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<mods:title id="F0A1E88CA25BF4A1A0CFFFA9C905E4DF">Fused and vaulted nasals of tyrannosaurid dinosaurs: Implications for cranial strength and feeding mechanics</mods:title>
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<mods:namePart id="94235FD904267B13669631623BBCFFCB">Eric Snively</mods:namePart>
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<mods:namePart id="99D5A68C745224EB11F7F5ACFCCB45F7">Donald M. Henderson</mods:namePart>
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<mods:namePart id="A97F57125A95F4549ACD320200850666">Doug S. Phillips</mods:namePart>
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<heading id="D0CA81F0EC2DFFCD537BF954FAB8F8D5" box="[812,1305,1761,1803]" fontSize="18" level="1" pageId="0" pageNumber="435" reason="1">Hypotheses and approach</heading>
</paragraph>
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The fusion and vaulting of tyrannosaurid nasals, and their position as the keystone (
<bibRefCitation id="EFAC4B6DEC2DFFCD541EF8E4FB41F8B4" author="Busbey, A. R." box="[1097,1248,1873,1898]" editor="J. J. Thomason" journalOrPublisher="Cambridge University Press, Cambridge" pageId="0" pageNumber="435" pagination="173 - 192" refId="ref11168" refString="Busbey, A. R. 1995. The structural consequences of cranium flattening in crocodilians. In: J. J. Thomason (ed.), Functional Morphology in Vertebrate Paleontology, 173 - 192. Cambridge University Press, Cambridge." title="The structural consequences of cranium flattening in crocodilians" type="book chapter" volumeTitle="Functional Morphology in Vertebrate Paleontology" year="1995">Busbey 1995</bibRefCitation>
) 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 (
<bibRefCitation id="EFAC4B6DEC2CFFCC5205F944FCA0F8D4" author="Thomson, K. S." box="[594,769,1777,1802]" journalOrPublisher="American Zoologist" pageId="1" pageNumber="436" pagination="379 - 397" part="6" refId="ref13337" refString="Thomson, K. S. 1966. The evolution of the tetrapod middle ear in the rhipidistian-tetrapod transition. American Zoologist 6: 379 - 397." title="The evolution of the tetrapod middle ear in the rhipidistian-tetrapod transition" type="journal article" year="1966">Thomson 1966</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC2CFFCC5031F8A7FF4FF8F4" author="Kemp, T. S." bookContentInfo="284 pp." box="[102,238,1809,1834]" journalOrPublisher="Oxford University Press, Oxford" pageId="1" pageNumber="436" refId="ref12444" refString="Kemp, T. S. 1999. Fossils &amp; Evolution. 284 pp. Oxford University Press, Oxford." title="Fossils &amp; Evolution" type="book" year="1999">Kemp 1999</bibRefCitation>
) towards a reinforced head skeleton and high bite power.
</paragraph>
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<paragraph id="8B82369CEC2CFFCC5031FA46FDC9F971" blockId="1.[102,775,1523,1711]" pageId="1" pageNumber="436">
Fig. 1. Comparison of cranial and nasal morphology of: 
<emphasis id="B949EA8EEC2CFFCC522FFA46FD29F9D9" bold="true" box="[632,648,1523,1543]" pageId="1" pageNumber="436">A</emphasis>
, the tyrannosaurid 
<taxonomicName id="4C3D4D1FEC2CFFCC50F2F9A5FEF3F9FC" authorityName="Osborn" authorityYear="1905" box="[165,338,1552,1570]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="1" pageNumber="436" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC2CFFCC50F2F9A5FEF3F9FC" box="[165,338,1552,1570]" italics="true" pageId="1" pageNumber="436">Tyrannosaurus rex</emphasis>
</taxonomicName>
(TMP 98.86.01; cast of BHI 2033) and 
<emphasis id="B949EA8EEC2CFFCC5299F9A5FD7CF9FD" bold="true" box="[718,733,1552,1571]" pageId="1" pageNumber="436">B</emphasis>
, the carnosaur 
<taxonomicName id="4C3D4D1FEC2CFFCC5093F99EFECFF9E1" authorityName="Marsh" authorityYear="1877" box="[196,366,1579,1599]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="1" pageNumber="436" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC2CFFCC5093F99EFECFF9E1" box="[196,366,1579,1599]" italics="true" pageId="1" pageNumber="436">Allosaurus fragilis</emphasis>
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(UUVP 1663/UMNH VP 9146; mirrored to depict a complete pair). Scale axes for crania are in meters. Nasals in their life positions are highlighted in lateral and dorsal cranial views, and rendered in oblique view (not to scale). The 
<taxonomicName id="4C3D4D1FEC2CFFCC518FF935FDACF94C" authorityName="Osborn" authorityYear="1905" box="[472,525,1664,1682]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="1" pageNumber="436" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC2CFFCC518FF935FDACF94C" box="[472,525,1664,1682]" italics="true" pageId="1" pageNumber="436">T. rex</emphasis>
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nasals are tall, vaulted, and fused, while the 
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<emphasis id="B949EA8EEC2CFFCC50ABF929FEF7F971" box="[252,342,1691,1711]" italics="true" pageId="1" pageNumber="436">A. fragilis</emphasis>
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nasals are lower and unfused.
</paragraph>
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<paragraph id="8B82369CEC2CFFCC537BF8A4FA25F837" blockId="1.[812,1486,1809,2025]" pageId="1" pageNumber="436">
Fig. 2. Comparison of vertical bending strengths of adult theropod dentaries, graphed as mid−dentary section modulus versus mandible length (data from 
<bibRefCitation id="EFAC4B6DEC2CFFCC537BF8FCFC43F883" author="Therrien, F. &amp; Henderson, D. M. &amp; Ruff. C. B." box="[812,994,1865,1885]" editor="K. Carpenter" journalOrPublisher="Indiana University Press, Bloomington" pageId="1" pageNumber="436" pagination="179 - 237" refId="ref13207" refString="Therrien, F., Henderson, D. M., and Ruff. C. B. 2005. Bite me: biomechanical models of theropod mandibles and implications for feeding behavior. In: K. Carpenter (ed.), The Carnivorous Dinosaurs, 179 - 237. Indiana University Press, Bloomington." title="Bite me: biomechanical models of theropod mandibles and implications for feeding behavior" type="book chapter" volumeTitle="The Carnivorous Dinosaurs" year="2005">Therrien et al. 2005</bibRefCitation>
). Lines fitted by least squares regression, by log transformed values for the tyrannosaurid data. Carnosaur dentary strengths scale linearly with dentary length, while tyrannosaurid dentary strengths show an exponential increase. The tyrannosaurid dentaries are stronger than those of carnosaurs for a given mandible length, indicating a relatively stronger bite. See Appendix 1 for specimen labels; Gc, 
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<emphasis id="B949EA8EEC2CFFCC54CAF863FADFF837" box="[1181,1406,2005,2025]" italics="true" pageId="1" pageNumber="436">Giganotosaurus carolinii</emphasis>
</taxonomicName>
.
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<paragraph id="8B82369CEC2CFFCC50DBF8E4FE74F837" blockId="1.[102,775,1777,2026]" pageId="1" pageNumber="436">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:</paragraph>
<paragraph id="8B82369CEC2CFFCC5305FF5DFA94FEFF" blockId="1.[812,1485,232,1089]" pageId="1" pageNumber="436">(1) Tyrannosaurid maxillary teeth were stronger in bending those of other large carnivorous dinosaurs.</paragraph>
<paragraph id="8B82369CEC2CFFCC5305FE9DFC6FFEBF" blockId="1.[812,1485,232,1089]" pageId="1" pageNumber="436">(2) Vaulting contributed significantly to tyrannosaurid nasal strength.</paragraph>
<paragraph id="8B82369CEC2CFFCC5305FEDDFA18FE7F" blockId="1.[812,1485,232,1089]" pageId="1" pageNumber="436">
(3) Fusion of tyrannosaurid nasals imparted higher torsional and shear strengths than those of 
<taxonomicName id="4C3D4D1FEC2CFFCC54BBFE3DFAC4FE7E" authorityName="Marsh" authorityYear="1877" box="[1260,1381,392,416]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="1" pageNumber="436" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC2CFFCC54BBFE3DFAC4FE7E" box="[1260,1381,392,416]" italics="true" pageId="1" pageNumber="436">Allosaurus</emphasis>
</taxonomicName>
nasals.
</paragraph>
<paragraph id="8B82369CEC2CFFCC5305FE1DFA99FE3F" blockId="1.[812,1485,232,1089]" pageId="1" pageNumber="436">(4) Tyrannosaurid crania were stronger in bending and torsion than carnosaur crania of similar length.</paragraph>
<paragraph id="8B82369CEC2CFFCC5305FE5CFA97FC9E" blockId="1.[812,1485,232,1089]" pageId="1" pageNumber="436">
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 (
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; 
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). 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.
</paragraph>
<paragraph id="8B82369CEC2CFFCC5305FCFCFB69FB9F" blockId="1.[812,1485,232,1089]" pageId="1" pageNumber="436">
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 (
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<bibRefCitation id="EFAC4B6DEC2CFFCC545DFC5DFAE8FBDF" author="Thomason, J. J. &amp; Russell, A. P." box="[1034,1353,1000,1025]" journalOrPublisher="Journal of Morphology" pageId="1" pageNumber="436" pagination="199 - 213" part="189" refId="ref13266" refString="Thomason, J. J. and Russell, A. P. 1986. Mechanical factors in the evolution of the mammalian secondary palate. Journal of Morphology 189: 199 - 213." title="Mechanical factors in the evolution of the mammalian secondary palate" type="journal article" year="1986">Thomason and Russell 1986</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC2CFFCC5502FC5DFCC9FBFF" author="Thompson, D. A." bookContentInfo="368 pp." editor="Bonner, J. T." journalOrPublisher="Cambridge University Press, Cambridge" pageId="1" pageNumber="436" refId="ref13301" refString="Thompson, D. A. 1917. On Growth and Form (edited by Bonner, J. T.). 368 pp. Cambridge University Press, Cambridge (1992 edition)." title="On Growth and Form" type="book" year="1917">Thompson 1917</bibRefCitation>
). Simple approximations are valuable for numerous reasons, especially in palaeontology.
</paragraph>
<caption id="DF426614EC2FFFCF5031F9ECFCDCF91F" ID-DOI="http://doi.org/10.5281/zenodo.3961063" ID-Zenodo-Dep="3961063" httpUri="https://zenodo.org/record/3961063/files/figure.png" pageId="2" pageNumber="437" startId="2.[102,135,1625,1645]" targetBox="[859,1446,938,1599]" targetPageId="2">
<paragraph id="8B82369CEC2FFFCF5031F9ECFCDCF91F" blockId="2.[102,1485,1625,1729]" pageId="2" pageNumber="437">
Fig. 3. Comparisons of mediolateral (
<emphasis id="B949EA8EEC2FFFCF51EFF9ECFE69F9B3" bold="true" box="[440,456,1625,1645]" pageId="2" pageNumber="437">A</emphasis>
, 
<emphasis id="B949EA8EEC2FFFCF5184F9EFFE43F9B3" bold="true" box="[467,482,1626,1645]" pageId="2" pageNumber="437">B</emphasis>
) and anteroposterior (
<emphasis id="B949EA8EEC2FFFCF52FCF9ECFD1AF9B3" bold="true" box="[683,699,1625,1645]" pageId="2" pageNumber="437">C</emphasis>
, 
<emphasis id="B949EA8EEC2FFFCF5290F9EFFD76F9B3" bold="true" box="[711,727,1626,1645]" pageId="2" pageNumber="437">D</emphasis>
) strengths of tyrannosaurid and non−tyrannosaurid theropod maxillary teeth, plotted against skull length. Regressions are by least squares, on log transformed data for the tyrannosaurids. Trend lines are allometric in the tyannosaurids but linear in non−tyrannosaurids. Tooth strengths of 
<taxonomicName id="4C3D4D1FEC2FFFCF51ACF927FD04F97A" authorityName="Osborn" authorityYear="1905" box="[507,677,1682,1700]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="2" pageNumber="437" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC2FFFCF51ACF927FD04F97A" box="[507,677,1682,1700]" italics="true" pageId="2" pageNumber="437">Tyrannosaurus rex</emphasis>
</taxonomicName>
are much higher than in any other examined taxon. Starting points of the small arrows indicate the position of the juvenile 
<taxonomicName id="4C3D4D1FEC2FFFCF51DFF91BFE1CF91E" authorityName="Osborn" authorityYear="1905" box="[392,445,1710,1728]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="2" pageNumber="437" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC2FFFCF51DFF91BFE1CF91E" box="[392,445,1710,1728]" italics="true" pageId="2" pageNumber="437">T. rex</emphasis>
</taxonomicName>
(TrJ). See Appendix 1 for other specimen labels.
</paragraph>
</caption>
<paragraph id="8B82369CEC2FFFCE50DBF95BFE24FE9F" blockId="2.[102,775,1774,2026]" lastBlockId="3.[102,775,232,1187]" lastPageId="3" lastPageNumber="438" pageId="2" pageNumber="437">
First, reductionist models allow efficient tests of strength hypotheses by equations of beam theory and its elaborations (
<bibRefCitation id="EFAC4B6DEC2FFFCF503AF89AFE33F896" author="Young, W. C. &amp; Budynas, R." bookContentInfo="832 pp." box="[109,402,1839,1864]" journalOrPublisher="McGraw-Hill, New York" pageId="2" pageNumber="437" refId="ref13586" refString="Young, W. C. and Budynas, R. 2001. Roark's Formulas for Stress and Strain. 832 pp. McGraw-Hill, New York." title="Roark's Formulas for Stress and Strain" type="book" year="2001">Young and Budynas 2001</bibRefCitation>
). These methods are applicable to cantilevered structures regardless of the proportions or shape of the beam (
<bibRefCitation id="EFAC4B6DEC2FFFCF50ACF8C5FE35F857" author="Molnar, R. E." box="[251,404,1904,1929]" journalOrPublisher="Gaia" pageId="2" pageNumber="437" pagination="193 - 218" part="15" refId="ref12650" refString="Molnar, R. E. 2000. Mechanical factors in the design of the cranium of Tyrannosaurus rex (Osborn 1905). Gaia 15: 193 - 218." title="Mechanical factors in the design of the cranium of Tyrannosaurus rex (Osborn 1905)" type="journal article" year="2000">Molnar 2000</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC2FFFCF51C8F8C5FDFAF857" author="Henderson, D. M." box="[415,603,1904,1929]" journalOrPublisher="Journal of Vertebrate Paleontology" pageId="2" pageNumber="437" pagination="766 - 778" part="22" refId="ref12007" refString="Henderson, D. M. 2002. The eyes have it: the sizes, shapes, and orientations of theropod orbits as indicators of cranium strength and bite force. Journal of Vertebrate Paleontology 22: 766 - 778." title="The eyes have it: the sizes, shapes, and orientations of theropod orbits as indicators of cranium strength and bite force" type="journal article" year="2002">Henderson 2002</bibRefCitation>
) or truss (
<bibRefCitation id="EFAC4B6DEC2FFFCF5299F8C5FF40F877" author="Rayfield, E. J." journalOrPublisher="Proceedings of the Royal Society of London B" pageId="2" pageNumber="437" pagination="1451 - 1459" part="271" refId="ref12756" refString="Rayfield, E. J. 2004. Cranial mechanics and feeding in Tyrannosaurus rex. Proceedings of the Royal Society of London B 271: 1451 - 1459." title="Cranial mechanics and feeding in Tyrannosaurus rex" type="journal article" year="2004">Rayfield 2004</bibRefCitation>
). 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 (
<bibRefCitation id="EFAC4B6DEC2FFFCF5506F95BFC2CF8F9" author="Rayfield, E. J. &amp; Norman, D. B. &amp; Horner, C. C. &amp; Horner, J. R. &amp; May Smith, P. &amp; Thomason, J. J. &amp; Upchurch, P." journalOrPublisher="Nature" pageId="2" pageNumber="437" pagination="1033 - 1037" part="409" refId="ref12823" refString="Rayfield, E. J., Norman, D. B., Horner, C. C., Horner, J. R., May Smith, P., Thomason, J. J., and Upchurch, P. 2001. Cranial design and function in a large theropod dinosaur. Nature 409: 1033 - 1037." title="Cranial design and function in a large theropod dinosaur" type="journal article" year="2001">Rayfield et al. 2001</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC2FFFCF53CAF8BBFB68F8F9" author="Snively, E. &amp; Russell, A. P." box="[925,1225,1806,1831]" journalOrPublisher="Senckenbergiana lethaea" pageId="2" pageNumber="437" pagination="35 - 42" part="82" refId="ref13043" refString="Snively, E. and Russell, A. P. 2002. The tyrannosaurid metatarsus: bone strain and inferred ligament function. Senckenbergiana lethaea 82: 35 - 42." title="The tyrannosaurid metatarsus: bone strain and inferred ligament function" type="journal article" year="2002">Snively and Russell 2002</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC2FFFCF5480F8BAFA69F8F9" author="Mazzetta, G. V. &amp; Cisilino, A. P. &amp; Blanco, R. E." box="[1239,1480,1806,1831]" journalOrPublisher="Ameghiniana" pageId="2" pageNumber="437" pagination="605 - 617" part="41" refId="ref12529" refString="Mazzetta, G. V., Cisilino, A. P., and Blanco, R. E. 2004. Distribucion de tensiones durante la mordita en la mandibula de Carnotaurus sastrei Bonaparte, 1985 (Theropoda: Abelisauridae). Ameghiniana 41: 605 - 617." title="Distribucion de tensiones durante la mordita en la mandibula de Carnotaurus sastrei Bonaparte, 1985 (Theropoda: Abelisauridae)" type="journal article" year="2004">Mazzetta et al. 2004</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC2FFFCF537BF89AFC71F896" author="Rayfield, E. J." box="[812,976,1839,1864]" journalOrPublisher="The Anatomical Record Part A" pageId="2" pageNumber="437" pagination="349 - 365" part="283" refId="ref12786" refString="Rayfield, E. J. 2005. Using finite element analysis to investigate suture morphology: a case study using large carnivorous dinosaurs. The Anatomical Record Part A 283 A: 349 - 365." title="Using finite element analysis to investigate suture morphology: a case study using large carnivorous dinosaurs" type="journal article" year="2005">Rayfield 2005</bibRefCitation>
). Third, simple analyses, as of skull and metatarsal function (
<bibRefCitation id="EFAC4B6DEC2FFFCF53BFF8FAFB25F8B6" author="Bakker, R. T." box="[1000,1156,1871,1896]" journalOrPublisher="Gaia" pageId="2" pageNumber="437" pagination="145 - 158" part="15" refId="ref11029" refString="Bakker, R. T. 2000. Brontosaur killers: Late Jurassic allosaurids as sabretoothed cat analogues. Gaia 15: 145 - 158." title="Brontosaur killers: Late Jurassic allosaurids as sabretoothed cat analogues" type="journal article" year="2000">Bakker 2000</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC2FFFCF54C2F8FAFABDF8B6" author="Holtz, T. R. Jr." box="[1173,1308,1871,1896]" journalOrPublisher="Journal of Paleontology" pageId="2" pageNumber="437" pagination="1100 - 1117" part="68" refId="ref12090" refString="Holtz, T. R. Jr. 1994. The phylogenetic position of the Tyrannosauridae: implications for theropod systematics. Journal of Paleontology 68: 1100 - 1117." title="The phylogenetic position of the Tyrannosauridae: implications for theropod systematics" type="journal article" year="1994">Holtz 1994</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC2FFFCF5579F8FAFA68F8B6" author="Molnar, R. E." bookContentInfo="447 pp." box="[1326,1481,1871,1896]" journalOrPublisher="University of California, Los Angeles" pageId="2" pageNumber="437" refId="ref12615" refString="Molnar, R. E. 1973. The Cranial Morphology and Mechanics of Tyrannosaurus rex (Reptilia: Saurischia). 447 pp. PhD thesis, University of California, Los Angeles." title="The Cranial Morphology and Mechanics of Tyrannosaurus rex (Reptilia: Saurischia)" type="book" year="1973">Molnar 1973</bibRefCitation>
, 
<bibRefCitation id="EFAC4B6DEC2FFFCF537BF8C5FCC9F857" author="Molnar, R. E." box="[812,872,1904,1929]" journalOrPublisher="Gaia" pageId="2" pageNumber="437" pagination="193 - 218" part="15" refId="ref12650" refString="Molnar, R. E. 2000. Mechanical factors in the design of the cranium of Tyrannosaurus rex (Osborn 1905). Gaia 15: 193 - 218." title="Mechanical factors in the design of the cranium of Tyrannosaurus rex (Osborn 1905)" type="journal article" year="2000">2000</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC2FFFCF5322F8C5FB38F857" author="Snively, E. &amp; Russell, A. P." box="[885,1177,1904,1929]" journalOrPublisher="Journal of Morphology" pageId="2" pageNumber="437" pagination="215 - 227" part="255" refId="ref13075" refString="Snively, E. and Russell, A. P. 2003. A kinematic model of tyrannosaurid (Dinosauria, Theropoda) arctometatarsus function. Journal of Morphology 255: 215 - 227." title="A kinematic model of tyrannosaurid (Dinosauria, Theropoda) arctometatarsus function" type="journal article" year="2003">Snively and Russell 2003</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC2FFFCF54F1F8C5FA21F857" author="Snively, E. &amp; Russell, A. P. &amp; Powell, G. L." box="[1190,1408,1904,1929]" journalOrPublisher="Zoological Journal of the Linnean Society" pageId="2" pageNumber="437" pagination="525 - 553" part="142" refId="ref13110" refString="Snively, E., Russell, A. P., and Powell, G. L. 2004. Evolutionary morphology of the coelurosaurian arctometatarsus: descriptive, morphometric, and phylogenetic approaches. Zoological Journal of the Linnean Society 142: 525 - 553." title="Evolutionary morphology of the coelurosaurian arctometatarsus: descriptive, morphometric, and phylogenetic approaches" type="journal article" year="2004">Snively et al. 2004</bibRefCitation>
), yield rapid generation of results and hypotheses that are testable by more sophisticated means (
<bibRefCitation id="EFAC4B6DEC2FFFCF543CF804FAFDF814" author="Rayfield, E. J. &amp; Norman, D. B. &amp; Horner, C. C. &amp; Horner, J. R. &amp; May Smith, P. &amp; Thomason, J. J. &amp; Upchurch, P." box="[1131,1372,1969,1994]" journalOrPublisher="Nature" pageId="2" pageNumber="437" pagination="1033 - 1037" part="409" refId="ref12823" refString="Rayfield, E. J., Norman, D. B., Horner, C. C., Horner, J. R., May Smith, P., Thomason, J. J., and Upchurch, P. 2001. Cranial design and function in a large theropod dinosaur. Nature 409: 1033 - 1037." title="Cranial design and function in a large theropod dinosaur" type="journal article" year="2001">Rayfield et al. 2001</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC2FFFCF553AF804FCC6F834" author="Rayfield, E. J." journalOrPublisher="Proceedings of the Royal Society of London B" pageId="2" pageNumber="437" pagination="1451 - 1459" part="271" refId="ref12756" refString="Rayfield, E. J. 2004. Cranial mechanics and feeding in Tyrannosaurus rex. Proceedings of the Royal Society of London B 271: 1451 - 1459." title="Cranial mechanics and feeding in Tyrannosaurus rex" type="journal article" year="2004">Rayfield 2004</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC2FFFCF5325F864FB30F834" author="Snively, E. &amp; Russell, A. P." box="[882,1169,2001,2026]" journalOrPublisher="Senckenbergiana lethaea" pageId="2" pageNumber="437" pagination="35 - 42" part="82" refId="ref13043" refString="Snively, E. and Russell, A. P. 2002. The tyrannosaurid metatarsus: bone strain and inferred ligament function. Senckenbergiana lethaea 82: 35 - 42." title="The tyrannosaurid metatarsus: bone strain and inferred ligament function" type="journal article" year="2002">Snively and Russell 2002</bibRefCitation>
). Conversely, elaborate tests (
<bibRefCitation id="EFAC4B6DEC2EFFCE503AFF5DFEF2FEDF" author="Rayfield, E. J. &amp; Norman, D. B. &amp; Horner, C. C. &amp; Horner, J. R. &amp; May Smith, P. &amp; Thomason, J. J. &amp; Upchurch, P." box="[109,339,232,257]" journalOrPublisher="Nature" pageId="3" pageNumber="438" pagination="1033 - 1037" part="409" refId="ref12823" refString="Rayfield, E. J., Norman, D. B., Horner, C. C., Horner, J. R., May Smith, P., Thomason, J. J., and Upchurch, P. 2001. Cranial design and function in a large theropod dinosaur. Nature 409: 1033 - 1037." title="Cranial design and function in a large theropod dinosaur" type="journal article" year="2001">Rayfield et al. 2001</bibRefCitation>
) are subject to refinement of assumptions, whose effects are more easily testable with simplified methods (
<bibRefCitation id="EFAC4B6DEC2EFFCE5084FE9DFED8FE9F" author="Rayfield, E. J." box="[211,377,296,321]" journalOrPublisher="Proceedings of the Royal Society of London B" pageId="3" pageNumber="438" pagination="1451 - 1459" part="271" refId="ref12756" refString="Rayfield, E. J. 2004. Cranial mechanics and feeding in Tyrannosaurus rex. Proceedings of the Royal Society of London B 271: 1451 - 1459." title="Cranial mechanics and feeding in Tyrannosaurus rex" type="journal article" year="2004">Rayfield 2004</bibRefCitation>
).
</paragraph>
<paragraph id="8B82369CEC2EFFCE50DBFEFCFE07FD1C" blockId="3.[102,775,232,1187]" pageId="3" pageNumber="438">
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 (
<bibRefCitation id="EFAC4B6DEC2EFFCE5089FE1CFE21FE1C" author="Rayfield, E. J." box="[222,384,425,450]" journalOrPublisher="The Anatomical Record Part A" pageId="3" pageNumber="438" pagination="349 - 365" part="283" refId="ref12786" refString="Rayfield, E. J. 2005. Using finite element analysis to investigate suture morphology: a case study using large carnivorous dinosaurs. The Anatomical Record Part A 283 A: 349 - 365." title="Using finite element analysis to investigate suture morphology: a case study using large carnivorous dinosaurs" type="journal article" year="2005">Rayfield 2005</bibRefCitation>
) 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 (
<bibRefCitation id="EFAC4B6DEC2EFFCE523EFD9CFCA3FD9C" author="Molnar, R. E." box="[617,770,553,578]" journalOrPublisher="Gaia" pageId="3" pageNumber="438" pagination="193 - 218" part="15" refId="ref12650" refString="Molnar, R. E. 2000. Mechanical factors in the design of the cranium of Tyrannosaurus rex (Osborn 1905). Gaia 15: 193 - 218." title="Mechanical factors in the design of the cranium of Tyrannosaurus rex (Osborn 1905)" type="journal article" year="2000">Molnar 2000</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC2EFFCE5031FDFCFEF0FDBC" author="Rayfield, E. J. &amp; Norman, D. B. &amp; Horner, C. C. &amp; Horner, J. R. &amp; May Smith, P. &amp; Thomason, J. J. &amp; Upchurch, P." box="[102,337,585,610]" journalOrPublisher="Nature" pageId="3" pageNumber="438" pagination="1033 - 1037" part="409" refId="ref12823" refString="Rayfield, E. J., Norman, D. B., Horner, C. C., Horner, J. R., May Smith, P., Thomason, J. J., and Upchurch, P. 2001. Cranial design and function in a large theropod dinosaur. Nature 409: 1033 - 1037." title="Cranial design and function in a large theropod dinosaur" type="journal article" year="2001">Rayfield et al. 2001</bibRefCitation>
), stress concentrations will be similar overall in shell−like and lattice models (
<bibRefCitation id="EFAC4B6DEC2EFFCE5276FDDCFD1AFD5C" author="Gordon, J. E." bookContentInfo="395 pp." box="[545,699,617,642]" journalOrPublisher="Plenum Publishing, New York" pageId="3" pageNumber="438" refId="ref11840" refString="Gordon, J. E. 1978. Structures: Or Why Things Don't Fall Down. 395 pp. Plenum Publishing, New York." title="Structures: Or Why Things Don't Fall Down" type="book" year="1978">Gordon 1978</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC2EFFCE5290FDDCFF6EFD7C" author="Greaves, W. S." journalOrPublisher="Journal of Zoology, London" pageId="3" pageNumber="438" pagination="125 - 136" part="207" refId="ref11896" refString="Greaves, W. S. 1985. The mammalian postorbital bar as a torsion-resisting helical strut. Journal of Zoology, London 207: 125 - 136." title="The mammalian postorbital bar as a torsion-resisting helical strut" type="journal article" year="1985">Greaves 1985</bibRefCitation>
), and a shell−like model does not obscure relative strengths of theropod crania.
</paragraph>
<paragraph id="8B82369CEC2EFFCE50DBFD7EFD89FB7C" blockId="3.[102,775,232,1187]" pageId="3" pageNumber="438">
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 (
<bibRefCitation id="EFAC4B6DEC2EFFCE50FAFCFFFEC8FCBD" author="Henderson, D. M." box="[173,361,842,867]" journalOrPublisher="Journal of Vertebrate Paleontology" pageId="3" pageNumber="438" pagination="766 - 778" part="22" refId="ref12007" refString="Henderson, D. M. 2002. The eyes have it: the sizes, shapes, and orientations of theropod orbits as indicators of cranium strength and bite force. Journal of Vertebrate Paleontology 22: 766 - 778." title="The eyes have it: the sizes, shapes, and orientations of theropod orbits as indicators of cranium strength and bite force" type="journal article" year="2002">Henderson 2002</bibRefCitation>
), and larger and presumably stronger ligamentous joints for resisting tension along the ventral bor− der of the cranium (
<bibRefCitation id="EFAC4B6DEC2EFFCE511EFC3FFE4EFC7D" author="Rayfield, E. J." box="[329,495,906,931]" journalOrPublisher="Proceedings of the Royal Society of London B" pageId="3" pageNumber="438" pagination="1451 - 1459" part="271" refId="ref12756" refString="Rayfield, E. J. 2004. Cranial mechanics and feeding in Tyrannosaurus rex. Proceedings of the Royal Society of London B 271: 1451 - 1459." title="Cranial mechanics and feeding in Tyrannosaurus rex" type="journal article" year="2004">Rayfield 2004</bibRefCitation>
). The anterior secondary palate of tyrannosaurids (
<bibRefCitation id="EFAC4B6DEC2EFFCE5129FC1FFE5CFC1D" author="Holtz, T. R. Jr." box="[382,509,938,963]" editor="P. H. Kelly &amp; M. Koweleski &amp; T. A. Hansen" journalOrPublisher="Kluwer / Plenum, New York" pageId="3" pageNumber="438" pagination="325 - 340" part="17" refId="ref12157" refString="Holtz, T. R. Jr. 2002. Theropod predation: evidence and ecomorphology. In: P. H. Kelly, M. Koweleski, and T. A. Hansen (eds.), Predator-Prey Interactions in the Fossil Record. Topics in Geobiology 17, 325 - 340. Kluwer / Plenum, New York." title="Theropod predation: evidence and ecomorphology" type="journal article" volumeTitle="Predator-Prey Interactions in the Fossil Record. Topics in Geobiology" year="2002">Holtz 2002</bibRefCitation>
) 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: 
<bibRefCitation id="EFAC4B6DEC2EFFCE5271FBBFFF6EFB9D" author="Thomason, J. J. &amp; Russell, A. P." journalOrPublisher="Journal of Morphology" pageId="3" pageNumber="438" pagination="199 - 213" part="189" refId="ref13266" refString="Thomason, J. J. and Russell, A. P. 1986. Mechanical factors in the evolution of the mammalian secondary palate. Journal of Morphology 189: 199 - 213." title="Mechanical factors in the evolution of the mammalian secondary palate" type="journal article" year="1986">Thomason and Russell 1986</bibRefCitation>
; 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.
</paragraph>
<paragraph id="8B82369CEC2EFFCE537BFF5DFA08FC96" blockId="3.[812,1486,232,840]" pageId="3" pageNumber="438">
<emphasis id="B949EA8EEC2EFFCE537BFF5DFBEEFEDE" box="[812,1103,232,256]" italics="true" pageId="3" pageNumber="438">Institutional abbreviations</emphasis>
.—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.
</paragraph>
<paragraph id="8B82369CEC2EFFCE537BFC22FA00FC1F" blockId="3.[812,1441,919,961]" box="[812,1441,919,961]" pageId="3" pageNumber="438">Strengths of large theropod teeth</paragraph>
<paragraph id="8B82369CEC2EFFCE537BFC5CFA6CFBDC" blockId="3.[812,1485,1001,1187]" box="[812,1485,1001,1026]" pageId="3" pageNumber="438">
<heading id="D0CA81F0EC2EFFCE537BFC5CFA6CFBDC" bold="true" box="[812,1485,1001,1026]" centered="true" fontSize="10" level="3" pageId="3" pageNumber="438" reason="0">
<emphasis id="B949EA8EEC2EFFCE537BFC5CFA6CFBDC" bold="true" box="[812,1485,1001,1026]" pageId="3" pageNumber="438">Materials and methods for testing tooth strength of large</emphasis>
</heading>
</paragraph>
<paragraph id="8B82369CEC2EFFC9537BFBBFFE81FEBF" blockId="3.[812,1485,1001,1187]" lastBlockId="4.[102,687,232,2026]" lastPageId="4" lastPageNumber="439" pageId="3" pageNumber="438">
<emphasis id="B949EA8EEC2EFFCE537BFBBFFC00FBFC" bold="true" box="[812,929,1034,1058]" pageId="3" pageNumber="438">theropods</emphasis>
.—We measured 
<emphasis id="B949EA8EEC2EFFCE543CFBBEFB12FBFC" box="[1131,1203,1035,1058]" italics="true" pageId="3" pageNumber="438">in situ</emphasis>
maxillary teeth of large theropods (
<tableCitation id="C6BF0327EC2EFFCE53F0FB9FFC5CFB9D" box="[935,1021,1066,1091]" captionStart="Table 1" captionStartId="3.[102,157,1231,1252]" captionTargetId="graphics@3.[102,1485,1359,2021]" captionTargetPageId="3" captionText="Table 1. Measured and computed properties of theropod maxillary teeth. N, number of teeth measured; CH, average crown height; FABL, average fore, aft basal length; MLBL, averge medolateral basal length; AP str., average anteroposterior bending strength indicator; ML str., mediolateral bending strength indicator; Skull l., skull length. Raw measurements of CH, FABL, and MLBL, not these averages, were used to calculate strength indicators." httpUri="http://table.plazi.org/id/DF426614EC2EFFCE5031FB7AFF6AFAE2" pageId="3" pageNumber="438" tableUuid="DF426614EC2EFFCE5031FB7AFF6AFAE2">Table 1</tableCitation>
, 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 
<taxonomicName id="4C3D4D1FEC29FFC95167FEBDFDCDFEFE" authorityName="Stovall &amp; Langston" authorityYear="1950" box="[304,620,264,288]" class="Reptilia" family="Carcharodontosauridae" genus="Acrocanthosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="439" phylum="Chordata" rank="species" species="atokensis">
<emphasis id="B949EA8EEC29FFC95167FEBDFDCDFEFE" box="[304,620,264,288]" italics="true" pageId="4" pageNumber="439">Acrocanthosaurus atokensis</emphasis>
</taxonomicName>
were obtained from the literature (
<bibRefCitation id="EFAC4B6DEC29FFC951F3FE9DFD8DFE9F" author="Harris, J. D." box="[420,556,296,321]" journalOrPublisher="New Mexico Museum of Nature and Science Bulletin" pageId="4" pageNumber="439" pagination="1 - 75" part="13" refId="ref11963" refString="Harris, J. D. 1998. A reanalysis of Acrocanthosaurus atokensis, its phylogenetic status, and paleobiogeographic implications, based on a new specimen from Texas. New Mexico Museum of Nature and Science Bulletin 13: 1 - 75." title="A reanalysis of Acrocanthosaurus atokensis, its phylogenetic status, and paleobiogeographic implications, based on a new specimen from Texas" type="journal article" year="1998">Harris 1998</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC29FFC9526EFE9DFEB4FEBF" author="Currie, P. J. &amp; Carpenter K." journalOrPublisher="Geodiversitas" pageId="4" pageNumber="439" pagination="207 - 246" part="22" refId="ref11425" refString="Currie, P. J. and Carpenter K. 2000. A new specimen of Acrocanthrosaurus atokensis (Theropoda, Dinosauria) from the Lower Cretaceous Antlers Formation (Lower Cretaceous, Aptian) of Oklahoma, USA. Geodiversitas 22: 207 - 246." title="A new specimen of Acrocanthrosaurus atokensis (Theropoda, Dinosauria) from the Lower Cretaceous Antlers Formation (Lower Cretaceous, Aptian) of Oklahoma, USA" type="journal article" year="2000">Currie and Carpenter 2000</bibRefCitation>
).
