THE UNIVERSITY OF CALGARY Eric Snively A ... - Ohio University

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$Introduction to Numerical Math and Matlab ... - Ohio University$

Table 2.4b Variancelmeasurement each PC ex~lains
positively with relative metatarsal gracility, while proximal width decreases with gracility. However, a high positive loading for HGlNGL may reflect the relatively high values for this measurement in the large tyrannosaurid specimens (see Discussion), and therefore may be correlated more with overall metatarsal length than with proximal narrowing. Grouping of speàmem by PCA Table 2.5 gives statistics for al1 specimens measured for PCA, including the total variance for each specimen, the amount of each specimen's variance explained by each PC (Varcamp), and the distance of the specimen from the origin of al1 PC axes. The last quantity gives the degree of deviation from a hypothetical average morphology in size and shape as deterrnined by the constituency of the entire data base. The value of distance from the origin is simply the square root of the variance, and is the number of standard deviation units (SD) a specimen plots away from the origin. The distribution of standard deviations (Distance: Table 2.5) facilitates the general identification of unusual and typical morphologies. Because PC1 , a size related component, explains 86.65% of total variance, distance from the origin in SD primarily shows deviations in overail size from the average of the sample. At 0.15 SD, the Elaphrosaurus MT III is closest to the average in linear dimensions. By far the most aberrant are Omzholestes and the smaller lngenia specimen, at distances of 1.474 and 1.480 SD, respectively. These are the smallest specimens in overall length. At the other extreme, Allosaurus (Saurophaganax) maximus (1 .O8 SD) and the larger Tjmnnosaurus rex specimen (1 -04 SD) have
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THE UNIVERSITY OF CALGARY Functiona
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Many figures in this thesis use col
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ACKNOWLEûGEM ENTS Many friends and
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Approval page Acknowledgements Tabi
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CONCLUDING COMMENTS Figures for Cha
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CHAPTER 5: Mechanical and phylogene
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LIST OF FIGURES Figure 1 .l. Phylog
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Figure 3.6. Osteological correlates
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AMNH GI HMN IVPP MOR NMC OMNH PIN P
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and constructional morphology revea
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1985, Bryant and Seymour 1990). If
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surfaces of a Tyrannosaurus rex spe
Page 26 and 27: 3. Troodontidae (Figure 1.2): Trwdo
Page 29 and 30: Hypothesized functions of the tyran
Page 31 and 32: 1. Atomization (Chapters 2 and 3).
Page 33 and 34: Figure 1.1. P hylogenetic diagram o
Page 35 and 36: Figure 1.2. Phylogenetic diagram of
Page 41: Figure 1 .S. Skeletal restorations
Page 44 and 45: did not quantify the degree of prox
Page 46 and 47: qualitative debate over arctometata
Page 48 and 49: This hypothesis focuses on tyrannos
Page 50 and 51: Table 2.1. Theropod and Plafeosauru
Page 52 and 53: specimens in the figures reflects a
Page 54 and 55: were not attempted. While this limi
Page 56 and 57: Chapter 3). 1 now address variation
Page 58 and 59: - Ç6'P 1 68'€tr 1 L'OC 99'66 L'9
Page 60 and 61: Table 2.3: Log-transformed values f
Page 62 and 63: experiences a sharp laterally indin
Page 64 and 65: ecause it can be cursorily dassifie
Page 66 and 67: arctometatarsalian specimens, the l
Page 68 and 69: ) Shaf€ and region of proximal ar
Page 70 and 71: a) Ginglymus. Figure 2.14 shows the
Page 72 and 73: ) Shaft and region of proximal arti
Page 74 and 75: measurements of width pV2S%TU-DE an
Page 78 and 79: the largest sum of linear measureme
Page 80 and 81: Table 2.5: Specimen statistics Herr
Page 82 and 83: and Sinraptor dongi specimens. With
Page 84 and 85: In addition, a hook like proximal a
Page 86 and 87: oth physical narrowing and elongati
Page 88 and 89: 1s the MT 111 shape segregation fun
Page 90 and 91: tyrannosaurids, ornithomimid, and t
Page 92 and 93: proximal constriction, white EImisa
Page 95: Figure 2.2. Tyrannosaurid, trwdonti
Page 99: Figure 2.4. Dromaeosaurid and carno
Page 102 and 103: - Anterior (flexor) surface medial
Page 105 and 106: Figure 2.7. Left MT III of Tyrannos
Page 107 and 108: Figure 2.8. Left MT III of Gorgosau
Page 109 and 110: Figure 2.9. Left MT III of an omith
Page 111 and 112: Figure 2.10. Left metatarsus of Tmd
Page 113 and 114: Figure 2.1 1. Left MT III of Elmisa
Page 115 and 116: Figure 2.12. Right MT III of Deinon
Page 117 and 118: Figure 2.13. Left MT III of Allosau
Page 119 and 120: Figure 2.14. Left metatarsus of Sin
Page 121 and 122: Figure 2.15. Plots of MT Ill specir
Page 123: Figure 2.16. Plot of third metatars
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tv . ... . Ri. . . .
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Figure 2.19. Plot of third metatars
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CHAPTER 3: Tensile keystone model o
