I’ve been lax in feeding the biomechanics demon [n1] with tasty brain food, and extremely lax in talking about a paper that was published quite some time ago, but is still quite interesting. A new paper from the author (on cranial morphometrics in Felidae, Sakamoto & Ruta, 2012) probably has nothing to do with spurring me to discuss this older paper.
It may be a puzzle to people that oviraptorids tend not to get included in modelling analyses of jaw function or morphology, until one realizes that the jaw anatomy of oviraptorids is very, very different from that of “typical” theropods, like Velociraptor mongoliensis. The jaws are relatively short, deep, and unlike other toothless theropod dinosaurs like ornithomimosaurids, the jaw muscles appear to insert far forward of their relative position in toothed animals.
What’s In A Jaw?
Dr. Manabu Sakamoto took the skull of a large range of theropods and estimated or determined the position of the origin and insertion of a variety of jaw adducting muscles; determined the point of articulation in the jaw and it’s size; and the leverage and force each of the muscles would have as the jaw “bit.” He then divided the range of dentition of the jaws (upper and lower) against the dentition range and computed the mechanical advantage if the animal to were bite at each tooth in this range. This results in a bite profile. (Dr. Sakamoto described the process in far more detail at his website, Raptor’s Nest.)
Typically, jaws are strongest closest to the jaw joint, but lack precision (it’s all about strength); alternately, jaws are weaker towards the tip, but increase in precision (it’s all about position). Thus, the bite profile for a typical animal will slope from the rear (at 0% of the jaw margin) down to the front (to 100% of the jaw margin), and create a sloping bite profile. Further, it is assumed the animal will prefer to bite at the point that is most efficient: for most animals, this is at the posterior end of the jaws. But in some cases, the skew towards or away from the rear of the jaw is such that the animal would seem to prefer the one method over the other.
Coelophysoids, in this analysis (seen in black, above), have a nearly L-shaped profile, showing such a skew toward the posterior end of the jaw that it almost certainly used the rostral end differently than the rear of the jaw. Oviraptorids, on the other hand, had such an even slope with high anterior jaw advantage that it is quite likely that the jaws were very employed in a very specific manner. Sakamoto stresses that taxa with long tooth rows, and thus with the posteriormost bite points at or close to the adductor musculature, have moderate mechanical advantage along the whole jaw while also supporting extremely high advantage at the rear. Coelophysoids merely have the highest posterior advantage of taxa assessed.
For oviraptorids and ornithomimosaurs, Sakamoto was unable to calculate tooth position, and so merely divided the effective jaw margin into discrete points every 10% and calculated his values along this margin. The results in comparison to various toothed theropods was different from both ornithomimosaurs and oviraptorids, but ornithomimosaurs at least shared a similar profile to toothed theropods, despite being toothless. Oviraptorids, however, did not.
Here, the profile is represented by several factors: the mechanical advantage, the degree of change in mechancial advantage over the tooth row (slope), and the degree of difference in mechanical advantage from point to point along the row (which results in a curvature of the slope). It should be cautioned that the slope profile does not represent positional advantage of the jaw, so that percentage represents which portion of the jaw is “strongest;” instead, the slope relates to calculating individual mechanical advantage at each percentage of the jaw’s margin against the entire jaw’s length. This, then indicates the relative advantage a portion of the jaw has over the whole: A steep curve indicates that mechanical advantage is segregated in the jaw, so that there are regions of the jaw that are better suited at high advantage, and others at lower; a shallow curve indicates the jaw has high mechanical advantage throughout.
(“Strength” may be presumed, but other analyses such as those employing FEA to calculate the stresses in the jaws, likely bite actions and so forth, are done separately.)
As one should note, oviraptorids, unlike virtually all other taxa sampled, have virtually no curvature of the slope, and the slope is shallow. This indicates that the total-jaw mechanical advantage (as opposed to a percentage of it) was very high for oviraptorids, while in typical theropods, total-jaw mechanical advantage ends up fairly low.
Relating strongly to the posterior position of the jaw adducting muscles, the analysis also purported a distinction between “weak/fast” and “high efficiency” jaws. A mandible with rostral insertions of the musculature has increased mechanical leverage as this increases the muscle moment to the jaw joint. When the jaw muscles of the upper cranium are closely aligned and posterior, the jaw produces a fast-closing action: this appears to be the case for ornithomimosaurs, which are also (largely) edentulous, as well as basal coelurosaurs, and birds in general. Conversely, anterior positioning of these muscles produces a slower, but more efficient bite: this appears to be the case for tyrannosaurids (and other large-skulled tetanuran and neoceratosaurian theropods) and oviraptorids.
Oviraptorids, like some “strong-jawed” theropods like tyrannosaurids, show high mechanical advantage, but then maintain this throughout the jaw, while tyrannosaurids are less efficient (but no less strong; see a recent albeit unpublished paper by Karl Bates and Peter Falkingham). Ornithomimosaurs have a higher curvature of the slope, but unlike all of the other taxa sampled, they start out with weak advantage, and end up with weaker advantage, and even in the same space as tyrannosaurids with regards to total-jaw efficiency.