</paragraph>
<caption id="DF426614EC2EFFCE5031FB7AFF6AFAE2" ID-Table-UUID="DF426614EC2EFFCE5031FB7AFF6AFAE2" httpUri="http://table.plazi.org/id/DF426614EC2EFFCE5031FB7AFF6AFAE2" pageId="3" pageNumber="438" startId="3.[102,157,1231,1252]" targetBox="[110,1450,1370,2018]" targetIsTable="true" targetPageId="3">
<paragraph id="8B82369CEC2EFFCE5031FB7AFF6AFAE2" blockId="3.[102,1485,1231,1340]" pageId="3" pageNumber="438">Table 1. Measured and computed properties of theropod maxillary teeth. N, number of teeth measured; CH, average crown height; FABL, average fore, aft basal length; MLBL, averge medolateral basal length; AP str., average anteroposterior bending strength indicator; ML str., mediolateral bending strength indicator; Skull l., skull length. Raw measurements of CH, FABL, and MLBL, not these averages, were used to calculate strength indicators.</paragraph>
</caption>
<paragraph id="8B82369CEC2EFFCE5210FADFFA3CF83F" pageId="3" pageNumber="438">
<table id="F93DC43CEC2E00325039FAEFFA0BF83C" box="[110,1450,1370,2018]" gridcols="8" gridrows="18" pageId="3" pageNumber="438">
<tr id="350D34DEEC2E00325039FAEFFA0BFA51" box="[110,1450,1370,1423]" gridrow="0" pageId="3" pageNumber="438" rowspan-0="1">
<th id="76DC5DA2EC2E00325214FAEFFDFAFA51" box="[579,603,1370,1423]" gridcol="1" gridrow="0" pageId="3" pageNumber="438">N</th>
<th id="76DC5DA2EC2E003252E9FAEFFD55FA51" box="[702,756,1370,1423]" gridcol="2" gridrow="0" pageId="3" pageNumber="438">CH (mm)</th>
<th id="76DC5DA2EC2E00325314FAEFFC21FA51" box="[835,896,1370,1423]" gridcol="3" gridrow="0" pageId="3" pageNumber="438">FABL (mm)</th>
<th id="76DC5DA2EC2E0032539DFAEFFBACFA51" box="[970,1037,1370,1423]" gridcol="4" gridrow="0" pageId="3" pageNumber="438">MLBL (mm)</th>
<th id="76DC5DA2EC2E00325403FAEFFB36FA51" box="[1108,1175,1370,1423]" gridcol="5" gridrow="0" pageId="3" pageNumber="438">AP str. m3</th>
<th id="76DC5DA2EC2E0032548DFAEFFA82FA51" box="[1242,1315,1370,1423]" gridcol="6" gridrow="0" pageId="3" pageNumber="438">ML str. m3</th>
<th id="76DC5DA2EC2E00325532FAEFFA0BFA51" box="[1381,1450,1370,1423]" gridcol="7" gridrow="0" pageId="3" pageNumber="438">Skull l. cm</th>
</tr>
<tr id="350D34DEEC2E00325039FA28FA0BFA6C" box="[110,1450,1437,1458]" gridrow="1" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039FA28FA0BFA6C" box="[110,1450,1437,1458]" colspan="8" colspanRight="7" gridcol="0" gridrow="1" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039FA28FEAEFA6C" box="[110,271,1437,1458]" class="Reptilia" family="Tyrannosauridae" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="family">Tyrannosauridae</taxonomicName>
</th>
</tr>
<tr id="350D34DEEC2E00325039FA75FA0BFA08" box="[110,1450,1472,1494]" gridrow="2" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039FA75FE0EFA08" box="[110,431,1472,1494]" gridcol="0" gridrow="2" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039FA74FE06FA0B" authority="(As)" baseAuthorityName="As" box="[110,423,1472,1494]" class="Reptilia" family="Tyrannosauridae" genus="Albertosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="species" species="sarcophagus">
<emphasis id="B949EA8EEC2EFFCE5039FA74FED6FA08" box="[110,375,1473,1494]" italics="true" pageId="3" pageNumber="438">Albertosaurus sarcophagus</emphasis>
(As)
</taxonomicName>
</th>
<td id="76DC5DA2EC2E00325214FA75FDFAFA08" box="[579,603,1472,1494]" gridcol="1" gridrow="2" pageId="3" pageNumber="438">7</td>
<td id="76DC5DA2EC2E003252E9FA75FD55FA08" box="[702,756,1472,1494]" gridcol="2" gridrow="2" pageId="3" pageNumber="438">70</td>
<td id="76DC5DA2EC2E00325314FA75FC21FA08" box="[835,896,1472,1494]" gridcol="3" gridrow="2" pageId="3" pageNumber="438">29.9</td>
<td id="76DC5DA2EC2E0032539DFA75FBACFA08" box="[970,1037,1472,1494]" gridcol="4" gridrow="2" pageId="3" pageNumber="438">17</td>
<td id="76DC5DA2EC2E00325403FA75FB36FA08" box="[1108,1175,1472,1494]" gridcol="5" gridrow="2" pageId="3" pageNumber="438">0.214</td>
<td id="76DC5DA2EC2E0032548DFA75FA82FA08" box="[1242,1315,1472,1494]" gridcol="6" gridrow="2" pageId="3" pageNumber="438">0.122</td>
<td id="76DC5DA2EC2E00325532FA75FA0BFA08" box="[1381,1450,1472,1494]" gridcol="7" gridrow="2" pageId="3" pageNumber="438">86.0</td>
</tr>
<tr id="350D34DEEC2E00325039FA56FA0BFA27" box="[110,1450,1507,1529]" gridrow="3" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039FA56FE0EFA27" box="[110,431,1507,1529]" gridcol="0" gridrow="3" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039FA51FEF3FA27" authorityName="Russell" authorityYear="1970" box="[110,338,1508,1529]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC2EFFCE5039FA51FEF3FA27" box="[110,338,1508,1529]" italics="true" pageId="3" pageNumber="438">Daspletosaurus torosus</emphasis>
</taxonomicName>
(DtS)
</th>
<td id="76DC5DA2EC2E00325214FA56FDFAFA27" box="[579,603,1507,1529]" gridcol="1" gridrow="3" pageId="3" pageNumber="438">9</td>
<td id="76DC5DA2EC2E003252E9FA56FD55FA27" box="[702,756,1507,1529]" gridcol="2" gridrow="3" pageId="3" pageNumber="438">37.9</td>
<td id="76DC5DA2EC2E00325314FA56FC21FA27" box="[835,896,1507,1529]" gridcol="3" gridrow="3" pageId="3" pageNumber="438">16.8</td>
<td id="76DC5DA2EC2E0032539DFA56FBACFA27" box="[970,1037,1507,1529]" gridcol="4" gridrow="3" pageId="3" pageNumber="438">11.1</td>
<td id="76DC5DA2EC2E00325403FA56FB36FA27" box="[1108,1175,1507,1529]" gridcol="5" gridrow="3" pageId="3" pageNumber="438">0.086</td>
<td id="76DC5DA2EC2E0032548DFA56FA82FA27" box="[1242,1315,1507,1529]" gridcol="6" gridrow="3" pageId="3" pageNumber="438">0.055</td>
<td id="76DC5DA2EC2E00325532FA56FA0BFA27" box="[1381,1450,1507,1529]" gridcol="7" gridrow="3" pageId="3" pageNumber="438">57.3</td>
</tr>
<tr id="350D34DEEC2E00325039F9B3FA0BF9C5" box="[110,1450,1542,1563]" gridrow="4" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039F9B3FE0EF9C5" box="[110,431,1542,1563]" gridcol="0" gridrow="4" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039F9B3FEF3F9C5" authorityName="Russell" authorityYear="1970" box="[110,338,1542,1563]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC2EFFCE5039F9B3FEF3F9C5" box="[110,338,1542,1563]" italics="true" pageId="3" pageNumber="438">Daspletosaurus torosus</emphasis>
</taxonomicName>
(DtL)
</th>
<td id="76DC5DA2EC2E00325214F9B3FDFAF9C5" box="[579,603,1542,1563]" gridcol="1" gridrow="4" pageId="3" pageNumber="438">6</td>
<td id="76DC5DA2EC2E003252E9F9B3FD55F9C5" box="[702,756,1542,1563]" gridcol="2" gridrow="4" pageId="3" pageNumber="438">72.5</td>
<td id="76DC5DA2EC2E00325314F9B3FC21F9C5" box="[835,896,1542,1563]" gridcol="3" gridrow="4" pageId="3" pageNumber="438">27.3</td>
<td id="76DC5DA2EC2E0032539DF9B3FBACF9C5" box="[970,1037,1542,1563]" gridcol="4" gridrow="4" pageId="3" pageNumber="438">19.7</td>
<td id="76DC5DA2EC2E00325403F9B3FB36F9C5" box="[1108,1175,1542,1563]" gridcol="5" gridrow="4" pageId="3" pageNumber="438">0.202</td>
<td id="76DC5DA2EC2E0032548DF9B3FA82F9C5" box="[1242,1315,1542,1563]" gridcol="6" gridrow="4" pageId="3" pageNumber="438">0.144</td>
<td id="76DC5DA2EC2E00325532F9B3FA0BF9C5" box="[1381,1450,1542,1563]" gridcol="7" gridrow="4" pageId="3" pageNumber="438">97.0</td>
</tr>
<tr id="350D34DEEC2E00325039F99CFA0BF9E0" box="[110,1450,1577,1598]" gridrow="5" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039F99CFE0EF9E0" box="[110,431,1577,1598]" gridcol="0" gridrow="5" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039F99CFECAF9E0" authority="(Gl)" baseAuthorityName="Gl" box="[110,363,1577,1598]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC2EFFCE5039F99CFE9FF9E0" box="[110,318,1577,1598]" italics="true" pageId="3" pageNumber="438">Gorgosaurus libratus</emphasis>
(Gl)
</taxonomicName>
</th>
<td id="76DC5DA2EC2E00325214F99CFDFAF9E0" box="[579,603,1577,1598]" gridcol="1" gridrow="5" pageId="3" pageNumber="438">13</td>
<td id="76DC5DA2EC2E003252E9F99CFD55F9E0" box="[702,756,1577,1598]" gridcol="2" gridrow="5" pageId="3" pageNumber="438">54.8</td>
<td id="76DC5DA2EC2E00325314F99CFC21F9E0" box="[835,896,1577,1598]" gridcol="3" gridrow="5" pageId="3" pageNumber="438">22.90</td>
<td id="76DC5DA2EC2E0032539DF99CFBACF9E0" box="[970,1037,1577,1598]" gridcol="4" gridrow="5" pageId="3" pageNumber="438">12.90</td>
<td id="76DC5DA2EC2E00325403F99CFB36F9E0" box="[1108,1175,1577,1598]" gridcol="5" gridrow="5" pageId="3" pageNumber="438">0.12</td>
<td id="76DC5DA2EC2E0032548DF99CFA82F9E0" box="[1242,1315,1577,1598]" gridcol="6" gridrow="5" pageId="3" pageNumber="438">0.213</td>
<td id="76DC5DA2EC2E00325532F99CFA0BF9E0" box="[1381,1450,1577,1598]" gridcol="7" gridrow="5" pageId="3" pageNumber="438">75.0</td>
</tr>
<tr id="350D34DEEC2E00325039F9F9FA0BF9BF" box="[110,1450,1612,1633]" gridrow="6" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039F9F9FE0EF9BF" box="[110,431,1612,1633]" gridcol="0" gridrow="6" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039F9F9FE9FF9BF" authority="Lambe, 1914" box="[110,318,1612,1633]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC2EFFCE5039F9F9FE9FF9BF" box="[110,318,1612,1633]" italics="true" pageId="3" pageNumber="438">Gorgosaurus libratus</emphasis>
</taxonomicName>
(GlL)
</th>
<td id="76DC5DA2EC2E00325214F9F9FDFAF9BF" box="[579,603,1612,1633]" gridcol="1" gridrow="6" pageId="3" pageNumber="438">11</td>
<td id="76DC5DA2EC2E003252E9F9F9FD55F9BF" box="[702,756,1612,1633]" gridcol="2" gridrow="6" pageId="3" pageNumber="438">57.1</td>
<td id="76DC5DA2EC2E00325314F9F9FC21F9BF" box="[835,896,1612,1633]" gridcol="3" gridrow="6" pageId="3" pageNumber="438">23.13</td>
<td id="76DC5DA2EC2E0032539DF9F9FBACF9BF" box="[970,1037,1612,1633]" gridcol="4" gridrow="6" pageId="3" pageNumber="438">22.6</td>
<td id="76DC5DA2EC2E00325403F9F9FB36F9BF" box="[1108,1175,1612,1633]" gridcol="5" gridrow="6" pageId="3" pageNumber="438">0.127</td>
<td id="76DC5DA2EC2E0032548DF9F9FA82F9BF" box="[1242,1315,1612,1633]" gridcol="6" gridrow="6" pageId="3" pageNumber="438">0.088</td>
<td id="76DC5DA2EC2E00325532F9F9FA0BF9BF" box="[1381,1450,1612,1633]" gridcol="7" gridrow="6" pageId="3" pageNumber="438">76.0</td>
</tr>
<tr id="350D34DEEC2E00325039F9DAFA0BF95A" box="[110,1450,1647,1668]" gridrow="7" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039F9DAFE0EF95A" box="[110,431,1647,1668]" gridcol="0" gridrow="7" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039F9DAFE85F95A" authorityName="Osborn" authorityYear="1905" box="[110,292,1647,1668]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC2EFFCE5039F9DAFE85F95A" box="[110,292,1647,1668]" italics="true" pageId="3" pageNumber="438">Tyrannosaurus rex</emphasis>
</taxonomicName>
(TrA)
</th>
<td id="76DC5DA2EC2E00325214F9DAFDFAF95A" box="[579,603,1647,1668]" gridcol="1" gridrow="7" pageId="3" pageNumber="438">10</td>
<td id="76DC5DA2EC2E003252E9F9DAFD55F95A" box="[702,756,1647,1668]" gridcol="2" gridrow="7" pageId="3" pageNumber="438">101.6</td>
<td id="76DC5DA2EC2E00325314F9DAFC21F95A" box="[835,896,1647,1668]" gridcol="3" gridrow="7" pageId="3" pageNumber="438">37.0</td>
<td id="76DC5DA2EC2E0032539DF9DAFBACF95A" box="[970,1037,1647,1668]" gridcol="4" gridrow="7" pageId="3" pageNumber="438">28.20</td>
<td id="76DC5DA2EC2E00325403F9DAFB36F95A" box="[1108,1175,1647,1668]" gridcol="5" gridrow="7" pageId="3" pageNumber="438">0.471</td>
<td id="76DC5DA2EC2E0032548DF9DAFA82F95A" box="[1242,1315,1647,1668]" gridcol="6" gridrow="7" pageId="3" pageNumber="438">0.630</td>
<td id="76DC5DA2EC2E00325532F9DAFA0BF95A" box="[1381,1450,1647,1668]" gridcol="7" gridrow="7" pageId="3" pageNumber="438">119.0</td>
</tr>
<tr id="350D34DEEC2E00325039F927FA0BF979" box="[110,1450,1682,1703]" gridrow="8" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039F927FE0EF979" box="[110,431,1682,1703]" gridcol="0" gridrow="8" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039F927FE85F979" authorityName="Osborn" authorityYear="1905" box="[110,292,1682,1703]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC2EFFCE5039F927FE85F979" box="[110,292,1682,1703]" italics="true" pageId="3" pageNumber="438">Tyrannosaurus rex</emphasis>
</taxonomicName>
(TrB)
</th>
<td id="76DC5DA2EC2E00325214F927FDFAF979" box="[579,603,1682,1703]" gridcol="1" gridrow="8" pageId="3" pageNumber="438">11</td>
<td id="76DC5DA2EC2E003252E9F927FD55F979" box="[702,756,1682,1703]" gridcol="2" gridrow="8" pageId="3" pageNumber="438">98.4</td>
<td id="76DC5DA2EC2E00325314F927FC21F979" box="[835,896,1682,1703]" gridcol="3" gridrow="8" pageId="3" pageNumber="438">45.0</td>
<td id="76DC5DA2EC2E0032539DF927FBACF979" box="[970,1037,1682,1703]" gridcol="4" gridrow="8" pageId="3" pageNumber="438">33.50</td>
<td id="76DC5DA2EC2E00325403F927FB36F979" box="[1108,1175,1682,1703]" gridcol="5" gridrow="8" pageId="3" pageNumber="438">0.864</td>
<td id="76DC5DA2EC2E0032548DF927FA82F979" box="[1242,1315,1682,1703]" gridcol="6" gridrow="8" pageId="3" pageNumber="438">1.154</td>
<td id="76DC5DA2EC2E00325532F927FA0BF979" box="[1381,1450,1682,1703]" gridcol="7" gridrow="8" pageId="3" pageNumber="438">140.0</td>
</tr>
<tr id="350D34DEEC2E00325039F900FA0BF914" box="[110,1450,1717,1738]" gridrow="9" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039F900FE0EF914" box="[110,431,1717,1738]" gridcol="0" gridrow="9" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039F900FE85F914" authorityName="Osborn" authorityYear="1905" box="[110,292,1717,1738]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC2EFFCE5039F900FE85F914" box="[110,292,1717,1738]" italics="true" pageId="3" pageNumber="438">Tyrannosaurus rex</emphasis>
</taxonomicName>
(TrL)
</th>
<td id="76DC5DA2EC2E00325214F900FDFAF914" box="[579,603,1717,1738]" gridcol="1" gridrow="9" pageId="3" pageNumber="438">9</td>
<td id="76DC5DA2EC2E003252E9F900FD55F914" box="[702,756,1717,1738]" gridcol="2" gridrow="9" pageId="3" pageNumber="438">78.6</td>
<td id="76DC5DA2EC2E00325314F900FC21F914" box="[835,896,1717,1738]" gridcol="3" gridrow="9" pageId="3" pageNumber="438">41.4</td>
<td id="76DC5DA2EC2E0032539DF900FBACF914" box="[970,1037,1717,1738]" gridcol="4" gridrow="9" pageId="3" pageNumber="438">25.70</td>
<td id="76DC5DA2EC2E00325403F900FB36F914" box="[1108,1175,1717,1738]" gridcol="5" gridrow="9" pageId="3" pageNumber="438">0.659</td>
<td id="76DC5DA2EC2E0032548DF900FA82F914" box="[1242,1315,1717,1738]" gridcol="6" gridrow="9" pageId="3" pageNumber="438">1.042</td>
<td id="76DC5DA2EC2E00325532F900FA0BF914" box="[1381,1450,1717,1738]" gridcol="7" gridrow="9" pageId="3" pageNumber="438">122.0</td>
</tr>
<tr id="350D34DEEC2E00325039F96DFA0BF933" box="[110,1450,1752,1773]" gridrow="10" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039F96DFE0EF933" box="[110,431,1752,1773]" gridcol="0" gridrow="10" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039F96DFE85F933" authorityName="Osborn" authorityYear="1905" box="[110,292,1752,1773]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC2EFFCE5039F96DFE85F933" box="[110,292,1752,1773]" italics="true" pageId="3" pageNumber="438">Tyrannosaurus rex</emphasis>
</taxonomicName>
juv. (TrJ)
</th>
<td id="76DC5DA2EC2E00325214F96DFDFAF933" box="[579,603,1752,1773]" gridcol="1" gridrow="10" pageId="3" pageNumber="438">11</td>
<td id="76DC5DA2EC2E003252E9F96DFD55F933" box="[702,756,1752,1773]" gridcol="2" gridrow="10" pageId="3" pageNumber="438">45.5</td>
<td id="76DC5DA2EC2E00325314F96DFC21F933" box="[835,896,1752,1773]" gridcol="3" gridrow="10" pageId="3" pageNumber="438">22.6</td>
<td id="76DC5DA2EC2E0032539DF96DFBACF933" box="[970,1037,1752,1773]" gridcol="4" gridrow="10" pageId="3" pageNumber="438">11.20</td>
<td id="76DC5DA2EC2E00325403F96DFB36F933" box="[1108,1175,1752,1773]" gridcol="5" gridrow="10" pageId="3" pageNumber="438">0.131</td>
<td id="76DC5DA2EC2E0032548DF96DFA82F933" box="[1242,1315,1752,1773]" gridcol="6" gridrow="10" pageId="3" pageNumber="438">0.065</td>
<td id="76DC5DA2EC2E00325532F96DFA0BF933" box="[1381,1450,1752,1773]" gridcol="7" gridrow="10" pageId="3" pageNumber="438">74.0</td>
</tr>
<tr id="350D34DEEC2E00325039F94EFA0BF8CE" box="[110,1450,1787,1808]" gridrow="11" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039F94EFA0BF8CE" box="[110,1450,1787,1808]" colspan="8" colspanRight="7" gridcol="0" gridrow="11" pageId="3" pageNumber="438">Non−tyrannosaurids</th>
</tr>
<tr id="350D34DEEC2E00325039F8ABFA0BF8ED" box="[110,1450,1822,1843]" gridrow="12" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039F8ABFE0EF8ED" box="[110,431,1822,1843]" gridcol="0" gridrow="12" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039F8ABFE0EF8ED" authority="(Aa)" authorityName="Stovall &amp; Langston" authorityYear="1950" baseAuthorityName="Aa" box="[110,431,1822,1843]" class="Reptilia" family="Carcharodontosauridae" genus="Acrocanthosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="species" species="atokensis">
<emphasis id="B949EA8EEC2EFFCE5039F8ABFEDCF8ED" box="[110,381,1822,1843]" italics="true" pageId="3" pageNumber="438">Acrocanthosaurus atokensis</emphasis>
(Aa)
</taxonomicName>
</th>
<td id="76DC5DA2EC2E00325214F8ABFDFAF8ED" box="[579,603,1822,1843]" gridcol="1" gridrow="12" pageId="3" pageNumber="438">1</td>
<td id="76DC5DA2EC2E003252E9F8ABFD55F8ED" box="[702,756,1822,1843]" gridcol="2" gridrow="12" pageId="3" pageNumber="438">84.0</td>
<td id="76DC5DA2EC2E00325314F8ABFC21F8ED" box="[835,896,1822,1843]" gridcol="3" gridrow="12" pageId="3" pageNumber="438">31.0</td>
<td id="76DC5DA2EC2E0032539DF8ABFBACF8ED" box="[970,1037,1822,1843]" gridcol="4" gridrow="12" pageId="3" pageNumber="438">19.5</td>
<td id="76DC5DA2EC2E00325403F8ABFB36F8ED" box="[1108,1175,1822,1843]" gridcol="5" gridrow="12" pageId="3" pageNumber="438">0.492</td>
<td id="76DC5DA2EC2E0032548DF8ABFA82F8ED" box="[1242,1315,1822,1843]" gridcol="6" gridrow="12" pageId="3" pageNumber="438">0.310</td>
<td id="76DC5DA2EC2E00325532F8ABFA0BF8ED" box="[1381,1450,1822,1843]" gridcol="7" gridrow="12" pageId="3" pageNumber="438">105.0</td>
</tr>
<tr id="350D34DEEC2E00325039F8F4FA0BF888" box="[110,1450,1857,1878]" gridrow="13" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039F8F4FE0EF888" box="[110,431,1857,1878]" gridcol="0" gridrow="13" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039F8F4FEF0F888" authority="(Af)" authorityName="Marsh" authorityYear="1877" baseAuthorityName="Af" box="[110,337,1857,1878]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC2EFFCE5039F8F4FE80F888" box="[110,289,1857,1878]" italics="true" pageId="3" pageNumber="438">Allosaurus fragilis</emphasis>
(Af)
</taxonomicName>
</th>
<td id="76DC5DA2EC2E00325214F8F4FDFAF888" box="[579,603,1857,1878]" gridcol="1" gridrow="13" pageId="3" pageNumber="438">14</td>
<td id="76DC5DA2EC2E003252E9F8F4FD55F888" box="[702,756,1857,1878]" gridcol="2" gridrow="13" pageId="3" pageNumber="438">44.3</td>
<td id="76DC5DA2EC2E00325314F8F4FC21F888" box="[835,896,1857,1878]" gridcol="3" gridrow="13" pageId="3" pageNumber="438">18.40</td>
<td id="76DC5DA2EC2E0032539DF8F4FBACF888" box="[970,1037,1857,1878]" gridcol="4" gridrow="13" pageId="3" pageNumber="438">12.70</td>
<td id="76DC5DA2EC2E00325403F8F4FB36F888" box="[1108,1175,1857,1878]" gridcol="5" gridrow="13" pageId="3" pageNumber="438">0.121</td>
<td id="76DC5DA2EC2E0032548DF8F4FA82F888" box="[1242,1315,1857,1878]" gridcol="6" gridrow="13" pageId="3" pageNumber="438">0.176</td>
<td id="76DC5DA2EC2E00325532F8F4FA0BF888" box="[1381,1450,1857,1878]" gridcol="7" gridrow="13" pageId="3" pageNumber="438">76.0</td>
</tr>
<tr id="350D34DEEC2E00325039F8D1FA0BF8A7" box="[110,1450,1892,1913]" gridrow="14" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039F8D1FE0EF8A7" box="[110,431,1892,1913]" gridcol="0" gridrow="14" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039F8D1FEFCF8A7" authority="(Cs)" authorityName="Bonaparte" authorityYear="1985" baseAuthorityName="Cs" box="[110,349,1892,1913]" class="Reptilia" family="Abelisauridae" genus="Carnotaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="species" species="sastrei">
<emphasis id="B949EA8EEC2EFFCE5039F8D1FE8EF8A7" box="[110,303,1892,1913]" italics="true" pageId="3" pageNumber="438">Carnotaurus sastrei</emphasis>
(Cs)
</taxonomicName>
</th>
<td id="76DC5DA2EC2E00325214F8D1FDFAF8A7" box="[579,603,1892,1913]" gridcol="1" gridrow="14" pageId="3" pageNumber="438">12</td>
<td id="76DC5DA2EC2E003252E9F8D1FD55F8A7" box="[702,756,1892,1913]" gridcol="2" gridrow="14" pageId="3" pageNumber="438">47.5</td>
<td id="76DC5DA2EC2E00325314F8D1FC21F8A7" box="[835,896,1892,1913]" gridcol="3" gridrow="14" pageId="3" pageNumber="438">22.60</td>
<td id="76DC5DA2EC2E0032539DF8D1FBACF8A7" box="[970,1037,1892,1913]" gridcol="4" gridrow="14" pageId="3" pageNumber="438">15.70</td>
<td id="76DC5DA2EC2E00325403F8D1FB36F8A7" box="[1108,1175,1892,1913]" gridcol="5" gridrow="14" pageId="3" pageNumber="438">0.211</td>
<td id="76DC5DA2EC2E0032548DF8D1FA82F8A7" box="[1242,1315,1892,1913]" gridcol="6" gridrow="14" pageId="3" pageNumber="438">0.310</td>
<td id="76DC5DA2EC2E00325532F8D1FA0BF8A7" box="[1381,1450,1892,1913]" gridcol="7" gridrow="14" pageId="3" pageNumber="438">56.0</td>
</tr>
<tr id="350D34DEEC2E00325039F833FA0BF842" box="[110,1450,1926,1948]" gridrow="15" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039F833FE0EF842" box="[110,431,1926,1948]" gridcol="0" gridrow="15" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039F832FE06F845" authority="(Cd)" baseAuthorityName="Cd" box="[110,423,1926,1948]" class="Reptilia" family="Ceratosauridae" genus="Ceratosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="species" species="dentisulcatus">
<emphasis id="B949EA8EEC2EFFCE5039F832FED7F842" box="[110,374,1927,1948]" italics="true" pageId="3" pageNumber="438">Ceratosaurus dentisulcatus</emphasis>
(Cd)
</taxonomicName>
</th>
<td id="76DC5DA2EC2E00325214F833FDFAF842" box="[579,603,1926,1948]" gridcol="1" gridrow="15" pageId="3" pageNumber="438">10</td>
<td id="76DC5DA2EC2E003252E9F833FD55F842" box="[702,756,1926,1948]" gridcol="2" gridrow="15" pageId="3" pageNumber="438">62.9</td>
<td id="76DC5DA2EC2E00325314F833FC21F842" box="[835,896,1926,1948]" gridcol="3" gridrow="15" pageId="3" pageNumber="438">26.10</td>
<td id="76DC5DA2EC2E0032539DF833FBACF842" box="[970,1037,1926,1948]" gridcol="4" gridrow="15" pageId="3" pageNumber="438">10.60</td>
<td id="76DC5DA2EC2E00325403F833FB36F842" box="[1108,1175,1926,1948]" gridcol="5" gridrow="15" pageId="3" pageNumber="438">0.079</td>
<td id="76DC5DA2EC2E0032548DF833FA82F842" box="[1242,1315,1926,1948]" gridcol="6" gridrow="15" pageId="3" pageNumber="438">0.193</td>
<td id="76DC5DA2EC2E00325532F833FA0BF842" box="[1381,1450,1926,1948]" gridcol="7" gridrow="15" pageId="3" pageNumber="438">63.0</td>
</tr>
<tr id="350D34DEEC2E00325039F81CFA0BF861" box="[110,1450,1961,1983]" gridrow="16" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039F81CFE0EF861" box="[110,431,1961,1983]" gridcol="0" gridrow="16" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039F81FFE2CF860" authority="(Mj)" baseAuthorityName="Mj" box="[110,397,1961,1983]" class="Reptilia" family="Ceratosauridae" genus="Monolophosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="species" species="jiangi">
<emphasis id="B949EA8EEC2EFFCE5039F81FFEFAF861" box="[110,347,1962,1983]" italics="true" pageId="3" pageNumber="438">Monolophosaurus jiangi</emphasis>
(Mj)
</taxonomicName>
</th>
<td id="76DC5DA2EC2E00325214F81CFDFAF861" box="[579,603,1961,1983]" gridcol="1" gridrow="16" pageId="3" pageNumber="438">13</td>
<td id="76DC5DA2EC2E003252E9F81CFD55F861" box="[702,756,1961,1983]" gridcol="2" gridrow="16" pageId="3" pageNumber="438">39.8</td>
<td id="76DC5DA2EC2E00325314F81CFC21F861" box="[835,896,1961,1983]" gridcol="3" gridrow="16" pageId="3" pageNumber="438">19.80</td>
<td id="76DC5DA2EC2E0032539DF81CFBACF861" box="[970,1037,1961,1983]" gridcol="4" gridrow="16" pageId="3" pageNumber="438">11.00</td>
<td id="76DC5DA2EC2E00325403F81CFB36F861" box="[1108,1175,1961,1983]" gridcol="5" gridrow="16" pageId="3" pageNumber="438">0.103</td>
<td id="76DC5DA2EC2E0032548DF81CFA82F861" box="[1242,1315,1961,1983]" gridcol="6" gridrow="16" pageId="3" pageNumber="438">0.187</td>
<td id="76DC5DA2EC2E00325532F81CFA0BF861" box="[1381,1450,1961,1983]" gridcol="7" gridrow="16" pageId="3" pageNumber="438">83.0</td>
</tr>
<tr id="350D34DEEC2E00325039F879FA0BF83C" box="[110,1450,1996,2018]" gridrow="17" pageId="3" pageNumber="438">
<th id="76DC5DA2EC2E00325039F879FE0EF83C" box="[110,431,1996,2018]" gridcol="0" gridrow="17" pageId="3" pageNumber="438">
<taxonomicName id="4C3D4D1FEC2EFFCE5039F878FE97F83F" authority="(Sd)" baseAuthorityName="Sd" box="[110,310,1996,2018]" class="Reptilia" family="Neovenatoridae" genus="Sinraptor" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="3" pageNumber="438" phylum="Chordata" rank="species" species="dongi">
<emphasis id="B949EA8EEC2EFFCE5039F878FEA6F83C" box="[110,263,1997,2018]" italics="true" pageId="3" pageNumber="438">Sinraptor dongi</emphasis>
(Sd)
</taxonomicName>
</th>
<td id="76DC5DA2EC2E00325214F879FDFAF83C" box="[579,603,1996,2018]" gridcol="1" gridrow="17" pageId="3" pageNumber="438">12</td>
<td id="76DC5DA2EC2E003252E9F879FD55F83C" box="[702,756,1996,2018]" gridcol="2" gridrow="17" pageId="3" pageNumber="438">47.5</td>
<td id="76DC5DA2EC2E00325314F879FC21F83C" box="[835,896,1996,2018]" gridcol="3" gridrow="17" pageId="3" pageNumber="438">22.60</td>
<td id="76DC5DA2EC2E0032539DF879FBACF83C" box="[970,1037,1996,2018]" gridcol="4" gridrow="17" pageId="3" pageNumber="438">15.70</td>
<td id="76DC5DA2EC2E00325403F879FB36F83C" box="[1108,1175,1996,2018]" gridcol="5" gridrow="17" pageId="3" pageNumber="438">0.211</td>
<td id="76DC5DA2EC2E0032548DF879FA82F83C" box="[1242,1315,1996,2018]" gridcol="6" gridrow="17" pageId="3" pageNumber="438">0.310</td>
<td id="76DC5DA2EC2E00325532F879FA0BF83C" box="[1381,1450,1996,2018]" gridcol="7" gridrow="17" pageId="3" pageNumber="438">84.0</td>
</tr>
</table>
</paragraph>
<paragraph id="8B82369CEC29FFC950DBFEDCFEE1FCDF" blockId="4.[102,687,232,2026]" pageId="4" pageNumber="439">
Measurements (with Mitutoyo 505–634 calipers) were crown height, fore−aft basal length (FABL) and mediolateral basal length (MLBL), 
<emphasis id="B949EA8EEC29FFC951B2FE1FFD80FE1F" box="[485,545,426,449]" italics="true" pageId="4" pageNumber="439">sensu</emphasis>
<bibRefCitation id="EFAC4B6DEC29FFC9527FFE1DFF10FE3F" author="Farlow, J. O. &amp; Brinkman, D. L. &amp; Abler, W. L. &amp; Currie, P. J." journalOrPublisher="Modern Geology" pageId="4" pageNumber="439" pagination="161 - 198" part="16" refId="ref11740" refString="Farlow, J. O., Brinkman, D. L., Abler, W. L., and Currie, P. J. 1991. Size, shape, and serration density of theropod dinosaur lateral teeth. Modern Geology 16: 161 - 198." title="Size, shape, and serration density of theropod dinosaur lateral teeth" type="journal article" year="1991">Farlow et al. (1991)</bibRefCitation>
. Because teeth of 
<taxonomicName id="4C3D4D1FEC29FFC95127FE7FFD9CFE3F" authorityName="Osborn" authorityYear="1905" box="[368,573,458,481]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="439" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC29FFC95127FE7FFD9CFE3F" box="[368,573,458,481]" italics="true" pageId="4" pageNumber="439">Tyrannosaurus rex</emphasis>
</taxonomicName>
<materialsCitation id="3B553CC1EC29FFC95214FE7CFD0FFE3F" ID-GBIF-Occurrence="2598685230" box="[579,686,456,481]" collectionCode="BHI" pageId="4" pageNumber="439" specimenCode="BHI 2033">BHI 2033</materialsCitation>
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 
<bibRefCitation id="EFAC4B6DEC29FFC95154FD1DFE77FD1F" author="Farlow, J. O. &amp; Brinkman, D. L. &amp; Abler, W. L. &amp; Currie, P. J." box="[259,470,680,705]" journalOrPublisher="Modern Geology" pageId="4" pageNumber="439" pagination="161 - 198" part="16" refId="ref11740" refString="Farlow, J. O., Brinkman, D. L., Abler, W. L., and Currie, P. J. 1991. Size, shape, and serration density of theropod dinosaur lateral teeth. Modern Geology 16: 161 - 198." title="Size, shape, and serration density of theropod dinosaur lateral teeth" type="journal article" year="1991">Farlow et al. (1991</bibRefCitation>
; assuming a rectangular cross−section), dividing by crown height, and assuming a unit force.
</paragraph>
<paragraph id="8B82369CEC29FFC950DBFCBCFD8FFB7C" blockId="4.[102,687,232,2026]" pageId="4" pageNumber="439">
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 
<bibRefCitation id="EFAC4B6DEC29FFC95031FC7CFEB1FC3C" author="Currie, P. J." box="[102,272,969,994]" journalOrPublisher="Canadian Journal of Earth Sciences" pageId="4" pageNumber="439" pagination="651 - 665" part="40" refId="ref11388" refString="Currie, P. J. 2003 b. Allometric growth in tyrannosaurids (Dinosauria: Theropoda) from the Upper Cretaceous of North America. Canadian Journal of Earth Sciences 40: 651 - 665." title="Allometric growth in tyrannosaurids (Dinosauria: Theropoda) from the Upper Cretaceous of North America" type="journal article" year="2003">Currie (2003b)</bibRefCitation>
. 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.
</paragraph>
<paragraph id="8B82369CEC29FFC95031FB07FEBBF834" blockId="4.[102,687,232,2026]" pageId="4" pageNumber="439">
<emphasis id="B949EA8EEC29FFC95031FB07FD2DFB14" bold="true" box="[102,652,1201,1226]" pageId="4" pageNumber="439">Results for maxillary tooth bending strengths</emphasis>
.— 
<tableCitation id="C6BF0327EC29FFC95031FB64FF67FB34" box="[102,198,1233,1258]" captionStart="Table 1" captionStartId="3.[102,157,1231,1252]" captionTargetId="graphics@3.[102,1485,1359,2021]" captionTargetPageId="3" captionText="Table 1. Measured and computed properties of theropod maxillary teeth. N, number of teeth measured; CH, average crown height; FABL, average fore, aft basal length; MLBL, averge medolateral basal length; AP str., average anteroposterior bending strength indicator; ML str., mediolateral bending strength indicator; Skull l., skull length. Raw measurements of CH, FABL, and MLBL, not these averages, were used to calculate strength indicators." httpUri="http://table.plazi.org/id/DF426614EC2EFFCE5031FB7AFF6AFAE2" pageId="4" pageNumber="439" tableUuid="DF426614EC2EFFCE5031FB7AFF6AFAE2">Table 1</tableCitation>
enumerates average measurements and strength results for theropod maxillary teeth, and 
<figureCitation id="13062A19EC29FFC952D4FB44FFD5FAF4" captionStart="Fig" captionStartId="2.[102,135,1625,1645]" captionTargetBox="[859,1446,938,1599]" captionTargetId="graphics@2.[924,1446,971,1546]" captionTargetPageId="2" captionText="Fig. 3. Comparisons of mediolateral (A, B) and anteroposterior (C, D) strengths of tyrannosaurid and non−tyrannosaurid theropod maxillary teeth, plotted against skull length. Regressions are by least squares, on log transformed data for the tyrannosaurids. Trend lines are allometric in the tyannosaurids but linear in non−tyrannosaurids. Tooth strengths of Tyrannosaurus rex are much higher than in any other examined taxon. Starting points of the small arrows indicate the position of the juvenile T. rex (TrJ). See Appendix 1 for other specimen labels." figureDoi="http://doi.org/10.5281/zenodo.3961063" httpUri="https://zenodo.org/record/3961063/files/figure.png" pageId="4" pageNumber="439">Fig. 3</figureCitation>
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 
<taxonomicName id="4C3D4D1FEC29FFC95113F9E7FE53F9B4" authority="Currie and Zhao, 1994" box="[324,498,1618,1642]" class="Reptilia" family="Neovenatoridae" genus="Sinraptor" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="439" phylum="Chordata" rank="species" species="dongi">
<emphasis id="B949EA8EEC29FFC95113F9E7FE53F9B4" box="[324,498,1618,1642]" italics="true" pageId="4" pageNumber="439">Sinraptor dongi</emphasis>
</taxonomicName>
and 
<taxonomicName id="4C3D4D1FEC29FFC95272F9E7FEBBF954" authorityName="Stovall &amp; Langston" authorityYear="1950" class="Reptilia" family="Carcharodontosauridae" genus="Acrocanthosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="439" phylum="Chordata" rank="species" species="atokensis">
<emphasis id="B949EA8EEC29FFC95272F9E7FEBBF954" italics="true" pageId="4" pageNumber="439">Acrocanthosaurus atokensis</emphasis>
</taxonomicName>
. 
<taxonomicName id="4C3D4D1FEC29FFC95171F9C6FE54F954" authorityName="Osborn" authorityYear="1905" box="[294,501,1651,1674]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="439" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC29FFC95171F9C6FE54F954" box="[294,501,1651,1674]" italics="true" pageId="4" pageNumber="439">Tyrannosaurus rex</emphasis>
</taxonomicName>
has much higher tooth strengths than these carnosaurs or other large tyrannosaurids. The average strengths of 
<taxonomicName id="4C3D4D1FEC29FFC95267F906FDD0F914" authorityName="Osborn" authorityYear="1905" box="[560,625,1715,1738]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="439" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC29FFC95267F906FDD0F914" box="[560,625,1715,1738]" italics="true" pageId="4" pageNumber="439">T. rex</emphasis>
</taxonomicName>
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 
<materialsCitation id="3B553CC1EC29FFC950B4F887FEDAF894" ID-GBIF-Occurrence="3396438301" box="[227,379,1841,1866]" collectionCode="AMNH" httpUri="http://research.amnh.org/paleontology/search.php?action=detail&amp;specimen_id=47761 " pageId="4" pageNumber="439" specimenCode="AMNH 5027">AMNH 5027</materialsCitation>
). 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.
</paragraph>
<caption id="DF426614EC29FFC95283F8D1FBB2F836" ID-DOI="http://doi.org/10.5281/zenodo.3739904" ID-Zenodo-Dep="3739904" httpUri="https://zenodo.org/record/3739904/files/figure.png" pageId="4" pageNumber="439" startId="4.[724,757,1892,1912]" targetBox="[729,1480,225,1865]" targetPageId="4">
<paragraph id="8B82369CEC29FFC95283F8D1FBB2F836" blockId="4.[724,1486,1892,2024]" pageId="4" pageNumber="439">
Fig. 4. CT reconstructions of tyrannosaurid nasals in side and top views. Anterior is to the right. 
<emphasis id="B949EA8EEC29FFC95367F835FCE1F84A" bold="true" box="[816,832,1920,1940]" pageId="4" pageNumber="439">A</emphasis>
. 
<taxonomicName id="4C3D4D1FEC29FFC95319F834FC5DF84D" authorityName="Osborn" authorityYear="1905" box="[846,1020,1921,1939]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="439" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC29FFC95319F834FC5DF84D" box="[846,1020,1921,1939]" italics="true" pageId="4" pageNumber="439">Tyrannosaurus rex</emphasis>
</taxonomicName>
(
<materialsCitation id="3B553CC1EC29FFC9545DF834FAE4F84A" ID-GBIF-Occurrence="2598685231" box="[1034,1349,1920,1940]" collectionCode="BHI" pageId="4" pageNumber="439" specimenCode="BHI 2033">TMP 98.86.01; cast of BHI 2033</materialsCitation>
). 
<emphasis id="B949EA8EEC29FFC95500F835FAC7F84D" bold="true" box="[1367,1382,1920,1939]" pageId="4" pageNumber="439">B</emphasis>
. 
<taxonomicName id="4C3D4D1FEC29FFC95523F835FCFCF871" authorityName="Russell" authorityYear="1970" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="439" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC29FFC95523F835FCFCF871" italics="true" pageId="4" pageNumber="439">Daspletosaurus torosus</emphasis>
</taxonomicName>
(TMP 98.48.1). 
<emphasis id="B949EA8EEC29FFC95457F829FBB1F86E" bold="true" box="[1024,1040,1948,1968]" pageId="4" pageNumber="439">C</emphasis>
. 
<taxonomicName id="4C3D4D1FEC29FFC95448F829FABCF86E" authority="Osborn, 1905 " box="[1055,1309,1948,1968]" class="Reptilia" family="Tyrannosauridae" genus="Albertosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="439" phylum="Chordata" rank="species">
<emphasis id="B949EA8EEC29FFC95448F829FABCF86E" box="[1055,1309,1948,1968]" italics="true" pageId="4" pageNumber="439">Albertosaurus sarcophagus</emphasis>
</taxonomicName>
(TMP 2000.12.1). 
<emphasis id="B949EA8EEC29FFC95283F80DFD45F815" bold="true" box="[724,740,1976,1995]" pageId="4" pageNumber="439">D</emphasis>
. Adult 
<taxonomicName id="4C3D4D1FEC29FFC95378F80CFC54F812" authority="Lambe, 1914" box="[815,1013,1976,1996]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="439" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC29FFC95378F80CFC54F812" box="[815,1013,1976,1996]" italics="true" pageId="4" pageNumber="439">Gorgosaurus libratus</emphasis>
</taxonomicName>
(TMP 86.64.1). 
<emphasis id="B949EA8EEC29FFC954C1F80DFB04F815" bold="true" box="[1174,1189,1976,1995]" pageId="4" pageNumber="439">E</emphasis>
. Juvenile 
<taxonomicName id="4C3D4D1FEC29FFC95550F80CFA6CF812" authority="Lambe, 1914" box="[1287,1485,1976,1996]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="4" pageNumber="439" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC29FFC95550F80CFA6CF812" box="[1287,1485,1976,1996]" italics="true" pageId="4" pageNumber="439">Gorgosaurus libratus</emphasis>
</taxonomicName>
(TMP 86.144.1). Scale bars 15 cm.
</paragraph>
</caption>
<paragraph id="8B82369CEC28FFC8537BFF58FBDCFE92" blockId="5.[812,1402,237,333]" pageId="5" pageNumber="440">
Strengths of tyrannosaurid and 
<taxonomicName id="4C3D4D1FEC28FFC8537BFE96FC5DFE93" authorityName="Marsh" authorityYear="1877" box="[812,1020,291,333]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="5" pageNumber="440" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC28FFC8537BFE96FC5DFE93" box="[812,1020,291,333]" italics="true" pageId="5" pageNumber="440">Allosaurus</emphasis>
</taxonomicName>
nasals
</paragraph>
<paragraph id="8B82369CEC28FFC8537BFEC1FC4DFE60" blockId="5.[812,1463,372,446]" pageId="5" pageNumber="440">Materials and methods for examining theropod nasal strength</paragraph>
<paragraph id="8B82369CEC28FFC8537BFE6CFA0DFD6F" blockId="5.[812,1486,472,1233]" pageId="5" pageNumber="440">
<emphasis id="B949EA8EEC28FFC8537BFE6CFC4DFE2F" bold="true" box="[812,1004,472,497]" pageId="5" pageNumber="440">Nasal specimens</emphasis>
.—Fossil nasal specimens included juvenile and adult specimens of 
<taxonomicName id="4C3D4D1FEC28FFC85417FE4CFA93FDCE" authority="Lambe, 1914" box="[1088,1330,504,528]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="5" pageNumber="440" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC28FFC85417FE4CFA93FDCE" box="[1088,1330,504,528]" italics="true" pageId="5" pageNumber="440">Gorgosaurus libratus</emphasis>
</taxonomicName>
, and a larger adult specimen of 
<taxonomicName id="4C3D4D1FEC28FFC853ABFDACFB2CFDEE" box="[1020,1165,537,560]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="5" pageNumber="440" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC28FFC853ABFDACFB2CFDEE" box="[1020,1165,537,560]" italics="true" pageId="5" pageNumber="440">Gorgosaurus</emphasis>
</taxonomicName>
̓s sister taxon 
<taxonomicName id="4C3D4D1FEC28FFC85565FDADFC18FD8E" authority="Osborn, 1905 " class="Reptilia" family="Tyrannosauridae" genus="Albertosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="5" pageNumber="440" phylum="Chordata" rank="species">
<emphasis id="B949EA8EEC28FFC85565FDADFC18FD8E" italics="true" pageId="5" pageNumber="440">Albertosaurus sarcophagus</emphasis>
</taxonomicName>
(
<figureCitation id="13062A19EC28FFC8539EFD8DFBAEFD8F" box="[969,1039,568,593]" captionStart="Fig" captionStartId="4.[724,757,1892,1912]" captionTargetBox="[729,1480,225,1865]" captionTargetId="figure@4.[729,1481,225,1865]" captionTargetPageId="4" captionText="Fig. 4. CT reconstructions of tyrannosaurid nasals in side and top views. Anterior is to the right. A. Tyrannosaurus rex (TMP 98.86.01; cast of BHI 2033). B. Daspletosaurus torosus (TMP 98.48.1). C. Albertosaurus sarcophagus (TMP 2000.12.1). D. Adult Gorgosaurus libratus (TMP 86.64.1). E. Juvenile Gorgosaurus libratus (TMP 86.144.1). Scale bars 15 cm." figureDoi="http://doi.org/10.5281/zenodo.3739904" httpUri="https://zenodo.org/record/3739904/files/figure.png" pageId="5" pageNumber="440">Fig. 4</figureCitation>
). These specimens are a tentative proxy for a nasal growth series of these tyrannosaurids, since the nasals share general morphological features (
<bibRefCitation id="EFAC4B6DEC28FFC85579FDCDFA64FD4F" author="Currie, P. J." box="[1326,1477,632,657]" journalOrPublisher="Acta Palaeontologica Polonica" pageId="5" pageNumber="440" pagination="191 - 226" part="48" refId="ref11356" refString="Currie, P. J. 2003 a. Cranial anatomy of tyrannosaurid dinosaurs from the Late Cretaceous of Alberta, Canada. Acta Palaeontologica Polonica 48: 191 - 226." title="Cranial anatomy of tyrannosaurid dinosaurs from the Late Cretaceous of Alberta, Canada" type="journal article" year="2003">Currie 2003a</bibRefCitation>
) and the animals reach identical adult sizes (
<bibRefCitation id="EFAC4B6DEC28FFC8555FFD2DFA3EFD6F" author="Currie, P. J." box="[1288,1439,664,689]" journalOrPublisher="Canadian Journal of Earth Sciences" pageId="5" pageNumber="440" pagination="651 - 665" part="40" refId="ref11388" refString="Currie, P. J. 2003 b. Allometric growth in tyrannosaurids (Dinosauria: Theropoda) from the Upper Cretaceous of North America. Canadian Journal of Earth Sciences 40: 651 - 665." title="Allometric growth in tyrannosaurids (Dinosauria: Theropoda) from the Upper Cretaceous of North America" type="journal article" year="2003">Currie 2003b</bibRefCitation>
).
