Tyrannosaurus rex Osborn 1905

Hypotheses and approach The fusion and vaulting of tyrannosaurid nasals, and their position as the keystone (Busbey 1995) of a broad, strongly articulated nasal−maxillary arch, suggest that the nasals enhanced the strength of the snout against compressive, bending, shear, and torsional forces. The confluence of unusual mandible, tooth, and nasal morphologies in the Tyrannosauridae suggests a correlated progression (Thomson 1966; Kemp 1999) towards a reinforced head skeleton and high bite power. Using data derived from CT cross−sections of theropod nasals, analysis of cross−sectional geometry of theropod crania, and measurements of maxillary teeth, we tested several hypotheses related to possible correlated progression of the tyrannosaurid feeding apparatus: (1) Tyrannosaurid maxillary teeth were stronger in bending those of other large carnivorous dinosaurs. (2) Vaulting contributed significantly to tyrannosaurid nasal strength. (3) Fusion of tyrannosaurid nasals imparted higher torsional and shear strengths than those of Allosaurus nasals. (4) Tyrannosaurid crania were stronger in bending and torsion than carnosaur crania of similar length. We approach these hypotheses inductively, proceeding from tooth to nasal to cranial strengths. The teeth were the elements that would first encounter resistance of prey tissues and would transmit food reaction forces to the cranium. Tyrannosaurid nasals were potentially adapted to resisting those forces, as dorsally positioned compressive members of the truss−like cranium (Molnar 2000; Rayfield 2004). We chose this order of investigation because each inductive stage can potentially falsify our overall hypothesis of correlated progression, and will build up to an integrated picture of the strengths of theropod feeding apparatus. To compare these strengths, we used simple engineering principles and calculations. Simplified models of biological structures have a rich history in the palaeontological and neontological literature (Alexander 1985; Farlow et al. 1995; Greaves 1978, 1991; Henderson 2002; Holtz 1995; Molnar 2000; Slijper 1946; Thomason and Russell 1986; Thompson 1917). Simple approximations are valuable for numerous reasons, especially in palaeontology. First, reductionist models allow efficient tests of strength hypotheses by equations of beam theory and its elaborations (Young and Budynas 2001). These methods are applicable to cantilevered structures regardless of the proportions or shape of the beam (Molnar 2000; Henderson 2002) or truss (Rayfield 2004). Second, simple computational models can be constructed quickly, enabling assessment of variation across taxa. In contrast, 3D finite element modeling is time consuming and usually encompasses one taxon at a time (Rayfield et al. 2001; Snively and Russell 2002; Mazzetta et al. 2004; Rayfield 2005). Third, simple analyses, as of skull and metatarsal function (Bakker 2000; Holtz 1994; Molnar 1973, 2000; Snively and Russell 2003; Snively et al. 2004), yield rapid generation of results and hypotheses that are testable by more sophisticated means (Rayfield et al. 2001; Rayfield 2004; Snively and Russell 2002). Conversely, elaborate tests (Rayfield et al. 2001) are subject to refinement of assumptions, whose effects are more easily testable with simplified methods (Rayfield 2004). Using shell−like theropod cranial models to test relative strengths exemplifies this approach. Models incorporating the influence of intracranial joints, cranial fenestration, and the palate (Rayfield 2005) will be valuable for future studies, because these factors affected second moments of area and hence bending and torsional strengths. We did not construct them here for several reasons. Fenestration occurred in areas where stresses would otherwise be minimal (Molnar 2000; Rayfield et al. 2001), stress concentrations will be similar overall in shell−like and lattice models (Gordon 1978; Greaves 1985), and a shell−like model does not obscure relative strengths of theropod crania. For our purposes, the main benefit of the shell−like models is that they isolate the effects of geometry from other factors contributing to cranial strength. Tyrannosaurid crania had proportionally more bone and smaller fenestrae than did carnosaurs (Henderson 2002), and larger and presumably stronger ligamentous joints for resisting tension along the ventral bor− der of the cranium (Rayfield 2004). The anterior secondary palate of tyrannosaurids (Holtz 2002) would greatly increase the torsional strength of the tyrannosaurid rostrum over that in some carnosaurs (contact of the palatal shelves in synapsids increased torsional strength immensely: Thomason and Russell 1986; Busby 1995). We gave the more open carnosaur specimens a relative advantage by approximating all crania as equally “closed” structures, effectively putting tyrannosaurid cranial geometry to a more stringent test. Institutional abbreviations.