The Nose Knows
In a more recent study, Brusatte et al. (2012; of whom Sakamoto is a co-author) expanded data by creating a databse of various theropod skulls in lateral aspect and applying a range of cranial landmarks to them, then assessing them in morphometric space using two sets of data: an expanded 36 taxon matrix with 13 landmarks (due to reduced preservation) and a smaller 26 taxon matrix but with 24 landmarks (for more complete skulls).
Calculating cranial shape variation by principal components analysis, and doing so without being influenced by the relative sizes of the skulls, the authors then ran several other analyses against the data, including Sakamoto (2010). They also segregated taxa through various imposed categories (taxonomic, inferred dietary, etc.) in order to find patterns in the data. After applying a range of tests to the data, and plotting Sakamoto’s data against a composite phylogeny, the authors further found that phylogeny range true: Taxa that are closely related to one another tend to stay close together, regardless of variation of skull shape.
This analysis produced in some oddities, however:
Allosauroids, perhaps because of their large, “boxy” skulls, grouped with taxa that also have large “boxy” skulls (here, tyrannosauroids).
Several toothless taxa were displaced from toothed taxa to which they are relate, such that Limusaurus inextricabilis (Xu et al., 2009) is far removed from “Ceratosauria” and rather placed within a bubble that defines the oviraptorosaurs and therizinosauroids.
Most bizarrely, oviraptorosaurs are skewed far away from other near-avian maniraptorans, while ornithomimosaurs and dromaeosaurids are closely associated.
Such results forced the authors to then duplicate their analyses again, this time while removing the oviraptorids from the sample. The result is the second plot above. While the authors noted that toothlessness does result in displacement, the high separation from the main plot of taxa was indicated strongly by shortening of the skull. Other theropod dinosaurs then tend to associate on the basis of phylogeny, then skull shape, even if that skull shape is similar to other, more distantly-related taxa. Because of the skull shape analysis is based on intricate details of the skull and not just outline, differences in the proportions of bones, size of various fenestra, and proportions of sections of skull (preorbital, postorbital) are relevant factors in demonstrating similarities.
The analysis also incorporated another portion of Sakamoto’s data, in assessing whether the phylogeny of taxa would show up grouping similar-shaped skulls with their bite profiles, and this is not the case: A shallow, high bite profile is present for carcharodontosaurids and for basal saurischians such as Plateosaurus engelhardti, but carcharodontosaurids at least are found nested within morphospace occupied by tyrannosaurs; similarly, ornithomimosaurs (low efficiency, shallow curve) are nested with dromaeosaurids (higher efficiency, steeper curve) and despite their lack of close relatedness. These aspects indicate that skull shape, bite efficiency, and bite strength result from a great many variables, and that a true “generalized” theropod skull may not be so easy to come by.
That the authors had to exclude oviraptorosaurs from their analysis to remove a bizarre outlier is no surprise, although it does little to influence the analysis itself. Nonetheless, just as oviraptorids are so peculiar in Sakamoto’s analysis, they are also in Brusatte et al.’s. Oviraptorid skull anatomy is extremely derived, with a highly foreshortened preorbital region of the skull, huge orbit, and large postorbital region retained despite overall skull shape. The mandible is deep, the snout declined from the angle of the jugal, and lots of stuff moved around the cranial skeleton to accommodate several of these changes. Brusatte et al. (p.369): “In other words, oviraptorosaurs are clearly the most aberrant theropods in terms of their skull shape,” a conclusion I cannot agree with more.
[n1] I am not an expert on biomechanics, although I profess a high interest in it, while I also lack as much of an understanding of biomechanical morphometrics as I should like. Because of this, this summary of work on the topics may come across as fantastically amateurish, for which I apologize. This deficiency is mitigated somewhat by conversations with Manabu Sakamoto, his own discussion of his 2010 paper, and my attempts to correct my lay knowledge and talking to several other biomechanics nuts. Please forgive the deficiencies of this post and I would be happy for you to point out corrections and improvements.
Brusatte, S. L., Sakamoto, M., Montanari, S. & Harcourt Smith, W. E. H. 2012. The evolution of cranial form and function in theropod dinosaurs: Insights from geometric morphometrics. Journal of Evolutionary Biology 25:365-377.
Sakamoto, M. 2010. Jaw biomechanics and the evolution of biting performance in theropod dinosaurs. Proceedings of the Royal Society of London, B: Biological Sciences 277:3327-3333. [PDF]
Sakamoto, M. & Ruta, M. 2012. Convergence and divergence in the evolution of cat skulls: Temporal and spatial patterns of morphological diversity. PLoS ONE 7(7):e39752.
Xu X., Clark, J. M., Mo J., Choiniere, J., Forster, C. A., Erickson, G. M., Hone, D. W. E., Sullivan, C., Eberth, D. A., Nesbitt, S., Zhao Q., Hernandez, R., Jia C.-k., Han F.-l. & and Guo Y. 2009. A Jurassic ceratosaur from China helps clarify avian digital homologies. Nature 459:940–944.
Zanno, L. E. & Makovicky, P. J. 2010. Herbivorous ecomorphology and specialization patterns in theropod dinosaur evolution. Proceedings of the National Academy of Sciences, Philadelphia 108:232-237. [PDF]