</paragraph>
<paragraph id="8B82369CEC28FFC85305FD0CFB91FB4E" blockId="5.[812,1486,472,1233]" pageId="5" pageNumber="440">
We also scanned fossilized nasals of a large adult 
<taxonomicName id="4C3D4D1FEC28FFC855C1FD0FFBA6FD2F" authorityName="Russell" authorityYear="1970" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="5" pageNumber="440" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC28FFC855C1FD0FFBA6FD2F" italics="true" pageId="5" pageNumber="440">Daspletosaurus torosus</emphasis>
</taxonomicName>
and a high−resolution cast of nasals from its close relative 
<taxonomicName id="4C3D4D1FEC28FFC853B1FD4FFB1BFCCF" authorityName="Osborn" authorityYear="1905" box="[998,1210,762,785]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="5" pageNumber="440" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC28FFC853B1FD4FFB1BFCCF" box="[998,1210,762,785]" italics="true" pageId="5" pageNumber="440">Tyrannosaurus rex</emphasis>
</taxonomicName>
(
<figureCitation id="13062A19EC28FFC8549EFD4DFAACFCCF" box="[1225,1293,760,785]" captionStart="Fig" captionStartId="4.[724,757,1892,1912]" captionTargetBox="[729,1480,225,1865]" captionTargetId="figure@4.[729,1481,225,1865]" captionTargetPageId="4" captionText="Fig. 4. CT reconstructions of tyrannosaurid nasals in side and top views. Anterior is to the right. A. Tyrannosaurus rex (TMP 98.86.01; cast of BHI 2033). B. Daspletosaurus torosus (TMP 98.48.1). C. Albertosaurus sarcophagus (TMP 2000.12.1). D. Adult Gorgosaurus libratus (TMP 86.64.1). E. Juvenile Gorgosaurus libratus (TMP 86.144.1). Scale bars 15 cm." figureDoi="http://doi.org/10.5281/zenodo.3739904" httpUri="https://zenodo.org/record/3739904/files/figure.png" pageId="5" pageNumber="440">Fig. 4</figureCitation>
). Scanning a cast to obtain cross−sections was appropriate for three reasons. Examination of the original specimen confirmed the fidelity of the cast, no other isolated 
<taxonomicName id="4C3D4D1FEC28FFC854D3FCEFFB68FCAF" authorityName="Osborn" authorityYear="1905" box="[1156,1225,858,881]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="5" pageNumber="440" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC28FFC854D3FCEFFB68FCAF" box="[1156,1225,858,881]" italics="true" pageId="5" pageNumber="440">T. rex</emphasis>
</taxonomicName>
nasal specimens were available, and cross−sectional geometry would be informative about strengths independently of internal architecture. A previous scan of a fossil 
<taxonomicName id="4C3D4D1FEC28FFC85423FC0FFB1BFC0F" authorityName="Osborn" authorityYear="1905" box="[1140,1210,954,977]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="5" pageNumber="440" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC28FFC85423FC0FFB1BFC0F" box="[1140,1210,954,977]" italics="true" pageId="5" pageNumber="440">T. rex</emphasis>
</taxonomicName>
skull (FMNH PR2081; 
<bibRefCitation id="EFAC4B6DEC28FFC8537BFC6DFC1FFC2F" author="Brochu, C. A." box="[812,958,984,1009]" journalOrPublisher="Journal of Vertebrate Paleontology" pageId="5" pageNumber="440" pagination="1 - 138" part="24 (Supplement 4)" refId="ref11126" refString="Brochu, C. A. 2003. Osteology of Tyrannosaurus rex: insights from a nearly complete skeleton and high-resolution computed tomographic analysis of the cranium. Journal of Vertebrate Paleontology 24 (Supplement 4): 1 - 138." title="Osteology of Tyrannosaurus rex: insights from a nearly complete skeleton and high-resolution computed tomographic analysis of the cranium" type="journal article" year="2003">Brochu 2003</bibRefCitation>
) demonstrated internal fusion of the nasals similar to that of other tyrannosaurids. We expect that the fossil template of our cast is internally similar to nearly all other tyrannosaurid nasals, and predict that CT sections of the fossil specimen (
<materialsCitation id="3B553CC1EC28FFC85394FBEDFB95FBAF" ID-GBIF-Occurrence="2598685229" box="[963,1076,1112,1137]" collectionCode="BHI" pageId="5" pageNumber="440" specimenCode="BHI 2033">BHI 2033</materialsCitation>
) would validate our strength calculations based on the cast.
</paragraph>
<paragraph id="8B82369CEC28FFCB5305FB2CFE51F952" blockId="5.[812,1486,472,1233]" lastBlockId="6.[102,775,1551,1838]" lastPageId="6" lastPageNumber="441" pageId="5" pageNumber="440">
We examined three individual left or right nasal specimens of the carnosaur 
<taxonomicName id="4C3D4D1FEC28FFC853BAFB0DFB1AFB0E" authorityName="Marsh" authorityYear="1877" box="[1005,1211,1208,1232]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="5" pageNumber="440" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC28FFC853BAFB0DFB1AFB0E" box="[1005,1211,1208,1232]" italics="true" pageId="5" pageNumber="440">Allosaurus fragilis</emphasis>
</taxonomicName>
(reconstructed and mirrored to represent paired nasals: 
<figureCitation id="13062A19EC2BFFCB5193F9BAFDA2F9F6" box="[452,515,1551,1576]" captionStart="Fig" captionStartId="5.[102,135,1750,1770]" captionTargetBox="[121,755,223,1724]" captionTargetId="figure@5.[121,755,223,1724]" captionTargetPageId="5" captionText="Fig. 5. CT cross sections and reconstructions of Allosaurus fragilis nasals: A, largest (UUVP 1663/UMNH VP 9146); B, midsize (UUVP 1913/ UMNH VP 9144); and C, smallest (UUVP 10854/UMNHVP 7784). Anterior is to the right. Cross sections are from the strongly pneumatized regions of the nasals, at positions indicated by the dashed lines. The slices are normalized to the same size to show the relative degree of pneumatic excavation, evident despite mineral infilling in some sections. Reconstructions are in lateral views and in dorsal views with single left or right specimens mirrored to replicate complete pairs. Specimen B is broken over the posterior part of the external nares. Scale bar 10 cm." figureDoi="http://doi.org/10.5281/zenodo.3739906" httpUri="https://zenodo.org/record/3739906/files/figure.png" pageId="6" pageNumber="441">Fig. 5</figureCitation>
) from the collections of UUVP. These nasals represent a growth series of 
<taxonomicName id="4C3D4D1FEC2BFFCB52C0F984FCA7F997" authorityName="Marsh" authorityYear="1877" box="[663,774,1585,1609]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="6" pageNumber="441" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC2BFFCB52C0F984FCA7F997" box="[663,774,1585,1609]" italics="true" pageId="6" pageNumber="441">A. fragilis</emphasis>
</taxonomicName>
ranging in size from juvenile to adult, and overlap the size range of the smaller tyrannosaurids.
</paragraph>
<caption id="DF426614EC28FFC85031F963FE4BF838" ID-DOI="http://doi.org/10.5281/zenodo.3739906" ID-Zenodo-Dep="3739906" httpUri="https://zenodo.org/record/3739906/files/figure.png" pageId="5" pageNumber="440" startId="5.[102,135,1750,1770]" targetBox="[121,755,223,1724]" targetPageId="5">
<paragraph id="8B82369CEC28FFC85031F963FE4BF838" blockId="5.[102,776,1750,2022]" pageId="5" pageNumber="440">
Fig. 5. CT cross sections and reconstructions of 
<taxonomicName id="4C3D4D1FEC28FFC8524DF962FD62F935" authorityName="Marsh" authorityYear="1877" box="[538,707,1751,1771]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="5" pageNumber="440" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC28FFC8524DF962FD62F935" box="[538,707,1751,1771]" italics="true" pageId="5" pageNumber="440">Allosaurus fragilis</emphasis>
</taxonomicName>
nasals: 
<emphasis id="B949EA8EEC28FFC85031F947FFD7F8D8" bold="true" box="[102,118,1778,1798]" pageId="5" pageNumber="440">A</emphasis>
, largest (UUVP 1663/UMNH VP 9146); 
<emphasis id="B949EA8EEC28FFC85246F946FD81F8D8" bold="true" box="[529,544,1779,1798]" pageId="5" pageNumber="440">B</emphasis>
, midsize (UUVP 1913/ UMNH VP 9144); and 
<emphasis id="B949EA8EEC28FFC8516FF8BBFEE9F8FC" bold="true" box="[312,328,1806,1826]" pageId="5" pageNumber="440">C</emphasis>
, smallest (UUVP 10854/UMNHVP 7784). Anterior is to the right. Cross sections are from the strongly pneumatized regions of the nasals, at positions indicated by the dashed lines. The slices are normalized to the same size to show the relative degree of pneumatic excavation, evident despite mineral infilling in some sections. Reconstructions are in lateral views and in dorsal views with single left or right specimens mirrored to replicate complete pairs. Specimen B is broken over the posterior part of the external nares. Scale bar 10 cm.
</paragraph>
</caption>
<caption id="DF426614EC28FFC8537BF89EFA0CF839" ID-DOI="http://doi.org/10.5281/zenodo.3739908" ID-Zenodo-Dep="3739908" httpUri="https://zenodo.org/record/3739908/files/figure.png" pageId="5" pageNumber="440" startId="5.[812,845,1835,1855]" targetBox="[855,1442,1260,1807]" targetPageId="5">
<paragraph id="8B82369CEC28FFC8537BF89EFA0CF839" blockId="5.[812,1485,1835,2023]" pageId="5" pageNumber="440">
Fig. 6. Geometry used to compute the area, centroid, and second moments of area of a nasal cross−section (from middle region of fused 
<taxonomicName id="4C3D4D1FEC28FFC85513F8FDFCE8F8A8" authorityName="Osborn" authorityYear="1905" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="5" pageNumber="440" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC28FFC85513F8FDFCE8F8A8" italics="true" pageId="5" pageNumber="440">Tyrannosaurus rex</emphasis>
</taxonomicName>
nasals: 
<materialsCitation id="3B553CC1EC28FFC853C0F8D1FB72F8A9" ID-GBIF-Occurrence="2598685232" box="[919,1235,1891,1911]" collectionCode="BHI" pageId="5" pageNumber="440" specimenCode="BHI 2033">TMP 98.86.01; cast of BHI 2033</materialsCitation>
). 
<emphasis id="B949EA8EEC28FFC854B2F8D6FB54F8A9" bold="true" box="[1253,1269,1891,1911]" pageId="5" pageNumber="440">A</emphasis>
. Decomposition of the cross−section to compute area by summing areas of triangles. Small “+”s are centroids of individual triangles. Large “+” is the centroid for the complete section. 
<emphasis id="B949EA8EEC28FFC853F0F802FC17F814" bold="true" box="[935,950,1975,1994]" pageId="5" pageNumber="440">B</emphasis>
. Cross−section partitioned into horizontal and vertical strips of known area and position, used to calculate second moments of area.
</paragraph>
</caption>
<caption id="DF426614EC2BFFCB5031FA2CFC33FA3B" ID-DOI="http://doi.org/10.5281/zenodo.3961065" ID-Zenodo-Dep="3961065" httpUri="https://zenodo.org/record/3961065/files/figure.png" pageId="6" pageNumber="441" startId="6.[102,135,1433,1453]" targetBox="[102,1485,226,1404]" targetPageId="6">
<paragraph id="8B82369CEC2BFFCB5031FA2CFC33FA3B" blockId="6.[102,1486,1432,1509]" pageId="6" pageNumber="441">
Fig. 7. CT−scanned cross−sections of fused tyrannosaurid nasals, showing greater vaulting and higher cross−sectional areas of bone in larger individuals. 
<emphasis id="B949EA8EEC2BFFCB55E0FA2DFA66FA72" bold="true" box="[1463,1479,1432,1452]" pageId="6" pageNumber="441">A</emphasis>
. 
<taxonomicName id="4C3D4D1FEC2BFFCB5031FA03FE8AFA17" authority="Lambe, 1914" box="[102,299,1461,1481]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="6" pageNumber="441" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC2BFFCB5031FA03FE8AFA17" box="[102,299,1461,1481]" italics="true" pageId="6" pageNumber="441">Gorgosaurus libratus</emphasis>
</taxonomicName>
(juvenile: TMP 86.144.1). 
<emphasis id="B949EA8EEC2BFFCB527CFA00FD9BFA16" bold="true" box="[555,570,1461,1480]" pageId="6" pageNumber="441">B</emphasis>
. 
<taxonomicName id="4C3D4D1FEC2BFFCB521FFA03FCACFA17" authority="Lambe, 1914" box="[584,781,1461,1481]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="6" pageNumber="441" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC2BFFCB521FFA03FCACFA17" box="[584,781,1461,1481]" italics="true" pageId="6" pageNumber="441">Gorgosaurus libratus</emphasis>
</taxonomicName>
(subadult: TMP 86.64.1). 
<emphasis id="B949EA8EEC2BFFCB5451FA01FBB7FA16" bold="true" box="[1030,1046,1460,1480]" pageId="6" pageNumber="441">C</emphasis>
. 
<taxonomicName id="4C3D4D1FEC2BFFCB5474FA00FB5DFA16" authorityName="Russell" authorityYear="1970" box="[1059,1276,1461,1481]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="6" pageNumber="441" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC2BFFCB5474FA00FB5DFA16" box="[1059,1276,1461,1481]" italics="true" pageId="6" pageNumber="441">Daspletosaurus torosus</emphasis>
</taxonomicName>
(adult: TMP 98.48.1). Numbers 1–4: cross−sections at topologically similar positions, from posterior to anterior.
</paragraph>
</caption>
<paragraph id="8B82369CEC2BFFCB50DBF920FD8BF8F0" blockId="6.[102,775,1551,1838]" pageId="6" pageNumber="441">
The specimens were CT scanned on a General Electric QX/1 scanner at Foothills Hospital, Calgary, Alberta. Scan settings of 120 KVp and 200 mA, at 5 mm thickness, produced good results. Thickness was reduced to 2.5 mm for the smaller 
<taxonomicName id="4C3D4D1FEC2BFFCB50E8F8A3FE10F8F0" authority="Lambe, 1914" box="[191,433,1814,1838]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="6" pageNumber="441" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC2BFFCB50E8F8A3FE10F8F0" box="[191,433,1814,1838]" italics="true" pageId="6" pageNumber="441">Gorgosaurus libratus</emphasis>
</taxonomicName>
specimen.
</paragraph>
<paragraph id="8B82369CEC2BFFCB5031F8E4FBB8F936" blockId="6.[102,775,1873,2026]" lastBlockId="6.[812,1486,1551,2026]" pageId="6" pageNumber="441">
<emphasis id="B949EA8EEC2BFFCB5031F8E4FD61F8B4" bold="true" box="[102,704,1873,1898]" pageId="6" pageNumber="441">Specimen comparisons and CT data processing</emphasis>
.—CT slices were viewed to evaluate internal anatomy of the nasals in Madena X (http://radonc.usc.edu/USCRadOnc/Madena/ Madena.html; Apple Macintosh OS X 10.3). Three−dimensional renderings (
<figureCitation id="13062A19EC2BFFCB5165F864FE3BF834" box="[306,410,2001,2026]" captionStart-0="Fig" captionStart-1="Fig" captionStart-2="Fig" captionStartId-0="1.[102,135,1523,1543]" captionStartId-1="1.[812,844,1809,1829]" captionStartId-2="2.[102,135,1625,1645]" captionTargetBox-0="[115,761,227,1497]" captionTargetBox-1="[856,1441,1117,1784]" captionTargetBox-2="[859,1446,938,1599]" captionTargetId-0="figure@1.[115,761,227,1497]" captionTargetId-1="graphics@1.[915,1440,1149,1726]" captionTargetId-2="graphics@2.[924,1446,971,1546]" captionTargetPageId-0="1" captionTargetPageId-1="1" captionTargetPageId-2="2" captionText-0="Fig. 1. Comparison of cranial and nasal morphology of: A, the tyrannosaurid Tyrannosaurus rex (TMP 98.86.01; cast of BHI 2033) and B, the carnosaur Allosaurus fragilis (UUVP 1663/UMNH VP 9146; mirrored to depict a complete pair). Scale axes for crania are in meters. Nasals in their life positions are highlighted in lateral and dorsal cranial views, and rendered in oblique view (not to scale). The T. rex nasals are tall, vaulted, and fused, while the A. fragilis nasals are lower and unfused." captionText-1="Fig. 2. Comparison of vertical bending strengths of adult theropod dentaries, graphed as mid−dentary section modulus versus mandible length (data from Therrien et al. 2005). Lines fitted by least squares regression, by log transformed values for the tyrannosaurid data. Carnosaur dentary strengths scale linearly with dentary length, while tyrannosaurid dentary strengths show an exponential increase. The tyrannosaurid dentaries are stronger than those of carnosaurs for a given mandible length, indicating a relatively stronger bite. See Appendix 1 for specimen labels; Gc, Giganotosaurus carolinii." captionText-2="Fig. 3. Comparisons of mediolateral (A, B) and anteroposterior (C, D) strengths of tyrannosaurid and non−tyrannosaurid theropod maxillary teeth, plotted against skull length. Regressions are by least squares, on log transformed data for the tyrannosaurids. Trend lines are allometric in the tyannosaurids but linear in non−tyrannosaurids. Tooth strengths of Tyrannosaurus rex are much higher than in any other examined taxon. Starting points of the small arrows indicate the position of the juvenile T. rex (TrJ). See Appendix 1 for other specimen labels." figureDoi-0="http://doi.org/10.5281/zenodo.3739900" figureDoi-1="http://doi.org/10.5281/zenodo.3961033" figureDoi-2="http://doi.org/10.5281/zenodo.3961063" httpUri-0="https://zenodo.org/record/3739900/files/figure.png" httpUri-1="https://zenodo.org/record/3961033/files/figure.png" httpUri-2="https://zenodo.org/record/3961063/files/figure.png" pageId="6" pageNumber="441">Figs. 1–3</figureCitation>
) and volume slicing for examining internal structure in context (
<figureCitation id="13062A19EC2BFFCB54F3F9BAFB49F9F6" box="[1188,1256,1551,1576]" captionStart="Fig" captionStartId="6.[102,135,1433,1453]" captionTargetBox="[102,1485,226,1404]" captionTargetId="figure@6.[102,1486,229,1405]" captionTargetPageId="6" captionText="Fig. 7. CT−scanned cross−sections of fused tyrannosaurid nasals, showing greater vaulting and higher cross−sectional areas of bone in larger individuals. A. Gorgosaurus libratus (juvenile: TMP 86.144.1). B. Gorgosaurus libratus (subadult: TMP 86.64.1). C. Daspletosaurus torosus (adult: TMP 98.48.1). Numbers 1–4: cross−sections at topologically similar positions, from posterior to anterior." figureDoi="http://doi.org/10.5281/zenodo.3961065" httpUri="https://zenodo.org/record/3961065/files/figure.png" pageId="6" pageNumber="441">Fig. 7</figureCitation>
) were performed in OsiriX (http://homepage.mac.com/rossetantoine/osirix/Index2.htm; Apple Macintosh OS X 10.3). To test if our CT manipulations correctly visualized the internal structure of the bone, we examined naturally broken tyrannosaurid nasal specimens of varying size (TMP 81.23.1, 86.36.36, 92.36.81, 94.12.414, 94.154.2, 96.12.404).
</paragraph>
<paragraph id="8B82369CEC2BFFCB5305F944FB94F837" blockId="6.[812,1486,1551,2026]" pageId="6" pageNumber="441">The raw CT data were imported into ImageJ (http://rsb. info.nih.gov/ij/) where contrast enhancement, thresholding, particle analysis and other image processing commands (to fill holes, for example) were executed to produce filled regions corresponding to the nasal cross−sections. Subsequently, custom software was used to determine the (x,y) coordinates of the bone perimeters. The resolution of the finished contours is estimated to be 0.5 mm.</paragraph>
<paragraph id="8B82369CEC2AFFCA5031FF5DFDCCFE1F" blockId="7.[102,775,232,449]" pageId="7" pageNumber="442">
<emphasis id="B949EA8EEC2AFFCA5031FF5DFE99FEDF" bold="true" box="[102,312,232,257]" pageId="7" pageNumber="442">Area calculations</emphasis>
.—With their positions along the top of the muzzle, the nasals are well positioned to receive the compressive forces associated with biting (
<bibRefCitation id="EFAC4B6DEC2AFFCA5276FE9DFD69FE9F" author="Rayfield, E. J." box="[545,712,296,321]" journalOrPublisher="Proceedings of the Royal Society of London B" pageId="7" pageNumber="442" pagination="1451 - 1459" part="271" refId="ref12756" refString="Rayfield, E. J. 2004. Cranial mechanics and feeding in Tyrannosaurus rex. Proceedings of the Royal Society of London B 271: 1451 - 1459." title="Cranial mechanics and feeding in Tyrannosaurus rex" type="journal article" year="2004">Rayfield 2004</bibRefCitation>
), and their resistance to these forces will be proportional to their cross−sectional areas. The areas of the irregular nasal crosssections were determined by the triangular decomposition method (
<figureCitation id="13062A19EC2AFFCA509EFE1DFEADFE1F" box="[201,268,424,449]" captionStart="Fig" captionStartId="5.[812,845,1835,1855]" captionTargetBox="[855,1442,1260,1807]" captionTargetId="graphics@5.[856,1408,1260,1807]" captionTargetPageId="5" captionText="Fig. 6. Geometry used to compute the area, centroid, and second moments of area of a nasal cross−section (from middle region of fused Tyrannosaurus rex nasals: TMP 98.86.01; cast of BHI 2033). A. Decomposition of the cross−section to compute area by summing areas of triangles. Small “+”s are centroids of individual triangles. Large “+” is the centroid for the complete section. B. Cross−section partitioned into horizontal and vertical strips of known area and position, used to calculate second moments of area." figureDoi="http://doi.org/10.5281/zenodo.3739908" httpUri="https://zenodo.org/record/3739908/files/figure.png" pageId="7" pageNumber="442">Fig. 6</figureCitation>
) outlined in 
<bibRefCitation id="EFAC4B6DEC2AFFCA51CCFE1DFDC8FE1F" author="Henderson, D. M." box="[411,617,424,449]" journalOrPublisher="Journal of Vertebrate Paleontology" pageId="7" pageNumber="442" pagination="766 - 778" part="22" refId="ref12007" refString="Henderson, D. M. 2002. The eyes have it: the sizes, shapes, and orientations of theropod orbits as indicators of cranium strength and bite force. Journal of Vertebrate Paleontology 22: 766 - 778." title="The eyes have it: the sizes, shapes, and orientations of theropod orbits as indicators of cranium strength and bite force" type="journal article" year="2002">Henderson (2002)</bibRefCitation>
.
</paragraph>
<paragraph id="8B82369CEC2AFFCA5031FE69FF7DFD6B" blockId="7.[102,775,476,921]" pageId="7" pageNumber="442">
<emphasis id="B949EA8EEC2AFFCA5031FE69FEFEFE2B" bold="true" box="[102,351,476,501]" pageId="7" pageNumber="442">Strength calculations</emphasis>
.—Both nasals and skulls were represented in three−dimensional, Cartesian coordinate space, with posterior edges set at X = 0. The midsagittal axis was defined as the X−axis, and the dorsoventral axis was set to the Y−axis. The Z−axis defined the mediolateral axis, with negative and positive Z−coordinates correspond to left and right sides, respectively.
</paragraph>
<paragraph id="8B82369CEC2AFFCA50DBFD0BFE86FC49" blockId="7.[102,775,476,921]" pageId="7" pageNumber="442">
Determination of the horizontal and vertical neutral axes of bending of the nasal slices came from determining the Z− and Y−axis centroids (horizontal and vertical, respectively) of the contour bounded regions, and this was facilitated by the triangular decompositions used to determine areas (
<figureCitation id="13062A19EC2AFFCA528EFC8BFF28FCA9" captionStart="Fig" captionStartId="5.[812,845,1835,1855]" captionTargetBox="[855,1442,1260,1807]" captionTargetId="graphics@5.[856,1408,1260,1807]" captionTargetPageId="5" captionText="Fig. 6. Geometry used to compute the area, centroid, and second moments of area of a nasal cross−section (from middle region of fused Tyrannosaurus rex nasals: TMP 98.86.01; cast of BHI 2033). A. Decomposition of the cross−section to compute area by summing areas of triangles. Small “+”s are centroids of individual triangles. Large “+” is the centroid for the complete section. B. Cross−section partitioned into horizontal and vertical strips of known area and position, used to calculate second moments of area." figureDoi="http://doi.org/10.5281/zenodo.3739908" httpUri="https://zenodo.org/record/3739908/files/figure.png" pageId="7" pageNumber="442">Fig. 6A</figureCitation>
) The centroid of the entire contour−bounded region (
<emphasis id="B949EA8EEC2AFFCA52A2FCEAFCA1FCA8" box="[757,768,863,886]" italics="true" pageId="7" pageNumber="442">z</emphasis>
, 
<emphasis id="B949EA8EEC2AFFCA5031FCCAFFD3FC48" box="[102,114,895,918]" italics="true" pageId="7" pageNumber="442">y</emphasis>
) 
<emphasis id="B949EA8EEC2AFFCA502CFC3CFF3CFC47" box="[123,157,905,921]" italics="true" pageId="7" pageNumber="442">
<subScript id="17B934D9EC2AFFCA502CFC3CFF3CFC47" attach="left" box="[123,157,905,921]" fontSize="7" pageId="7" pageNumber="442">slice</subScript>
</emphasis>
is given by:
</paragraph>
<caption id="DF426614EC2AFFCA51CBFC4FFE1CFBCD" ID-DOI="http://doi.org/10.5281/zenodo.5196278" ID-Zenodo-Dep="5196278" box="[412,445,1018,1043]" httpUri="https://zenodo.org/record/5196278/files/figure.png" inLine="true" pageId="7" pageNumber="442" startId="7.[412,423,1018,1043]" targetBox="[140,392,938,1110]" targetPageId="7">
<paragraph id="8B82369CEC2AFFCA51CBFC4FFE1CFBCD" blockId="7.[412,445,1018,1043]" box="[412,445,1018,1043]" pageId="7" pageNumber="442">(1)</paragraph>
</caption>
<paragraph id="8B82369CEC2AFFCA5031FBDDFDE9FB1F" blockId="7.[102,775,1128,1315]" pageId="7" pageNumber="442">
where N is the number of triangles in a contour decomposition, and (
<emphasis id="B949EA8EEC2AFFCA5089FB3CFEB8FB7A" box="[222,281,1161,1188]" italics="true" pageId="7" pageNumber="442">
<subScript id="17B934D9EC2AFFCA5089FB3CFF53FB7A" attach="left" box="[222,242,1161,1188]" fontSize="7" pageId="7" pageNumber="442">zn</subScript>
, 
<subScript id="17B934D9EC2AFFCA5153FB3CFEB8FB7A" attach="left" box="[260,281,1161,1188]" fontSize="7" pageId="7" pageNumber="442">yn</subScript>
</emphasis>
) and 
<emphasis id="B949EA8EEC2AFFCA5137FB3DFEDBFB7A" box="[352,378,1160,1188]" italics="true" pageId="7" pageNumber="442">
<subScript id="17B934D9EC2AFFCA5137FB3DFEDBFB7A" attach="left" box="[352,378,1160,1188]" fontSize="7" pageId="7" pageNumber="442">An</subScript>
</emphasis>
are the centroid and area, respectively, of the 
<superScript id="7C489BD4EC2AFFCA50ACFB1CFEB9FB68" attach="left" box="[251,280,1190,1216]" fontSize="7" pageId="7" pageNumber="442">nth</superScript>
sub−triangle (Appendix 2).
</paragraph>
<paragraph id="8B82369CEC2AFFCA50DBFB7FFF50FAFD" blockId="7.[102,775,1128,1315]" pageId="7" pageNumber="442">The second moments of area of a nasal cross−section with respect to the two axes were determined with the following expressions:</paragraph>
<paragraph id="8B82369CEC2AFFCA50B7FA86FEBCFAA8" blockId="7.[140,552,1330,1398]" pageId="7" pageNumber="442">
<emphasis id="B949EA8EEC2AFFCA50B7FA86FF44FA9F" box="[224,229,1331,1345]" italics="true" pageId="7" pageNumber="442">I</emphasis>
–1 
<emphasis id="B949EA8EEC2AFFCA5157FA87FEACFA9D" box="[256,269,1330,1347]" italics="true" pageId="7" pageNumber="442">
J 
<subScript id="17B934D9EC2AFFCA515EFA8FFEACFA9D" attach="left" box="[265,269,1338,1347]" fontSize="4" pageId="7" pageNumber="442">I</subScript>
</emphasis>
–1 
<emphasis id="B949EA8EEC2AFFCA50DBFAF2FE98FABD" italics="true" pageId="7" pageNumber="442">I nasal = Ʃ Ʃ y 2 · area (h _ strip) z i</emphasis>
(
<emphasis id="B949EA8EEC2AFFCA5256FAE0FDA4FABD" box="[513,517,1365,1379]" italics="true" pageId="7" pageNumber="442">i</emphasis>
, 
<emphasis id="B949EA8EEC2AFFCA5258FAE0FDB2FABD" box="[527,531,1365,1379]" italics="true" pageId="7" pageNumber="442">j</emphasis>
) 
<emphasis id="B949EA8EEC2AFFCA50B7FADDFF45FAA8" box="[224,228,1384,1398]" italics="true" pageId="7" pageNumber="442">i</emphasis>
= 0 
<emphasis id="B949EA8EEC2AFFCA5152FADDFEA8FAA8" box="[261,265,1384,1398]" italics="true" pageId="7" pageNumber="442">j</emphasis>
= 0
</paragraph>
<paragraph id="8B82369CEC2AFFCA5210FAF3FDC9FA81" blockId="7.[583,616,1350,1375]" box="[583,616,1350,1375]" pageId="7" pageNumber="442">(2)</paragraph>
<paragraph id="8B82369CEC2AFFCA5088FA3BFEBAFA0F" blockId="7.[140,541,1421,1489]" pageId="7" pageNumber="442">
<emphasis id="B949EA8EEC2AFFCA5088FA3BFF47FA42" box="[223,230,1422,1436]" italics="true" pageId="7" pageNumber="442">J</emphasis>
–1 
<emphasis id="B949EA8EEC2AFFCA5157FA38FEAAFA40" box="[256,267,1421,1438]" italics="true" pageId="7" pageNumber="442">
I 
<subScript id="17B934D9EC2AFFCA5150FA20FEAAFA40" attach="left" box="[263,267,1429,1438]" fontSize="4" pageId="7" pageNumber="442">I</subScript>
</emphasis>
–1 
<emphasis id="B949EA8EEC2AFFCA50DBFA16FE97FA60" italics="true" pageId="7" pageNumber="442">I nasal = Ʃ Ʃ z 2 · area (v_ strip) y j</emphasis>
(
<emphasis id="B949EA8EEC2AFFCA51AFFA05FE5DFA60" box="[504,508,1456,1470]" italics="true" pageId="7" pageNumber="442">j</emphasis>
, 
<emphasis id="B949EA8EEC2AFFCA5253FA05FDA9FA60" box="[516,520,1456,1470]" italics="true" pageId="7" pageNumber="442">i</emphasis>
) 
<emphasis id="B949EA8EEC2AFFCA50B6FA76FF44FA0F" box="[225,229,1475,1489]" italics="true" pageId="7" pageNumber="442">j</emphasis>
= 0 
<emphasis id="B949EA8EEC2AFFCA5154FA76FEA6FA0F" box="[259,263,1475,1489]" italics="true" pageId="7" pageNumber="442">i</emphasis>
= 0
</paragraph>
<paragraph id="8B82369CEC2AFFCA5214FA14FDC5FA64" blockId="7.[579,612,1441,1466]" box="[579,612,1441,1466]" pageId="7" pageNumber="442">(3)</paragraph>
<paragraph id="8B82369CEC2AFFCA50DBFA5BFDF7F97B" blockId="7.[102,775,1516,1701]" pageId="7" pageNumber="442">
<emphasis id="B949EA8EEC2AFFCA50DBFA5BFF34F9DB" box="[140,149,1518,1541]" italics="true" pageId="7" pageNumber="442">I</emphasis>
and 
<emphasis id="B949EA8EEC2AFFCA509EFA5BFF74F9DB" box="[201,213,1518,1541]" italics="true" pageId="7" pageNumber="442">J</emphasis>
are the numbers of horizontal and vertical slices, 
<emphasis id="B949EA8EEC2AFFCA52AFFA5BFCA7F9D6" box="[760,774,1518,1544]" italics="true" pageId="7" pageNumber="442">
<subScript id="17B934D9EC2AFFCA52AFFA5BFCA7F9D6" attach="left" box="[760,774,1518,1544]" fontSize="7" pageId="7" pageNumber="442">Ij</subScript>
</emphasis>
and 
<emphasis id="B949EA8EEC2AFFCA50C3F9BBFF07F9F6" box="[148,166,1550,1576]" italics="true" pageId="7" pageNumber="442">
<subScript id="17B934D9EC2AFFCA50C3F9BBFF07F9F6" attach="left" box="[148,166,1550,1576]" fontSize="7" pageId="7" pageNumber="442">Ji</subScript>
</emphasis>
are the numbers of separate strips on 
<emphasis id="B949EA8EEC2AFFCA521FF9BBFDF0F9FB" box="[584,593,1550,1573]" italics="true" pageId="7" pageNumber="442">I</emphasis>
<superScript id="7C489BD4EC2AFFCA5205F9BFFDC0F9C4" attach="left" box="[594,609,1546,1562]" fontSize="7" pageId="7" pageNumber="442">th</superScript>
horizontal and 
<emphasis id="B949EA8EEC2AFFCA5031F99BFFD3F99B" box="[102,114,1582,1605]" italics="true" pageId="7" pageNumber="442">J</emphasis>
<superScript id="7C489BD4EC2AFFCA5025F99FFF20F9E4" attach="left" box="[114,129,1578,1594]" fontSize="7" pageId="7" pageNumber="442">th</superScript>
vertical slices, 
<emphasis id="B949EA8EEC2AFFCA517AF99BFE98F99B" box="[301,313,1582,1605]" italics="true" pageId="7" pageNumber="442">y</emphasis>
<subScript id="17B934D9EC2AFFCA516EF98DFE9FF996" attach="left" box="[313,318,1592,1608]" fontSize="7" pageId="7" pageNumber="442">i</subScript>
and 
<emphasis id="B949EA8EEC2AFFCA5123F99BFEDEF99B" box="[372,383,1582,1605]" italics="true" pageId="7" pageNumber="442">z</emphasis>
<subScript id="17B934D9EC2AFFCA5128F98DFE25F996" attach="left" box="[383,388,1592,1608]" fontSize="7" pageId="7" pageNumber="442">i</subScript>
are the vertical and horizontal distances of strips from the centroid, and 
<emphasis id="B949EA8EEC2AFFCA525AF9F8FDFDF9BB" box="[525,604,1613,1637]" italics="true" pageId="7" pageNumber="442">h_strip</emphasis>
and 
<emphasis id="B949EA8EEC2AFFCA52C6F9FBFD7FF9BB" box="[657,734,1614,1637]" italics="true" pageId="7" pageNumber="442">v_strip</emphasis>
are the areas of sets of individual strips taken in the vertical and horizontal directions, respectively (
<figureCitation id="13062A19EC2AFFCA51A6F939FDE8F97B" box="[497,585,1676,1701]" captionStart="Fig" captionStartId="5.[812,845,1835,1855]" captionTargetBox="[855,1442,1260,1807]" captionTargetId="graphics@5.[856,1408,1260,1807]" captionTargetPageId="5" captionText="Fig. 6. Geometry used to compute the area, centroid, and second moments of area of a nasal cross−section (from middle region of fused Tyrannosaurus rex nasals: TMP 98.86.01; cast of BHI 2033). A. Decomposition of the cross−section to compute area by summing areas of triangles. Small “+”s are centroids of individual triangles. Large “+” is the centroid for the complete section. B. Cross−section partitioned into horizontal and vertical strips of known area and position, used to calculate second moments of area." figureDoi="http://doi.org/10.5281/zenodo.3739908" httpUri="https://zenodo.org/record/3739908/files/figure.png" pageId="7" pageNumber="442">Fig. 6B</figureCitation>
).
</paragraph>
<caption id="DF426614EC2AFFCA537BF9EAFBEEF8E9" ID-DOI="http://doi.org/10.5281/zenodo.3961039" ID-Zenodo-Dep="3961039" httpUri="https://zenodo.org/record/3961039/files/figure.png" pageId="7" pageNumber="442" startId="7.[812,845,1631,1651]" targetBox="[817,1481,230,1606]" targetPageId="7">
<paragraph id="8B82369CEC2AFFCA537BF9EAFBEEF8E9" blockId="7.[812,1486,1631,1847]" pageId="7" pageNumber="442">
Fig. 8. Average strengths of nasal cross−sections in tyrannosaurids and 
<taxonomicName id="4C3D4D1FEC2AFFCA537BF9C9FC77F94E" authorityName="Marsh" authorityYear="1877" box="[812,982,1660,1680]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="7" pageNumber="442" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC2AFFCA537BF9C9FC77F94E" box="[812,982,1660,1680]" italics="true" pageId="7" pageNumber="442">Allosaurus fragilis</emphasis>
</taxonomicName>
, plotted against nasal length. 
<emphasis id="B949EA8EEC2AFFCA54BDF9CEFB5BF951" bold="true" box="[1258,1274,1659,1679]" pageId="7" pageNumber="442">A</emphasis>
. Cross−sectional areas, proportional to compression strengths. 
<emphasis id="B949EA8EEC2AFFCA54DCF92DFB3BF975" bold="true" box="[1163,1178,1688,1707]" pageId="7" pageNumber="442">B</emphasis>
. Second moment of area, proportional to vertical bending strength. 
<emphasis id="B949EA8EEC2AFFCA5435F906FBD3F919" bold="true" box="[1122,1138,1715,1735]" pageId="7" pageNumber="442">C</emphasis>
. Second moment of area, proportional to lateral bending strength. Values for the 
<taxonomicName id="4C3D4D1FEC2AFFCA54F1F965FAA1F93A" authorityName="Marsh" authorityYear="1877" box="[1190,1280,1744,1764]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="7" pageNumber="442" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC2AFFCA54F1F965FAA1F93A" box="[1190,1280,1744,1764]" italics="true" pageId="7" pageNumber="442">A. fragilis</emphasis>
</taxonomicName>
nasals are uncorrected for the hollowness of the sections, which would reduce their strengths. Lines fitted to the tyrannosaurid values are derived from log transformed data. See Appendix 1 for labels.
</paragraph>
</caption>
<paragraph id="8B82369CEC2AFFCA5031F975FCA7F906" blockId="7.[100,775,1728,2026]" box="[102,774,1728,1753]" pageId="7" pageNumber="442">
<heading id="D0CA81F0EC2AFFCA5031F975FCA7F906" bold="true" box="[102,774,1728,1753]" centered="true" fontSize="10" level="3" pageId="7" pageNumber="442" reason="0">
<emphasis id="B949EA8EEC2AFFCA5031F975FD45F907" bold="true" box="[102,740,1728,1753]" pageId="7" pageNumber="442">Influence of vaulting on tyrannosaurid nasals strengths</emphasis>
.—
</heading>
</paragraph>
<paragraph id="8B82369CEC2AFFCA5031F954FC7CF877" blockId="7.[100,775,1728,2026]" lastBlockId="7.[812,1485,1905,2029]" pageId="7" pageNumber="442">
We investigated the influence of vaulting on vertical strength by normalizing 
<emphasis id="B949EA8EEC2AFFCA514DF8B7FE89F8C3" box="[282,296,1794,1821]" italics="true" pageId="7" pageNumber="442">
I 
<subScript id="17B934D9EC2AFFCA5174F8A4FE89F8C3" attach="left" box="[291,296,1809,1821]" fontSize="5" pageId="7" pageNumber="442">z</subScript>
</emphasis>
for cross−sectional area of every tyrannosaurid CT slice, using the expression 
<emphasis id="B949EA8EEC2AFFCA5248F892FDEBF89D" box="[543,586,1831,1859]" italics="true" pageId="7" pageNumber="442">
h 
<subScript id="17B934D9EC2AFFCA527AF880FDEBF89D" attach="left" box="[557,586,1845,1859]" fontSize="6" pageId="7" pageNumber="442">slice</subScript>
</emphasis>
= 
<emphasis id="B949EA8EEC2AFFCA52D7F89DFD0AF8EE" box="[640,683,1826,1859]" italics="true" pageId="7" pageNumber="442">
I 
<subScript id="17B934D9EC2AFFCA52DBF880FD33F89D" attach="left" box="[652,658,1845,1859]" fontSize="6" pageId="7" pageNumber="442">z</subScript>
<superScript id="7C489BD4EC2AFFCA52D9F897FD0AF8EE" attach="left" box="[654,683,1826,1840]" fontSize="6" pageId="7" pageNumber="442">slice</superScript>
</emphasis>
/ 
<emphasis id="B949EA8EEC2AFFCA529DF892FD58F89D" box="[714,761,1831,1859]" italics="true" pageId="7" pageNumber="442">
A 
<subScript id="17B934D9EC2AFFCA528BF880FD58F89D" attach="left" box="[732,761,1845,1859]" fontSize="6" pageId="7" pageNumber="442">slice</subScript>
</emphasis>
. The term 
<emphasis id="B949EA8EEC2AFFCA5084F8E7FF5FF8B0" box="[211,254,1874,1902]" italics="true" pageId="7" pageNumber="442">
h 
<subScript id="17B934D9EC2AFFCA50B6F8D5FF5FF8B0" attach="left" box="[225,254,1888,1902]" fontSize="6" pageId="7" pageNumber="442">slice</subScript>
</emphasis>
is the height of a rectangular cross−section, of area equal to that of the real slice (
<emphasis id="B949EA8EEC2AFFCA51B0F8C7FDAEF850" box="[487,527,1906,1934]" italics="true" pageId="7" pageNumber="442">
A 
<subScript id="17B934D9EC2AFFCA51A0F837FDAEF850" attach="left" box="[503,527,1922,1934]" fontSize="5" pageId="7" pageNumber="442">slice</subScript>
</emphasis>
), which would have a vertical second moment of area equal to that of the real slice (
<emphasis id="B949EA8EEC2AFFCA5039F806FF38F865" box="[110,153,1965,1998]" italics="true" pageId="7" pageNumber="442">
I 
<subScript id="17B934D9EC2AFFCA502DF875FF21F810" attach="left" box="[122,128,1984,1998]" fontSize="6" pageId="7" pageNumber="442">z</subScript>
<superScript id="7C489BD4EC2AFFCA502BF818FF38F865" attach="left" box="[124,153,1965,1979]" fontSize="6" pageId="7" pageNumber="442">slice</superScript>
</emphasis>
). Dividing 
<emphasis id="B949EA8EEC2AFFCA514AF807FEE9F810" box="[285,328,1970,1998]" italics="true" pageId="7" pageNumber="442">
h 
<subScript id="17B934D9EC2AFFCA517CF875FEE9F810" attach="left" box="[299,328,1984,1998]" fontSize="6" pageId="7" pageNumber="442">slice</subScript>
</emphasis>
by the length of the nasals converts 
<emphasis id="B949EA8EEC2AFFCA5280F807FCA0F810" box="[727,769,1970,1998]" italics="true" pageId="7" pageNumber="442">
h 
<subScript id="17B934D9EC2AFFCA52B3F875FCA0F810" attach="left" box="[740,769,1984,1998]" fontSize="6" pageId="7" pageNumber="442">slice</subScript>
</emphasis>
to a relative height, a dimensionless “vaulting index”, that allows comparison of the degree of vaulting between cross−sections of all taxa.
