluding tooth on dentary, 3, last occluding maxillary/dentary tooth. (b) Calculated Euclidean distances between studied taxa for undeformed models and for different bite scenarios. Pale background colours indicate models scaled to same surface area. Full size image

Plant stress distribution

The effects of bite force and position on different sized food items were tested for all taxa. For the larger plant model (10 mm in diameter), the stress distribution for all bite positions is largely similar for the scaled skull models and shows only low stress magnitudes (Fig. 5). However, for Stegosaurus stenops and Plateosaurus engelhardti the stress magnitudes are highest in the caudal bite scenario. The smaller plant models (5 mm in diameter) display more variable stress distributions. While a bite at the tip of the skull produces very low magnitudes, stress increases with a shift of the bite point (and coincident increase in bite force) caudally. Among these three taxa, stress magnitudes are highest for Plateosaurus engelhardti for each bite scenario across the width of the plant model. For all taxa, contour plots of the smaller plant models show marked asymmetries in stress distribution. This can be explained by the fact that the tooth positions, orientations and eruption stages and thus the force vectors of the left and right sides of the skull and jaw, are subject to natural variation.