—AMNH, American Museum of Natural History, New York, New York, USA; BHI, Black Hills Institute of Geological Research, Hill City, South Dakota, USA; BMRP, Burpee Museum of Natural History, Rockford, Illinois, USA; FMNH, Field Museum of Natural History, Chicago, Illinois, USA; IVPP, Institute of Vertebrate Palaeontology and Palaeoanthropology, Bejing, China; LACM, Natural History Museum of Los Angeles County, Los Angeles, California, USA; ROM, Royal Ontario Museum, Toronto, Ontario, Canada; MACN, Museo Argentino de Ciencias Naturales, Buenos Aires, Argentina; MOR, Museum of the Rockies, Bozeman, Montana, USA; MWC, Museum of Western Colorado, Grand Junction, Colorado, USA; NCSM, North Carolina State Museum of Natural Sciences, Raleigh, North Carolina, USA; SGM, Ministere de l̓Energie et des Mines, Rabat, Morocco; TCMI, The Children̓s Museum of Indianapolis, Indianapolis, Indiana, USA; TMP, Royal Tyrrell Museum of Palaeontology, Drumheller, Alberta, Canada; UUVP, University of Utah Vertebrate Paleontology, Salt Lake City, Utah, USA. Strengths of large theropod teeth Materials and methods for testing tooth strength of large theropods.—We measured in situ maxillary teeth of large theropods (Table 1, Appendix 1) to determine if the tyrannosaurid teeth were stronger than those of non−tyrannosaurids, and to reveal any trends in tooth strength with increases in body size. Specimens included tyrannosaurids, carnosaurs, and neoceratosaurians. Maxillary tooth measurements of the carnosaur Acrocanthosaurus atokensis were obtained from the literature (Harris 1998; Currie and Carpenter 2000). Measurements (with Mitutoyo 505–634 calipers) were crown height, fore−aft basal length (FABL) and mediolateral basal length (MLBL), sensu Farlow et al. (1991). Because teeth of Tyrannosaurus rex BHI 2033 had taphonomically slipped out of the alveoli, their cross sectional measurements were taken from the proximal base of the enamel, and crown heights measured from this point as well. Strength indicators for maxillary teeth in mediolateral and anteroposterior bending were determined by calculating their section modulus after Farlow et al. (1991; assuming a rectangular cross−section), dividing by crown height, and assuming a unit force. These tooth strength indicators were plotted against skull length. Skull lengths (from the anterior tip of the premaxilla to the posterior edge of the quadrates in lateral view) were measured with a tape measure, taken from the literature, or calculated from maxillary measurements and the log form of regression equations in Currie (2003b). The predicted lengths of measured skulls were within 3% of their actual lengths. However, for disarticulated skulls whose lengths were calculated using the regression equations (TCMI 2001.89.01; TMP 1994.143.1, 2001.36.1, and 2004.03.03), future published lengths from reconstructed skulls will be more definitive than those calculated here. Results for maxillary tooth bending strengths.— Table 1 enumerates average measurements and strength results for theropod maxillary teeth, and Fig. 3 plots mean maxillary tooth strengths versus theropod skull lengths. Fitted trend lines (using least squares regression) are shown for tyrannosaurids and carnosaurs, with the neoceratosaurians plotted as well. Smaller tyrannosaurid teeth are generally weaker in anteroposterior and mediolateral bending than teeth of non−tyrannosaurids. Maxillary teeth of most large tyrannosaurids are as strong or slightly stronger in mediolateral bending and stronger in anteroposterior bending than teeth of non−tyrannosaurids, except for the large carnosaurs Sinraptor dongi and Acrocanthosaurus atokensis. Tyrannosaurus rex has much higher tooth strengths than these carnosaurs or other large tyrannosaurids. The average strengths of T. rex teeth are extraordinary high relative to skull length, despite marked discrepancies in tooth sizes along each specimen̓s maxillary row (evident in the lower average strength in AMNH 5027). The patterns of increasing tooth strength with skull length differ between tyrannosaurids and other large theropods. The line of best fit for the non−tyrannosaurids is linear, while that for the tyrannosaurids is best described by an exponential function. Strengths of tyrannosaurid and Allosaurus nasals Materials and methods for examining theropod nasal strength Nasal specimens.—Fossil nasal specimens included juvenile and adult specimens of Gorgosaurus libratus, and a larger adult specimen of Gorgosaurus ̓s sister taxon Albertosaurus sarcophagus (Fig. 4). These specimens are a tentative proxy for a nasal growth series of these tyrannosaurids, since the nasals share general morphological features (Currie 2003a) and the animals reach identical adult sizes (Currie 2003b). We also scanned fossilized nasals of a large adult Daspletosaurus torosus and a high−resolution cast of nasals from its close relative Tyrannosaurus rex (Fig. 4). Scanning a cast to obtain cross−sections was appropriate for three reasons. Examination of the original specimen

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