</paragraph>
<paragraph id="8B82369CEC2AFFC5536FF807FE55F837" blockId="7.[812,1485,1905,2029]" lastBlockId="8.[102,775,1823,2030]" lastPageId="8" lastPageNumber="443" pageId="7" pageNumber="442">
We also investigated the influence of allometry in nasal width on lateral strength by normalizing 
<emphasis id="B949EA8EEC2AFFCA5550F866FAB9F833" box="[1287,1304,2003,2029]" italics="true" pageId="7" pageNumber="442">
<subScript id="17B934D9EC2AFFCA5550F866FAB9F833" attach="left" box="[1287,1304,2003,2029]" fontSize="7" pageId="7" pageNumber="442">Iy</subScript>
</emphasis>
for slice crosssectional area. By the expression 
<emphasis id="B949EA8EEC25FFC5518EF890FDA2F89F" box="[473,515,1829,1857]" italics="true" pageId="8" pageNumber="443">
s 
<subScript id="17B934D9EC25FFC551B1F886FDA2F89F" attach="left" box="[486,515,1843,1857]" fontSize="6" pageId="8" pageNumber="443">slice</subScript>
</emphasis>
=, 
<emphasis id="B949EA8EEC25FFC55292F890FD4EF89F" box="[709,751,1829,1857]" italics="true" pageId="8" pageNumber="443">
s 
<subScript id="17B934D9EC25FFC55285F886FD4EF89F" attach="left" box="[722,751,1843,1857]" fontSize="6" pageId="8" pageNumber="443">slice</subScript>
</emphasis>
is the span (width) of a rectangle of area equal to 
<emphasis id="B949EA8EEC25FFC552CFF8E4FD6AF8B2" box="[664,715,1873,1900]" italics="true" pageId="8" pageNumber="443">
<subScript id="17B934D9EC25FFC552CFF8E4FD6AF8B2" attach="left" box="[664,715,1873,1900]" fontSize="7" pageId="8" pageNumber="443">Aslice</subScript>
</emphasis>
, that would have the same lateral second moment of area as the real slice. Dividing 
<emphasis id="B949EA8EEC25FFC55117F827FECBF870" box="[320,362,1938,1966]" italics="true" pageId="8" pageNumber="443">
s 
<subScript id="17B934D9EC25FFC5511AF815FECBF870" attach="left" box="[333,362,1952,1966]" fontSize="6" pageId="8" pageNumber="443">slice</subScript>
</emphasis>
for every slice by the lengths of their respective nasals yields a dimensionless “span index” for the contribution of slice widths to 
<emphasis id="B949EA8EEC25FFC551EAF867FE49F804" box="[445,488,1996,2030]" italics="true" pageId="8" pageNumber="443">
I 
<subScript id="17B934D9EC25FFC5519EF855FE71F830" attach="left" box="[457,464,2016,2030]" fontSize="6" pageId="8" pageNumber="443">y</subScript>
<superScript id="7C489BD4EC25FFC5519CF879FE49F804" attach="left" box="[459,488,1996,2010]" fontSize="6" pageId="8" pageNumber="443">slice</superScript>
</emphasis>
.
</paragraph>
<caption id="DF426614EC25FFC55031F921FAE4F93E" ID-DOI="http://doi.org/10.5281/zenodo.3739912" ID-Zenodo-Dep="3739912" httpUri="https://zenodo.org/record/3739912/files/figure.png" pageId="8" pageNumber="443" startId="8.[102,135,1684,1704]" targetBox="[108,1479,227,1655]" targetPageId="8">
<paragraph id="8B82369CEC25FFC55031F921FAE4F93E" blockId="8.[102,1485,1684,1764]" pageId="8" pageNumber="443">
Fig. 9. Comparison of theropod nasal strengths at multiple transverse sections. Horizontal (
<emphasis id="B949EA8EEC25FFC553CCF920FC08F972" box="[923,937,1685,1708]" italics="true" pageId="8" pageNumber="443">
<subScript id="17B934D9EC25FFC553CCF920FC08F972" attach="left" box="[923,937,1685,1708]" fontSize="6" pageId="8" pageNumber="443">Iy</subScript>
</emphasis>
) and vertical (
<emphasis id="B949EA8EEC25FFC5547AF920FB9BF972" box="[1069,1082,1685,1708]" italics="true" pageId="8" pageNumber="443">
<subScript id="17B934D9EC25FFC5547AF920FB9BF972" attach="left" box="[1069,1082,1685,1708]" fontSize="6" pageId="8" pageNumber="443">Iz</subScript>
</emphasis>
) second moments of area of nasal cross−sections of 
<taxonomicName id="4C3D4D1FEC25FFC550F8F905FEF6F91A" authorityName="Marsh" authorityYear="1877" box="[175,343,1712,1732]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="8" pageNumber="443" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC25FFC550F8F905FEF6F91A" box="[175,343,1712,1732]" italics="true" pageId="8" pageNumber="443">Allosaurus fragilis</emphasis>
</taxonomicName>
(upper two graphs) and tyrannosaurids (lower two graphs). Second moments of area are proportional to lateral (
<emphasis id="B949EA8EEC25FFC5551FF904FAF6F916" box="[1352,1367,1713,1736]" italics="true" pageId="8" pageNumber="443">
<subScript id="17B934D9EC25FFC5551FF904FAF6F916" attach="left" box="[1352,1367,1713,1736]" fontSize="6" pageId="8" pageNumber="443">Iy</subScript>
</emphasis>
) and vertical (
<emphasis id="B949EA8EEC25FFC5503AF978FFDAF93A" box="[109,123,1741,1764]" italics="true" pageId="8" pageNumber="443">
<subScript id="17B934D9EC25FFC5503AF978FFDAF93A" attach="right" box="[109,123,1741,1764]" fontSize="6" pageId="8" pageNumber="443">Iz</subScript>
</emphasis>
) bending strengths. X−axes of graphs show relative position of slices along the long axes of the bones: 0.0 is posterior and 1.0 anterior.
</paragraph>
</caption>
<paragraph id="8B82369CEC25FFC5537BF8AAFC00F8B4" blockId="8.[812,1389,1823,1898]" pageId="8" pageNumber="443">Results of nasal morphology and strength analyses</paragraph>
<paragraph id="8B82369CEC25FFC4537BF825FD6CFC3B" blockId="8.[812,1485,1936,2026]" lastBlockId="9.[102,775,652,2026]" lastPageId="9" lastPageNumber="444" pageId="8" pageNumber="443">
<figureCitation id="13062A19EC25FFC5537BF825FCCFF876" box="[812,878,1936,1961]" captionStart="Fig" captionStartId="6.[102,135,1433,1453]" captionTargetBox="[102,1485,226,1404]" captionTargetId="figure@6.[102,1486,229,1405]" captionTargetPageId="6" captionText="Fig. 7. CT−scanned cross−sections of fused tyrannosaurid nasals, showing greater vaulting and higher cross−sectional areas of bone in larger individuals. A. Gorgosaurus libratus (juvenile: TMP 86.144.1). B. Gorgosaurus libratus (subadult: TMP 86.64.1). C. Daspletosaurus torosus (adult: TMP 98.48.1). Numbers 1–4: cross−sections at topologically similar positions, from posterior to anterior." figureDoi="http://doi.org/10.5281/zenodo.3961065" httpUri="https://zenodo.org/record/3961065/files/figure.png" pageId="8" pageNumber="443">Fig. 7</figureCitation>
depicts several CT cross−sections through selected tyrannosaurid nasals. All are minimally fused to unfused anteriorly, strongly fused and vaulted in the middle sections, and flatter posteriorly. Cortical bone was extensive, and the struts comprising the spongy bone in the nasals̓ interiors were so densely packed that they were only clearly visible under high contrast in the CT images. Observations of naturally broken specimens corroborate that the high density apparent in CT slices was not an artifact of inaccurate visualization. CT slices of larger specimens appear proportionally more highly vaulted, wider relative to the element̓s length, and consequently more robust than in the juvenile 
<taxonomicName id="4C3D4D1FEC24FFC45198FC38FD1CFC7A" authority="Lambe, 1914" box="[463,701,908,932]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC24FFC45198FC38FD1CFC7A" box="[463,701,908,932]" italics="true" pageId="9" pageNumber="444">Gorgosaurus libratus</emphasis>
</taxonomicName>
specimen (
<figureCitation id="13062A19EC24FFC450FFFC19FEA2FC1B" box="[168,259,940,965]" captionStart="Fig" captionStartId="6.[102,135,1433,1453]" captionTargetBox="[102,1485,226,1404]" captionTargetId="figure@6.[102,1486,229,1405]" captionTargetPageId="6" captionText="Fig. 7. CT−scanned cross−sections of fused tyrannosaurid nasals, showing greater vaulting and higher cross−sectional areas of bone in larger individuals. A. Gorgosaurus libratus (juvenile: TMP 86.144.1). B. Gorgosaurus libratus (subadult: TMP 86.64.1). C. Daspletosaurus torosus (adult: TMP 98.48.1). Numbers 1–4: cross−sections at topologically similar positions, from posterior to anterior." figureDoi="http://doi.org/10.5281/zenodo.3961065" httpUri="https://zenodo.org/record/3961065/files/figure.png" pageId="9" pageNumber="444">Fig. 7A</figureCitation>
). The 
<taxonomicName id="4C3D4D1FEC24FFC45118FC19FDF7FC1A" authorityName="Russell" authorityYear="1970" box="[335,598,940,964]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC24FFC45118FC19FDF7FC1A" box="[335,598,940,964]" italics="true" pageId="9" pageNumber="444">Daspletosaurus torosus</emphasis>
</taxonomicName>
specimen (
<figureCitation id="13062A19EC24FFC4528DFC19FF26FC3B" captionStart="Fig" captionStartId="6.[102,135,1433,1453]" captionTargetBox="[102,1485,226,1404]" captionTargetId="figure@6.[102,1486,229,1405]" captionTargetPageId="6" captionText="Fig. 7. CT−scanned cross−sections of fused tyrannosaurid nasals, showing greater vaulting and higher cross−sectional areas of bone in larger individuals. A. Gorgosaurus libratus (juvenile: TMP 86.144.1). B. Gorgosaurus libratus (subadult: TMP 86.64.1). C. Daspletosaurus torosus (adult: TMP 98.48.1). Numbers 1–4: cross−sections at topologically similar positions, from posterior to anterior." figureDoi="http://doi.org/10.5281/zenodo.3961065" httpUri="https://zenodo.org/record/3961065/files/figure.png" pageId="9" pageNumber="444">Fig. 7C</figureCitation>
) appears especially massive and tall in cross section.
</paragraph>
<caption id="DF426614EC24FFC45031FF52FD30FF22" ID-Table-UUID="DF426614EC24FFC45031FF52FD30FF22" box="[102,657,231,252]" httpUri="http://table.plazi.org/id/DF426614EC24FFC45031FF52FD30FF22" pageId="9" pageNumber="444" startId="9.[102,157,231,252]" targetBox="[110,1463,282,604]" targetIsTable="true" targetPageId="9">
<paragraph id="8B82369CEC24FFC45031FF52FD30FF22" blockId="9.[102,657,231,252]" box="[102,657,231,252]" pageId="9" pageNumber="444">Table 2. Computed strength properties of theropod nasals</paragraph>
</caption>
<paragraph id="8B82369CEC24FFC452C7FF52FD35FF22" blockId="9.[656,660,231,252]" box="[656,660,231,252]" pageId="9" pageNumber="444">.</paragraph>
<paragraph id="8B82369CEC24FFC4520CFEA9FAF1FD82" pageId="9" pageNumber="444">
<table id="F93DC43CEC2400325039FEAFFA16FD82" box="[110,1463,282,604]" gridcols="5" gridrows="9" pageId="9" pageNumber="444">
<tr id="350D34DEEC2400325039FEAFFA16FE91" box="[110,1463,282,335]" gridrow="0" pageId="9" pageNumber="444" rowspan-0="1">
<th id="76DC5DA2EC240032520CFEAFFD3EFE91" box="[603,671,282,335]" gridcol="1" gridrow="0" pageId="9" pageNumber="444">Length (cm)</th>
<th id="76DC5DA2EC2400325371FEAFFC29FE91" box="[806,904,282,335]" gridcol="2" gridrow="0" pageId="9" pageNumber="444">Iz (m4×10–8)</th>
<th id="76DC5DA2EC2400325457FEAFFBC3FE91" box="[1024,1122,282,335]" gridcol="3" gridrow="0" pageId="9" pageNumber="444">Iy (m4×10–9)</th>
<th id="76DC5DA2EC24003254E2FEAFFA16FE91" box="[1205,1463,282,335]" gridcol="4" gridrow="0" pageId="9" pageNumber="444">Avg. Cross−Sectional Area (m2×10–4)</th>
</tr>
<tr id="350D34DEEC2400325039FEEEFA16FEAF" box="[110,1463,347,369]" gridrow="1" pageId="9" pageNumber="444">
<th id="76DC5DA2EC2400325039FEEEFE73FEAF" box="[110,466,347,369]" gridcol="0" gridrow="1" pageId="9" pageNumber="444">
<taxonomicName id="4C3D4D1FEC24FFC45039FEE9FE9FFEAF" authority="Lambe, 1914" box="[110,318,348,369]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC24FFC45039FEE9FE9FFEAF" box="[110,318,348,369]" italics="true" pageId="9" pageNumber="444">Gorgosaurus libratus</emphasis>
</taxonomicName>
(juvenile) (Gl)
</th>
<td id="76DC5DA2EC240032520CFEEEFD3EFEAF" box="[603,671,347,369]" gridcol="1" gridrow="1" pageId="9" pageNumber="444">31.0</td>
<td id="76DC5DA2EC2400325371FEEEFC29FEAF" box="[806,904,347,369]" gridcol="2" gridrow="1" pageId="9" pageNumber="444">2.935</td>
<td id="76DC5DA2EC2400325457FEEEFBC3FEAF" box="[1024,1122,347,369]" gridcol="3" gridrow="1" pageId="9" pageNumber="444">3.515</td>
<td id="76DC5DA2EC24003254E2FEEEFA16FEAF" box="[1205,1463,347,369]" gridcol="4" gridrow="1" pageId="9" pageNumber="444">2.335</td>
</tr>
<tr id="350D34DEEC2400325039FEC8FA16FE4C" box="[110,1463,381,402]" gridrow="2" pageId="9" pageNumber="444">
<th id="76DC5DA2EC2400325039FEC8FE73FE4C" box="[110,466,381,402]" gridcol="0" gridrow="2" pageId="9" pageNumber="444">
<taxonomicName id="4C3D4D1FEC24FFC45039FEC8FE9FFE4C" authority="Lambe, 1914" box="[110,318,381,402]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC24FFC45039FEC8FE9FFE4C" box="[110,318,381,402]" italics="true" pageId="9" pageNumber="444">Gorgosaurus libratus</emphasis>
</taxonomicName>
(subadult) (Gl)
</th>
<td id="76DC5DA2EC240032520CFEC8FD3EFE4C" box="[603,671,381,402]" gridcol="1" gridrow="2" pageId="9" pageNumber="444">46.5</td>
<td id="76DC5DA2EC2400325371FEC8FC29FE4C" box="[806,904,381,402]" gridcol="2" gridrow="2" pageId="9" pageNumber="444">21.94</td>
<td id="76DC5DA2EC2400325457FEC8FBC3FE4C" box="[1024,1122,381,402]" gridcol="3" gridrow="2" pageId="9" pageNumber="444">45.55</td>
<td id="76DC5DA2EC24003254E2FEC8FA16FE4C" box="[1205,1463,381,402]" gridcol="4" gridrow="2" pageId="9" pageNumber="444">7.709</td>
</tr>
<tr id="350D34DEEC2400325039FE2AFA16FE6A" box="[110,1463,415,436]" gridrow="3" pageId="9" pageNumber="444">
<th id="76DC5DA2EC2400325039FE2AFE73FE6A" box="[110,466,415,436]" gridcol="0" gridrow="3" pageId="9" pageNumber="444">
<taxonomicName id="4C3D4D1FEC24FFC45039FE2AFE06FE6A" authority="(As)" baseAuthorityName="As" box="[110,423,415,436]" class="Reptilia" family="Tyrannosauridae" genus="Albertosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="sarcophagus">
<emphasis id="B949EA8EEC24FFC45039FE2AFED6FE6A" box="[110,375,415,436]" italics="true" pageId="9" pageNumber="444">Albertosaurus sarcophagus</emphasis>
(As)
</taxonomicName>
</th>
<td id="76DC5DA2EC240032520CFE2AFD3EFE6A" box="[603,671,415,436]" gridcol="1" gridrow="3" pageId="9" pageNumber="444">68.7</td>
<td id="76DC5DA2EC2400325371FE2AFC29FE6A" box="[806,904,415,436]" gridcol="2" gridrow="3" pageId="9" pageNumber="444">93.30</td>
<td id="76DC5DA2EC2400325457FE2AFBC3FE6A" box="[1024,1122,415,436]" gridcol="3" gridrow="3" pageId="9" pageNumber="444">302.6</td>
<td id="76DC5DA2EC24003254E2FE2AFA16FE6A" box="[1205,1463,415,436]" gridcol="4" gridrow="3" pageId="9" pageNumber="444">19.44</td>
</tr>
<tr id="350D34DEEC2400325039FE75FA16FE0B" box="[110,1463,448,469]" gridrow="4" pageId="9" pageNumber="444">
<th id="76DC5DA2EC2400325039FE75FE73FE0B" box="[110,466,448,469]" gridcol="0" gridrow="4" pageId="9" pageNumber="444">
<taxonomicName id="4C3D4D1FEC24FFC45039FE75FEDEFE0B" authority="(Dt)" authorityName="Russell" authorityYear="1970" baseAuthorityName="Dt" box="[110,383,448,469]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC24FFC45039FE75FEF3FE0B" box="[110,338,448,469]" italics="true" pageId="9" pageNumber="444">Daspletosaurus torosus</emphasis>
(Dt)
</taxonomicName>
</th>
<td id="76DC5DA2EC240032520CFE75FD3EFE0B" box="[603,671,448,469]" gridcol="1" gridrow="4" pageId="9" pageNumber="444">68.0</td>
<td id="76DC5DA2EC2400325371FE75FC29FE0B" box="[806,904,448,469]" gridcol="2" gridrow="4" pageId="9" pageNumber="444">187.5</td>
<td id="76DC5DA2EC2400325457FE75FBC3FE0B" box="[1024,1122,448,469]" gridcol="3" gridrow="4" pageId="9" pageNumber="444">519.0</td>
<td id="76DC5DA2EC24003254E2FE75FA16FE0B" box="[1205,1463,448,469]" gridcol="4" gridrow="4" pageId="9" pageNumber="444">27.69</td>
</tr>
<tr id="350D34DEEC2400325039FE57FA16FE29" box="[110,1463,482,503]" gridrow="5" pageId="9" pageNumber="444">
<th id="76DC5DA2EC2400325039FE57FE73FE29" box="[110,466,482,503]" gridcol="0" gridrow="5" pageId="9" pageNumber="444">
<taxonomicName id="4C3D4D1FEC24FFC45039FE57FEF1FE29" authority="(Tr)" authorityName="Osborn" authorityYear="1905" baseAuthorityName="Tr" box="[110,336,482,503]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC24FFC45039FE57FE85FE29" box="[110,292,482,503]" italics="true" pageId="9" pageNumber="444">Tyrannosaurus rex</emphasis>
(Tr)
</taxonomicName>
</th>
<td id="76DC5DA2EC240032520CFE57FD3EFE29" box="[603,671,482,503]" gridcol="1" gridrow="5" pageId="9" pageNumber="444">81.0</td>
<td id="76DC5DA2EC2400325371FE57FC29FE29" box="[806,904,482,503]" gridcol="2" gridrow="5" pageId="9" pageNumber="444">496.3</td>
<td id="76DC5DA2EC2400325457FE57FBC3FE29" box="[1024,1122,482,503]" gridcol="3" gridrow="5" pageId="9" pageNumber="444">769.7</td>
<td id="76DC5DA2EC24003254E2FE57FA16FE29" box="[1205,1463,482,503]" gridcol="4" gridrow="5" pageId="9" pageNumber="444">33.30</td>
</tr>
<tr id="350D34DEEC2400325039FDB6FA16FDC7" box="[110,1463,515,537]" gridrow="6" pageId="9" pageNumber="444">
<th id="76DC5DA2EC2400325039FDB6FE73FDC7" box="[110,466,515,537]" gridcol="0" gridrow="6" pageId="9" pageNumber="444">
<taxonomicName id="4C3D4D1FEC24FFC45039FDB1FE80FDC7" authorityName="Marsh" authorityYear="1877" box="[110,289,516,537]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC24FFC45039FDB1FE80FDC7" box="[110,289,516,537]" italics="true" pageId="9" pageNumber="444">Allosaurus fragilis</emphasis>
</taxonomicName>
(small) (Af)
</th>
<td id="76DC5DA2EC240032520CFDB6FD3EFDC7" box="[603,671,515,537]" gridcol="1" gridrow="6" pageId="9" pageNumber="444">24.1</td>
<td id="76DC5DA2EC2400325371FDB6FC29FDC7" box="[806,904,515,537]" gridcol="2" gridrow="6" pageId="9" pageNumber="444">3.881</td>
<td id="76DC5DA2EC2400325457FDB6FBC3FDC7" box="[1024,1122,515,537]" gridcol="3" gridrow="6" pageId="9" pageNumber="444">17.01</td>
<td id="76DC5DA2EC24003254E2FDB6FA16FDC7" box="[1205,1463,515,537]" gridcol="4" gridrow="6" pageId="9" pageNumber="444">4.376</td>
</tr>
<tr id="350D34DEEC2400325039FD90FA16FDE4" box="[110,1463,549,570]" gridrow="7" pageId="9" pageNumber="444">
<th id="76DC5DA2EC2400325039FD90FE73FDE4" box="[110,466,549,570]" gridcol="0" gridrow="7" pageId="9" pageNumber="444">
<taxonomicName id="4C3D4D1FEC24FFC45039FD90FE80FDE4" authorityName="Marsh" authorityYear="1877" box="[110,289,549,570]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC24FFC45039FD90FE80FDE4" box="[110,289,549,570]" italics="true" pageId="9" pageNumber="444">Allosaurus fragilis</emphasis>
</taxonomicName>
(medium) (Af)
</th>
<td id="76DC5DA2EC240032520CFD90FD3EFDE4" box="[603,671,549,570]" gridcol="1" gridrow="7" pageId="9" pageNumber="444">28.0</td>
<td id="76DC5DA2EC2400325371FD90FC29FDE4" box="[806,904,549,570]" gridcol="2" gridrow="7" pageId="9" pageNumber="444">7.186</td>
<td id="76DC5DA2EC2400325457FD90FBC3FDE4" box="[1024,1122,549,570]" gridcol="3" gridrow="7" pageId="9" pageNumber="444">45.53</td>
<td id="76DC5DA2EC24003254E2FD90FA16FDE4" box="[1205,1463,549,570]" gridcol="4" gridrow="7" pageId="9" pageNumber="444">6.725</td>
</tr>
<tr id="350D34DEEC2400325039FDF2FA16FD82" box="[110,1463,583,604]" gridrow="8" pageId="9" pageNumber="444">
<th id="76DC5DA2EC2400325039FDF2FE73FD82" box="[110,466,583,604]" gridcol="0" gridrow="8" pageId="9" pageNumber="444">
<taxonomicName id="4C3D4D1FEC24FFC45039FDF2FE80FD82" authorityName="Marsh" authorityYear="1877" box="[110,289,583,604]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC24FFC45039FDF2FE80FD82" box="[110,289,583,604]" italics="true" pageId="9" pageNumber="444">Allosaurus fragilis</emphasis>
</taxonomicName>
(large) (Af)
</th>
<td id="76DC5DA2EC240032520CFDF2FD3EFD82" box="[603,671,583,604]" gridcol="1" gridrow="8" pageId="9" pageNumber="444">40.5</td>
<td id="76DC5DA2EC2400325371FDF2FC29FD82" box="[806,904,583,604]" gridcol="2" gridrow="8" pageId="9" pageNumber="444">24.62</td>
<td id="76DC5DA2EC2400325457FDF2FBC3FD82" box="[1024,1122,583,604]" gridcol="3" gridrow="8" pageId="9" pageNumber="444">115.3</td>
<td id="76DC5DA2EC24003254E2FDF2FA16FD82" box="[1205,1463,583,604]" gridcol="4" gridrow="8" pageId="9" pageNumber="444">13.04</td>
</tr>
</table>
</paragraph>
<paragraph id="8B82369CEC24FFC450DBFC58FD4DFB58" blockId="9.[102,775,652,2026]" pageId="9" pageNumber="444">
Nasal cross−sectional areas, which correlate positively with compressional strength (Gordon 1979), are much higher in the adult tyrannosaurids than in other specimens (
<tableCitation id="C6BF0327EC24FFC452FEFB98FCA0FB98" box="[681,769,1069,1094]" captionStart="Table 2" captionStartId="9.[102,157,231,252]" captionTargetBox="[110,1463,282,604]" captionTargetId="graphics@9.[102,1485,271,607]" captionText="Table 2. Computed strength properties of theropod nasals" httpUri="http://table.plazi.org/id/DF426614EC24FFC45031FF52FD30FF22" pageId="9" pageNumber="444" tableUuid="DF426614EC24FFC45031FF52FD30FF22">Table 2</tableCitation>
, 
<figureCitation id="13062A19EC24FFC45031FBF8FF08FBB8" box="[102,169,1101,1126]" captionStart="Fig" captionStartId="7.[812,845,1631,1651]" captionTargetBox="[817,1481,230,1606]" captionTargetId="graphics@7.[917,1470,726,1087]" captionText="Fig. 8. Average strengths of nasal cross−sections in tyrannosaurids and Allosaurus fragilis, plotted against nasal length. A. Cross−sectional areas, proportional to compression strengths. B. Second moment of area, proportional to vertical bending strength. C. Second moment of area, proportional to lateral bending strength. Values for the A. fragilis nasals are uncorrected for the hollowness of the sections, which would reduce their strengths. Lines fitted to the tyrannosaurid values are derived from log transformed data. See Appendix 1 for labels." figureDoi="http://doi.org/10.5281/zenodo.3961039" httpUri="https://zenodo.org/record/3961039/files/figure.png" pageId="9" pageNumber="444">Fig. 8</figureCitation>
). Areas for 
<taxonomicName id="4C3D4D1FEC24FFC45178FBF8FD98FBB8" authorityName="Russell" authorityYear="1970" box="[303,569,1101,1126]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC24FFC45178FBF8FD98FBB8" box="[303,569,1101,1126]" italics="true" pageId="9" pageNumber="444">Daspletosaurus torosus</emphasis>
</taxonomicName>
are higher than in the 
<emphasis id="B949EA8EEC24FFC450D8FBD8FE65FB5B" box="[143,452,1133,1157]" italics="true" pageId="9" pageNumber="444">Albertosaurus sarcophagus</emphasis>
nasals of the same length.
</paragraph>
<paragraph id="8B82369CEC24FFC450DBFB3AFD7BFA56" blockId="9.[102,775,652,2026]" pageId="9" pageNumber="444">
<tableCitation id="C6BF0327EC24FFC450DBFB3AFF42FB76" box="[140,227,1167,1192]" captionStart="Table 2" captionStartId="9.[102,157,231,252]" captionTargetBox="[110,1463,282,604]" captionTargetId="graphics@9.[102,1485,271,607]" captionText="Table 2. Computed strength properties of theropod nasals" httpUri="http://table.plazi.org/id/DF426614EC24FFC45031FF52FD30FF22" pageId="9" pageNumber="444" tableUuid="DF426614EC24FFC45031FF52FD30FF22">Table 2</tableCitation>
reports average second moments of area 
<emphasis id="B949EA8EEC24FFC45293FB25FD75FB74" box="[708,724,1168,1194]" italics="true" pageId="9" pageNumber="444">
<subScript id="17B934D9EC24FFC45293FB25FD75FB74" attach="left" box="[708,724,1168,1194]" fontSize="7" pageId="9" pageNumber="444">Iz</subScript>
</emphasis>
and 
<emphasis id="B949EA8EEC24FFC45031FB05FFD6FB14" box="[102,119,1200,1226]" italics="true" pageId="9" pageNumber="444">
<subScript id="17B934D9EC24FFC45031FB05FFD6FB14" attach="left" box="[102,119,1200,1226]" fontSize="7" pageId="9" pageNumber="444">Iy</subScript>
</emphasis>
, which respectively indicate vertical and lateral bending strengths, and average cross−sectional area, for all examined tyrannosaurid and 
<taxonomicName id="4C3D4D1FEC24FFC4512AFB5AFE58FAD9" authorityName="Marsh" authorityYear="1877" box="[381,505,1263,1287]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC4512AFB5AFE58FAD9" box="[381,505,1263,1287]" italics="true" pageId="9" pageNumber="444">Allosaurus</emphasis>
</taxonomicName>
nasals. The average 
<emphasis id="B949EA8EEC24FFC452A2FB45FCA7FAD4" box="[757,774,1264,1290]" italics="true" pageId="9" pageNumber="444">
<subScript id="17B934D9EC24FFC452A2FB45FCA7FAD4" attach="left" box="[757,774,1264,1290]" fontSize="7" pageId="9" pageNumber="444">Iz</subScript>
</emphasis>
for resistance to vertical bending increases faster than nasal length. While lateral strength indicators 
<emphasis id="B949EA8EEC24FFC4527AFA85FD9FFA94" box="[557,574,1328,1354]" italics="true" pageId="9" pageNumber="444">
<subScript id="17B934D9EC24FFC4527AFA85FD9FFA94" attach="left" box="[557,574,1328,1354]" fontSize="7" pageId="9" pageNumber="444">Iy</subScript>
</emphasis>
are not as high as those for vertical bending, the discrepancies between small and large specimens are even more dramatic (
<tableCitation id="C6BF0327EC24FFC45226FADAFD6DFA56" box="[625,716,1391,1416]" captionStart="Table 2" captionStartId="9.[102,157,231,252]" captionTargetBox="[110,1463,282,604]" captionTargetId="graphics@9.[102,1485,271,607]" captionText="Table 2. Computed strength properties of theropod nasals" httpUri="http://table.plazi.org/id/DF426614EC24FFC45031FF52FD30FF22" pageId="9" pageNumber="444" tableUuid="DF426614EC24FFC45031FF52FD30FF22">Table 2</tableCitation>
).
</paragraph>
<paragraph id="8B82369CEC24FFC450DBFA25FEAFF917" blockId="9.[102,775,652,2026]" pageId="9" pageNumber="444">
The 
<taxonomicName id="4C3D4D1FEC24FFC450EAFA25FEC8FA76" authorityName="Russell" authorityYear="1970" box="[189,361,1424,1448]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC450EAFA25FEC8FA76" box="[189,361,1424,1448]" italics="true" pageId="9" pageNumber="444">Daspletosaurus</emphasis>
</taxonomicName>
and 
<taxonomicName id="4C3D4D1FEC24FFC451CAFA24FDE5FA76" authorityName="Osborn" authorityYear="1905" box="[413,580,1425,1448]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC451CAFA24FDE5FA76" box="[413,580,1425,1448]" italics="true" pageId="9" pageNumber="444">Tyrannosaurus</emphasis>
</taxonomicName>
nasals had higher average indicators for vertical bending strength than in the adult 
<taxonomicName id="4C3D4D1FEC24FFC450FEFA64FE9BFA36" box="[169,314,1489,1512]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC450FEFA64FE9BFA36" box="[169,314,1489,1512]" italics="true" pageId="9" pageNumber="444">Gorgosaurus</emphasis>
</taxonomicName>
and 
<taxonomicName id="4C3D4D1FEC24FFC4512BFA65FDB6FA36" box="[380,535,1488,1512]" class="Reptilia" family="Tyrannosauridae" genus="Albertosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC4512BFA65FDB6FA36" box="[380,535,1488,1512]" italics="true" pageId="9" pageNumber="444">Albertosaurus</emphasis>
</taxonomicName>
. 
<emphasis id="B949EA8EEC24FFC4527CFA64FD9DFA32" box="[555,572,1489,1516]" italics="true" pageId="9" pageNumber="444">
<subScript id="17B934D9EC24FFC4527CFA64FD9DFA32" attach="left" box="[555,572,1489,1516]" fontSize="7" pageId="9" pageNumber="444">Iy</subScript>
</emphasis>
of the 
<taxonomicName id="4C3D4D1FEC24FFC452CDFA65FF0EF9D6" authorityName="Russell" authorityYear="1970" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC452CDFA65FF0EF9D6" italics="true" pageId="9" pageNumber="444">Daspletosaurus</emphasis>
</taxonomicName>
nasals is almost twice that of the equivalently long adult 
<taxonomicName id="4C3D4D1FEC24FFC450F4F9A5FE9FF9F6" box="[163,318,1552,1576]" class="Reptilia" family="Tyrannosauridae" genus="Albertosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC450F4F9A5FE9FF9F6" box="[163,318,1552,1576]" italics="true" pageId="9" pageNumber="444">Albertosaurus</emphasis>
</taxonomicName>
specimen (
<figureCitation id="13062A19EC24FFC451EBF9A5FE5EF9F7" box="[444,511,1552,1577]" captionStart="Fig" captionStartId="7.[812,845,1631,1651]" captionTargetBox="[817,1481,230,1606]" captionTargetId="graphics@7.[917,1470,726,1087]" captionText="Fig. 8. Average strengths of nasal cross−sections in tyrannosaurids and Allosaurus fragilis, plotted against nasal length. A. Cross−sectional areas, proportional to compression strengths. B. Second moment of area, proportional to vertical bending strength. C. Second moment of area, proportional to lateral bending strength. Values for the A. fragilis nasals are uncorrected for the hollowness of the sections, which would reduce their strengths. Lines fitted to the tyrannosaurid values are derived from log transformed data. See Appendix 1 for labels." figureDoi="http://doi.org/10.5281/zenodo.3961039" httpUri="https://zenodo.org/record/3961039/files/figure.png" pageId="9" pageNumber="444">Fig. 8</figureCitation>
). The 
<taxonomicName id="4C3D4D1FEC24FFC45211F9A5FD1CF9F6" authorityName="Marsh" authorityYear="1877" box="[582,701,1552,1576]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC45211F9A5FD1CF9F6" box="[582,701,1552,1576]" italics="true" pageId="9" pageNumber="444">Allosaurus</emphasis>
</taxonomicName>
nasals had relatively high strength indicators 
<emphasis id="B949EA8EEC24FFC4524BF984FD8CF992" box="[540,557,1585,1612]" italics="true" pageId="9" pageNumber="444">
<subScript id="17B934D9EC24FFC4524BF984FD8CF992" attach="left" box="[540,557,1585,1612]" fontSize="7" pageId="9" pageNumber="444">Iy</subScript>
</emphasis>
and 
<emphasis id="B949EA8EEC24FFC4523EF984FDD8F992" box="[617,633,1585,1612]" italics="true" pageId="9" pageNumber="444">
<subScript id="17B934D9EC24FFC4523EF984FDD8F992" attach="left" box="[617,633,1585,1612]" fontSize="7" pageId="9" pageNumber="444">Iz</subScript>
</emphasis>
for bending when compared with tyrannosaurid nasals of a given length (
<figureCitation id="13062A19EC24FFC45039F9C5FF15F957" box="[110,180,1648,1673]" captionStart="Fig" captionStartId="7.[812,845,1631,1651]" captionTargetBox="[817,1481,230,1606]" captionTargetId="graphics@7.[917,1470,726,1087]" captionText="Fig. 8. Average strengths of nasal cross−sections in tyrannosaurids and Allosaurus fragilis, plotted against nasal length. A. Cross−sectional areas, proportional to compression strengths. B. Second moment of area, proportional to vertical bending strength. C. Second moment of area, proportional to lateral bending strength. Values for the A. fragilis nasals are uncorrected for the hollowness of the sections, which would reduce their strengths. Lines fitted to the tyrannosaurid values are derived from log transformed data. See Appendix 1 for labels." figureDoi="http://doi.org/10.5281/zenodo.3961039" httpUri="https://zenodo.org/record/3961039/files/figure.png" pageId="9" pageNumber="444">Fig. 8</figureCitation>
), although their increases in nasal bending strength with increases in nasal length are less dramatic than in the tyrannosaurids.
</paragraph>
<paragraph id="8B82369CEC24FFC450DBF964FE52F834" blockId="9.[102,775,652,2026]" pageId="9" pageNumber="444">
<figureCitation id="13062A19EC24FFC450DBF964FF6CF934" box="[140,205,1745,1770]" captionStart="Fig" captionStartId="8.[102,135,1684,1704]" captionTargetBox="[108,1479,227,1655]" captionTargetPageId="8" captionText="Fig. 9. Comparison of theropod nasal strengths at multiple transverse sections. Horizontal (Iy) and vertical (Iz) second moments of area of nasal cross−sections of Allosaurus fragilis (upper two graphs) and tyrannosaurids (lower two graphs). Second moments of area are proportional to lateral (Iy) and vertical (Iz) bending strengths. X−axes of graphs show relative position of slices along the long axes of the bones: 0.0 is posterior and 1.0 anterior." figureDoi="http://doi.org/10.5281/zenodo.3739912" httpUri="https://zenodo.org/record/3739912/files/figure.png" pageId="9" pageNumber="444">Fig. 9</figureCitation>
graphs the distribution of second moments of area for individual nasal cross−sections. For resistance to vertical bending 
<taxonomicName id="4C3D4D1FEC24FFC4509FF8A7FEE0F8F4" authorityName="Marsh" authorityYear="1877" box="[200,321,1810,1834]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC4509FF8A7FEE0F8F4" box="[200,321,1810,1834]" italics="true" pageId="9" pageNumber="444">Allosaurus</emphasis>
</taxonomicName>
and tyrannosaurid nasals have higher 
<emphasis id="B949EA8EEC24FFC452A1F8A6FCA7F8F3" box="[758,774,1811,1837]" italics="true" pageId="9" pageNumber="444">
<subScript id="17B934D9EC24FFC452A1F8A6FCA7F8F3" attach="left" box="[758,774,1811,1837]" fontSize="7" pageId="9" pageNumber="444">Iz</subScript>
</emphasis>
anteriorly than posteriorly. At posterior sections in 
<taxonomicName id="4C3D4D1FEC24FFC452E3F887FF10F8B4" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC452E3F887FF10F8B4" italics="true" pageId="9" pageNumber="444">Gorgosaurus</emphasis>
</taxonomicName>
and 
<taxonomicName id="4C3D4D1FEC24FFC450BAF8E7FE0DF8B3" authority=", Iz" authorityName="Iz" box="[237,428,1874,1901]" class="Reptilia" family="Tyrannosauridae" genus="Albertosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC450BAF8E7FE2DF8B4" box="[237,396,1874,1898]" italics="true" pageId="9" pageNumber="444">Albertosaurus</emphasis>
, 
<emphasis id="B949EA8EEC24FFC451CBF8E6FE0DF8B3" box="[412,428,1875,1901]" italics="true" pageId="9" pageNumber="444">
<subScript id="17B934D9EC24FFC451CBF8E6FE0DF8B3" attach="left" box="[412,428,1875,1901]" fontSize="7" pageId="9" pageNumber="444">Iz</subScript>
</emphasis>
</taxonomicName>
falls off more rapidly than in 
<taxonomicName id="4C3D4D1FEC24FFC45031F8C6FEB1F854" authorityName="Osborn" authorityYear="1905" box="[102,272,1907,1930]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC45031F8C6FEB1F854" box="[102,272,1907,1930]" italics="true" pageId="9" pageNumber="444">Tyrannosaurus</emphasis>
</taxonomicName>
and 
<taxonomicName id="4C3D4D1FEC24FFC45104F8C7FDA2F854" authorityName="Russell" authorityYear="1970" box="[339,515,1906,1930]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC45104F8C7FDA2F854" box="[339,515,1906,1930]" italics="true" pageId="9" pageNumber="444">Daspletosaurus</emphasis>
</taxonomicName>
. Resistance to lateral bending 
<emphasis id="B949EA8EEC24FFC45091F826FF79F873" box="[198,216,1939,1965]" italics="true" pageId="9" pageNumber="444">
<subScript id="17B934D9EC24FFC45091F826FF79F873" attach="left" box="[198,216,1939,1965]" fontSize="7" pageId="9" pageNumber="444">Iy</subScript>
</emphasis>
generally increases posteriorly in 
<taxonomicName id="4C3D4D1FEC24FFC45203F827FD6CF874" authorityName="Marsh" authorityYear="1877" box="[596,717,1938,1962]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC45203F827FD6CF874" box="[596,717,1938,1962]" italics="true" pageId="9" pageNumber="444">Allosaurus</emphasis>
</taxonomicName>
. The lateral strength indicators peak anteriorly in tyrannosaurids, and in general decrease posteriorly.
</paragraph>
<paragraph id="8B82369CEC24FFC45305FD38FA67FCDB" blockId="9.[812,1485,652,1445]" pageId="9" pageNumber="444">
In all specimens the anterior− and posteriormost second moments of area are low. Other bones articulate with the nasals in these areas, however, and presumably compensate for low strengths here of the nasals themselves (
<figureCitation id="13062A19EC24FFC45560FD59FA25FCDB" box="[1335,1412,748,773]" captionStart="Fig" captionStartId="5.[102,135,1750,1770]" captionTargetBox="[121,755,223,1724]" captionTargetId="figure@5.[121,755,223,1724]" captionTargetPageId="5" captionText="Fig. 5. CT cross sections and reconstructions of Allosaurus fragilis nasals: A, largest (UUVP 1663/UMNH VP 9146); B, midsize (UUVP 1913/ UMNH VP 9144); and C, smallest (UUVP 10854/UMNHVP 7784). Anterior is to the right. Cross sections are from the strongly pneumatized regions of the nasals, at positions indicated by the dashed lines. The slices are normalized to the same size to show the relative degree of pneumatic excavation, evident despite mineral infilling in some sections. Reconstructions are in lateral views and in dorsal views with single left or right specimens mirrored to replicate complete pairs. Specimen B is broken over the posterior part of the external nares. Scale bar 10 cm." figureDoi="http://doi.org/10.5281/zenodo.3739906" httpUri="https://zenodo.org/record/3739906/files/figure.png" pageId="9" pageNumber="444">Figs. 5</figureCitation>
, 
<figureCitation id="13062A19EC24FFC455D9FD58FA3FFCDA" box="[1422,1438,749,772]" captionStart="Fig" captionStartId="6.[102,135,1433,1453]" captionTargetBox="[102,1485,226,1404]" captionTargetId="figure@6.[102,1486,229,1405]" captionTargetPageId="6" captionText="Fig. 7. CT−scanned cross−sections of fused tyrannosaurid nasals, showing greater vaulting and higher cross−sectional areas of bone in larger individuals. A. Gorgosaurus libratus (juvenile: TMP 86.144.1). B. Gorgosaurus libratus (subadult: TMP 86.64.1). C. Daspletosaurus torosus (adult: TMP 98.48.1). Numbers 1–4: cross−sections at topologically similar positions, from posterior to anterior." figureDoi="http://doi.org/10.5281/zenodo.3961065" httpUri="https://zenodo.org/record/3961065/files/figure.png" pageId="9" pageNumber="444">7</figureCitation>
, 
<figureCitation id="13062A19EC24FFC455FFFD59FA19FCDB" box="[1448,1464,748,773]" captionStart="Fig" captionStartId="7.[812,845,1631,1651]" captionTargetBox="[817,1481,230,1606]" captionTargetId="graphics@7.[917,1470,726,1087]" captionText="Fig. 8. Average strengths of nasal cross−sections in tyrannosaurids and Allosaurus fragilis, plotted against nasal length. A. Cross−sectional areas, proportional to compression strengths. B. Second moment of area, proportional to vertical bending strength. C. Second moment of area, proportional to lateral bending strength. Values for the A. fragilis nasals are uncorrected for the hollowness of the sections, which would reduce their strengths. Lines fitted to the tyrannosaurid values are derived from log transformed data. See Appendix 1 for labels." figureDoi="http://doi.org/10.5281/zenodo.3961039" httpUri="https://zenodo.org/record/3961039/files/figure.png" pageId="9" pageNumber="444">8</figureCitation>
).