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dynamically transmitted Iommotor fo
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Table 3.1 . Metatarsi examined in t
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interrnetatarsal dynamics in these
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compelled analysis of movement evid
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Once prepared, TMP 94.1 2.602 and i
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Daspletosaurus tomsus (MOR 590), an
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2. Freedom of movement inferred fro
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Table 3.2. Surface areas of intemet
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phylogenetic bracketing Wtmer 1995)
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4) Forces from anterior displacerne
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e expected for tyrannosaurid interm
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The preceding discussion derives fr
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weapons sparring), and the arctomet
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Figure 3.1. Schematic representatio
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Figure 3.3. CT reconstruction of ri
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Figure 3.5. MT II (left element) an
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Figure 3.1 1 ae. The metatarsal rec
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Figure 3.13. Ligament contribution
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Figure 3.15. Anatorny of the equid
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Figure 3.16. Cornparison of loading
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(nodes), and solving stresslstrain
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The practicality of the finite elem
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collective density of trabeculae (K
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A FORCE INPUTS AND MATERIAL PROPERT
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Alexander et al. (1 979) rewrded a
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The preceding loading regime entait
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detemined by using the photographic
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2. Preparation of data for contour
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. - Elastic modulus (GP4 Ex EY Ez P
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conversion. Volume-to-nuages facili
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maintained. An angle of 2 degrees p
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of MT III (Figure 4.4, pinpointed b
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anterodorsal rotation of the distal
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allowed to stretch slightly under t
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Figure 4.1. Initial loads and bound
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Figure 4.3. Finite element mesh of
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Figure 4.5. Strain distribution in
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CHAPTER 5: Mechanical and evolution
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y distal intermetatarsal ligaments,
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Probable fundion of the tyrannosaur
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Ornitholestes, and camosaurs) incre
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morphology matches in degree the co
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discussion elucidates the evolution
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face of the skull met part of the m
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Alternately, a morphological novelt
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outgroup to ail theropods, and the
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convincingly evident in figures of
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parsimonious scenarios are outlined
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dromaeosaurids], and a dade compris
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arctometatarsalian forrns. The conv
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Proximal intermetatarsal ligaments
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witti a surfeit of potentially supp
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Figure 5.2. Phylogeny of the Therop
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Bock W.J. and von Wahlert G. Evolut
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Cume P.J. 1997. Theropoda. In: Fari
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Grenard S. 1991. Handbook of Alliga
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Liem K.F. and Osse J.W.M. 1975. Bio
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Richtsmeier J.T. and Cheverud J.M.
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Woo S., Maynard J., Butler O. 1987.
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Different variables in a PCA will h
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THE UNIVERSITY OF CALGARY Eric Snively A ... - Ohio University

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