</paragraph>
<paragraph id="8B82369CEC24FFC45305FCB9FAD8FB1B" blockId="9.[812,1485,652,1445]" pageId="9" pageNumber="444">
Our “vaulting index” measures the effects of shape on nasal strength (
<figureCitation id="13062A19EC24FFC453E2FC99FBBBFC9B" box="[949,1050,812,837]" captionStart="Fig" captionStartId="10.[102,135,1356,1376]" captionTargetBox="[106,770,225,1318]" captionTargetId="graphics@10.[106,769,259,1263]" captionTargetPageId="10" captionText="Fig. 10. Heights and widths of tyrannosaurid nasal slices normalized for slice area and bone length. A. Normalized heights (“vaulting index”) showing convergence of vaulting pattern at large size. B. Normalized widths (“span index”) showing isometric form in most specimens, but exaggerated relative width in Tyrannosaurus rex nasals. Points of maximum vaulting and span are indicated on nasals of T. rex (TMP 98.86.01; cast of BHI 2033). Symbols as per Fig. 9." figureDoi="http://doi.org/10.5281/zenodo.3739914" httpUri="https://zenodo.org/record/3739914/files/figure.png" pageId="9" pageNumber="444">Fig. 10A</figureCitation>
), and shows that the vertical second moment of area would be greater in the adult tyrannosaurids, even if corresponding slices in all tyrannosaurid specimens were scaled to the same cross sectional areas. Above the largest maxillary teeth, the adult 
<taxonomicName id="4C3D4D1FEC24FFC45414FC19FB7FFC1A" box="[1091,1246,940,964]" class="Reptilia" family="Tyrannosauridae" genus="Albertosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC45414FC19FB7FFC1A" box="[1091,1246,940,964]" italics="true" pageId="9" pageNumber="444">Albertosaurus</emphasis>
</taxonomicName>
, 
<taxonomicName id="4C3D4D1FEC24FFC454BBFC19FA39FC1A" authorityName="Russell" authorityYear="1970" box="[1260,1432,940,964]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC454BBFC19FA39FC1A" box="[1260,1432,940,964]" italics="true" pageId="9" pageNumber="444">Daspletosaurus</emphasis>
</taxonomicName>
, and 
<taxonomicName id="4C3D4D1FEC24FFC4537BFC78FC72FC3A" authorityName="Osborn" authorityYear="1905" box="[812,979,973,996]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC4537BFC78FC72FC3A" box="[812,979,973,996]" italics="true" pageId="9" pageNumber="444">Tyrannosaurus</emphasis>
</taxonomicName>
nasals are more highly vaulted than in the juvenile 
<taxonomicName id="4C3D4D1FEC24FFC45322FC58FBA7FBDA" box="[885,1030,1005,1028]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC45322FC58FBA7FBDA" box="[885,1030,1005,1028]" italics="true" pageId="9" pageNumber="444">Gorgosaurus</emphasis>
</taxonomicName>
. The subadult 
<taxonomicName id="4C3D4D1FEC24FFC454F2FC58FA97FBDA" box="[1189,1334,1005,1028]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC454F2FC58FA97FBDA" box="[1189,1334,1005,1028]" italics="true" pageId="9" pageNumber="444">Gorgosaurus</emphasis>
</taxonomicName>
specimen approaches the degree of vaulting seen in the adult 
<taxonomicName id="4C3D4D1FEC24FFC45525FBB9FCD4FB9A" class="Reptilia" family="Tyrannosauridae" genus="Albertosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC45525FBB9FCD4FB9A" italics="true" pageId="9" pageNumber="444">Albertosaurus</emphasis>
</taxonomicName>
, possibly indicating that the nasals of these taxa increased little in vaulting after a certain stage of growth. Posteriorly the 
<taxonomicName id="4C3D4D1FEC24FFC453C0FBD9FBE2FB5A" authorityName="Russell" authorityYear="1970" box="[919,1091,1132,1156]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC453C0FBD9FBE2FB5A" box="[919,1091,1132,1156]" italics="true" pageId="9" pageNumber="444">Daspletosaurus</emphasis>
</taxonomicName>
and 
<taxonomicName id="4C3D4D1FEC24FFC45420FBD8FABFFB5A" authorityName="Osborn" authorityYear="1905" box="[1143,1310,1133,1156]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC24FFC45420FBD8FABFFB5A" box="[1143,1310,1133,1156]" italics="true" pageId="9" pageNumber="444">Tyrannosaurus</emphasis>
</taxonomicName>
nasals are more vaulted than in the other taxa, and which may have contributed to greater relative bending strength of these elements.
</paragraph>
<paragraph id="8B82369CEC24FFC45305FB79FA0FFA7B" blockId="9.[812,1485,652,1445]" pageId="9" pageNumber="444">
The “span index” (
<figureCitation id="13062A19EC24FFC45472FB79FB28FB3B" box="[1061,1161,1228,1253]" captionStart="Fig" captionStartId="10.[102,135,1356,1376]" captionTargetBox="[106,770,225,1318]" captionTargetId="graphics@10.[106,769,259,1263]" captionTargetPageId="10" captionText="Fig. 10. Heights and widths of tyrannosaurid nasal slices normalized for slice area and bone length. A. Normalized heights (“vaulting index”) showing convergence of vaulting pattern at large size. B. Normalized widths (“span index”) showing isometric form in most specimens, but exaggerated relative width in Tyrannosaurus rex nasals. Points of maximum vaulting and span are indicated on nasals of T. rex (TMP 98.86.01; cast of BHI 2033). Symbols as per Fig. 9." figureDoi="http://doi.org/10.5281/zenodo.3739914" httpUri="https://zenodo.org/record/3739914/files/figure.png" pageId="9" pageNumber="444">Fig. 10B</figureCitation>
) indicates that allometric expansion in width had little effect on lateral second moment of area 
<emphasis id="B949EA8EEC24FFC45336FAB8FCD3FAF6" box="[865,882,1293,1320]" italics="true" pageId="9" pageNumber="444">
<subScript id="17B934D9EC24FFC45336FAB8FCD3FAF6" attach="left" box="[865,882,1293,1320]" fontSize="7" pageId="9" pageNumber="444">Iy</subScript>
</emphasis>
for most of the tyrannosaurids, because their area−normalized scores for 
<emphasis id="B949EA8EEC24FFC453AAFA98FBAFFA96" box="[1021,1038,1325,1352]" italics="true" pageId="9" pageNumber="444">
<subScript id="17B934D9EC24FFC453AAFA98FBAFFA96" attach="left" box="[1021,1038,1325,1352]" fontSize="7" pageId="9" pageNumber="444">Iy</subScript>
</emphasis>
overlap. However, 
<emphasis id="B949EA8EEC24FFC454BEFA98FB5BFA96" box="[1257,1274,1325,1352]" italics="true" pageId="9" pageNumber="444">
<subScript id="17B934D9EC24FFC454BEFA98FB5BFA96" attach="left" box="[1257,1274,1325,1352]" fontSize="7" pageId="9" pageNumber="444">Iy</subScript>
</emphasis>
values of the anterior 
<taxonomicName id="4C3D4D1FEC24FFC4530DFAF8FB8BFABA" authorityName="Osborn" authorityYear="1905" box="[858,1066,1357,1380]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC24FFC4530DFAF8FB8BFABA" box="[858,1066,1357,1380]" italics="true" pageId="9" pageNumber="444">Tyrannosaurus rex</emphasis>
</taxonomicName>
cross−sections were much higher than in the other taxa, indicating that allometric lateral expansion increased the relative lateral bending strength of its nasals.
</paragraph>
<paragraph id="8B82369CEC24FFC4537BFA53FAD0F99B" blockId="9.[812,1393,1510,1605]" pageId="9" pageNumber="444">
<heading id="D0CA81F0EC24FFC4537BFA53FB60F9CE" box="[812,1217,1510,1552]" fontSize="18" level="1" pageId="9" pageNumber="444" reason="1">Cranium strengths of</heading>
tyrannosaurids and carnosaurs
</paragraph>
<paragraph id="8B82369CEC24FFC4537BF9DBFBB7F969" blockId="9.[812,1469,1646,1719]" pageId="9" pageNumber="444">Materials and methods for calculating theropod cranium strength</paragraph>
<paragraph id="8B82369CEC24FFC4537BF967FB22F834" blockId="9.[812,1485,1745,2026]" pageId="9" pageNumber="444">
<emphasis id="B949EA8EEC24FFC4537BF967FB4DF934" bold="true" box="[812,1260,1745,1770]" pageId="9" pageNumber="444">External geometry of theropod crania</emphasis>
.—We produced 3D numerical representations of theropod crania (
<figureCitation id="13062A19EC24FFC45567F944FA21F8D4" box="[1328,1408,1777,1802]" captionStart="Fig" captionStartId="11.[812,845,1343,1363]" captionTargetBox="[101,1485,237,1477]" captionTargetPageId="11" captionText="Fig. 11. Top and side views of theropod crania used to reconstruct crosssectional shapes, and oblique views of reconstructed plinge cross−sections for each cranium. Second moments of area of the plinges were calculated as indices of bending and torsional cranium strengths. A–D, carnosaurs; E–G, tyrannosaurids." figureDoi="http://doi.org/10.5281/zenodo.3961067" httpUri="https://zenodo.org/record/3961067/files/figure.png" pageId="9" pageNumber="444">Fig. 11</figureCitation>
) in or− der to examine the correspondence between cranium shape and strength. We chose tyrannosaurid and carnosaur specimens of similar skull lengths, approximately matching the tyrannosaurids 
<taxonomicName id="4C3D4D1FEC24FFC4538DF8C7FB6CF854" authority="Lambe, 1914" box="[986,1229,1906,1930]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC24FFC4538DF8C7FB6CF854" box="[986,1229,1906,1930]" italics="true" pageId="9" pageNumber="444">Gorgosaurus libratus</emphasis>
</taxonomicName>
, 
<taxonomicName id="4C3D4D1FEC24FFC4548AF8C7FCF1F874" authorityName="Russell" authorityYear="1970" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC24FFC4548AF8C7FCF1F874" italics="true" pageId="9" pageNumber="444">Daspletosaurus torosus</emphasis>
</taxonomicName>
, and a medium sized 
<taxonomicName id="4C3D4D1FEC24FFC45411F826FABDF874" authorityName="Osborn" authorityYear="1905" box="[1094,1308,1939,1962]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC24FFC45411F826FABDF874" box="[1094,1308,1939,1962]" italics="true" pageId="9" pageNumber="444">Tyrannosaurus rex</emphasis>
</taxonomicName>
with the carnosaurs 
<taxonomicName id="4C3D4D1FEC24FFC45339F807FBE1F814" authorityName="Marsh" authorityYear="1877" box="[878,1088,1970,1994]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC24FFC45339F807FBE1F814" box="[878,1088,1970,1994]" italics="true" pageId="9" pageNumber="444">Allosaurus fragilis</emphasis>
</taxonomicName>
, 
<taxonomicName id="4C3D4D1FEC24FFC45419F807FAA3F814" authority="Currie and Zhao, 1994" box="[1102,1282,1970,1994]" class="Reptilia" family="Neovenatoridae" genus="Sinraptor" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="dongi">
<emphasis id="B949EA8EEC24FFC45419F807FAA3F814" box="[1102,1282,1970,1994]" italics="true" pageId="9" pageNumber="444">Sinraptor dongi</emphasis>
</taxonomicName>
, and 
<taxonomicName id="4C3D4D1FEC24FFC45516F807FC47F834" authorityName="Stovall &amp; Langston" authorityYear="1950" class="Reptilia" family="Carcharodontosauridae" genus="Acrocanthosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="9" pageNumber="444" phylum="Chordata" rank="species" species="atokensis">
<emphasis id="B949EA8EEC24FFC45516F807FC47F834" italics="true" pageId="9" pageNumber="444">Acrocanthosaurus atokensis</emphasis>
</taxonomicName>
, respectively.
</paragraph>
<caption id="DF426614EC27FFC75031FAF9FED0F9D6" ID-DOI="http://doi.org/10.5281/zenodo.3739914" ID-Zenodo-Dep="3739914" httpUri="https://zenodo.org/record/3739914/files/figure.png" pageId="10" pageNumber="445" startId="10.[102,135,1356,1376]" targetBox="[106,770,225,1318]" targetPageId="10">
<paragraph id="8B82369CEC27FFC75031FAF9FED0F9D6" blockId="10.[102,774,1356,1544]" pageId="10" pageNumber="445">
Fig. 10. Heights and widths of tyrannosaurid nasal slices normalized for slice area and bone length. 
<emphasis id="B949EA8EEC27FFC75100FADDFEC6FAA2" bold="true" box="[343,359,1384,1404]" pageId="10" pageNumber="445">A</emphasis>
. Normalized heights (“vaulting index”) showing convergence of vaulting pattern at large size. 
<emphasis id="B949EA8EEC27FFC7526DFA30FDE8FA46" bold="true" box="[570,585,1413,1432]" pageId="10" pageNumber="445">B</emphasis>
. Normalized widths (“span index”) showing isometric form in most specimens, but exaggerated relative width in 
<taxonomicName id="4C3D4D1FEC27FFC75152FA0BFE12FA0E" authorityName="Osborn" authorityYear="1905" box="[261,435,1470,1488]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="10" pageNumber="445" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC27FFC75152FA0BFE12FA0E" box="[261,435,1470,1488]" italics="true" pageId="10" pageNumber="445">Tyrannosaurus rex</emphasis>
</taxonomicName>
nasals. Points of maximum vaulting and span are indicated on nasals of 
<emphasis id="B949EA8EEC27FFC751ECFA6FFE52FA32" box="[443,499,1498,1516]" italics="true" pageId="10" pageNumber="445">T. rex</emphasis>
(TMP 98.86.01; cast of BHI 2033). Symbols as per Fig. 9.
</paragraph>
</caption>
<paragraph id="8B82369CEC27FFC750DBF987FE65F834" blockId="10.[102,775,1585,2026]" pageId="10" pageNumber="445">
To encompass the upper end of the theropod size range, we reconstructed the cranium of a large 
<taxonomicName id="4C3D4D1FEC27FFC75256F9E6FD72F9B4" authorityName="Osborn" authorityYear="1905" box="[513,723,1619,1642]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="10" pageNumber="445" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC27FFC75256F9E6FD72F9B4" box="[513,723,1619,1642]" italics="true" pageId="10" pageNumber="445">Tyrannosaurus rex</emphasis>
</taxonomicName>
(1.4 m; FMNH PR2081) and the similarly huge 
<taxonomicName id="4C3D4D1FEC27FFC75203F9C7FE82F974" authority="Depéret &amp; Savornin, 1925" class="Reptilia" family="Carcharodontosauridae" genus="Carcharodontosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="10" pageNumber="445" phylum="Chordata" rank="species" species="saharicus">
<emphasis id="B949EA8EEC27FFC75203F9C7FE82F974" italics="true" pageId="10" pageNumber="445">Carcharodontosaurus saharicus</emphasis>
</taxonomicName>
(1.6 m; SGM−Din 1). The larger 
<taxonomicName id="4C3D4D1FEC27FFC752F7F926FF79F914" authorityName="Osborn" authorityYear="1905" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="10" pageNumber="445" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC27FFC752F7F926FF79F914" italics="true" pageId="10" pageNumber="445">Tyrannosaurus rex</emphasis>
</taxonomicName>
cranium (FMNH PR2081) was crushed during fossilization, but we were able to reconstruct it based on measurements in its description (
<bibRefCitation id="EFAC4B6DEC27FFC75123F944FDA6F8D4" author="Brochu, C. A." box="[372,519,1777,1802]" journalOrPublisher="Journal of Vertebrate Paleontology" pageId="10" pageNumber="445" pagination="1 - 138" part="24 (Supplement 4)" refId="ref11126" refString="Brochu, C. A. 2003. Osteology of Tyrannosaurus rex: insights from a nearly complete skeleton and high-resolution computed tomographic analysis of the cranium. Journal of Vertebrate Paleontology 24 (Supplement 4): 1 - 138." title="Osteology of Tyrannosaurus rex: insights from a nearly complete skeleton and high-resolution computed tomographic analysis of the cranium" type="journal article" year="2003">Brochu 2003</bibRefCitation>
) and comparisons with other 
<emphasis id="B949EA8EEC27FFC750F0F8A6FF48F8F4" box="[167,233,1811,1834]" italics="true" pageId="10" pageNumber="445">T. rex</emphasis>
crania. The 
<emphasis id="B949EA8EEC27FFC75120F8A7FDA4F8F4" box="[375,517,1810,1834]" italics="true" pageId="10" pageNumber="445">C. saharicus</emphasis>
cranium (SGM−Din 1) lacks the premaxilla but the specimen̓s width and height are known. Because bending and torsional strength scale linearly with length but with the square of width and height, a different length than restored for the 
<taxonomicName id="4C3D4D1FEC27FFC751C5F827FD24F874" authorityName="Stromer" authorityYear="1931" box="[402,645,1938,1962]" class="Reptilia" family="Carcharodontosauridae" genus="Carcharodontosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="10" pageNumber="445" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC27FFC751C5F827FD24F874" box="[402,645,1938,1962]" italics="true" pageId="10" pageNumber="445">Carcharodontosaurus</emphasis>
</taxonomicName>
cranium by 
<bibRefCitation id="EFAC4B6DEC27FFC75031F804FEE2F814" author="Sereno, P. C. &amp; Dutheil, D. B. &amp; Iarochene, M. &amp; Larsson, H. C. E. &amp; Lyon, G. H. &amp; Magwene, P. M. &amp; Sidor, C. A. &amp; Varricchio, D. J. &amp; Wilson, J. A." box="[102,323,1969,1994]" journalOrPublisher="Science" pageId="10" pageNumber="445" pagination="986 - 991" part="272" refId="ref12919" refString="Sereno, P. C., Dutheil, D. B., Iarochene, M., Larsson, H. C. E., Lyon, G. H., Magwene, P. M., Sidor, C. A., Varricchio, D. J., and Wilson, J. A. 1996. Predatory dinosaurs from the Sahara and late cretaceous faunal differentiation. Science 272: 986 - 991." title="Predatory dinosaurs from the Sahara and late cretaceous faunal differentiation" type="journal article" year="1996">Sereno et al. (1996)</bibRefCitation>
would have a relatively minor effect on the specimen̓s strength indices.
</paragraph>
<paragraph id="8B82369CEC27FFC7537BFF5CFAA1FC9C" blockId="10.[812,1485,232,835]" pageId="10" pageNumber="445">
<emphasis id="B949EA8EEC27FFC7537BFF5CFB52FEDF" bold="true" box="[812,1267,232,257]" pageId="10" pageNumber="445">Data collection for cranium geometry</emphasis>
.—Isometric dorsal and lateral images of the crania from published illustrations were scanned on a flatbed scanner, and the dorsal and lateral profiles of the crania were traced in Canvas 7 (Deneba Software Inc.; 
<figureCitation id="13062A19EC27FFC753F4FEDCFC55FE5C" box="[931,1012,361,386]" captionStart="Fig" captionStartId="11.[812,845,1343,1363]" captionTargetBox="[101,1485,237,1477]" captionTargetPageId="11" captionText="Fig. 11. Top and side views of theropod crania used to reconstruct crosssectional shapes, and oblique views of reconstructed plinge cross−sections for each cranium. Second moments of area of the plinges were calculated as indices of bending and torsional cranium strengths. A–D, carnosaurs; E–G, tyrannosaurids." figureDoi="http://doi.org/10.5281/zenodo.3961067" httpUri="https://zenodo.org/record/3961067/files/figure.png" pageId="10" pageNumber="445">Fig. 11</figureCitation>
). The bending and torsional strengths of a cranium depend on its transverse cross−sectional shapes, and on how these shapes vary along the cranium̓s length. All the crania were therefore represented in mathematical form as sets of horizontally stacked, transverse, two−dimensional plinges (flat−topped corbelled vaults: Gordon 1984; 
<figureCitation id="13062A19EC27FFC7552EFDBCFA66FDFC" box="[1401,1479,521,546]" captionStart="Fig" captionStartId="7.[812,845,1631,1651]" captionTargetBox="[817,1481,230,1606]" captionTargetId="graphics@7.[917,1470,726,1087]" captionText="Fig. 8. Average strengths of nasal cross−sections in tyrannosaurids and Allosaurus fragilis, plotted against nasal length. A. Cross−sectional areas, proportional to compression strengths. B. Second moment of area, proportional to vertical bending strength. C. Second moment of area, proportional to lateral bending strength. Values for the A. fragilis nasals are uncorrected for the hollowness of the sections, which would reduce their strengths. Lines fitted to the tyrannosaurid values are derived from log transformed data. See Appendix 1 for labels." figureDoi="http://doi.org/10.5281/zenodo.3961039" httpUri="https://zenodo.org/record/3961039/files/figure.png" pageId="10" pageNumber="445">Figs. 8</figureCitation>
, 
<figureCitation id="13062A19EC27FFC7537BFD9CFC9DFD9C" box="[812,828,553,578]" captionStart="Fig" captionStartId="8.[102,135,1684,1704]" captionTargetBox="[108,1479,227,1655]" captionTargetPageId="8" captionText="Fig. 9. Comparison of theropod nasal strengths at multiple transverse sections. Horizontal (Iy) and vertical (Iz) second moments of area of nasal cross−sections of Allosaurus fragilis (upper two graphs) and tyrannosaurids (lower two graphs). Second moments of area are proportional to lateral (Iy) and vertical (Iz) bending strengths. X−axes of graphs show relative position of slices along the long axes of the bones: 0.0 is posterior and 1.0 anterior." figureDoi="http://doi.org/10.5281/zenodo.3739912" httpUri="https://zenodo.org/record/3739912/files/figure.png" pageId="10" pageNumber="445">9</figureCitation>
). Unlike the strong nasals, the crania of most dinosaurs are found in slightly to very distorted states (e.g., the American and Field Museum 
<taxonomicName id="4C3D4D1FEC27FFC75446FDDEFB4BFD5C" authorityName="Osborn" authorityYear="1905" box="[1041,1258,619,642]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="10" pageNumber="445" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC27FFC75446FDDEFB4BFD5C" box="[1041,1258,619,642]" italics="true" pageId="10" pageNumber="445">Tyrannosaurus rex</emphasis>
</taxonomicName>
specimens, respectively). This leads to uncertainty regarding the exact form of the original uncrushed cranium. With the nasals, their original geometry is well preserved and it was felt worthwhile to use precise CT methods to capture their shape. In contrast, the uncertainties of cranial preservation made a first order approximation adequate for our purposes.
</paragraph>
<paragraph id="8B82369CEC27FFC7537BFCD4FB78FB45" blockId="10.[812,1485,865,1179]" pageId="10" pageNumber="445">
<emphasis id="B949EA8EEC27FFC7537BFCD4FBA3FCA4" bold="true" box="[812,1026,865,890]" pageId="10" pageNumber="445">Area calculations</emphasis>
.—Calculating areas of cranium plinge sections is fundamental, as all other mechanical properties of the cranium depend on the areas in some way. All theropod crania have a typical form that results in all transverse slices being laterally symmetrical quadrilaterals (“trapezoids”) with a ventral (lower) edge that is wider than the accompanying dorsal (upper) edge (
<figureCitation id="13062A19EC27FFC7541AFB97FB34FBE5" box="[1101,1173,1058,1083]" captionStart="Fig" captionStartId="8.[102,135,1684,1704]" captionTargetBox="[108,1479,227,1655]" captionTargetPageId="8" captionText="Fig. 9. Comparison of theropod nasal strengths at multiple transverse sections. Horizontal (Iy) and vertical (Iz) second moments of area of nasal cross−sections of Allosaurus fragilis (upper two graphs) and tyrannosaurids (lower two graphs). Second moments of area are proportional to lateral (Iy) and vertical (Iz) bending strengths. X−axes of graphs show relative position of slices along the long axes of the bones: 0.0 is posterior and 1.0 anterior." figureDoi="http://doi.org/10.5281/zenodo.3739912" httpUri="https://zenodo.org/record/3739912/files/figure.png" pageId="10" pageNumber="445">Fig. 9</figureCitation>
). The areas of these trapezoidal cross−sections, and excised areas representing the interior of each plinge (see below), were computed using the method outlined in 
<bibRefCitation id="EFAC4B6DEC27FFC75450FB37FB74FB45" author="Henderson, D. M." box="[1031,1237,1154,1179]" journalOrPublisher="Journal of Vertebrate Paleontology" pageId="10" pageNumber="445" pagination="766 - 778" part="22" refId="ref12007" refString="Henderson, D. M. 2002. The eyes have it: the sizes, shapes, and orientations of theropod orbits as indicators of cranium strength and bite force. Journal of Vertebrate Paleontology 22: 766 - 778." title="The eyes have it: the sizes, shapes, and orientations of theropod orbits as indicators of cranium strength and bite force" type="journal article" year="2002">Henderson (2002)</bibRefCitation>
.
</paragraph>
<paragraph id="8B82369CEC27FFC7537BFB0DFC2FF9ED" blockId="10.[812,1485,1208,1943]" pageId="10" pageNumber="445">
<emphasis id="B949EA8EEC27FFC7537BFB0DFB96FB0F" bold="true" box="[812,1079,1208,1233]" pageId="10" pageNumber="445">Strength calculations</emphasis>
.—Dorsoventral and mediolateral modes of bending are relevant to the study of the cranium mechanics of predatory dinosaurs. In each mode the side of the cranium where a force is being applied will experience tension, while the opposite side will be in compression. Somewhere between the compressed and tensed sides is an infinitesimally thin zone, the neutral axis, that does not experience any stress. For dorsoventral bending this neutral axis is equivalent to the horizontal, y−axis centroid, 
<emphasis id="B949EA8EEC27FFC7556DFA0EFAE7FA0C" box="[1338,1350,1467,1490]" italics="true" pageId="10" pageNumber="445">y</emphasis>
. As the crania and their transverse slices are left−right symmetrical, the central Y−axis (Z = 0) is the neutral axis for mediolateral bending.
</paragraph>
<paragraph id="8B82369CEC27FFC75305F988FBFEF8EB" blockId="10.[812,1485,1208,1943]" pageId="10" pageNumber="445">
A cranium̓s bending strength at a particular point depends on two parameters—the second moment of area of the corresponding cross−section, and its distance from the point of force application. The first parameter is a measure of how the material comprising the slice is distributed about the neutral axis of the slice (
<bibRefCitation id="EFAC4B6DEC27FFC7544DF968FB17F928" author="Gordon, J. E." bookContentInfo="395 pp." box="[1050,1206,1757,1782]" journalOrPublisher="Plenum Publishing, New York" pageId="10" pageNumber="445" refId="ref11840" refString="Gordon, J. E. 1978. Structures: Or Why Things Don't Fall Down. 395 pp. Plenum Publishing, New York." title="Structures: Or Why Things Don't Fall Down" type="book" year="1978">Gordon 1978</bibRefCitation>
). For dorsoventral bending this quantity, 
<emphasis id="B949EA8EEC27FFC753B8F94BFBBAF8D8" box="[1007,1051,1784,1818]" italics="true" pageId="10" pageNumber="445">
I 
<subScript id="17B934D9EC27FFC753ACF8B9FBA0F8C4" attach="left" box="[1019,1025,1804,1818]" fontSize="6" pageId="10" pageNumber="445">z</subScript>
<superScript id="7C489BD4EC27FFC753AAF94DFBBAF8D8" attach="right" box="[1021,1051,1784,1798]" fontSize="6" pageId="10" pageNumber="445">skull</superScript>
</emphasis>
, is computed relative to the horizontal Z−axis, and is expressed as:
</paragraph>
<paragraph id="8B82369CEC27FFC753F0F8F2FC14F889" blockId="10.[812,1485,1208,1943]" box="[935,949,1863,1879]" pageId="10" pageNumber="445">
<emphasis id="B949EA8EEC27FFC753F0F8F2FC14F889" box="[935,949,1863,1879]" italics="true" pageId="10" pageNumber="445">yc</emphasis>
</paragraph>
<paragraph id="8B82369CEC27FFC7530EF8D4FB95F8A6" blockId="10.[812,1485,1208,1943]" box="[857,1076,1883,1927]" pageId="10" pageNumber="445">
<emphasis id="B949EA8EEC27FFC7530EF8D4FC24F8B7" box="[857,901,1883,1917]" italics="true" pageId="10" pageNumber="445">I z skull</emphasis>
= I 
<emphasis id="B949EA8EEC27FFC753EAF8D4FC68F8A6" box="[957,969,1889,1912]" italics="true" pageId="10" pageNumber="445">y</emphasis>
2 
<emphasis id="B949EA8EEC27FFC7538EF8D5FC59F8A6" box="[985,1016,1888,1912]" italics="true" pageId="10" pageNumber="445">dA</emphasis>
(4)
</paragraph>
<paragraph id="8B82369CEC27FFC753FFF832FC14F849" blockId="10.[812,1485,1208,1943]" box="[936,949,1927,1943]" pageId="10" pageNumber="445">
<emphasis id="B949EA8EEC27FFC753FFF832FC14F849" box="[936,949,1927,1943]" italics="true" pageId="10" pageNumber="445">yt</emphasis>
</paragraph>
<paragraph id="8B82369CEC27FFC6537BF804FEA4F953" blockId="10.[812,1485,1969,2026]" lastBlockId="11.[102,775,1520,1839]" lastPageId="11" lastPageNumber="446" pageId="10" pageNumber="445">
where 
<emphasis id="B949EA8EEC27FFC75320F806FC2AF813" box="[887,907,1971,1997]" italics="true" pageId="10" pageNumber="445">
<subScript id="17B934D9EC27FFC75320F806FC2AF813" attach="left" box="[887,907,1971,1997]" fontSize="7" pageId="10" pageNumber="445">yc</subScript>
</emphasis>
and 
<emphasis id="B949EA8EEC27FFC753E8F806FC70F813" box="[959,977,1971,1997]" italics="true" pageId="10" pageNumber="445">
<subScript id="17B934D9EC27FFC753E8F806FC70F813" attach="left" box="[959,977,1971,1997]" fontSize="7" pageId="10" pageNumber="445">yt</subScript>
</emphasis>
are the distances from 
<emphasis id="B949EA8EEC27FFC75486F806FB7CF814" box="[1233,1245,1971,1994]" italics="true" pageId="10" pageNumber="445">y</emphasis>
to the top and bottom edges of the cross−section that experience compression and tension, respectively, and 
<emphasis id="B949EA8EEC26FFC651DFFA45FE06F9D6" box="[392,423,1520,1544]" italics="true" pageId="11" pageNumber="446">dA</emphasis>
is a horizontal strip of area that will vary with height (
<figureCitation id="13062A19EC26FFC65109F9A4FE67F9F4" box="[350,454,1553,1578]" captionStart="Fig" captionStartId="12.[102,135,1158,1178]" captionTargetBox="[82,784,206,1136]" captionTargetPageId="12" captionText="Fig. 12. Schematic trapezoidal cross−sections of theropod crania, with geometry and expressions for computing second moments of area. A. Determining moments with respect to the horizontal (Z) axis. The width of a strip of area is a function of its vertical (Y) coordinate. B. Determining moments with respect to the vertical (Y) axis; the cross−section is partitioned into two central rectangular areas, and two lateral triangular regions." figureDoi="http://doi.org/10.5281/zenodo.3961043" httpUri="https://zenodo.org/record/3961043/files/figure.png" pageId="11" pageNumber="446">Fig. 12A</figureCitation>
). For a theropod biting prey, and with the impact force directed upwards, the dorsal side of the cranium will be under compression and the ventral side under tension.
</paragraph>
<caption id="DF426614EC26FFC6537BFA8AFC18FA1D" ID-DOI="http://doi.org/10.5281/zenodo.3961067" ID-Zenodo-Dep="3961067" httpUri="https://zenodo.org/record/3961067/files/figure.png" pageId="11" pageNumber="446" startId="11.[812,845,1343,1363]" targetBox="[101,1485,237,1477]" targetPageId="11">
<paragraph id="8B82369CEC26FFC6537BFA8AFC18FA1D" pageId="11" pageNumber="446">
Fig. 11. Top and side views of theropod crania used to reconstruct crosssectional shapes, and oblique views of reconstructed plinge cross−sections for each cranium. Second moments of area of the plinges were calculated as indices of bending and torsional cranium strengths. 
<emphasis id="B949EA8EEC26FFC654AEFA26FA84FA79" bold="true" box="[1273,1317,1427,1447]" pageId="11" pageNumber="446">A–D</emphasis>
, carnosaurs; 
<emphasis id="B949EA8EEC26FFC655CCFA21FA69FA79" bold="true" box="[1435,1480,1427,1447]" pageId="11" pageNumber="446">E–G</emphasis>
, tyrannosaurids.
</paragraph>
</caption>
<paragraph id="8B82369CEC26FFC650DBF92DFD5FF90E" blockId="11.[102,775,1520,1839]" pageId="11" pageNumber="446">
For mediolateral bending the expression for second moment of area with respect to the vertical axis, 
<emphasis id="B949EA8EEC26FFC65211F90DFDD3F91E" box="[582,626,1714,1748]" italics="true" pageId="11" pageNumber="446">
I 
<subScript id="17B934D9EC26FFC65205F973FDF8F90A" attach="left" box="[594,601,1734,1748]" fontSize="6" pageId="11" pageNumber="446">y</subScript>
<superScript id="7C489BD4EC26FFC65203F907FDD3F91E" attach="right" box="[596,626,1714,1728]" fontSize="6" pageId="11" pageNumber="446">skull</superScript>
</emphasis>
, is given by:
</paragraph>
<paragraph id="8B82369CEC26FFC650AAF954FEAFF92C" blockId="11.[102,775,1520,1839]" box="[253,270,1761,1778]" pageId="11" pageNumber="446">
<emphasis id="B949EA8EEC26FFC650AAF954FEAFF92C" box="[253,270,1761,1778]" italics="true" pageId="11" pageNumber="446">zD</emphasis>
</paragraph>
<paragraph id="8B82369CEC26FFC650DBF94EFE7DF8CC" blockId="11.[102,775,1520,1839]" box="[140,476,1781,1825]" pageId="11" pageNumber="446">
<emphasis id="B949EA8EEC26FFC650DBF94EFF19F8DD" box="[140,184,1781,1815]" italics="true" pageId="11" pageNumber="446">I y skull</emphasis>
= 2 · I 
<emphasis id="B949EA8EEC26FFC65145F94EFEBCF8CC" box="[274,285,1787,1810]" italics="true" pageId="11" pageNumber="446">z</emphasis>
2 · (
<emphasis id="B949EA8EEC26FFC65119F94EFE05F8C9" box="[334,420,1787,1815]" italics="true" pageId="11" pageNumber="446">y D – y V</emphasis>
) 
<emphasis id="B949EA8EEC26FFC651EFF94FFE70F8CC" box="[440,465,1786,1810]" italics="true" pageId="11" pageNumber="446">dz</emphasis>
+
</paragraph>
<paragraph id="8B82369CEC26FFC650AEF894FEB2F8F1" blockId="11.[102,775,1520,1839]" box="[249,275,1825,1839]" pageId="11" pageNumber="446">
<emphasis id="B949EA8EEC26FFC650AEF894FF5EF8F1" box="[249,255,1825,1839]" italics="true" pageId="11" pageNumber="446">z</emphasis>
= 0
</paragraph>
<paragraph id="8B82369CEC26FFC650ECF8F2FF66F889" blockId="11.[140,579,1863,1943]" box="[187,199,1863,1879]" pageId="11" pageNumber="446">
<emphasis id="B949EA8EEC26FFC650ECF8F2FF66F889" box="[187,199,1863,1879]" italics="true" pageId="11" pageNumber="446">z V</emphasis>
</paragraph>
<paragraph id="8B82369CEC26FFC650DBF8D5FF72F849" blockId="11.[140,579,1863,1943]" pageId="11" pageNumber="446">
+ 2 I 
<emphasis id="B949EA8EEC26FFC65099F8D4FF78F8A6" box="[206,217,1889,1912]" italics="true" pageId="11" pageNumber="446">z</emphasis>
2[
<emphasis id="B949EA8EEC26FFC650A0F8D4FE99F8A3" box="[247,312,1889,1917]" italics="true" pageId="11" pageNumber="446">m lateral</emphasis>
(
<emphasis id="B949EA8EEC26FFC6511BF8D4FE2CF8A3" box="[332,397,1888,1917]" italics="true" pageId="11" pageNumber="446">z – z D</emphasis>
) + 
<emphasis id="B949EA8EEC26FFC651E8F8D4FDB5F8A3" box="[447,532,1888,1917]" italics="true" pageId="11" pageNumber="446">y D – y V</emphasis>
] 
<emphasis id="B949EA8EEC26FFC6527DF8D5FF17F84B" italics="true" pageId="11" pageNumber="446">dz z</emphasis>
= 
<emphasis id="B949EA8EEC26FFC65095F832FF72F849" box="[194,211,1927,1943]" italics="true" pageId="11" pageNumber="446">
z 
<subScript id="17B934D9EC26FFC6509CF83BFF72F849" attach="left" box="[203,211,1934,1943]" fontSize="4" pageId="11" pageNumber="446">D</subScript>
</emphasis>
</paragraph>
<paragraph id="8B82369CEC26FFC65209F8EAFDDEF8A6" blockId="11.[606,639,1887,1912]" box="[606,639,1887,1912]" pageId="11" pageNumber="446">(5)</paragraph>
<paragraph id="8B82369CEC26FFC65031F804FC57F976" blockId="11.[102,774,1969,2026]" lastBlockId="11.[812,1485,1520,2026]" pageId="11" pageNumber="446">
where the first term is for a rectangular region immediately adjacent to the central, vertical neutral axis, which is bounded vertically by 
<emphasis id="B949EA8EEC26FFC65396FA44FC7BF9D2" box="[961,986,1521,1548]" italics="true" pageId="11" pageNumber="446">
<subScript id="17B934D9EC26FFC65396FA44FC7BF9D2" attach="left" box="[961,986,1521,1548]" fontSize="7" pageId="11" pageNumber="446">yD</subScript>
</emphasis>
, and 
<emphasis id="B949EA8EEC26FFC6544BFA44FB92F9D2" box="[1052,1075,1521,1548]" italics="true" pageId="11" pageNumber="446">
<subScript id="17B934D9EC26FFC6544BFA44FB92F9D2" attach="left" box="[1052,1075,1521,1548]" fontSize="7" pageId="11" pageNumber="446">yV</subScript>
</emphasis>
, and laterally by z 
<emphasis id="B949EA8EEC26FFC65550FA49FAB5F9D2" box="[1287,1300,1532,1548]" italics="true" pageId="11" pageNumber="446">
<subScript id="17B934D9EC26FFC65550FA49FAB5F9D2" attach="left" box="[1287,1300,1532,1548]" fontSize="7" pageId="11" pageNumber="446">D</subScript>
</emphasis>
(
<figureCitation id="13062A19EC26FFC65571FA45FA2CF9D7" box="[1318,1421,1520,1545]" captionStart="Fig" captionStartId="12.[102,135,1158,1178]" captionTargetBox="[82,784,206,1136]" captionTargetPageId="12" captionText="Fig. 12. Schematic trapezoidal cross−sections of theropod crania, with geometry and expressions for computing second moments of area. A. Determining moments with respect to the horizontal (Z) axis. The width of a strip of area is a function of its vertical (Y) coordinate. B. Determining moments with respect to the vertical (Y) axis; the cross−section is partitioned into two central rectangular areas, and two lateral triangular regions." figureDoi="http://doi.org/10.5281/zenodo.3961043" httpUri="https://zenodo.org/record/3961043/files/figure.png" pageId="11" pageNumber="446">Fig. 12B</figureCitation>
). The second term is for a laterally positioned triangular region which is bounded along its top edge by the lateral side of the plinge, and extends along its lower edge to 
<emphasis id="B949EA8EEC26FFC6555FF9E4FABFF9B2" box="[1288,1310,1617,1644]" italics="true" pageId="11" pageNumber="446">
<subScript id="17B934D9EC26FFC6555FF9E4FABFF9B2" attach="left" box="[1288,1310,1617,1644]" fontSize="7" pageId="11" pageNumber="446">zV</subScript>
</emphasis>
. To account for the left−right symmetry of the trapezoidal shape each term is multiplied by two.
</paragraph>
<paragraph id="8B82369CEC26FFC15305F904FE2FF9CE" blockId="11.[812,1485,1520,2026]" lastBlockId="12.[102,775,1367,1808]" lastPageId="12" lastPageNumber="447" pageId="11" pageNumber="446">
The above expressions for second moments of area are for solids, but crania are not solid blocks of bone. To represent for the hollowness of the cranial vault, a second inner shell was defined. The mean thickness of bones comprising a cranium was estimated to be 5% of the cranium length. This thickness was subtracted from the dimensions defining the outer cranium contours, with the original and reduced trapezoids sharing the same bottom edge. Second moments of area were computed for the reduced internal cranium shapes, and the resulting values were subtracted from second moments of area of the original, external geometries following the methods of 
<bibRefCitation id="EFAC4B6DEC21FFC15158FAC2FE4FFA4E" author="Farlow, J. O. &amp; Smith, M. B. &amp; Robinson, J. M." box="[271,494,1399,1424]" journalOrPublisher="Journal of Vertebrate Paleontology" pageId="12" pageNumber="447" pagination="713 - 725" part="15" refId="ref11791" refString="Farlow, J. O., Smith, M. B., and Robinson, J. M. 1995. Body mass, bone &quot; strength indicator, &quot; and cursorial potential of Tyrannosaurus rex. Journal of Vertebrate Paleontology 15: 713 - 725." title="Body mass, bone &quot; strength indicator, &quot; and cursorial potential of Tyrannosaurus rex" type="journal article" year="1995">Farlow et al. (1995)</bibRefCitation>
. We used the mean of the second moments of area all the slices as a strength indicator for the cranium as a whole. This was appropriate for our present interest in correlations between nasal bone strengths and general cranium strengths.
</paragraph>
<caption id="DF426614EC21FFC15031FB33FD23FAF8" ID-DOI="http://doi.org/10.5281/zenodo.3961043" ID-Zenodo-Dep="3961043" httpUri="https://zenodo.org/record/3961043/files/figure.png" pageId="12" pageNumber="447" startId="12.[102,135,1158,1178]" targetBox="[82,784,206,1136]" targetPageId="12">
<paragraph id="8B82369CEC21FFC15031FB33FD23FAF8" blockId="12.[102,775,1158,1318]" pageId="12" pageNumber="447">
Fig. 12. Schematic trapezoidal cross−sections of theropod crania, with geometry and expressions for computing second moments of area. 
<emphasis id="B949EA8EEC21FFC152E6FB17FD60FB68" bold="true" box="[689,705,1186,1206]" pageId="12" pageNumber="447">A</emphasis>
. Determining moments with respect to the horizontal (Z) axis. The width of a strip of area is a function of its vertical (Y) coordinate. 
<emphasis id="B949EA8EEC21FFC15274FB6EFD93FB30" bold="true" box="[547,562,1243,1262]" pageId="12" pageNumber="447">B</emphasis>
. Determining moments with respect to the vertical (Y) axis; the cross−section is partitioned into two central rectangular areas, and two lateral triangular regions.
</paragraph>
</caption>
<paragraph id="8B82369CEC21FFC150DBF9ADFD38F8CE" blockId="12.[102,775,1367,1808]" pageId="12" pageNumber="447">
In addition to the two modes of bending deformation, there is also the potential for the torsional deformation as the cranium twists about its long axis during feeding activities. The torsional strength of the cranium is proportional to the polar second moment of area (
<emphasis id="B949EA8EEC21FFC15199F92DFE7BF971" box="[462,474,1688,1711]" italics="true" pageId="12" pageNumber="447">J</emphasis>
). For each cranium slice, 
<emphasis id="B949EA8EEC21FFC15031F90DFFD3F911" box="[102,114,1720,1743]" italics="true" pageId="12" pageNumber="447">J</emphasis>
was computed as the sum of the two orthogonal second moments of area, 
<emphasis id="B949EA8EEC21FFC1515AF96DFEBFF92C" box="[269,286,1752,1778]" italics="true" pageId="12" pageNumber="447">
<subScript id="17B934D9EC21FFC1515AF96DFEBFF92C" attach="left" box="[269,286,1752,1778]" fontSize="7" pageId="12" pageNumber="447">Iz</subScript>
</emphasis>
and 
<emphasis id="B949EA8EEC21FFC15101F96DFEC9F92C" box="[342,360,1752,1778]" italics="true" pageId="12" pageNumber="447">
<subScript id="17B934D9EC21FFC15101F96DFEC9F92C" attach="left" box="[342,360,1752,1778]" fontSize="7" pageId="12" pageNumber="447">Iy</subScript>
</emphasis>
(
<bibRefCitation id="EFAC4B6DEC21FFC15120F962FD88F92E" author="Biewener, A. A." box="[375,553,1751,1776]" editor="A. A. Biewener" journalOrPublisher="Oxford University Press, Oxford" pageId="12" pageNumber="447" pagination="1 - 20" refId="ref11055" refString="Biewener, A. A. 1992. Overview of structural mechanics. In: A. A. Biewener (ed.). Biomechanics-Structures and Systems, 1 - 20. Oxford University Press, Oxford." title="Overview of structural mechanics" type="book chapter" volumeTitle="Biomechanics-Structures and Systems" year="1992">Biewener 1992</bibRefCitation>
). The mean value 
<emphasis id="B949EA8EEC21FFC152ADF96DFCA7F931" box="[762,774,1752,1775]" italics="true" pageId="12" pageNumber="447">J</emphasis>
for all the slices was then assigned to the cranium.
</paragraph>
<paragraph id="8B82369CEC21FFC15031F88DFE06F889" blockId="12.[102,423,1848,1879]" box="[102,423,1848,1879]" pageId="12" pageNumber="447">
<heading id="D0CA81F0EC21FFC15031F88DFE06F889" box="[102,423,1848,1879]" fontSize="13" level="2" pageId="12" pageNumber="447" reason="1">Cranial strength results</heading>
</paragraph>
<paragraph id="8B82369CEC21FFC15031F8C4FB0FFD7F" blockId="12.[102,774,1905,2026]" lastBlockId="12.[812,1485,232,673]" pageId="12" pageNumber="447">
The results in 
<figureCitation id="13062A19EC21FFC1515DF8C4FEFDF854" box="[266,348,1905,1930]" captionStart="Fig" captionStartId="12.[812,845,1921,1941]" captionTargetBox="[823,1475,731,1894]" captionTargetId="graphics@12.[927,1475,1162,1441]" captionTargetPageId="12" captionText="Fig. 13. Strength indicators computed for theropod crania under mediolateral (A), dorsoventral (B), and torsional (C) loadings. Tyrannosaurid crania are invariably stronger than those of carnosaurs for a given skull length. See Appendix 1 for labels." figureDoi="http://doi.org/10.5281/zenodo.3961069" httpUri="https://zenodo.org/record/3961069/files/figure.png" pageId="12" pageNumber="447">Fig. 13</figureCitation>
and 
<tableCitation id="C6BF0327EC21FFC151C1F8C4FE4CF854" box="[406,493,1905,1930]" captionStart="Table 3" captionStartId="13.[812,867,231,252]" captionTargetId="graphics@13.[812,1485,271,619]" captionTargetPageId="13" captionText="Table 3. Computed strength properties of theropod crania." httpUri="http://table.plazi.org/id/DF426614EC20FFC0537BFF52FAFAFF22" pageId="12" pageNumber="447" tableUuid="DF426614EC20FFC0537BFF52FAFAFF22">Table 3</tableCitation>
show that tyrannosaurid crania had generally higher second moments of area and higher torsional strength indicators than carnosaur crania of equivalent length. Tyrannosaurid cranium geometry there− fore conferred generally higher strength in torsion and in lateral and dorsoventral bending. The results for 
<taxonomicName id="4C3D4D1FEC21FFC15532FEBFFC09FE9F" authorityName="Osborn" authorityYear="1905" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="12" pageNumber="447" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC21FFC15532FEBFFC09FE9F" italics="true" pageId="12" pageNumber="447">Tyrannosaurus rex</emphasis>
</taxonomicName>
amplify the trend towards higher strengths in tyrannosaurids than in carnosaurs. The smaller 
<taxonomicName id="4C3D4D1FEC21FFC15505FEFFFA36FEBF" authorityName="Osborn" authorityYear="1905" box="[1362,1431,330,353]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="12" pageNumber="447" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC21FFC15505FEFFFA36FEBF" box="[1362,1431,330,353]" italics="true" pageId="12" pageNumber="447">T. rex</emphasis>
</taxonomicName>
cranium (TrA) shows approximately twice the dorsoventral bending and torsional strengths, and three times the mediolateral bending strength, of the equally long cranium of 
<taxonomicName id="4C3D4D1FEC21FFC1537BFE7DFB0AFE3F" authority="(Aa)" authorityName="Stovall &amp; Langston" authorityYear="1950" baseAuthorityName="Aa" box="[812,1195,456,481]" class="Reptilia" family="Carcharodontosauridae" genus="Acrocanthosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="12" pageNumber="447" phylum="Chordata" rank="species" species="atokensis">
<emphasis id="B949EA8EEC21FFC1537BFE7DFBCAFE3E" box="[812,1131,456,480]" italics="true" pageId="12" pageNumber="447">Acrocanthosaurus atokensis</emphasis>
(Aa)
</taxonomicName>
. This 
<emphasis id="B949EA8EEC21FFC154A4FE7FFA96FE3F" box="[1267,1335,458,481]" italics="true" pageId="12" pageNumber="447">T. rex</emphasis>
cranium had higher torsional and lateral bending strength indicators than the much longer cranium of 
<taxonomicName id="4C3D4D1FEC21FFC15435FDBDFCC1FD9F" authority="(Cs)" baseAuthorityName="Cs" class="Reptilia" family="Carcharodontosauridae" genus="Carcharodontosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="12" pageNumber="447" phylum="Chordata" rank="species" species="saharicus">
<emphasis id="B949EA8EEC21FFC15435FDBDFA6CFDFE" box="[1122,1485,520,544]" italics="true" pageId="12" pageNumber="447">Carcharodontosaurus saharicus</emphasis>
(Cs)
</taxonomicName>
. The larger 
<emphasis id="B949EA8EEC21FFC153B3FD9FFB84FD9F" box="[996,1061,554,577]" italics="true" pageId="12" pageNumber="447">T. rex</emphasis>
cranium TrF is 12.5% longer than the smaller TrA, but its substantially higher strength reflects the non−linear increase in second moment of area with increasing linear size (equations 4 and 5).
</paragraph>
<caption id="DF426614EC21FFC1537BF834FBBFF837" ID-DOI="http://doi.org/10.5281/zenodo.3961069" ID-Zenodo-Dep="3961069" httpUri="https://zenodo.org/record/3961069/files/figure.png" pageId="12" pageNumber="447" startId="12.[812,845,1921,1941]" targetBox="[823,1475,731,1894]" targetPageId="12">
<paragraph id="8B82369CEC21FFC1537BF834FBBFF837" blockId="12.[812,1486,1921,2025]" pageId="12" pageNumber="447">
Fig. 13. Strength indicators computed for theropod crania under mediolateral (
<emphasis id="B949EA8EEC21FFC15327F829FC21F86E" bold="true" box="[880,896,1948,1968]" pageId="12" pageNumber="447">A</emphasis>
), dorsoventral (
<emphasis id="B949EA8EEC21FFC15458F828FBBFF86E" bold="true" box="[1039,1054,1949,1968]" pageId="12" pageNumber="447">B</emphasis>
), and torsional (
<emphasis id="B949EA8EEC21FFC154F8F829FB1EF86E" bold="true" box="[1199,1215,1948,1968]" pageId="12" pageNumber="447">C</emphasis>
) loadings. Tyrannosaurid crania are invariably stronger than those of carnosaurs for a given skull length. See Appendix 1 for labels.
</paragraph>
</caption>
<paragraph id="8B82369CEC20FFC05031FF58FE98FEC9" blockId="13.[102,313,237,279]" box="[102,313,237,279]" pageId="13" pageNumber="448">
<heading id="D0CA81F0EC20FFC05031FF58FE98FEC9" box="[102,313,237,279]" fontSize="18" level="1" pageId="13" pageNumber="448" reason="1">Discussion</heading>
</paragraph>
<caption id="DF426614EC20FFC0537BFF52FAFAFF22" ID-Table-UUID="DF426614EC20FFC0537BFF52FAFAFF22" box="[812,1371,231,252]" httpUri="http://table.plazi.org/id/DF426614EC20FFC0537BFF52FAFAFF22" pageId="13" pageNumber="448" startId="13.[812,867,231,252]" targetBox="[817,1480,282,615]" targetIsTable="true" targetPageId="13">
<paragraph id="8B82369CEC20FFC0537BFF52FAFAFF22" blockId="13.[812,1371,231,252]" box="[812,1371,231,252]" pageId="13" pageNumber="448">Table 3. Computed strength properties of theropod crania.</paragraph>
</caption>
<paragraph id="8B82369CEC20FFC054FCFEA8FA13FDB9" pageId="13" pageNumber="448">
<table id="F93DC43CEC2000325366FEAFFA69FDB9" box="[817,1480,282,615]" gridcols="4" gridrows="9" pageId="13" pageNumber="448">
<tr id="350D34DEEC2000325366FEAFFA69FE91" box="[817,1480,282,335]" gridrow="0" pageId="13" pageNumber="448" rowspan-0="1">
<th id="76DC5DA2EC20003254FCFEAFFB4EFE91" box="[1195,1263,282,335]" gridcol="1" gridrow="0" pageId="13" pageNumber="448">Length (cm)</th>
<th id="76DC5DA2EC20003254ACFEAFFA69FE91" box="[1275,1480,282,335]" colspan="2" colspanRight="1" gridcol="2" gridrow="0" pageId="13" pageNumber="448">Iz Iy (m4×10–5) (m4×10–6)</th>
</tr>
<tr id="350D34DEEC2000325366FEE8FA69FEAD" box="[817,1480,349,371]" gridrow="1" pageId="13" pageNumber="448">
<th id="76DC5DA2EC2000325366FEE8FB37FEAD" box="[817,1174,349,371]" gridcol="0" gridrow="1" pageId="13" pageNumber="448">
<taxonomicName id="4C3D4D1FEC20FFC05366FEEBFBB5FEAC" authority="(Af)" authorityName="Marsh" authorityYear="1877" baseAuthorityName="Af" box="[817,1044,349,371]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC20FFC05366FEEBFC45FEAD" box="[817,996,350,371]" italics="true" pageId="13" pageNumber="448">Allosaurus fragilis</emphasis>
(Af)
</taxonomicName>
</th>
<td id="76DC5DA2EC20003254FCFEE8FB4EFEAD" box="[1195,1263,349,371]" gridcol="1" gridrow="1" pageId="13" pageNumber="448">79.1</td>
<td id="76DC5DA2EC20003254ACFEE8FAE6FEAD" box="[1275,1351,349,371]" gridcol="2" gridrow="1" pageId="13" pageNumber="448">1.411</td>
<td id="76DC5DA2EC200032552BFEE8FA69FEAD" box="[1404,1480,349,371]" gridcol="3" gridrow="1" pageId="13" pageNumber="448">2.975</td>
</tr>
<tr id="350D34DEEC2000325366FE35FA69FE48" box="[817,1480,384,406]" gridrow="2" pageId="13" pageNumber="448">
<th id="76DC5DA2EC2000325366FE35FB37FE48" box="[817,1174,384,406]" gridcol="0" gridrow="2" pageId="13" pageNumber="448">
<taxonomicName id="4C3D4D1FEC20FFC05366FE34FC58FE4B" authority="(Sd)" baseAuthorityName="Sd" box="[817,1017,384,406]" class="Reptilia" family="Neovenatoridae" genus="Sinraptor" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="dongi">
<emphasis id="B949EA8EEC20FFC05366FE34FC6BFE48" box="[817,970,385,406]" italics="true" pageId="13" pageNumber="448">Sinraptor dongi</emphasis>
(Sd)
</taxonomicName>
</th>
<td id="76DC5DA2EC20003254FCFE35FB4EFE48" box="[1195,1263,384,406]" gridcol="1" gridrow="2" pageId="13" pageNumber="448">84.2</td>
<td id="76DC5DA2EC20003254ACFE35FAE6FE48" box="[1275,1351,384,406]" gridcol="2" gridrow="2" pageId="13" pageNumber="448">5.083</td>
<td id="76DC5DA2EC200032552BFE35FA69FE48" box="[1404,1480,384,406]" gridcol="3" gridrow="2" pageId="13" pageNumber="448">12.93</td>
</tr>
<tr id="350D34DEEC2000325366FE16FA69FE66" box="[817,1480,419,440]" gridrow="3" pageId="13" pageNumber="448">
<th id="76DC5DA2EC2000325366FE16FB37FE66" box="[817,1174,419,440]" gridcol="0" gridrow="3" pageId="13" pageNumber="448">
<taxonomicName id="4C3D4D1FEC20FFC05366FE16FBDAFE66" authority="(Aa)" authorityName="Stovall &amp; Langston" authorityYear="1950" baseAuthorityName="Aa" box="[817,1147,419,440]" class="Reptilia" family="Carcharodontosauridae" genus="Acrocanthrosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="atokensis">
<emphasis id="B949EA8EEC20FFC05366FE16FBE8FE66" box="[817,1097,419,440]" italics="true" pageId="13" pageNumber="448">Acrocanthrosaurus atokensis</emphasis>
(Aa)
</taxonomicName>
</th>
<td id="76DC5DA2EC20003254FCFE16FB4EFE66" box="[1195,1263,419,440]" gridcol="1" gridrow="3" pageId="13" pageNumber="448">124</td>
<td id="76DC5DA2EC20003254ACFE16FAE6FE66" box="[1275,1351,419,440]" gridcol="2" gridrow="3" pageId="13" pageNumber="448">16.68</td>
<td id="76DC5DA2EC200032552BFE16FA69FE66" box="[1404,1480,419,440]" gridcol="3" gridrow="3" pageId="13" pageNumber="448">36.26</td>
</tr>
<tr id="350D34DEEC2000325366FE73FA69FE05" box="[817,1480,454,475]" gridrow="4" pageId="13" pageNumber="448">
<th id="76DC5DA2EC2000325366FE73FB37FE05" box="[817,1174,454,475]" gridcol="0" gridrow="4" pageId="13" pageNumber="448">
<taxonomicName id="4C3D4D1FEC20FFC05366FE73FB37FE05" authority="(Cs)" baseAuthorityName="Cs" box="[817,1174,454,475]" class="Reptilia" family="Carcharodontosauridae" genus="Carcharodontosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="saharicus">
<emphasis id="B949EA8EEC20FFC05366FE73FBC9FE05" box="[817,1128,454,475]" italics="true" pageId="13" pageNumber="448">Carcharodontosaurus saharicus</emphasis>
(Cs)
</taxonomicName>
</th>
<td id="76DC5DA2EC20003254FCFE73FB4EFE05" box="[1195,1263,454,475]" gridcol="1" gridrow="4" pageId="13" pageNumber="448">160</td>
<td id="76DC5DA2EC20003254ACFE73FAE6FE05" box="[1275,1351,454,475]" gridcol="2" gridrow="4" pageId="13" pageNumber="448">37.61</td>
<td id="76DC5DA2EC200032552BFE73FA69FE05" box="[1404,1480,454,475]" gridcol="3" gridrow="4" pageId="13" pageNumber="448">65.11</td>
</tr>
<tr id="350D34DEEC2000325366FE5CFA69FE20" box="[817,1480,489,510]" gridrow="5" pageId="13" pageNumber="448">
<th id="76DC5DA2EC2000325366FE5CFB37FE20" box="[817,1174,489,510]" gridcol="0" gridrow="5" pageId="13" pageNumber="448">
<taxonomicName id="4C3D4D1FEC20FFC05366FE5CFB8FFE20" authority="(Al)" baseAuthorityName="Al" box="[817,1070,489,510]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC20FFC05366FE5CFBA1FE20" box="[817,1024,489,510]" italics="true" pageId="13" pageNumber="448">Gorgosaurus libratus</emphasis>
(Al)
</taxonomicName>
</th>
<td id="76DC5DA2EC20003254FCFE5CFB4EFE20" box="[1195,1263,489,510]" gridcol="1" gridrow="5" pageId="13" pageNumber="448">75.0</td>
<td id="76DC5DA2EC20003254ACFE5CFAE6FE20" box="[1275,1351,489,510]" gridcol="2" gridrow="5" pageId="13" pageNumber="448">2.304</td>
<td id="76DC5DA2EC200032552BFE5CFA69FE20" box="[1404,1480,489,510]" gridcol="3" gridrow="5" pageId="13" pageNumber="448">8.296</td>
</tr>
<tr id="350D34DEEC2000325366FDB9FA69FDFF" box="[817,1480,524,545]" gridrow="6" pageId="13" pageNumber="448">
<th id="76DC5DA2EC2000325366FDB9FB37FDFF" box="[817,1174,524,545]" gridcol="0" gridrow="6" pageId="13" pageNumber="448">
<taxonomicName id="4C3D4D1FEC20FFC05366FDB9FBE3FDFF" authority="(Dt)" authorityName="Russell" authorityYear="1970" baseAuthorityName="Dt" box="[817,1090,524,545]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC20FFC05366FDB9FBB5FDFF" box="[817,1044,524,545]" italics="true" pageId="13" pageNumber="448">Daspletosaurus torosus</emphasis>
(Dt)
</taxonomicName>
</th>
<td id="76DC5DA2EC20003254FCFDB9FB4EFDFF" box="[1195,1263,524,545]" gridcol="1" gridrow="6" pageId="13" pageNumber="448">104</td>
<td id="76DC5DA2EC20003254ACFDB9FAE6FDFF" box="[1275,1351,524,545]" gridcol="2" gridrow="6" pageId="13" pageNumber="448">9.911</td>
<td id="76DC5DA2EC200032552BFDB9FA69FDFF" box="[1404,1480,524,545]" gridcol="3" gridrow="6" pageId="13" pageNumber="448">28.85</td>
</tr>
<tr id="350D34DEEC2000325366FD9AFA69FD9A" box="[817,1480,559,580]" gridrow="7" pageId="13" pageNumber="448">
<th id="76DC5DA2EC2000325366FD9AFB37FD9A" box="[817,1174,559,580]" gridcol="0" gridrow="7" pageId="13" pageNumber="448">
<taxonomicName id="4C3D4D1FEC20FFC05366FD9AFC46FD9A" authorityName="Osborn" authorityYear="1905" box="[817,999,559,580]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC20FFC05366FD9AFC46FD9A" box="[817,999,559,580]" italics="true" pageId="13" pageNumber="448">Tyrannosaurus rex</emphasis>
</taxonomicName>
(TrA)
</th>
<td id="76DC5DA2EC20003254FCFD9AFB4EFD9A" box="[1195,1263,559,580]" gridcol="1" gridrow="7" pageId="13" pageNumber="448">125</td>
<td id="76DC5DA2EC20003254ACFD9AFAE6FD9A" box="[1275,1351,559,580]" gridcol="2" gridrow="7" pageId="13" pageNumber="448">34.02</td>
<td id="76DC5DA2EC200032552BFD9AFA69FD9A" box="[1404,1480,559,580]" gridcol="3" gridrow="7" pageId="13" pageNumber="448">122.5</td>
</tr>
<tr id="350D34DEEC2000325366FDE7FA69FDB9" box="[817,1480,594,615]" gridrow="8" pageId="13" pageNumber="448">
<th id="76DC5DA2EC2000325366FDE7FB37FDB9" box="[817,1174,594,615]" gridcol="0" gridrow="8" pageId="13" pageNumber="448">
<taxonomicName id="4C3D4D1FEC20FFC05366FDE7FC46FDB9" authorityName="Osborn" authorityYear="1905" box="[817,999,594,615]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC20FFC05366FDE7FC46FDB9" box="[817,999,594,615]" italics="true" pageId="13" pageNumber="448">Tyrannosaurus rex</emphasis>
</taxonomicName>
(TrF)
</th>
<td id="76DC5DA2EC20003254FCFDE7FB4EFDB9" box="[1195,1263,594,615]" gridcol="1" gridrow="8" pageId="13" pageNumber="448">140</td>
<td id="76DC5DA2EC20003254ACFDE7FAE6FDB9" box="[1275,1351,594,615]" gridcol="2" gridrow="8" pageId="13" pageNumber="448">53.53</td>
<td id="76DC5DA2EC200032552BFDE7FA69FDB9" box="[1404,1480,594,615]" gridcol="3" gridrow="8" pageId="13" pageNumber="448">192.8</td>
</tr>
</table>
</paragraph>
<paragraph id="8B82369CEC20FFC05031FEF0FDACFE51" blockId="13.[102,721,325,399]" pageId="13" pageNumber="448">Are hypotheses of tyrannosaurid tooth, nasal and cranial strength validated?</paragraph>
<paragraph id="8B82369CEC20FFC05031FE1EFCA6FE1A" blockId="13.[102,775,427,1413]" box="[102,775,427,452]" pageId="13" pageNumber="448">
<heading id="D0CA81F0EC20FFC05031FE1EFCA6FE1A" bold="true" box="[102,775,427,452]" centered="true" fontSize="10" level="3" pageId="13" pageNumber="448" reason="0">
<emphasis id="B949EA8EEC20FFC05031FE1EFCA6FE1A" bold="true" box="[102,775,427,452]" pageId="13" pageNumber="448">Tyrannosaurid maxillary teeth were stronger in bending</emphasis>
</heading>
</paragraph>
<paragraph id="8B82369CEC20FFC05031FE7EFD57FBBA" blockId="13.[102,775,427,1413]" pageId="13" pageNumber="448">
<emphasis id="B949EA8EEC20FFC05031FE7EFD13FE3A" bold="true" box="[102,690,459,484]" pageId="13" pageNumber="448">than those of other large carnivorous dinosaurs</emphasis>
.—This hypothesis is partly falsified in that the average maxillary tooth strengths of most tyrannosaurids are not substantially higher than those of carnosaurs at equivalent skull lengths. The teeth of the carnosaur 
<taxonomicName id="4C3D4D1FEC20FFC051C9FDF9FDF2FDBD" authority="Currie and Zhao, 1994" box="[414,595,587,611]" class="Reptilia" family="Neovenatoridae" genus="Sinraptor" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="dongi">
<emphasis id="B949EA8EEC20FFC051C9FDF9FDF2FDBD" box="[414,595,587,611]" italics="true" pageId="13" pageNumber="448">Sinraptor dongi</emphasis>
</taxonomicName>
are notably robust; while not as thick at the base as most tyrannosaurid teeth they have lower crown heights and low bending moments arms. However, tyrannosaurid teeth vary more in size along the maxillary row than in other theropods, and the strengths of the largest maxillary tooth tend to be higher in tyrannosaurids relative to skull length. The average and maximum tooth strengths of 
<taxonomicName id="4C3D4D1FEC20FFC05120FC99FDEAFC9D" authorityName="Osborn" authorityYear="1905" box="[375,587,812,835]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC20FFC05120FC99FDEAFC9D" box="[375,587,812,835]" italics="true" pageId="13" pageNumber="448">Tyrannosaurus rex</emphasis>
</taxonomicName>
are much higher than those of non−tyrannosaurids when normalized for skull size. High mediolateral bending strength of 
<taxonomicName id="4C3D4D1FEC20FFC05204FCD9FD34FC5D" authorityName="Osborn" authorityYear="1905" box="[595,661,876,899]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC20FFC05204FCD9FD34FC5D" box="[595,661,876,899]" italics="true" pageId="13" pageNumber="448">T. rex</emphasis>
</taxonomicName>
teeth corresponds with Meers̓ (2003) observation that 
<taxonomicName id="4C3D4D1FEC20FFC0522DFC39FD1FFC7D" authorityName="Osborn" authorityYear="1905" box="[634,702,908,931]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC20FFC0522DFC39FD1FFC7D" box="[634,702,908,931]" italics="true" pageId="13" pageNumber="448">T. rex</emphasis>
</taxonomicName>
rostra were broader than the mediolateral span of the dentaries. If the animals bit into bone often and food was caught between the tooth rows, this jaw arrangement would impose lateral bending forces on the maxillary teeth and medial forces on the dentary teeth. A high mediolateral section modulus would reduce stress that these forces imposed on the teeth.
</paragraph>
<paragraph id="8B82369CEC20FFC050DBFBD9FECFFA5B" blockId="13.[102,775,427,1413]" pageId="13" pageNumber="448">
The trends of increase in tooth strength with skull length are markedly different between tyrannosaurids and other large theropods. The high strengths of 
<taxonomicName id="4C3D4D1FEC20FFC05279FB18FCA6FB1A" authorityName="Osborn" authorityYear="1905" box="[558,775,1197,1220]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC20FFC05279FB18FCA6FB1A" box="[558,775,1197,1220]" italics="true" pageId="13" pageNumber="448">Tyrannosaurus rex</emphasis>
</taxonomicName>
teeth contribute to the non−linear trend in the tyrannosaurids. The particularly strong maxillary teeth of 
<taxonomicName id="4C3D4D1FEC20FFC05215FB58FD24FADA" authorityName="Osborn" authorityYear="1905" box="[578,645,1261,1284]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC20FFC05215FB58FD24FADA" box="[578,645,1261,1284]" italics="true" pageId="13" pageNumber="448">T. rex</emphasis>
</taxonomicName>
are consistent with high bite forces (
<bibRefCitation id="EFAC4B6DEC20FFC051D3FAB9FDC3FAFB" author="Erickson, G. M. &amp; Olson, K. H." box="[388,610,1292,1317]" journalOrPublisher="Journal of Vertebrate Paleontology" pageId="13" pageNumber="448" pagination="175 - 178" part="16" refId="ref11520" refString="Erickson, G. M. and Olson, K. H. 1996. Bite marks attributable to Tyrannosaurus rex: a preliminary description and implications. Journal of Vertebrate Paleontology 16: 175 - 178." title="Bite marks attributable to Tyrannosaurus rex: a preliminary description and implications" type="journal article" year="1996">Erickson et al. 1996</bibRefCitation>
) and mandible strength (
<bibRefCitation id="EFAC4B6DEC20FFC05099FA99FE0DFA9B" author="Therrien, F. &amp; Henderson, D. M. &amp; Ruff. C. B." box="[206,428,1324,1349]" editor="K. Carpenter" journalOrPublisher="Indiana University Press, Bloomington" pageId="13" pageNumber="448" pagination="179 - 237" refId="ref13207" refString="Therrien, F., Henderson, D. M., and Ruff. C. B. 2005. Bite me: biomechanical models of theropod mandibles and implications for feeding behavior. In: K. Carpenter (ed.), The Carnivorous Dinosaurs, 179 - 237. Indiana University Press, Bloomington." title="Bite me: biomechanical models of theropod mandibles and implications for feeding behavior" type="book chapter" volumeTitle="The Carnivorous Dinosaurs" year="2005">Therrien et al. 2005</bibRefCitation>
) found for this taxon, and indicate that its feeding apparatus was stronger than expected for a tyrannosaurid its size.
</paragraph>
<paragraph id="8B82369CEC20FFC05031FA2BFCA7FA69" blockId="13.[102,775,1438,1816]" box="[102,774,1438,1463]" pageId="13" pageNumber="448">
<heading id="D0CA81F0EC20FFC05031FA2BFCA7FA69" bold="true" box="[102,774,1438,1463]" centered="true" fontSize="10" level="3" pageId="13" pageNumber="448" reason="0">
<emphasis id="B949EA8EEC20FFC05031FA2BFCA7FA69" bold="true" box="[102,774,1438,1463]" pageId="13" pageNumber="448">Vaulting contributed significantly to tyrannosaurid nasal</emphasis>
</heading>
</paragraph>
<paragraph id="8B82369CEC20FFC05031FA0AFD78F8C6" blockId="13.[102,775,1438,1816]" pageId="13" pageNumber="448">
<emphasis id="B949EA8EEC20FFC05031FA0AFF68FA09" bold="true" box="[102,201,1471,1495]" pageId="13" pageNumber="448">strength</emphasis>
.—The nasal “vaulting index” (
<figureCitation id="13062A19EC20FFC0527BFA0AFD32FA06" box="[556,659,1471,1496]" captionStart="Fig" captionStartId="10.[102,135,1356,1376]" captionTargetBox="[106,770,225,1318]" captionTargetId="graphics@10.[106,769,259,1263]" captionTargetPageId="10" captionText="Fig. 10. Heights and widths of tyrannosaurid nasal slices normalized for slice area and bone length. A. Normalized heights (“vaulting index”) showing convergence of vaulting pattern at large size. B. Normalized widths (“span index”) showing isometric form in most specimens, but exaggerated relative width in Tyrannosaurus rex nasals. Points of maximum vaulting and span are indicated on nasals of T. rex (TMP 98.86.01; cast of BHI 2033). Symbols as per Fig. 9." figureDoi="http://doi.org/10.5281/zenodo.3739914" httpUri="https://zenodo.org/record/3739914/files/figure.png" pageId="13" pageNumber="448">Fig. 10A</figureCitation>
) indicates that the vertical second moments of area in large tyrannosaurids is higher than expected if they retained the same cross−sectional shapes of the smaller specimens. Thus vaulting of the nasals, more than increased cross−sectional area, increased their second moments of area and strengths of large tyrannosaurid nasals in bending and torsion. We predict that analysis including more juvenile specimens will uphold these findings. Our “span index” (
<figureCitation id="13062A19EC20FFC051B7F90AFDE2F906" box="[480,579,1727,1752]" captionStart="Fig" captionStartId="10.[102,135,1356,1376]" captionTargetBox="[106,770,225,1318]" captionTargetId="graphics@10.[106,769,259,1263]" captionTargetPageId="10" captionText="Fig. 10. Heights and widths of tyrannosaurid nasal slices normalized for slice area and bone length. A. Normalized heights (“vaulting index”) showing convergence of vaulting pattern at large size. B. Normalized widths (“span index”) showing isometric form in most specimens, but exaggerated relative width in Tyrannosaurus rex nasals. Points of maximum vaulting and span are indicated on nasals of T. rex (TMP 98.86.01; cast of BHI 2033). Symbols as per Fig. 9." figureDoi="http://doi.org/10.5281/zenodo.3739914" httpUri="https://zenodo.org/record/3739914/files/figure.png" pageId="13" pageNumber="448">Fig. 10B</figureCitation>
) shows that anterior broadening of the nasals in the 
<taxonomicName id="4C3D4D1FEC20FFC051BDF955FD1FF929" authorityName="Osborn" authorityYear="1905" box="[490,702,1760,1783]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC20FFC051BDF955FD1FF929" box="[490,702,1760,1783]" italics="true" pageId="13" pageNumber="448">Tyrannosaurus rex</emphasis>
</taxonomicName>
specimen increased its lateral bending strength in this region.
</paragraph>
<paragraph id="8B82369CEC20FFC05031F887FCA6F894" blockId="13.[102,775,1841,2026]" box="[102,775,1841,1866]" pageId="13" pageNumber="448">
<heading id="D0CA81F0EC20FFC05031F887FCA6F894" bold="true" box="[102,775,1841,1866]" centered="true" fontSize="10" level="3" pageId="13" pageNumber="448" reason="0">
<emphasis id="B949EA8EEC20FFC05031F887FCA6F894" bold="true" box="[102,775,1841,1866]" pageId="13" pageNumber="448">Fused tyrannosaurid nasals were stronger than unfused</emphasis>
</heading>
</paragraph>
<paragraph id="8B82369CEC20FFC05031F8E7FCA7F837" blockId="13.[102,775,1841,2026]" pageId="13" pageNumber="448">
<emphasis id="B949EA8EEC20FFC05031F8E7FE91F8B4" bold="true" box="[102,304,1874,1898]" pageId="13" pageNumber="448">carnosaur nasals</emphasis>
.—Our results for the geometric contributions to nasal strength artificially exaggerate the strengths of the 
<taxonomicName id="4C3D4D1FEC20FFC050D8F827FEC0F874" authorityName="Marsh" authorityYear="1877" box="[143,353,1938,1962]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC20FFC050D8F827FEC0F874" box="[143,353,1938,1962]" italics="true" pageId="13" pageNumber="448">Allosaurus fragilis</emphasis>
</taxonomicName>
nasals, and diminish those of 
<taxonomicName id="4C3D4D1FEC20FFC052E3F827FEB0F814" authority="Lambe, 1914" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC20FFC052E3F827FEB0F814" italics="true" pageId="13" pageNumber="448">Gorgosaurus libratus</emphasis>
</taxonomicName>
and 
<taxonomicName id="4C3D4D1FEC20FFC05119F807FD27F814" authority="Osborn, 1905 " box="[334,646,1970,1994]" class="Reptilia" family="Tyrannosauridae" genus="Albertosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species">
<emphasis id="B949EA8EEC20FFC05119F807FD27F814" box="[334,646,1970,1994]" italics="true" pageId="13" pageNumber="448">Albertosaurus sarcophagus</emphasis>
</taxonomicName>
. The computed average strengths of 
<taxonomicName id="4C3D4D1FEC20FFC051FAF867FD24F834" authorityName="Marsh" authorityYear="1877" box="[429,645,2002,2026]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC20FFC051FAF867FD24F834" box="[429,645,2002,2026]" italics="true" pageId="13" pageNumber="448">Allosaurus fragilis</emphasis>
</taxonomicName>
nasals are
</paragraph>
<paragraph id="8B82369CEC20FFC0537BFD1CFB7FFBFC" blockId="13.[812,1485,681,2026]" pageId="13" pageNumber="448">
higher than those of the albertosaurine tyrannosaurids when plotted against nasal length (
<figureCitation id="13062A19EC20FFC05426FD7CFB17FD3C" box="[1137,1206,713,738]" captionStart="Fig" captionStartId="7.[812,845,1631,1651]" captionTargetBox="[817,1481,230,1606]" captionTargetId="graphics@7.[917,1470,726,1087]" captionText="Fig. 8. Average strengths of nasal cross−sections in tyrannosaurids and Allosaurus fragilis, plotted against nasal length. A. Cross−sectional areas, proportional to compression strengths. B. Second moment of area, proportional to vertical bending strength. C. Second moment of area, proportional to lateral bending strength. Values for the A. fragilis nasals are uncorrected for the hollowness of the sections, which would reduce their strengths. Lines fitted to the tyrannosaurid values are derived from log transformed data. See Appendix 1 for labels." figureDoi="http://doi.org/10.5281/zenodo.3961039" httpUri="https://zenodo.org/record/3961039/files/figure.png" pageId="13" pageNumber="448">Fig. 8</figureCitation>
). However, averages for the albertosaurine tyrannosaurid nasals are reduced by strength properties of their flat caudal projection, where articulating bones would augment the nasal strengths. The anterior, vaulted portions of the albertosaurine nasals, where they would receive the brunt of forces from the maxillae, have higher strengths than the 
<taxonomicName id="4C3D4D1FEC20FFC054CBFC3FFAB0FC7C" authorityName="Marsh" authorityYear="1877" box="[1180,1297,906,930]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC20FFC054CBFC3FFAB0FC7C" box="[1180,1297,906,930]" italics="true" pageId="13" pageNumber="448">A. fragilis</emphasis>
</taxonomicName>
nasals (
<figureCitation id="13062A19EC20FFC05522FC3CFA1EFC7C" box="[1397,1471,905,930]" captionStart="Fig" captionStartId="8.[102,135,1684,1704]" captionTargetBox="[108,1479,227,1655]" captionTargetPageId="8" captionText="Fig. 9. Comparison of theropod nasal strengths at multiple transverse sections. Horizontal (Iy) and vertical (Iz) second moments of area of nasal cross−sections of Allosaurus fragilis (upper two graphs) and tyrannosaurids (lower two graphs). Second moments of area are proportional to lateral (Iy) and vertical (Iz) bending strengths. X−axes of graphs show relative position of slices along the long axes of the bones: 0.0 is posterior and 1.0 anterior." figureDoi="http://doi.org/10.5281/zenodo.3739912" httpUri="https://zenodo.org/record/3739912/files/figure.png" pageId="13" pageNumber="448">Fig. 9</figureCitation>
). Also, pneumaticity of the 
<taxonomicName id="4C3D4D1FEC20FFC0541CFC1FFB1BFC1C" authorityName="Marsh" authorityYear="1877" box="[1099,1210,938,962]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC20FFC0541CFC1FFB1BFC1C" box="[1099,1210,938,962]" italics="true" pageId="13" pageNumber="448">A. fragilis</emphasis>
</taxonomicName>
nasals (
<figureCitation id="13062A19EC20FFC05545FC1CFAF2FC1C" box="[1298,1363,937,962]" captionStart="Fig" captionStartId="5.[102,135,1750,1770]" captionTargetBox="[121,755,223,1724]" captionTargetId="figure@5.[121,755,223,1724]" captionTargetPageId="5" captionText="Fig. 5. CT cross sections and reconstructions of Allosaurus fragilis nasals: A, largest (UUVP 1663/UMNH VP 9146); B, midsize (UUVP 1913/ UMNH VP 9144); and C, smallest (UUVP 10854/UMNHVP 7784). Anterior is to the right. Cross sections are from the strongly pneumatized regions of the nasals, at positions indicated by the dashed lines. The slices are normalized to the same size to show the relative degree of pneumatic excavation, evident despite mineral infilling in some sections. Reconstructions are in lateral views and in dorsal views with single left or right specimens mirrored to replicate complete pairs. Specimen B is broken over the posterior part of the external nares. Scale bar 10 cm." figureDoi="http://doi.org/10.5281/zenodo.3739906" httpUri="https://zenodo.org/record/3739906/files/figure.png" pageId="13" pageNumber="448">Fig. 5</figureCitation>
) would reduce their strengths somewhat. The average compressional strengths would decrease by approximately 30%, and second moments of area by approximately 6%
</paragraph>
<paragraph id="8B82369CEC20FFC05305FB99FA38FA1B" blockId="13.[812,1485,681,2026]" pageId="13" pageNumber="448">
The extensive fusion seen in tyrannosaurid CT sections would increase their torsional and compressive strengths, with benefits for feeding function. Tooth marks show that large theropods applied powerful bites that cut bone (
<bibRefCitation id="EFAC4B6DEC20FFC055D0FB39FC04FB1B" author="Chure, D. J. &amp; Fiorillo, A. R. &amp; Jacobsen, A." journalOrPublisher="Gaia" pageId="13" pageNumber="448" pagination="227 - 232" part="15" refId="ref11302" refString="Chure, D. J., Fiorillo, A. R., and Jacobsen, A. 2000. Prey bone utilization by predatory dinosaurs in the Late Jurassic of North America, with comments on prey bone use by dinosaurs throughout the Mesozoic. Gaia 15: 227 - 232." title="Prey bone utilization by predatory dinosaurs in the Late Jurassic of North America, with comments on prey bone use by dinosaurs throughout the Mesozoic" type="journal article" year="2000">Chure et al. 2000</bibRefCitation>
). With unilateral biting, unfused nasals would experience vertical shear between left and right halves, causing dorsal displacement of one side of the snout relative to the other and straining ligaments that connected the nasals. In tyrannosaurids, fusion added bone to the midline of the nasals where the structures are notably tall in cross−section (
<figureCitation id="13062A19EC20FFC05362FAD9FCD9FA5B" box="[821,888,1388,1413]" captionStart="Fig" captionStartId="5.[812,845,1835,1855]" captionTargetBox="[855,1442,1260,1807]" captionTargetId="graphics@5.[856,1408,1260,1807]" captionTargetPageId="5" captionText="Fig. 6. Geometry used to compute the area, centroid, and second moments of area of a nasal cross−section (from middle region of fused Tyrannosaurus rex nasals: TMP 98.86.01; cast of BHI 2033). A. Decomposition of the cross−section to compute area by summing areas of triangles. Small “+”s are centroids of individual triangles. Large “+” is the centroid for the complete section. B. Cross−section partitioned into horizontal and vertical strips of known area and position, used to calculate second moments of area." figureDoi="http://doi.org/10.5281/zenodo.3739908" httpUri="https://zenodo.org/record/3739908/files/figure.png" pageId="13" pageNumber="448">Fig. 6</figureCitation>
). Because shear strength is proportional to the dimension of a structure parallel to shear forces, increased height of bone along the midline would resist dorsoventral shear.
</paragraph>
<paragraph id="8B82369CEC20FFC05305FA7AFA25F919" blockId="13.[812,1485,681,2026]" pageId="13" pageNumber="448">
The combination of fusion and high second moments of area gave the dorsal portion of tyrannosaurid nasals the properties of a torsion tube resistant to twisting forces (similar to the entire muzzles of crocodilians: 
<bibRefCitation id="EFAC4B6DEC20FFC054E7F99AFAE4F996" author="Busbey, A. R." box="[1200,1349,1583,1608]" editor="J. J. Thomason" journalOrPublisher="Cambridge University Press, Cambridge" pageId="13" pageNumber="448" pagination="173 - 192" refId="ref11168" refString="Busbey, A. R. 1995. The structural consequences of cranium flattening in crocodilians. In: J. J. Thomason (ed.), Functional Morphology in Vertebrate Paleontology, 173 - 192. Cambridge University Press, Cambridge." title="The structural consequences of cranium flattening in crocodilians" type="book chapter" volumeTitle="Functional Morphology in Vertebrate Paleontology" year="1995">Busbey 1995</bibRefCitation>
). With bone rather than ligaments resisting the tensile components of shear and torsion, and bone resisting compressive torsional components, the food would have experienced a greater proportion of the full bite force in tyrannosaurids than in carnosaurs.
</paragraph>
<paragraph id="8B82369CEC20FFC35305F964FD7CFEFF" blockId="13.[812,1485,681,2026]" lastBlockId="14.[102,774,232,289]" lastPageId="14" lastPageNumber="449" pageId="13" pageNumber="448">
High proportions of bone in cross−sections of tyrannosaurid nasals indicate higher compressional strength than the collective strength of 
<taxonomicName id="4C3D4D1FEC20FFC05449F8A7FB34F8F4" authorityName="Marsh" authorityYear="1877" box="[1054,1173,1810,1834]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC20FFC05449F8A7FB34F8F4" box="[1054,1173,1810,1834]" italics="true" pageId="13" pageNumber="448">Allosaurus</emphasis>
</taxonomicName>
nasals. CT sections (
<figureCitation id="13062A19EC20FFC055D4F8A4FA69F8F4" box="[1411,1480,1809,1834]" captionStart="Fig" captionStartId="5.[102,135,1750,1770]" captionTargetBox="[121,755,223,1724]" captionTargetId="figure@5.[121,755,223,1724]" captionTargetPageId="5" captionText="Fig. 5. CT cross sections and reconstructions of Allosaurus fragilis nasals: A, largest (UUVP 1663/UMNH VP 9146); B, midsize (UUVP 1913/ UMNH VP 9144); and C, smallest (UUVP 10854/UMNHVP 7784). Anterior is to the right. Cross sections are from the strongly pneumatized regions of the nasals, at positions indicated by the dashed lines. The slices are normalized to the same size to show the relative degree of pneumatic excavation, evident despite mineral infilling in some sections. Reconstructions are in lateral views and in dorsal views with single left or right specimens mirrored to replicate complete pairs. Specimen B is broken over the posterior part of the external nares. Scale bar 10 cm." figureDoi="http://doi.org/10.5281/zenodo.3739906" httpUri="https://zenodo.org/record/3739906/files/figure.png" pageId="13" pageNumber="448">Fig. 5</figureCitation>
; Emily Rayfield, personal communication 2004) and openings into the bones (
<bibRefCitation id="EFAC4B6DEC20FFC053B5F8E4FBDDF8B4" author="Witmer, L. M." box="[994,1148,1873,1898]" journalOrPublisher="Journal of Vertebrate Paleontology" pageId="13" pageNumber="448" pagination="1 - 73" part="17 (Supplement 1)" refId="ref13418" refString="Witmer, L. M. 1997. The evolution of the antorbital cavity of archosaurs: a study in soft-tissue reconstruction in the fossil record with an analysis of the function of pneumaticity. Journal of Vertebrate Paleontology 17 (Supplement 1): 1 - 73." title="The evolution of the antorbital cavity of archosaurs: a study in soft-tissue reconstruction in the fossil record with an analysis of the function of pneumaticity" type="journal article" year="1997">Witmer 1997</bibRefCitation>
) show that 
<taxonomicName id="4C3D4D1FEC20FFC0555FF8E7FADEF8B4" authorityName="Marsh" authorityYear="1877" box="[1288,1407,1874,1898]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="13" pageNumber="448" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC20FFC0555FF8E7FADEF8B4" box="[1288,1407,1874,1898]" italics="true" pageId="13" pageNumber="448">Allosaurus</emphasis>
</taxonomicName>
nasals were hollowed out through much of their length (
<figureCitation id="13062A19EC20FFC0550BF8C4FA01F854" box="[1372,1440,1905,1930]" captionStart="Fig" captionStartId="5.[102,135,1750,1770]" captionTargetBox="[121,755,223,1724]" captionTargetId="figure@5.[121,755,223,1724]" captionTargetPageId="5" captionText="Fig. 5. CT cross sections and reconstructions of Allosaurus fragilis nasals: A, largest (UUVP 1663/UMNH VP 9146); B, midsize (UUVP 1913/ UMNH VP 9144); and C, smallest (UUVP 10854/UMNHVP 7784). Anterior is to the right. Cross sections are from the strongly pneumatized regions of the nasals, at positions indicated by the dashed lines. The slices are normalized to the same size to show the relative degree of pneumatic excavation, evident despite mineral infilling in some sections. Reconstructions are in lateral views and in dorsal views with single left or right specimens mirrored to replicate complete pairs. Specimen B is broken over the posterior part of the external nares. Scale bar 10 cm." figureDoi="http://doi.org/10.5281/zenodo.3739906" httpUri="https://zenodo.org/record/3739906/files/figure.png" pageId="13" pageNumber="448">Fig. 5</figureCitation>
) by pneumatizing tissues, reducing their cross−sectional area and compressive strength. In contrast, CT sections and broken fossilized specimens show that tyrannosaurid nasals had extensive cortical bone, high densities of trabecular bone, and small vascular canals (
<bibRefCitation id="EFAC4B6DEC23FFC3514CFEBDFE0FFEFF" author="Currie, P. J." box="[283,430,264,289]" journalOrPublisher="Acta Palaeontologica Polonica" pageId="14" pageNumber="449" pagination="191 - 226" part="48" refId="ref11356" refString="Currie, P. J. 2003 a. Cranial anatomy of tyrannosaurid dinosaurs from the Late Cretaceous of Alberta, Canada. Acta Palaeontologica Polonica 48: 191 - 226." title="Cranial anatomy of tyrannosaurid dinosaurs from the Late Cretaceous of Alberta, Canada" type="journal article" year="2003">Currie 2003a</bibRefCitation>
) but no pneumatic cavities.
</paragraph>
<paragraph id="8B82369CEC23FFC35031FE88FE50FDA8" blockId="14.[102,775,317,630]" pageId="14" pageNumber="449">
<emphasis id="B949EA8EEC23FFC35031FE88FF4CFEA8" bold="true" pageId="14" pageNumber="449">
<heading id="D0CA81F0EC23FFC35031FE88FF3AFEAB" bold="true" centered="true" fontSize="10" level="3" pageId="14" pageNumber="449" reason="0">Tyrannosaurid crania were stronger overall than carnosaur</heading>
crania
</emphasis>
.—The results confirm that tyrannosaurid crania were stronger than those of other theropods of similar skull length (
<tableCitation id="C6BF0327EC23FFC350E8FE28FEBCFE68" box="[191,285,413,438]" captionStart="Table 3" captionStartId="13.[812,867,231,252]" captionTargetId="graphics@13.[812,1485,271,619]" captionTargetPageId="13" captionText="Table 3. Computed strength properties of theropod crania." httpUri="http://table.plazi.org/id/DF426614EC20FFC0537BFF52FAFAFF22" pageId="14" pageNumber="449" tableUuid="DF426614EC20FFC0537BFF52FAFAFF22">Table 3</tableCitation>
). The 
<taxonomicName id="4C3D4D1FEC23FFC35138FE2BFDC6FE6B" authority="Lambe, 1914" box="[367,615,413,437]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC23FFC35138FE2BFDC6FE6B" box="[367,615,413,437]" italics="true" pageId="14" pageNumber="449">Gorgosaurus libratus</emphasis>
</taxonomicName>
cranium was minimally 1.5 times stronger (in vertical bending) than a slightly longer cranium of 
<taxonomicName id="4C3D4D1FEC23FFC351D9FE68FDFEFE2B" authorityName="Marsh" authorityYear="1877" box="[398,607,477,501]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC23FFC351D9FE68FDFEFE2B" box="[398,607,477,501]" italics="true" pageId="14" pageNumber="449">Allosaurus fragilis</emphasis>
</taxonomicName>
. The 
<taxonomicName id="4C3D4D1FEC23FFC352C9FE6BFF7BFDCB" authorityName="Osborn" authorityYear="1905" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC23FFC352C9FE6BFF7BFDCB" italics="true" pageId="14" pageNumber="449">Tyrannosaurus rex</emphasis>
</taxonomicName>
crania were much stronger than equivalently sized or larger carnosaur crania, except for a modestly higher vertical bending indicator for 
<taxonomicName id="4C3D4D1FEC23FFC351C2FD88FCA7FD8B" authority="Depéret &amp; Savornin, 1925" box="[405,774,573,597]" class="Reptilia" family="Carcharodontosauridae" genus="Carcharodontosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="saharicus">
<emphasis id="B949EA8EEC23FFC351C2FD88FCA7FD8B" box="[405,774,573,597]" italics="true" pageId="14" pageNumber="449">Carcharodontosaurus saharicus</emphasis>
</taxonomicName>
versus the smaller 
<taxonomicName id="4C3D4D1FEC23FFC35160FDEBFED8FDAB" authorityName="Osborn" authorityYear="1905" box="[311,377,606,629]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC23FFC35160FDEBFED8FDAB" box="[311,377,606,629]" italics="true" pageId="14" pageNumber="449">T. rex</emphasis>
</taxonomicName>
specimen.
</paragraph>
<paragraph id="8B82369CEC23FFC35031FD12FD8EFD2F" blockId="14.[102,592,679,753]" pageId="14" pageNumber="449">Pattern of correlated progression of tyrannosaurid feeding mechanics</paragraph>
<paragraph id="8B82369CEC23FFC35031FCBBFE77FBF9" blockId="14.[102,775,782,2026]" pageId="14" pageNumber="449">
<bibRefCitation id="EFAC4B6DEC23FFC35031FCBBFE90FCF9" author="Thomson, K. S." box="[102,305,782,807]" journalOrPublisher="American Zoologist" pageId="14" pageNumber="449" pagination="379 - 397" part="6" refId="ref13337" refString="Thomson, K. S. 1966. The evolution of the tetrapod middle ear in the rhipidistian-tetrapod transition. American Zoologist 6: 379 - 397." title="The evolution of the tetrapod middle ear in the rhipidistian-tetrapod transition" type="journal article" year="1966">Thomson̓s (1966)</bibRefCitation>
concept of correlated progression involves the evolutionary integration of adaptive features (
<figureCitation id="13062A19EC23FFC352C5FC9BFD5BFC99" box="[658,762,814,839]" captionStart="Fig" captionStartId="15.[102,135,1656,1676]" captionTargetBox="[212,1379,225,1629]" captionTargetId="graphics@15.[325,856,629,1619]" captionTargetPageId="15" captionText="Fig. 14. A. Functional integration of strengths of the tyrannosaurid head skeleton when subjected to feeding forces. Dark arrows represent direct influences of forces on structures, and direct integration of structural strengths. Light arrows represent less direct influences of structures on one another. B. Correlated progression of tyrannosauroid feeding adaptations mapped onto a tyrannosauroid cladogram after Xu et al. (2004) and Holtz (2004). Arrow at left represents phyletic increases that likely occurred at all ingroup nodes except G. libratus + A. sarcophagus." figureDoi="http://doi.org/10.5281/zenodo.3961071" httpUri="https://zenodo.org/record/3961071/files/figure.png" pageId="14" pageNumber="449">Fig. 14A</figureCitation>
). Structural modifications of the tyrannosauroid feeding apparatus suggest integration of faculties towards reduction of large prey. We adopt the phrase “correlated progression” with the caveat that it does not imply universal adaptive improvement. Escalating performance in one area may lead to loss of capability in others, such as a reduced ability of the adults of larger predators to capture smaller prey.
</paragraph>
<paragraph id="8B82369CEC23FFC350DBFB85FDB6FAF7" blockId="14.[102,775,782,2026]" pageId="14" pageNumber="449">
Correlated progression is testable by examining correspondences between rates of performance increase for various structures. The nasals, teeth, dentaries, and crania of tyrannosaurids show consistent patterns of positive allometric increase in strength when plotted against cranium or dentary length (
<figureCitation id="13062A19EC23FFC3514AFB65FED1FB37" box="[285,368,1232,1257]" captionStart="Fig" captionStartId="1.[812,844,1809,1829]" captionTargetBox="[856,1441,1117,1784]" captionTargetId="graphics@1.[915,1440,1149,1726]" captionTargetPageId="1" captionText="Fig. 2. Comparison of vertical bending strengths of adult theropod dentaries, graphed as mid−dentary section modulus versus mandible length (data from Therrien et al. 2005). Lines fitted by least squares regression, by log transformed values for the tyrannosaurid data. Carnosaur dentary strengths scale linearly with dentary length, while tyrannosaurid dentary strengths show an exponential increase. The tyrannosaurid dentaries are stronger than those of carnosaurs for a given mandible length, indicating a relatively stronger bite. See Appendix 1 for specimen labels; Gc, Giganotosaurus carolinii." figureDoi="http://doi.org/10.5281/zenodo.3961033" httpUri="https://zenodo.org/record/3961033/files/figure.png" pageId="14" pageNumber="449">Figs. 2</figureCitation>
, 
<figureCitation id="13062A19EC23FFC35128FB65FE2FFB37" box="[383,398,1232,1257]" captionStart="Fig" captionStartId="2.[102,135,1625,1645]" captionTargetBox="[859,1446,938,1599]" captionTargetId="graphics@2.[924,1446,971,1546]" captionTargetPageId="2" captionText="Fig. 3. Comparisons of mediolateral (A, B) and anteroposterior (C, D) strengths of tyrannosaurid and non−tyrannosaurid theropod maxillary teeth, plotted against skull length. Regressions are by least squares, on log transformed data for the tyrannosaurids. Trend lines are allometric in the tyannosaurids but linear in non−tyrannosaurids. Tooth strengths of Tyrannosaurus rex are much higher than in any other examined taxon. Starting points of the small arrows indicate the position of the juvenile T. rex (TrJ). See Appendix 1 for other specimen labels." figureDoi="http://doi.org/10.5281/zenodo.3961063" httpUri="https://zenodo.org/record/3961063/files/figure.png" pageId="14" pageNumber="449">3</figureCitation>
, 
<figureCitation id="13062A19EC23FFC351C8FB65FE0FFB37" box="[415,430,1232,1257]" captionStart="Fig" captionStartId="7.[812,845,1631,1651]" captionTargetBox="[817,1481,230,1606]" captionTargetId="graphics@7.[917,1470,726,1087]" captionText="Fig. 8. Average strengths of nasal cross−sections in tyrannosaurids and Allosaurus fragilis, plotted against nasal length. A. Cross−sectional areas, proportional to compression strengths. B. Second moment of area, proportional to vertical bending strength. C. Second moment of area, proportional to lateral bending strength. Values for the A. fragilis nasals are uncorrected for the hollowness of the sections, which would reduce their strengths. Lines fitted to the tyrannosaurid values are derived from log transformed data. See Appendix 1 for labels." figureDoi="http://doi.org/10.5281/zenodo.3961039" httpUri="https://zenodo.org/record/3961039/files/figure.png" pageId="14" pageNumber="449">8</figureCitation>
, 
<figureCitation id="13062A19EC23FFC351E9FB65FE7CFB37" box="[446,477,1232,1257]" captionStart="Fig" captionStartId="12.[812,845,1921,1941]" captionTargetBox="[823,1475,731,1894]" captionTargetId="graphics@12.[927,1475,1162,1441]" captionTargetPageId="12" captionText="Fig. 13. Strength indicators computed for theropod crania under mediolateral (A), dorsoventral (B), and torsional (C) loadings. Tyrannosaurid crania are invariably stronger than those of carnosaurs for a given skull length. See Appendix 1 for labels." figureDoi="http://doi.org/10.5281/zenodo.3961069" httpUri="https://zenodo.org/record/3961069/files/figure.png" pageId="14" pageNumber="449">13</figureCitation>
). In contrast, elements of other large theropods show linear increases in strength with increasing skull size (
<figureCitation id="13062A19EC23FFC3510FFAA5FE06FAF7" box="[344,423,1296,1321]" captionStart="Fig" captionStartId="1.[812,844,1809,1829]" captionTargetBox="[856,1441,1117,1784]" captionTargetId="graphics@1.[915,1440,1149,1726]" captionTargetPageId="1" captionText="Fig. 2. Comparison of vertical bending strengths of adult theropod dentaries, graphed as mid−dentary section modulus versus mandible length (data from Therrien et al. 2005). Lines fitted by least squares regression, by log transformed values for the tyrannosaurid data. Carnosaur dentary strengths scale linearly with dentary length, while tyrannosaurid dentary strengths show an exponential increase. The tyrannosaurid dentaries are stronger than those of carnosaurs for a given mandible length, indicating a relatively stronger bite. See Appendix 1 for specimen labels; Gc, Giganotosaurus carolinii." figureDoi="http://doi.org/10.5281/zenodo.3961033" httpUri="https://zenodo.org/record/3961033/files/figure.png" pageId="14" pageNumber="449">Figs. 2</figureCitation>
, 
<figureCitation id="13062A19EC23FFC351E4FAA5FE63FAF7" box="[435,450,1296,1321]" captionStart="Fig" captionStartId="2.[102,135,1625,1645]" captionTargetBox="[859,1446,938,1599]" captionTargetId="graphics@2.[924,1446,971,1546]" captionTargetPageId="2" captionText="Fig. 3. Comparisons of mediolateral (A, B) and anteroposterior (C, D) strengths of tyrannosaurid and non−tyrannosaurid theropod maxillary teeth, plotted against skull length. Regressions are by least squares, on log transformed data for the tyrannosaurids. Trend lines are allometric in the tyannosaurids but linear in non−tyrannosaurids. Tooth strengths of Tyrannosaurus rex are much higher than in any other examined taxon. Starting points of the small arrows indicate the position of the juvenile T. rex (TrJ). See Appendix 1 for other specimen labels." figureDoi="http://doi.org/10.5281/zenodo.3961063" httpUri="https://zenodo.org/record/3961063/files/figure.png" pageId="14" pageNumber="449">3</figureCitation>
, 
<figureCitation id="13062A19EC23FFC35198FAA5FE7FFAF7" box="[463,478,1296,1321]" captionStart="Fig" captionStartId="7.[812,845,1631,1651]" captionTargetBox="[817,1481,230,1606]" captionTargetId="graphics@7.[917,1470,726,1087]" captionText="Fig. 8. Average strengths of nasal cross−sections in tyrannosaurids and Allosaurus fragilis, plotted against nasal length. A. Cross−sectional areas, proportional to compression strengths. B. Second moment of area, proportional to vertical bending strength. C. Second moment of area, proportional to lateral bending strength. Values for the A. fragilis nasals are uncorrected for the hollowness of the sections, which would reduce their strengths. Lines fitted to the tyrannosaurid values are derived from log transformed data. See Appendix 1 for labels." figureDoi="http://doi.org/10.5281/zenodo.3961039" httpUri="https://zenodo.org/record/3961039/files/figure.png" pageId="14" pageNumber="449">8</figureCitation>
, 
<figureCitation id="13062A19EC23FFC351BCFAA5FDABFAF7" box="[491,522,1296,1321]" captionStart="Fig" captionStartId="12.[812,845,1921,1941]" captionTargetBox="[823,1475,731,1894]" captionTargetId="graphics@12.[927,1475,1162,1441]" captionTargetPageId="12" captionText="Fig. 13. Strength indicators computed for theropod crania under mediolateral (A), dorsoventral (B), and torsional (C) loadings. Tyrannosaurid crania are invariably stronger than those of carnosaurs for a given skull length. See Appendix 1 for labels." figureDoi="http://doi.org/10.5281/zenodo.3961069" httpUri="https://zenodo.org/record/3961069/files/figure.png" pageId="14" pageNumber="449">13</figureCitation>
).
</paragraph>
<paragraph id="8B82369CEC23FFC350DBFA84FBF0FE5F" blockId="14.[102,775,782,2026]" lastBlockId="14.[812,1485,232,706]" pageId="14" pageNumber="449">
The tyrannosaurid trends reveal a more complex, mosaic pattern of correlated progression than lock−step increases in strength for all structures. With most comparable structures, adult tyrannosaurine taxa (
<taxonomicName id="4C3D4D1FEC23FFC351E2FA27FD6BFA74" authorityName="Russell" authorityYear="1970" box="[437,714,1426,1450]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC23FFC351E2FA27FD6BFA74" box="[437,714,1426,1450]" italics="true" pageId="14" pageNumber="449">Daspletosaurus torosus</emphasis>
</taxonomicName>
and 
<taxonomicName id="4C3D4D1FEC23FFC35031FA06FE9FFA14" authorityName="Osborn" authorityYear="1905" box="[102,318,1459,1482]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC23FFC35031FA06FE9FFA14" box="[102,318,1459,1482]" italics="true" pageId="14" pageNumber="449">Tyrannosaurus rex</emphasis>
</taxonomicName>
) have higher size−normalized strengths than the albertosaurine forms, and 
<taxonomicName id="4C3D4D1FEC23FFC351A5FA66FD94FA34" authorityName="Osborn" authorityYear="1905" box="[498,565,1491,1514]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC23FFC351A5FA66FD94FA34" box="[498,565,1491,1514]" italics="true" pageId="14" pageNumber="449">T. rex</emphasis>
</taxonomicName>
in turn has higher strengths than 
<taxonomicName id="4C3D4D1FEC23FFC3515DFA46FEDEF9D4" authorityName="Russell" authorityYear="1970" box="[266,383,1523,1546]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC23FFC3515DFA46FEDEF9D4" box="[266,383,1523,1546]" italics="true" pageId="14" pageNumber="449">D. torosus</emphasis>
</taxonomicName>
. Because these taxa represent successively more derived forms (
<bibRefCitation id="EFAC4B6DEC23FFC35196F9A4FDE4F9F4" author="Holtz, T. R. Jr." box="[449,581,1553,1578]" editor="D. B. Weishampel &amp; P. Dodson &amp; H. Osmolska" journalOrPublisher="University of California Press. Berkeley" pageId="14" pageNumber="449" pagination="111 - 136" refId="ref12220" refString="Holtz, T. R. Jr. 2004. Tyrannosauroidea. In: D. B. Weishampel, P. Dodson, and H. Osmolska (eds.), The Dinosauria, 111 - 136. University of California Press. Berkeley." title="Tyrannosauroidea" type="book chapter" volumeTitle="The Dinosauria" year="2004">Holtz 2004</bibRefCitation>
), similar patterns of strength increase for all examined structures support the hypothesis of correlated progression of the tyrannosaurid feeding apparatus (
<figureCitation id="13062A19EC23FFC3516CF9C4FE00F954" box="[315,417,1649,1674]" captionStart="Fig" captionStartId="15.[102,135,1656,1676]" captionTargetBox="[212,1379,225,1629]" captionTargetId="graphics@15.[325,856,629,1619]" captionTargetPageId="15" captionText="Fig. 14. A. Functional integration of strengths of the tyrannosaurid head skeleton when subjected to feeding forces. Dark arrows represent direct influences of forces on structures, and direct integration of structural strengths. Light arrows represent less direct influences of structures on one another. B. Correlated progression of tyrannosauroid feeding adaptations mapped onto a tyrannosauroid cladogram after Xu et al. (2004) and Holtz (2004). Arrow at left represents phyletic increases that likely occurred at all ingroup nodes except G. libratus + A. sarcophagus." figureDoi="http://doi.org/10.5281/zenodo.3961071" httpUri="https://zenodo.org/record/3961071/files/figure.png" pageId="14" pageNumber="449">Fig. 14B</figureCitation>
). However, the adult 
<emphasis id="B949EA8EEC23FFC352C5F9C6FCA7F954" box="[658,774,1651,1674]" italics="true" pageId="14" pageNumber="449">D. torosus</emphasis>
maxillary teeth are no stronger than those of the 
<taxonomicName id="4C3D4D1FEC23FFC352FEF927FF10F914" class="Reptilia" family="Tyrannosauridae" genus="Albertosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC23FFC352FEF927FF10F914" italics="true" pageId="14" pageNumber="449">Albertosaurus</emphasis>
</taxonomicName>
specimen, while 
<taxonomicName id="4C3D4D1FEC23FFC351DFF906FE6EF914" authorityName="Osborn" authorityYear="1905" box="[392,463,1715,1738]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC23FFC351DFF906FE6EF914" box="[392,463,1715,1738]" italics="true" pageId="14" pageNumber="449">T. rex</emphasis>
</taxonomicName>
maxillary teeth are much stronger than either. Rather than showing an insensibly continuous trend, the allometric increase for maxillary teeth probably reflects a quantum jump in strength from the condition in 
<taxonomicName id="4C3D4D1FEC23FFC350EEF887FEF9F894" box="[185,344,1842,1866]" class="Reptilia" family="Tyrannosauridae" genus="Albertosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC23FFC350EEF887FEF9F894" box="[185,344,1842,1866]" italics="true" pageId="14" pageNumber="449">Albertosaurus</emphasis>
</taxonomicName>
and 
<taxonomicName id="4C3D4D1FEC23FFC351C5F887FDE3F894" authorityName="Russell" authorityYear="1970" box="[402,578,1842,1866]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC23FFC351C5F887FDE3F894" box="[402,578,1842,1866]" italics="true" pageId="14" pageNumber="449">Daspletosaurus</emphasis>
</taxonomicName>
to that of 
<taxonomicName id="4C3D4D1FEC23FFC352EBF886FCA1F894" authorityName="Osborn" authorityYear="1905" box="[700,768,1843,1866]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC23FFC352EBF886FCA1F894" box="[700,768,1843,1866]" italics="true" pageId="14" pageNumber="449">T. rex</emphasis>
</taxonomicName>
. The more gradual increase in nasal and cranial strengths indicates that robustness of these structures preceded acquisition of particularly strong teeth in adult 
<taxonomicName id="4C3D4D1FEC23FFC351B1F826FD84F874" authorityName="Osborn" authorityYear="1905" box="[486,549,1939,1962]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC23FFC351B1F826FD84F874" box="[486,549,1939,1962]" italics="true" pageId="14" pageNumber="449">T. rex</emphasis>
</taxonomicName>
(
<figureCitation id="13062A19EC23FFC35265F824FD36F874" box="[562,663,1937,1962]" captionStart="Fig" captionStartId="15.[102,135,1656,1676]" captionTargetBox="[212,1379,225,1629]" captionTargetId="graphics@15.[325,856,629,1619]" captionTargetPageId="15" captionText="Fig. 14. A. Functional integration of strengths of the tyrannosaurid head skeleton when subjected to feeding forces. Dark arrows represent direct influences of forces on structures, and direct integration of structural strengths. Light arrows represent less direct influences of structures on one another. B. Correlated progression of tyrannosauroid feeding adaptations mapped onto a tyrannosauroid cladogram after Xu et al. (2004) and Holtz (2004). Arrow at left represents phyletic increases that likely occurred at all ingroup nodes except G. libratus + A. sarcophagus." figureDoi="http://doi.org/10.5281/zenodo.3961071" httpUri="https://zenodo.org/record/3961071/files/figure.png" pageId="14" pageNumber="449">Fig. 14B</figureCitation>
). If the giant 
<taxonomicName id="4C3D4D1FEC23FFC350C7F807FED3F814" authorityName="Russell" authorityYear="1970" box="[144,370,1970,1994]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC23FFC350C7F807FED3F814" box="[144,370,1970,1994]" italics="true" pageId="14" pageNumber="449">Tarbosaurus bataar</emphasis>
</taxonomicName>
experienced a “growth spurt” similar to that of 
<taxonomicName id="4C3D4D1FEC23FFC350A0F866FE98F834" authorityName="Osborn" authorityYear="1905" box="[247,313,2003,2026]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC23FFC350A0F866FE98F834" box="[247,313,2003,2026]" italics="true" pageId="14" pageNumber="449">T. rex</emphasis>
</taxonomicName>
(
<bibRefCitation id="EFAC4B6DEC23FFC35110F864FD8FF834" author="Erickson, G. M. &amp; Makovicky, P. J. &amp; Currie, P. J. &amp; Norell, M. A. &amp; Yerby, S. A. &amp; Brochu, C. A." box="[327,558,2001,2026]" journalOrPublisher="Nature" pageId="14" pageNumber="449" pagination="772 - 775" part="430" refId="ref11617" refString="Erickson, G. M., Makovicky, P. J., Currie, P. J., Norell, M. A., Yerby, S. A., and Brochu, C. A. 2004. Gigantism and comparative life-history parameters of tyrannosaurid dinosaurs. Nature 430: 772 - 775." title="Gigantism and comparative life-history parameters of tyrannosaurid dinosaurs" type="journal article" year="2004">Erickson et al. 2004</bibRefCitation>
), its narrower skull (
<bibRefCitation id="EFAC4B6DEC23FFC35363FF5DFBE8FEDF" author="Hurum, J. H. &amp; Sabath, K." box="[820,1097,232,257]" journalOrPublisher="Acta Palaeontologica Polonica" pageId="14" pageNumber="449" pagination="161 - 190" part="48" refId="ref12267" refString="Hurum, J. H. and Sabath, K. 2003. Giant theropod dinosaurs from Asia and North America: crania of Tarbosaurus bataar and Tyrannosaurus rex compared. Acta Palaeontologica Polonica 48: 161 - 190." title="Giant theropod dinosaurs from Asia and North America: crania of Tarbosaurus bataar and Tyrannosaurus rex compared" type="journal article" year="2003">Hurum and Sabath 2003</bibRefCitation>
) indicates that it may have continued the ontogenetic trajectory of strength increase seen in smaller tyrannosaurids. 
<taxonomicName id="4C3D4D1FEC23FFC3546CFE9FFBDCFE9F" authorityName="Osborn" authorityYear="1905" box="[1083,1149,298,321]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC23FFC3546CFE9FFBDCFE9F" box="[1083,1149,298,321]" italics="true" pageId="14" pageNumber="449">T. rex</emphasis>
</taxonomicName>
, in contrast, probably experienced greater hypermorphosis of tooth and cranial strengths during this growth period.
</paragraph>
<paragraph id="8B82369CEC23FFC35305FE3CFB49FD1C" blockId="14.[812,1485,232,706]" pageId="14" pageNumber="449">
Tooth, nasal, and cranial strengths likely increased in parallel with jaw adductor forces. Bite forces were probably enhanced in tyrannosaurids through enlarged muscle origins from midsagittal and nuchal crests (m. adductor mandibulae externus medialis) and perhaps the expanded quadratojugalsquamosal contact (
<bibRefCitation id="EFAC4B6DEC23FFC3545DFD9CFB00FD9C" author="Molnar, R. E." bookContentInfo="447 pp." box="[1034,1185,553,578]" journalOrPublisher="University of California, Los Angeles" pageId="14" pageNumber="449" refId="ref12615" refString="Molnar, R. E. 1973. The Cranial Morphology and Mechanics of Tyrannosaurus rex (Reptilia: Saurischia). 447 pp. PhD thesis, University of California, Los Angeles." title="The Cranial Morphology and Mechanics of Tyrannosaurus rex (Reptilia: Saurischia)" type="book" year="1973">Molnar 1973</bibRefCitation>
), and increased size of the adductor chamber. These trends in feeding strengths are elucidated by consideration of how tyrannosaurid nasals contributed to cranium strength, and possible behavioural consequences of skull strengths in theropods.
</paragraph>
<paragraph id="8B82369CEC23FFC3537BFD59FB82FCEB" blockId="14.[812,1440,748,821]" pageId="14" pageNumber="449">Mechanical integration of theropod nasal and cranium strengths</paragraph>
<paragraph id="8B82369CEC23FFC3537BFCE5FA6AFAD6" blockId="14.[812,1485,848,2026]" pageId="14" pageNumber="449">
Our results for nasal compressional strength support 
<bibRefCitation id="EFAC4B6DEC23FFC355C0FCE4FC63FC57" author="Rayfield, E. J." journalOrPublisher="Proceedings of the Royal Society of London B" pageId="14" pageNumber="449" pagination="1451 - 1459" part="271" refId="ref12756" refString="Rayfield, E. J. 2004. Cranial mechanics and feeding in Tyrannosaurus rex. Proceedings of the Royal Society of London B 271: 1451 - 1459." title="Cranial mechanics and feeding in Tyrannosaurus rex" type="journal article" year="2004">Rayfield̓s (2004)</bibRefCitation>
hypothesis that the nasals strengthened the cranium in vertical bending. 
<bibRefCitation id="EFAC4B6DEC23FFC35412FC25FB55FC77" author="Rayfield, E. J." box="[1093,1268,912,937]" journalOrPublisher="Proceedings of the Royal Society of London B" pageId="14" pageNumber="449" pagination="1451 - 1459" part="271" refId="ref12756" refString="Rayfield, E. J. 2004. Cranial mechanics and feeding in Tyrannosaurus rex. Proceedings of the Royal Society of London B 271: 1451 - 1459." title="Cranial mechanics and feeding in Tyrannosaurus rex" type="journal article" year="2004">Rayfield (2004)</bibRefCitation>
ran a finite element analysis of the skull of 
<taxonomicName id="4C3D4D1FEC23FFC35417FC07FAB5FC17" authorityName="Osborn" authorityYear="1905" box="[1088,1300,946,969]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC23FFC35417FC07FAB5FC17" box="[1088,1300,946,969]" italics="true" pageId="14" pageNumber="449">Tyrannosaurus rex</emphasis>
</taxonomicName>
(BHI 2033, the specimen that was cast for our 
<taxonomicName id="4C3D4D1FEC23FFC35421FC67FB15FC37" authorityName="Osborn" authorityYear="1905" box="[1142,1204,978,1001]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC23FFC35421FC67FB15FC37" box="[1142,1204,978,1001]" italics="true" pageId="14" pageNumber="449">T. rex</emphasis>
</taxonomicName>
nasals: TMP 98.86.01) as a plate−like lateral projection. With the joints between ventral cranium bones treated realistically as unfused, the model showed high compressional stress over the anterior maxillary teeth (as predicted by 
<bibRefCitation id="EFAC4B6DEC23FFC35471FBE5FB18FBB7" author="Molnar, R. E." bookContentInfo="447 pp." box="[1062,1209,1104,1129]" journalOrPublisher="University of California, Los Angeles" pageId="14" pageNumber="449" refId="ref12615" refString="Molnar, R. E. 1973. The Cranial Morphology and Mechanics of Tyrannosaurus rex (Reptilia: Saurischia). 447 pp. PhD thesis, University of California, Los Angeles." title="The Cranial Morphology and Mechanics of Tyrannosaurus rex (Reptilia: Saurischia)" type="book" year="1973">Molnar 1973</bibRefCitation>
, 
<bibRefCitation id="EFAC4B6DEC23FFC35491FBE5FAA3FBB7" author="Molnar, R. E." box="[1222,1282,1104,1129]" journalOrPublisher="Gaia" pageId="14" pageNumber="449" pagination="193 - 218" part="15" refId="ref12650" refString="Molnar, R. E. 2000. Mechanical factors in the design of the cranium of Tyrannosaurus rex (Osborn 1905). Gaia 15: 193 - 218." title="Mechanical factors in the design of the cranium of Tyrannosaurus rex (Osborn 1905)" type="journal article" year="2000">2000</bibRefCitation>
). This is precisely where 
<taxonomicName id="4C3D4D1FEC23FFC35320FBC7FBE9FB57" authorityName="Osborn" authorityYear="1905" box="[887,1096,1138,1161]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC23FFC35320FBC7FBE9FB57" box="[887,1096,1138,1161]" italics="true" pageId="14" pageNumber="449">Tyrannosaurus rex</emphasis>
</taxonomicName>
nasals, and those of other tyrannosaurids, show the highest cross−sectional areas. With a large cross−sectional area the nasals could withstand high compressional forces, such as those incurred during dorsal bending of the rostrum, without experiencing unusually high stress.
</paragraph>
<paragraph id="8B82369CEC23FFC35305FAA4FAE7F954" blockId="14.[812,1485,848,2026]" pageId="14" pageNumber="449">
Adult specimens 
<taxonomicName id="4C3D4D1FEC23FFC35446FAA7FB45FAF7" authorityName="Osborn" authorityYear="1905" box="[1041,1252,1298,1321]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC23FFC35446FAA7FB45FAF7" box="[1041,1252,1298,1321]" italics="true" pageId="14" pageNumber="449">Tyrannosaurus rex</emphasis>
</taxonomicName>
, and similarly gigantic adults of the tyrannosaurid 
<taxonomicName id="4C3D4D1FEC23FFC354CAFA84FA25FA97" authorityName="Russell" authorityYear="1970" box="[1181,1412,1329,1353]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC23FFC354CAFA84FA25FA97" box="[1181,1412,1329,1353]" italics="true" pageId="14" pageNumber="449">Tarbosaurus bataar</emphasis>
</taxonomicName>
, have staircase−style interdigitating sutures, with triangular pegs and sockets, between the nasals and maxillae (
<bibRefCitation id="EFAC4B6DEC23FFC3551EFAC4FC1AFA74" author="Hurum, J. H. &amp; Sabath, K." journalOrPublisher="Acta Palaeontologica Polonica" pageId="14" pageNumber="449" pagination="161 - 190" part="48" refId="ref12267" refString="Hurum, J. H. and Sabath, K. 2003. Giant theropod dinosaurs from Asia and North America: crania of Tarbosaurus bataar and Tyrannosaurus rex compared. Acta Palaeontologica Polonica 48: 161 - 190." title="Giant theropod dinosaurs from Asia and North America: crania of Tarbosaurus bataar and Tyrannosaurus rex compared" type="journal article" year="2003">Hurum and Sabath 2003</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC23FFC3539FFA24FBCAFA74" author="Rayfield, E. J." box="[968,1131,1425,1450]" journalOrPublisher="Proceedings of the Royal Society of London B" pageId="14" pageNumber="449" pagination="1451 - 1459" part="271" refId="ref12756" refString="Rayfield, E. J. 2004. Cranial mechanics and feeding in Tyrannosaurus rex. Proceedings of the Royal Society of London B 271: 1451 - 1459." title="Cranial mechanics and feeding in Tyrannosaurus rex" type="journal article" year="2004">Rayfield 2004</bibRefCitation>
; 
<figureCitation id="13062A19EC23FFC3542FFA24FB6AFA74" box="[1144,1227,1425,1450]" captionStart="Fig" captionStartId="16.[102,135,1681,1701]" captionTargetBox="[105,772,232,1654]" captionTargetId="figure@16.[105,772,232,1654]" captionTargetPageId="16" captionText="Fig. 15. Nasal articulations with maxillae in juvenile Gorgosaurus libratus (nasals at top; TMP 86.144.1) adult Tyrannosaurus rex (nasals in middle and maxilla below; TMP 98.86.01; cast of BHI 2033). The interlocking, staircase−style articulation in the adult Tyrannosaurus rex efficiently transmitted compressional forces and increased the shear strength of the articulation. Dashed lines show the extent of the staircased articulation, and the solid line indicates a projection on the nasals and the corresponding depression in the maxilla." figureDoi="http://doi.org/10.5281/zenodo.3961073" httpUri="https://zenodo.org/record/3961073/files/figure.png" pageId="14" pageNumber="449">Fig. 15</figureCitation>
). This staircasing does not occur in a juvenile specimen of 
<taxonomicName id="4C3D4D1FEC23FFC354B1FA04FA6CFA17" authorityName="Russell" authorityYear="1970" box="[1254,1485,1457,1481]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC23FFC354B1FA04FA6CFA17" box="[1254,1485,1457,1481]" italics="true" pageId="14" pageNumber="449">Tarbosaurus bataar</emphasis>
</taxonomicName>
(TMP 2000.50.5; cast), or in adults of other examined tyrannosaurids (including the large, robust 
<taxonomicName id="4C3D4D1FEC23FFC3554AFA44FCDFF9F7" authorityName="Russell" authorityYear="1970" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC23FFC3554AFA44FCDFF9F7" italics="true" pageId="14" pageNumber="449">Daspletosaurus torosus</emphasis>
</taxonomicName>
specimen). This additional reinforcement of the nasal−maxillary suture may be exclusive to adult 
<taxonomicName id="4C3D4D1FEC23FFC3556AF984FA6DF997" authorityName="Maleev" authorityYear="1955" box="[1341,1484,1585,1609]" class="Reptilia" family="Tyrannosauridae" genus="Tarbosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC23FFC3556AF984FA6DF997" box="[1341,1484,1585,1609]" italics="true" pageId="14" pageNumber="449">Tarbosaurus</emphasis>
</taxonomicName>
and 
<taxonomicName id="4C3D4D1FEC23FFC3530AF9E7FBA6F9B7" authorityName="Osborn" authorityYear="1905" box="[861,1031,1618,1641]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC23FFC3530AF9E7FBA6F9B7" box="[861,1031,1618,1641]" italics="true" pageId="14" pageNumber="449">Tyrannosaurus</emphasis>
</taxonomicName>
, and related to increased feeding forces involved with engaging larger prey (see below).
</paragraph>
<paragraph id="8B82369CEC23FFC35305F924FB7EF857" blockId="14.[812,1485,848,2026]" pageId="14" pageNumber="449">
<bibRefCitation id="EFAC4B6DEC23FFC35305F924FBADF974" author="Rayfield, E. J." box="[850,1036,1681,1706]" journalOrPublisher="Proceedings of the Royal Society of London B" pageId="14" pageNumber="449" pagination="1451 - 1459" part="271" refId="ref12756" refString="Rayfield, E. J. 2004. Cranial mechanics and feeding in Tyrannosaurus rex. Proceedings of the Royal Society of London B 271: 1451 - 1459." title="Cranial mechanics and feeding in Tyrannosaurus rex" type="journal article" year="2004">Rayfield (2004)</bibRefCitation>
noted that nasal−maxilla interlocking would brace the joint against high concentrations of shear stress in the region between the nasals and maxillae of 
<taxonomicName id="4C3D4D1FEC23FFC3537BF947FBA0F8D7" authorityName="Osborn" authorityYear="1905" box="[812,1025,1778,1801]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC23FFC3537BF947FBA0F8D7" box="[812,1025,1778,1801]" italics="true" pageId="14" pageNumber="449">Tyrannosaurus rex</emphasis>
</taxonomicName>
, and efficiently channel compressive biting stress from the maxillae to the nasals. The staircasing would also brace the joints against shear induced by lateral bending and torsion of the snout, and complement high nasal and rostrum strengths found for 
<taxonomicName id="4C3D4D1FEC23FFC354C1F8C7FB79F857" authorityName="Osborn" authorityYear="1905" box="[1174,1240,1906,1929]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC23FFC354C1F8C7FB79F857" box="[1174,1240,1906,1929]" italics="true" pageId="14" pageNumber="449">T. rex</emphasis>
</taxonomicName>
.
</paragraph>
<paragraph id="8B82369CEC23FFC25305F824FF69F834" blockId="14.[812,1485,848,2026]" lastBlockId="15.[102,775,1809,2026]" lastPageId="15" lastPageNumber="450" pageId="14" pageNumber="449">
High second moments of area of the tyrannosaurid nasals relative to those of 
<taxonomicName id="4C3D4D1FEC23FFC35444F807FB49F814" authorityName="Marsh" authorityYear="1877" box="[1043,1256,1970,1994]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="14" pageNumber="449" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC23FFC35444F807FB49F814" box="[1043,1256,1970,1994]" italics="true" pageId="14" pageNumber="449">Allosaurus fragilis</emphasis>
</taxonomicName>
demonstrate higher strength of the dorsal part of the snout, and emphasize how the tyrannosaurids̓ nasals contributed to overall cranium strength. The breadth of the nasals (
<figureCitation id="13062A19EC22FFC251BBF884FD96F894" box="[492,567,1841,1866]" captionStart="Fig" captionStartId="4.[724,757,1892,1912]" captionTargetBox="[729,1480,225,1865]" captionTargetId="figure@4.[729,1481,225,1865]" captionTargetPageId="4" captionText="Fig. 4. CT reconstructions of tyrannosaurid nasals in side and top views. Anterior is to the right. A. Tyrannosaurus rex (TMP 98.86.01; cast of BHI 2033). B. Daspletosaurus torosus (TMP 98.48.1). C. Albertosaurus sarcophagus (TMP 2000.12.1). D. Adult Gorgosaurus libratus (TMP 86.64.1). E. Juvenile Gorgosaurus libratus (TMP 86.144.1). Scale bars 15 cm." figureDoi="http://doi.org/10.5281/zenodo.3739904" httpUri="https://zenodo.org/record/3739904/files/figure.png" pageId="15" pageNumber="450">Figs. 4</figureCitation>
and 
<figureCitation id="13062A19EC22FFC2523DF884FD26F894" box="[618,647,1841,1866]" captionStart="Fig" captionStartId="10.[102,135,1356,1376]" captionTargetBox="[106,770,225,1318]" captionTargetId="graphics@10.[106,769,259,1263]" captionTargetPageId="10" captionText="Fig. 10. Heights and widths of tyrannosaurid nasal slices normalized for slice area and bone length. A. Normalized heights (“vaulting index”) showing convergence of vaulting pattern at large size. B. Normalized widths (“span index”) showing isometric form in most specimens, but exaggerated relative width in Tyrannosaurus rex nasals. Points of maximum vaulting and span are indicated on nasals of T. rex (TMP 98.86.01; cast of BHI 2033). Symbols as per Fig. 9." figureDoi="http://doi.org/10.5281/zenodo.3739914" httpUri="https://zenodo.org/record/3739914/files/figure.png" pageId="15" pageNumber="450">10</figureCitation>
) gave them a high lateral second moment of area, and increased the width of the snout by laterally displacing the maxillae. The great width of the rostrum greatly increased its lateral second moment of area, and overall strength in torsion and lateral bending.
</paragraph>
<caption id="DF426614EC22FFC25031F9CDFC6BF93E" ID-DOI="http://doi.org/10.5281/zenodo.3961071" ID-Zenodo-Dep="3961071" httpUri="https://zenodo.org/record/3961071/files/figure.png" pageId="15" pageNumber="450" startId="15.[102,135,1656,1676]" targetBox="[212,1379,225,1629]" targetPageId="15">
<paragraph id="8B82369CEC22FFC25031F9CDFC6BF93E" blockId="15.[102,1486,1656,1761]" pageId="15" pageNumber="450">
Fig. 14. 
<emphasis id="B949EA8EEC22FFC250F8F9CDFF1EF952" bold="true" box="[175,191,1656,1676]" pageId="15" pageNumber="450">A</emphasis>
. Functional integration of strengths of the tyrannosaurid head skeleton when subjected to feeding forces. Dark arrows represent direct influences of forces on structures, and direct integration of structural strengths. Light arrows represent less direct influences of structures on one another. 
<emphasis id="B949EA8EEC22FFC25503F920FAC2F976" bold="true" box="[1364,1379,1685,1704]" pageId="15" pageNumber="450">B</emphasis>
. Correlated progression of tyrannosauroid feeding adaptations mapped onto a tyrannosauroid cladogram after 
<bibRefCitation id="EFAC4B6DEC22FFC2539BF904FBF7F91A" author="Xu X. &amp; Norell, M. A. &amp; Kuang, X. &amp; Wang, X. &amp; Zhao, Q. &amp; Jia, C." box="[972,1110,1712,1732]" journalOrPublisher="Nature" pageId="15" pageNumber="450" pagination="680 - 684" part="431" refId="ref13535" refString="Xu X., Norell, M. A., Kuang, X., Wang, X., Zhao, Q., and Jia, C. 2004. Basal tyrannosauroids from China and evidence for protofeathers in tyrannosauroids. Nature 431: 680 - 684." title="Basal tyrannosauroids from China and evidence for protofeathers in tyrannosauroids" type="journal article" year="2004">Xu et al. (2004)</bibRefCitation>
and 
<bibRefCitation id="EFAC4B6DEC22FFC25428F905FB54F91A" author="Holtz, T. R. Jr." box="[1151,1269,1712,1732]" editor="D. B. Weishampel &amp; P. Dodson &amp; H. Osmolska" journalOrPublisher="University of California Press. Berkeley" pageId="15" pageNumber="450" pagination="111 - 136" refId="ref12220" refString="Holtz, T. R. Jr. 2004. Tyrannosauroidea. In: D. B. Weishampel, P. Dodson, and H. Osmolska (eds.), The Dinosauria, 111 - 136. University of California Press. Berkeley." title="Tyrannosauroidea" type="book chapter" volumeTitle="The Dinosauria" year="2004">Holtz (2004)</bibRefCitation>
. Arrow at left represents phyletic increases that likely occurred at all ingroup nodes except 
<taxonomicName id="4C3D4D1FEC22FFC252EBF978FCBFF93F" authority="Lambe, 1914" box="[700,798,1741,1761]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="15" pageNumber="450" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC22FFC252EBF978FCBFF93F" box="[700,798,1741,1761]" italics="true" pageId="15" pageNumber="450">G. libratus</emphasis>
</taxonomicName>
+ 
<taxonomicName id="4C3D4D1FEC22FFC25360F978FC65F93F" authority="Osborn, 1905 " box="[823,964,1741,1761]" class="Reptilia" family="Tyrannosauridae" genus="Albertosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="15" pageNumber="450" phylum="Chordata" rank="species">
<emphasis id="B949EA8EEC22FFC25360F978FC65F93F" box="[823,964,1741,1761]" italics="true" pageId="15" pageNumber="450">A. sarcophagus</emphasis>
</taxonomicName>
.
</paragraph>
</caption>
<paragraph id="8B82369CEC22FFC25305F8A7FC59F834" blockId="15.[812,1485,1809,2026]" pageId="15" pageNumber="450">
In contrast, the nasals of 
<taxonomicName id="4C3D4D1FEC22FFC25430F8A4FB41F8F7" authorityName="Marsh" authorityYear="1877" box="[1127,1248,1809,1833]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="15" pageNumber="450" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC22FFC25430F8A4FB41F8F7" box="[1127,1248,1809,1833]" italics="true" pageId="15" pageNumber="450">Allosaurus</emphasis>
</taxonomicName>
and other carnosaurs are narrow between the articulations with the maxillae (
<bibRefCitation id="EFAC4B6DEC22FFC255D9F884FC34F8B4" author="Madsen, J. H. Jr." journalOrPublisher="Utah Geological Survey Bulletin" pageId="15" pageNumber="450" pagination="1 - 163" part="109" refId="ref12502" refString="Madsen, J. H. Jr. 1976. Allosaurus fragilis: a revised osteology. Utah Geological Survey Bulletin 109: 1 - 163." title="Allosaurus fragilis: a revised osteology" type="journal article" year="1976">Madsen 1976</bibRefCitation>
), the maxillae arch outward less, and the muzzle is consequently narrow (
<bibRefCitation id="EFAC4B6DEC22FFC2547EF8C4FB17F854" author="Meers, M. B." box="[1065,1206,1905,1930]" journalOrPublisher="Historical Biology" pageId="15" pageNumber="450" pagination="1 - 12" part="16" refId="ref12580" refString="Meers, M. B. 2003. Maximum bite force and prey size of Tyrannosaurus rex and their relationship to the inference of feeding behaviour. Historical Biology 16: 1 - 12." title="Maximum bite force and prey size of Tyrannosaurus rex and their relationship to the inference of feeding behaviour" type="journal article" year="2003">Meers 2003</bibRefCitation>
). The narrower rostra of carnosaurs conferred lower lateral bending and torsional strength relative to cranium length than in tyrannosaurids (
<figureCitation id="13062A19EC22FFC25362F864FC26F834" box="[821,903,2001,2026]" captionStart="Fig" captionStartId="11.[812,845,1343,1363]" captionTargetBox="[101,1485,237,1477]" captionTargetPageId="11" captionText="Fig. 11. Top and side views of theropod crania used to reconstruct crosssectional shapes, and oblique views of reconstructed plinge cross−sections for each cranium. Second moments of area of the plinges were calculated as indices of bending and torsional cranium strengths. A–D, carnosaurs; E–G, tyrannosaurids." figureDoi="http://doi.org/10.5281/zenodo.3961067" httpUri="https://zenodo.org/record/3961067/files/figure.png" pageId="15" pageNumber="450">Fig. 11</figureCitation>
, 
<tableCitation id="C6BF0327EC22FFC253C4F864FC4AF834" box="[915,1003,2001,2026]" captionStart="Table 2" captionStartId="9.[102,157,231,252]" captionTargetBox="[110,1463,282,604]" captionTargetId="graphics@9.[102,1485,271,607]" captionText="Table 2. Computed strength properties of theropod nasals" httpUri="http://table.plazi.org/id/DF426614EC24FFC45031FF52FD30FF22" pageId="15" pageNumber="450" tableUuid="DF426614EC24FFC45031FF52FD30FF22">Table 2</tableCitation>
).
</paragraph>
<paragraph id="8B82369CEC3DFFDD537BFF5DFBD2FEBF" blockId="16.[812,1485,232,353]" pageId="16" pageNumber="451">
theropods. Combined with strong articulations between bones of the palate, strong nasals and wide muzzles suggest that adult tyrannosaurids engaged in different feeding behaviours than carnosaurs (
<bibRefCitation id="EFAC4B6DEC3DFFDD53B1FEFDFBC9FEBF" author="Holtz, T. R. Jr." box="[998,1128,328,353]" editor="P. H. Kelly &amp; M. Koweleski &amp; T. A. Hansen" journalOrPublisher="Kluwer / Plenum, New York" pageId="16" pageNumber="451" pagination="325 - 340" part="17" refId="ref12157" refString="Holtz, T. R. Jr. 2002. Theropod predation: evidence and ecomorphology. In: P. H. Kelly, M. Koweleski, and T. A. Hansen (eds.), Predator-Prey Interactions in the Fossil Record. Topics in Geobiology 17, 325 - 340. Kluwer / Plenum, New York." title="Theropod predation: evidence and ecomorphology" type="journal article" volumeTitle="Predator-Prey Interactions in the Fossil Record. Topics in Geobiology" year="2002">Holtz 2002</bibRefCitation>
).
</paragraph>
<paragraph id="8B82369CEC3DFFDD537BFE39FC3DFE0B" blockId="16.[812,1406,396,469]" pageId="16" pageNumber="451">Behavioural implications of theropod skull strength</paragraph>
<caption id="DF426614EC3DFFDD5031F924FEB4F8B7" ID-DOI="http://doi.org/10.5281/zenodo.3961073" ID-Zenodo-Dep="3961073" httpUri="https://zenodo.org/record/3961073/files/figure.png" pageId="16" pageNumber="451" startId="16.[102,135,1681,1701]" targetBox="[105,772,232,1654]" targetPageId="16">
<paragraph id="8B82369CEC3DFFDD5031F924FEB4F8B7" blockId="16.[102,775,1681,1897]" pageId="16" pageNumber="451">
Fig. 15. Nasal articulations with maxillae in juvenile 
<taxonomicName id="4C3D4D1FEC3DFFDD5214F927FCA7F97B" authority="Lambe, 1914" box="[579,774,1681,1701]" class="Reptilia" family="Tyrannosauridae" genus="Gorgosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="16" pageNumber="451" phylum="Chordata" rank="species" species="libratus">
<emphasis id="B949EA8EEC3DFFDD5214F927FCA7F97B" box="[579,774,1681,1701]" italics="true" pageId="16" pageNumber="451">Gorgosaurus libratus</emphasis>
</taxonomicName>
(nasals at top; TMP 86.144.1) adult 
<taxonomicName id="4C3D4D1FEC3DFFDD51E2F91BFDC3F91E" authorityName="Osborn" authorityYear="1905" box="[437,610,1710,1728]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="16" pageNumber="451" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC3DFFDD51E2F91BFDC3F91E" box="[437,610,1710,1728]" italics="true" pageId="16" pageNumber="451">Tyrannosaurus rex</emphasis>
</taxonomicName>
(nasals in middle and maxilla below; TMP 98.86.01; cast of BHI 2033). The interlocking, staircase−style articulation in the adult 
<taxonomicName id="4C3D4D1FEC3DFFDD5196F953FDCDF926" authorityName="Osborn" authorityYear="1905" box="[449,620,1766,1784]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="16" pageNumber="451" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC3DFFDD5196F953FDCDF926" box="[449,620,1766,1784]" italics="true" pageId="16" pageNumber="451">Tyrannosaurus rex</emphasis>
</taxonomicName>
efficiently transmitted compressional forces and increased the shear strength of the articulation. Dashed lines show the extent of the staircased articulation, and the solid line indicates a projection on the nasals and the corresponding depression in the maxilla.
</paragraph>
</caption>
<paragraph id="8B82369CEC3DFFDD50DBF824FCD5FCF7" blockId="16.[102,774,1937,2026]" lastBlockId="16.[812,1486,496,2026]" pageId="16" pageNumber="451">
High torsional strengths of tyrannosaurid crania and nasals support Holtz̓s (2002) hypothesis that tyrannosaurids could subject their crania to greater torsional loads than could other The longer nasal specimens of the tyrannosaurids are stronger than expected than if they were geometrically similar to the nasals of smaller individuals (
<figureCitation id="13062A19EC3DFFDD5421FD85FB68FD97" box="[1142,1225,560,585]" captionStart="Fig" captionStartId="10.[102,135,1356,1376]" captionTargetBox="[106,770,225,1318]" captionTargetId="graphics@10.[106,769,259,1263]" captionTargetPageId="10" captionText="Fig. 10. Heights and widths of tyrannosaurid nasal slices normalized for slice area and bone length. A. Normalized heights (“vaulting index”) showing convergence of vaulting pattern at large size. B. Normalized widths (“span index”) showing isometric form in most specimens, but exaggerated relative width in Tyrannosaurus rex nasals. Points of maximum vaulting and span are indicated on nasals of T. rex (TMP 98.86.01; cast of BHI 2033). Symbols as per Fig. 9." figureDoi="http://doi.org/10.5281/zenodo.3739914" httpUri="https://zenodo.org/record/3739914/files/figure.png" pageId="16" pageNumber="451">Fig. 10</figureCitation>
). The skulls of juvenile tyrannosaurids were proportionally lower than adult skulls (
<bibRefCitation id="EFAC4B6DEC3DFFDD5363FDC5FC04FD57" author="Carr, T. D." box="[820,933,624,649]" journalOrPublisher="Journal of Vertebrate Paleontology" pageId="16" pageNumber="451" pagination="497 - 520" part="19" refId="ref11234" refString="Carr, T. D. 1999. Craniofacial ontogeny in Tyrannosauridae (Dinosauria, Coelurosauria). Journal of Vertebrate Paleontology 19: 497 - 520." title="Craniofacial ontogeny in Tyrannosauridae (Dinosauria, Coelurosauria)" type="journal article" year="1999">Carr 1999</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC3DFFDD53F9FDC5FBE3FD57" author="Currie, P. J." box="[942,1090,624,649]" journalOrPublisher="Canadian Journal of Earth Sciences" pageId="16" pageNumber="451" pagination="651 - 665" part="40" refId="ref11388" refString="Currie, P. J. 2003 b. Allometric growth in tyrannosaurids (Dinosauria: Theropoda) from the Upper Cretaceous of North America. Canadian Journal of Earth Sciences 40: 651 - 665." title="Allometric growth in tyrannosaurids (Dinosauria: Theropoda) from the Upper Cretaceous of North America" type="journal article" year="2003">Currie 2003b</bibRefCitation>
), and concomitantly much weaker in vertical bending. Much stronger nasals and allometrically taller skulls in adult tyrannosaurids than in juveniles (
<bibRefCitation id="EFAC4B6DEC3DFFDD55D2FD05FCD2FD37" author="Currie, P. J." journalOrPublisher="Canadian Journal of Earth Sciences" pageId="16" pageNumber="451" pagination="651 - 665" part="40" refId="ref11388" refString="Currie, P. J. 2003 b. Allometric growth in tyrannosaurids (Dinosauria: Theropoda) from the Upper Cretaceous of North America. Canadian Journal of Earth Sciences 40: 651 - 665." title="Allometric growth in tyrannosaurids (Dinosauria: Theropoda) from the Upper Cretaceous of North America" type="journal article" year="2003">Currie 2003b</bibRefCitation>
) support hypotheses of dramatic shifts in dietary niche between juveniles and adults (
<bibRefCitation id="EFAC4B6DEC3DFFDD5425FD45FA26FCD7" author="Molnar, R. E. &amp; Farlow J. O." box="[1138,1415,752,777]" editor="D. B. Weishampel &amp; P. Dodson &amp; H. Osmolska" journalOrPublisher="University of California Press, Berkeley" pageId="16" pageNumber="451" pagination="221 - 224" refId="ref12681" refString="Molnar, R. E. and Farlow J. O. 1990 Carnosaur paleobiology. In: D. B. Weishampel, P. Dodson, and H. Osmolska (eds.), The Dinosauria, 221 - 224. University of California Press, Berkeley." title="Carnosaur paleobiology" type="book chapter" volumeTitle="The Dinosauria" year="1990">Molnar and Farlow 1990</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC3DFFDD55C7FD45FCC9FCF7" author="Holtz, T. R. Jr." editor="P. H. Kelly &amp; M. Koweleski &amp; T. A. Hansen" journalOrPublisher="Kluwer / Plenum, New York" pageId="16" pageNumber="451" pagination="325 - 340" part="17" refId="ref12157" refString="Holtz, T. R. Jr. 2002. Theropod predation: evidence and ecomorphology. In: P. H. Kelly, M. Koweleski, and T. A. Hansen (eds.), Predator-Prey Interactions in the Fossil Record. Topics in Geobiology 17, 325 - 340. Kluwer / Plenum, New York." title="Theropod predation: evidence and ecomorphology" type="journal article" volumeTitle="Predator-Prey Interactions in the Fossil Record. Topics in Geobiology" year="2002">Holtz 2002</bibRefCitation>
).
</paragraph>
<paragraph id="8B82369CEC3DFFDD5305FC84FBB1FBF4" blockId="16.[812,1486,496,2026]" pageId="16" pageNumber="451">
This ecological partitioning would be similar to that seen in varanid lizards and crocodilians (
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; 
<bibRefCitation id="EFAC4B6DEC3DFFDD5322FCC7FBA6FC54" author="Hutton, J. M." box="[885,1031,881,906]" journalOrPublisher="Journal of Animal Ecology" pageId="16" pageNumber="451" pagination="25 - 38" part="56" refId="ref12411" refString="Hutton, J. M. 1987. Growth and feeding ecology of the Nile crocodile Crocodylus niloticus at Ngezi, Zimbabwe. Journal of Animal Ecology 56: 25 - 38." title="Growth and feeding ecology of the Nile crocodile Crocodylus niloticus at Ngezi, Zimbabwe" type="journal article" year="1987">Hutton 1987</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC3DFFDD5442FCC7FA89FC54" author="Losos, J. B. &amp; Greene, H. W." box="[1045,1320,881,906]" journalOrPublisher="Biological Journal of the Linnean Society" pageId="16" pageNumber="451" pagination="379 - 407" part="35" refId="ref12465" refString="Losos, J. B. and Greene, H. W. 1988. Ecological and evolutionary implications of diet in monitor lizards. Biological Journal of the Linnean Society 35: 379 - 407." title="Ecological and evolutionary implications of diet in monitor lizards" type="journal article" year="1988">Losos and Greene 1988</bibRefCitation>
), in which the young subsist upon small prey (including insects) and adults tackle much larger animals. Proportionally stronger nasals and crania of adult tyrannosaurids versus juveniles indicate that the adults could probably engage larger prey relative to their own body size.
</paragraph>
<paragraph id="8B82369CEC3DFFDD5305FB87FAC0FA17" blockId="16.[812,1486,496,2026]" pageId="16" pageNumber="451">
In the adult cranial specimens examined for this study, the discrepancy in vertical bending strength between tyrannosaurid and carnosaur crania is less than that for lateral strength. With relatively tall, narrow crania, carnosaurs were well equipped to rake down and backwards into the flesh of prey with their upper teeth (
<bibRefCitation id="EFAC4B6DEC3DFFDD542CFB64FAB7FB34" author="Bakker, R. T." box="[1147,1302,1233,1258]" journalOrPublisher="Gaia" pageId="16" pageNumber="451" pagination="145 - 158" part="15" refId="ref11029" refString="Bakker, R. T. 2000. Brontosaur killers: Late Jurassic allosaurids as sabretoothed cat analogues. Gaia 15: 145 - 158." title="Brontosaur killers: Late Jurassic allosaurids as sabretoothed cat analogues" type="journal article" year="2000">Bakker 2000</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC3DFFDD5571FB64FCC6FAD4" author="Rayfield, E. J. &amp; Norman, D. B. &amp; Horner, C. C. &amp; Horner, J. R. &amp; May Smith, P. &amp; Thomason, J. J. &amp; Upchurch, P." journalOrPublisher="Nature" pageId="16" pageNumber="451" pagination="1033 - 1037" part="409" refId="ref12823" refString="Rayfield, E. J., Norman, D. B., Horner, C. C., Horner, J. R., May Smith, P., Thomason, J. J., and Upchurch, P. 2001. Cranial design and function in a large theropod dinosaur. Nature 409: 1033 - 1037." title="Cranial design and function in a large theropod dinosaur" type="journal article" year="2001">Rayfield et al. 2001</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC3DFFDD5325FB44FB95FAD4" author="Anton, M. &amp; Sanchez I. M. &amp; Salesa M. J. &amp; Turner, A." box="[882,1076,1265,1290]" journalOrPublisher="Estudios Geologicos" pageId="16" pageNumber="451" pagination="313 - 323" part="59" refId="ref10956" refString="Anton, M., Sanchez I. M., Salesa M. J., and Turner, A. 2003. The muscle-powered bite of Allosaurus (Dinosauria; Theropoda): an interpretation of cranio-dental morphology. Estudios Geologicos 59: 313 - 323." title="The muscle-powered bite of Allosaurus (Dinosauria; Theropoda): an interpretation of cranio-dental morphology" type="journal article" year="2003">Antón et al. 2003</bibRefCitation>
). Finite element analysis (
<bibRefCitation id="EFAC4B6DEC3DFFDD5506FB44FC27FAF4" author="Rayfield, E. J. &amp; Norman, D. B. &amp; Horner, C. C. &amp; Horner, J. R. &amp; May Smith, P. &amp; Thomason, J. J. &amp; Upchurch, P." journalOrPublisher="Nature" pageId="16" pageNumber="451" pagination="1033 - 1037" part="409" refId="ref12823" refString="Rayfield, E. J., Norman, D. B., Horner, C. C., Horner, J. R., May Smith, P., Thomason, J. J., and Upchurch, P. 2001. Cranial design and function in a large theropod dinosaur. Nature 409: 1033 - 1037." title="Cranial design and function in a large theropod dinosaur" type="journal article" year="2001">Rayfield et al. 2001</bibRefCitation>
) and consideration of the moment arms of neck muscles (
<bibRefCitation id="EFAC4B6DEC3DFFDD533AFA84FBA9FA94" author="Bakker, R. T." box="[877,1032,1329,1354]" journalOrPublisher="Gaia" pageId="16" pageNumber="451" pagination="145 - 158" part="15" refId="ref11029" refString="Bakker, R. T. 2000. Brontosaur killers: Late Jurassic allosaurids as sabretoothed cat analogues. Gaia 15: 145 - 158." title="Brontosaur killers: Late Jurassic allosaurids as sabretoothed cat analogues" type="journal article" year="2000">Bakker 2000</bibRefCitation>
) demonstrate the probable success of these activities in 
<taxonomicName id="4C3D4D1FEC3DFFDD53A0FAE4FB68FAB7" authorityName="Marsh" authorityYear="1877" box="[1015,1225,1361,1385]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="16" pageNumber="451" phylum="Chordata" rank="species" species="fragilis">
<emphasis id="B949EA8EEC3DFFDD53A0FAE4FB68FAB7" box="[1015,1225,1361,1385]" italics="true" pageId="16" pageNumber="451">Allosaurus fragilis</emphasis>
</taxonomicName>
. High vertical bending strengths of the crania of 
<taxonomicName id="4C3D4D1FEC3DFFDD541BFAC4FA28FA57" authorityName="Stovall &amp; Langston" authorityYear="1950" box="[1100,1417,1393,1417]" class="Reptilia" family="Carcharodontosauridae" genus="Acrocanthosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="16" pageNumber="451" phylum="Chordata" rank="species" species="atokensis">
<emphasis id="B949EA8EEC3DFFDD541BFAC4FA28FA57" box="[1100,1417,1393,1417]" italics="true" pageId="16" pageNumber="451">Acrocanthosaurus atokensis</emphasis>
</taxonomicName>
, 
<taxonomicName id="4C3D4D1FEC3DFFDD55CFFAC7FBD0FA77" authority="Depéret &amp; Savornin, 1925" class="Reptilia" family="Carcharodontosauridae" genus="Carcharodontosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="16" pageNumber="451" phylum="Chordata" rank="species" species="saharicus">
<emphasis id="B949EA8EEC3DFFDD55CFFAC7FBD0FA77" italics="true" pageId="16" pageNumber="451">Carcharodontosaurus saharicus</emphasis>
</taxonomicName>
, and 
<taxonomicName id="4C3D4D1FEC3DFFDD54E0FA27FACFFA77" authority="Currie and Zhao, 1994" box="[1207,1390,1425,1449]" class="Reptilia" family="Neovenatoridae" genus="Sinraptor" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="16" pageNumber="451" phylum="Chordata" rank="species" species="dongi">
<emphasis id="B949EA8EEC3DFFDD54E0FA27FACFFA77" box="[1207,1390,1425,1449]" italics="true" pageId="16" pageNumber="451">Sinraptor dongi</emphasis>
</taxonomicName>
suggest the suitability of this strategy for other carnosaurs.
</paragraph>
<paragraph id="8B82369CEC3DFFDC5305FA64FECDFE9F" blockId="16.[812,1486,496,2026]" lastBlockId="17.[102,775,232,1507]" lastPageId="17" lastPageNumber="452" pageId="16" pageNumber="451">
Tyrannosaurid crania were nevertheless relatively stronger dorsoventrally than carnosaur crania, and much stronger in lateral bending and torsion (
<bibRefCitation id="EFAC4B6DEC3DFFDD5409F9A4FB7FF9F4" author="Holtz, T. R. Jr." box="[1118,1246,1553,1578]" editor="P. H. Kelly &amp; M. Koweleski &amp; T. A. Hansen" journalOrPublisher="Kluwer / Plenum, New York" pageId="16" pageNumber="451" pagination="325 - 340" part="17" refId="ref12157" refString="Holtz, T. R. Jr. 2002. Theropod predation: evidence and ecomorphology. In: P. H. Kelly, M. Koweleski, and T. A. Hansen (eds.), Predator-Prey Interactions in the Fossil Record. Topics in Geobiology 17, 325 - 340. Kluwer / Plenum, New York." title="Theropod predation: evidence and ecomorphology" type="journal article" volumeTitle="Predator-Prey Interactions in the Fossil Record. Topics in Geobiology" year="2002">Holtz 2002</bibRefCitation>
). As discussed above, the cranium and nasals would experience high torsional forces from uneven bites, with higher food reaction forces on one side of the skull than the other. Ornithischian fossils damaged during apparently unilateral bites by tyrannosaurids (
<bibRefCitation id="EFAC4B6DEC3DFFDD553DF924FC45F914" author="Erickson, G. M. &amp; Olson, K. H." journalOrPublisher="Journal of Vertebrate Paleontology" pageId="16" pageNumber="451" pagination="175 - 178" part="16" refId="ref11520" refString="Erickson, G. M. and Olson, K. H. 1996. Bite marks attributable to Tyrannosaurus rex: a preliminary description and implications. Journal of Vertebrate Paleontology 16: 175 - 178." title="Bite marks attributable to Tyrannosaurus rex: a preliminary description and implications" type="journal article" year="1996">Erickson and Olson 1996</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC3DFFDD53A6F904FB50F914" author="Wegweiser, M. &amp; Breithaupt, B. &amp; Chapman, R." box="[1009,1265,1713,1738]" journalOrPublisher="Journal of Vertebrate Paleontology" pageId="16" pageNumber="451" pagination="127" part="24 (Supplement 3)" refId="ref13365" refString="Wegweiser, M., Breithaupt, B., and Chapman, R. 2004. Attack behavior of tyrannosaurid dinosaur (s): Cretaceous crime scenes, really old evidence, and &quot; smoking guns &quot;. Journal of Vertebrate Paleontology 24 (Supplement 3): 127 A." title="Attack behavior of tyrannosaurid dinosaur (s): Cretaceous crime scenes, really old evidence, and &quot; smoking guns" type="journal article" year="2004">Wegweiser et al. 2004</bibRefCitation>
) indicate that these theropods imposed this loading regime on their crania (
<bibRefCitation id="EFAC4B6DEC3DFFDD55D8F964FCC9F8D4" author="Holtz, T. R. Jr." editor="P. H. Kelly &amp; M. Koweleski &amp; T. A. Hansen" journalOrPublisher="Kluwer / Plenum, New York" pageId="16" pageNumber="451" pagination="325 - 340" part="17" refId="ref12157" refString="Holtz, T. R. Jr. 2002. Theropod predation: evidence and ecomorphology. In: P. H. Kelly, M. Koweleski, and T. A. Hansen (eds.), Predator-Prey Interactions in the Fossil Record. Topics in Geobiology 17, 325 - 340. Kluwer / Plenum, New York." title="Theropod predation: evidence and ecomorphology" type="journal article" volumeTitle="Predator-Prey Interactions in the Fossil Record. Topics in Geobiology" year="2002">Holtz 2002</bibRefCitation>
). Adaptations for this biting behaviour would include the great width and height of tyrannosaurid nasals and rostra, a stronger palate than in other theropods (
<bibRefCitation id="EFAC4B6DEC3DFFDD54B0F884FAC9F894" author="Holtz, T. R. Jr." box="[1255,1384,1841,1866]" editor="P. H. Kelly &amp; M. Koweleski &amp; T. A. Hansen" journalOrPublisher="Kluwer / Plenum, New York" pageId="16" pageNumber="451" pagination="325 - 340" part="17" refId="ref12157" refString="Holtz, T. R. Jr. 2002. Theropod predation: evidence and ecomorphology. In: P. H. Kelly, M. Koweleski, and T. A. Hansen (eds.), Predator-Prey Interactions in the Fossil Record. Topics in Geobiology 17, 325 - 340. Kluwer / Plenum, New York." title="Theropod predation: evidence and ecomorphology" type="journal article" volumeTitle="Predator-Prey Interactions in the Fossil Record. Topics in Geobiology" year="2002">Holtz 2002</bibRefCitation>
), and the interdigitating, posteriorly declined mandibular symphysis (
<bibRefCitation id="EFAC4B6DEC3DFFDD5364F8C4FBB4F854" author="Therrien, F. &amp; Henderson, D. M. &amp; Ruff. C. B." box="[819,1045,1905,1930]" editor="K. Carpenter" journalOrPublisher="Indiana University Press, Bloomington" pageId="16" pageNumber="451" pagination="179 - 237" refId="ref13207" refString="Therrien, F., Henderson, D. M., and Ruff. C. B. 2005. Bite me: biomechanical models of theropod mandibles and implications for feeding behavior. In: K. Carpenter (ed.), The Carnivorous Dinosaurs, 179 - 237. Indiana University Press, Bloomington." title="Bite me: biomechanical models of theropod mandibles and implications for feeding behavior" type="book chapter" volumeTitle="The Carnivorous Dinosaurs" year="2005">Therrien et al. 2005</bibRefCitation>
), which increased the torsional strength of the cranium and articulated lower jaws. Additional strength imparted by the staircase−like nasal−maxillary joint of adult 
<taxonomicName id="4C3D4D1FEC3DFFDD537BF867FBAFF834" authorityName="Russell" authorityYear="1970" box="[812,1038,2002,2026]" class="Reptilia" family="Tyrannosauridae" genus="Daspletosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="16" pageNumber="451" phylum="Chordata" rank="species" species="torosus">
<emphasis id="B949EA8EEC3DFFDD537BF867FBAFF834" box="[812,1038,2002,2026]" italics="true" pageId="16" pageNumber="451">Tarbosaurus bataar</emphasis>
</taxonomicName>
and 
<taxonomicName id="4C3D4D1FEC3DFFDD5419F866FA85F834" authorityName="Osborn" authorityYear="1905" box="[1102,1316,2003,2026]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="16" pageNumber="451" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC3DFFDD5419F866FA85F834" box="[1102,1316,2003,2026]" italics="true" pageId="16" pageNumber="451">Tyrannosaurus rex</emphasis>
</taxonomicName>
would benefit these 5–10 tonne giants (
<bibRefCitation id="EFAC4B6DEC3CFFDC5128FF5DFE55FEDF" author="Paul, G. S." bookContentInfo="464 pp." box="[383,500,232,257]" journalOrPublisher="Simon and Schuster, New York" pageId="17" pageNumber="452" refId="ref12732" refString="Paul, G. S. 1988. Predatory Dinosaurs of the World. 464 pp. Simon and Schuster, New York." title="Predatory Dinosaurs of the World" type="book" year="1988">Paul 1988</bibRefCitation>
, 
<bibRefCitation id="EFAC4B6DEC3CFFDC5255FF5DFF3EFEFF" author="Henderson D. M. &amp; Snively E." journalOrPublisher="Proceedings of the Royal Society B, Biology Letters" pageId="17" pageNumber="452" pagination="S 57 - S 60" part="271" refId="ref12049" refString="Henderson D. M. and Snively E. 2003. Tyrannosaurus en pointe: Allometry minimized rotational inertia of large carnivorous dinosaurs. Proceedings of the Royal Society B, Biology Letters 271: S 57 - S 60." title="Tyrannosaurus en pointe: Allometry minimized rotational inertia of large carnivorous dinosaurs" type="journal article" year="2003">Henderson and Snively 2003</bibRefCitation>
) when reducing larger prey animals beyond the capacity of other tyrannosaurids.
</paragraph>
<paragraph id="8B82369CEC3CFFDC50DBFEFCFE41FD9C" blockId="17.[102,775,232,1507]" pageId="17" pageNumber="452">
Potential tyrannosaurid prey (including ceratopsians and hadrosaurs: 
<bibRefCitation id="EFAC4B6DEC3CFFDC50BBFEDCFEDCFE5C" author="Russell, D. A." box="[236,381,361,386]" journalOrPublisher="National Museum of Natural Sciences, Publications in Palaeontology" pageId="17" pageNumber="452" pagination="1 - 34" part="1" refId="ref12888" refString="Russell, D. A. 1970 Tyrannosaurs of the Late Cretaceous of western Canada. National Museum of Natural Sciences, Publications in Palaeontology 1: 1 - 34." title="Tyrannosaurs of the Late Cretaceous of western Canada" type="journal article" year="1970">Russell 1970</bibRefCitation>
) were generally smaller than the giant, long−necked sauropods that 
<taxonomicName id="4C3D4D1FEC3CFFDC5187FE3CFDE8FE7F" authorityName="Marsh" authorityYear="1877" box="[464,585,393,417]" class="Reptilia" family="Allosauridae" genus="Allosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="17" pageNumber="452" phylum="Chordata" rank="genus">
<emphasis id="B949EA8EEC3CFFDC5187FE3CFDE8FE7F" box="[464,585,393,417]" italics="true" pageId="17" pageNumber="452">Allosaurus</emphasis>
</taxonomicName>
and other carnosaurs more often encountered. It is therefore possible that tyrannosaurids bit into bone more often than would carnosaurs biting into the flesh of larger prey, although fragments in a coprolite (
<bibRefCitation id="EFAC4B6DEC3CFFDC5155FDBCFE1DFDFC" author="Stone, D. W. &amp; Crisp, E. L. &amp; Bishop J. R." box="[258,444,521,546]" journalOrPublisher="Geological Society of America Annual Meeting. Abstracts with Programs" pageId="17" pageNumber="452" pagination="220" part="32" refId="ref13158" refString="Stone, D. W., Crisp, E. L., and Bishop J. R. 2000. A large meat-eating dinosaur coprolite from the Jurassic Morrison Formation of Utah. Geological Society of America Annual Meeting. Abstracts with Programs 32: 220." title="A large meat-eating dinosaur coprolite from the Jurassic Morrison Formation of Utah" type="journal article" year="2000">Stone et al. 2000</bibRefCitation>
) suggest that large carnosaurs splintered bones before ingestion.
</paragraph>
</subSubSection>
<subSubSection id="C3276517EC3CFFDC50DBFDFCFD17FA3D" pageId="17" pageNumber="452" type="nomenclature">
<paragraph id="8B82369CEC3CFFDC50DBFDFCFD7DFC7C" blockId="17.[102,775,232,1507]" pageId="17" pageNumber="452">
High bending and torsional (
<bibRefCitation id="EFAC4B6DEC3CFFDC5185FDFCFDF4FDBC" author="Holtz, T. R. Jr." box="[466,597,585,610]" editor="P. H. Kelly &amp; M. Koweleski &amp; T. A. Hansen" journalOrPublisher="Kluwer / Plenum, New York" pageId="17" pageNumber="452" pagination="325 - 340" part="17" refId="ref12157" refString="Holtz, T. R. Jr. 2002. Theropod predation: evidence and ecomorphology. In: P. H. Kelly, M. Koweleski, and T. A. Hansen (eds.), Predator-Prey Interactions in the Fossil Record. Topics in Geobiology 17, 325 - 340. Kluwer / Plenum, New York." title="Theropod predation: evidence and ecomorphology" type="journal article" volumeTitle="Predator-Prey Interactions in the Fossil Record. Topics in Geobiology" year="2002">Holtz 2002</bibRefCitation>
) strength of tyrannosaurid crania and nasals are consistent with biting into bone, but also with adeptness at tearing bone and flesh from large prey (
<bibRefCitation id="EFAC4B6DEC3CFFDC50B5FD1CFDB6FD1C" author="Farlow, J. O. &amp; Brinkman, D. L." box="[226,535,681,706]" editor="G. D. Rosenberg &amp; D. L. Wolberg" journalOrPublisher="Palaeontological Society Special Publications" pageId="17" pageNumber="452" pagination="165 - 175" part="7" refId="ref11677" refString="Farlow, J. O. and Brinkman, D. L. 1994. Wear surfaces on the teeth of tyrannosaurs. In: G. D. Rosenberg and D. L. Wolberg (eds.), Dino Fest; Proceedings of a Conference for the General Public. Palaeontological Society Special Publications 7: 165 - 175." title="Wear surfaces on the teeth of tyrannosaurs" type="journal article" volumeTitle="Dino Fest; Proceedings of a Conference for the General Public" year="1994">Farlow and Brinkman 1994</bibRefCitation>
). High strength in lateral bending suggests the cranium was well equipped to withstand lateral movements of the head and neck while the teeth were embedded in the prey. The great posterior width of tyrannosaurid crania (especially in 
<taxonomicName id="4C3D4D1FEC3CFFDC5251FC9EFD78FC9C" authorityName="Osborn" authorityYear="1905" box="[518,729,811,834]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="17" pageNumber="452" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC3CFFDC5251FC9EFD78FC9C" box="[518,729,811,834]" italics="true" pageId="17" pageNumber="452">Tyrannosaurus rex</emphasis>
</taxonomicName>
) indicates high leverage for muscles that would turn the head (m. longissimus capitis superficialis) or turn and raise it at the same time (m. complexus) during unilateral contraction.
</paragraph>
<paragraph id="8B82369CEC3CFFDC50DBFC1FFEFDFB5C" blockId="17.[102,775,232,1507]" pageId="17" pageNumber="452">
These results complement findings, from tooth marks and finite element analysis, that 
<taxonomicName id="4C3D4D1FEC3CFFDC51F9FC7EFD27FC3C" authorityName="Osborn" authorityYear="1905" box="[430,646,971,994]" class="Reptilia" family="Tyrannosauridae" genus="Tyrannosaurus" higherTaxonomySource="GBIF" kingdom="Animalia" order="Dinosauria" pageId="17" pageNumber="452" phylum="Chordata" rank="species" species="rex">
<emphasis id="B949EA8EEC3CFFDC51F9FC7EFD27FC3C" box="[430,646,971,994]" italics="true" pageId="17" pageNumber="452">Tyrannosaurus rex</emphasis>
</taxonomicName>
was proficient at “puncture and pull” feeding by retraction of the head (
<bibRefCitation id="EFAC4B6DEC3CFFDC503AFBBFFEF1FBFD" author="Erickson, G. M. &amp; Olson, K. H." box="[109,336,1034,1059]" journalOrPublisher="Journal of Vertebrate Paleontology" pageId="17" pageNumber="452" pagination="175 - 178" part="16" refId="ref11520" refString="Erickson, G. M. and Olson, K. H. 1996. Bite marks attributable to Tyrannosaurus rex: a preliminary description and implications. Journal of Vertebrate Paleontology 16: 175 - 178." title="Bite marks attributable to Tyrannosaurus rex: a preliminary description and implications" type="journal article" year="1996">Erickson et al. 1996</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC3CFFDC510CFBBFFE5EFBFD" author="Rayfield, E. J." box="[347,511,1034,1059]" journalOrPublisher="Proceedings of the Royal Society of London B" pageId="17" pageNumber="452" pagination="1451 - 1459" part="271" refId="ref12756" refString="Rayfield, E. J. 2004. Cranial mechanics and feeding in Tyrannosaurus rex. Proceedings of the Royal Society of London B 271: 1451 - 1459." title="Cranial mechanics and feeding in Tyrannosaurus rex" type="journal article" year="2004">Rayfield 2004</bibRefCitation>
). The high lateral bending strength of tyrannosaurid crania indicates that the animals could have augmented linear retraction with vigorous sideways movements.
</paragraph>
<paragraph id="8B82369CEC3CFFDC50DBFB3FFD17FA3D" blockId="17.[102,775,232,1507]" pageId="17" pageNumber="452">
High strength of nasals and crania would augment a variety of feeding functions in tyrannosaurids, including the infliction of tissue damage without the need to secure food with their reduced forelimbs (
<bibRefCitation id="EFAC4B6DEC3CFFDC5138FB5FFE4EFADD" author="Holtz, T. R. Jr." box="[367,495,1258,1283]" editor="D. B. Weishampel &amp; P. Dodson &amp; H. Osmolska" journalOrPublisher="University of California Press. Berkeley" pageId="17" pageNumber="452" pagination="111 - 136" refId="ref12220" refString="Holtz, T. R. Jr. 2004. Tyrannosauroidea. In: D. B. Weishampel, P. Dodson, and H. Osmolska (eds.), The Dinosauria, 111 - 136. University of California Press. Berkeley." title="Tyrannosauroidea" type="book chapter" volumeTitle="The Dinosauria" year="2004">Holtz 2004</bibRefCitation>
). Modern carnivorous animals employ forceful bites and lateral tearing of flesh whether killing or eating prey (
<bibRefCitation id="EFAC4B6DEC3CFFDC5109FA9FFD81FA9D" author="Auffenberg, W." bookContentInfo="406 pp." box="[350,544,1322,1347]" journalOrPublisher="Univeristy of Florida Press, Gainsville" pageId="17" pageNumber="452" refId="ref11005" refString="Auffenberg, W. 1981. The Behavioral Ecology of the Komodo Monitor. 406 pp. Univeristy of Florida Press, Gainsville." title="The Behavioral Ecology of the Komodo Monitor" type="book" year="1981">Auffenberg 1981</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC3CFFDC527BFA9FFF00FABD" author="Erickson, G. M. &amp; Olson, K. H." journalOrPublisher="Journal of Vertebrate Paleontology" pageId="17" pageNumber="452" pagination="175 - 178" part="16" refId="ref11520" refString="Erickson, G. M. and Olson, K. H. 1996. Bite marks attributable to Tyrannosaurus rex: a preliminary description and implications. Journal of Vertebrate Paleontology 16: 175 - 178." title="Bite marks attributable to Tyrannosaurus rex: a preliminary description and implications" type="journal article" year="1996">Erickson and Olson 1996</bibRefCitation>
), and inference of these actions in tyrannosaurids is uninformative for debates over scavenging or predation frequency (
<bibRefCitation id="EFAC4B6DEC3CFFDC503AFA3FFF4FFA7D" author="Holtz, T. R. Jr." box="[109,238,1418,1443]" editor="P. H. Kelly &amp; M. Koweleski &amp; T. A. Hansen" journalOrPublisher="Kluwer / Plenum, New York" pageId="17" pageNumber="452" pagination="325 - 340" part="17" refId="ref12157" refString="Holtz, T. R. Jr. 2002. Theropod predation: evidence and ecomorphology. In: P. H. Kelly, M. Koweleski, and T. A. Hansen (eds.), Predator-Prey Interactions in the Fossil Record. Topics in Geobiology 17, 325 - 340. Kluwer / Plenum, New York." title="Theropod predation: evidence and ecomorphology" type="journal article" volumeTitle="Predator-Prey Interactions in the Fossil Record. Topics in Geobiology" year="2002">Holtz 2002</bibRefCitation>
). However, high strength of tyrannosaurid crania indicates that they could afford indelicacy during attempted killing bites (
<bibRefCitation id="EFAC4B6DEC3CFFDC50A1FA7FFE07FA3D" author="Carpenter, K." box="[246,422,1482,1507]" journalOrPublisher="Gaia" pageId="17" pageNumber="452" pagination="136 - 144" part="15" refId="ref11213" refString="Carpenter, K. 2000. Evidence of predatory behavior by carnivorous dinosaurs. Gaia 15: 136 - 144." title="Evidence of predatory behavior by carnivorous dinosaurs" type="journal article" year="2000">Carpenter 2000</bibRefCitation>
; 
<bibRefCitation id="EFAC4B6DEC3CFFDC51E7FA7FFD0AFA3D" author="Wegweiser, M. &amp; Breithaupt, B. &amp; Chapman, R." box="[432,683,1482,1507]" journalOrPublisher="Journal of Vertebrate Paleontology" pageId="17" pageNumber="452" pagination="127" part="24 (Supplement 3)" refId="ref13365" refString="Wegweiser, M., Breithaupt, B., and Chapman, R. 2004. Attack behavior of tyrannosaurid dinosaur (s): Cretaceous crime scenes, really old evidence, and &quot; smoking guns &quot;. Journal of Vertebrate Paleontology 24 (Supplement 3): 127 A." title="Attack behavior of tyrannosaurid dinosaur (s): Cretaceous crime scenes, really old evidence, and &quot; smoking guns" type="journal article" year="2004">Wegweiser et al. 2004</bibRefCitation>
).
</paragraph>
</subSubSection>
</treatment>
</document>