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

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Woo S., Maynard J., Butler O. 1987. Ligament, tendon, and joint capsure insertions to bone. In: Woo S., Buckwalter J.A (eds.) Injury and Repair of the Musculoskeletal Sof? rssues. Arnerican Academy of Orthopaedic Surgeons. Park Ridge. IL. Yalden D.W. 1971. The functional morphology of the carpus in ungulate animais. Acta Anat. 78: 461 -487. Zani P.A. 2000. The comparative evolution of lizard claw and toe morphology and dinging performance. J. Evol. Bid. 13:316-325. Zweers G.A. 1979. Explanation of structure by optirniration and systemization. Neth. J. Zool. 29:418-440. Zweers, GA. 1991. Transformation of avian feeding mechanisms: a deductive method. Acta Biotheoretica 39: 15-36.
APPENDIX Principal Components Analysis The mechanics and theory behind morphological Principal Components Analysis (PCA) are relatively simple. Dimensions between landmarks on an anatomical structure, or angles subtended by its contours, are measured for a number of specimens. These data are typically log transforrned and entered into a matrix of measurements versus specimens. The variables for these rneasurements represent coordinate axes in multidimensional space. Each specimen is plotted in a given position in a multidimensional cloud of points (Sokal and Rohlf 1995). PCA determines the variance and covariance of measured dimensions. Important elements of variance and covariance describe the shape of this cloud of points, much like the length and width axes that might describe the shape of an elipse. These principal axes that represent important aspects of variation are called eigenvectors, and values which denote variance along the axes are called eigenvalues (Sokal and Rohlf 1995). Eigenvalues reveal the relative contribution of principal axes to overall variation. These important contributing factors of variation are called Principal Components (abbreviated as PC). Because diierent eigenvalues can represent either variance or covariance, they can reveal the importance size or shape. Measures of linear size might be responsible for the most variation, or a measure of shape, such as ratios of variables, might contribute more. To reveal what kind of variation a principal component represents, we must examine the impact that individuai variables have on that principal component.
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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
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3. Troodontidae (Figure 1.2): Trwdo
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Hypothesized functions of the tyran
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1. Atomization (Chapters 2 and 3).
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Figure 1.1. P hylogenetic diagram o
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Figure 1.2. Phylogenetic diagram of
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Figure 1 .S. Skeletal restorations
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did not quantify the degree of prox
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qualitative debate over arctometata
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This hypothesis focuses on tyrannos
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Table 2.1. Theropod and Plafeosauru
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specimens in the figures reflects a
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were not attempted. While this limi
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Chapter 3). 1 now address variation
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- Ç6'P 1 68'€tr 1 L'OC 99'66 L'9
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Table 2.3: Log-transformed values f
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experiences a sharp laterally indin
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ecause it can be cursorily dassifie
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arctometatarsalian specimens, the l
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) Shaf€ and region of proximal ar
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a) Ginglymus. Figure 2.14 shows the
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) Shaft and region of proximal arti
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measurements of width pV2S%TU-DE an
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Table 2.4b Variancelmeasurement eac
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the largest sum of linear measureme
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Table 2.5: Specimen statistics Herr
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and Sinraptor dongi specimens. With
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In addition, a hook like proximal a
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oth physical narrowing and elongati
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1s the MT 111 shape segregation fun
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tyrannosaurids, ornithomimid, and t
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proximal constriction, white EImisa
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Figure 2.2. Tyrannosaurid, trwdonti
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Figure 2.4. Dromaeosaurid and carno
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- Anterior (flexor) surface medial
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Figure 2.7. Left MT III of Tyrannos
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Figure 2.8. Left MT III of Gorgosau
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Figure 2.9. Left MT III of an omith
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Figure 2.10. Left metatarsus of Tmd
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Figure 2.1 1. Left MT III of Elmisa
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Figure 2.12. Right MT III of Deinon
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Figure 2.13. Left MT III of Allosau
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Figure 2.14. Left metatarsus of Sin
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Figure 2.15. Plots of MT Ill specir
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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
Page 238 and 239: y distal intermetatarsal ligaments,
Page 240 and 241: Probable fundion of the tyrannosaur
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Page 248 and 249: face of the skull met part of the m
Page 250 and 251: Alternately, a morphological novelt
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Page 258 and 259: dromaeosaurids], and a dade compris
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Page 262 and 263: Proximal intermetatarsal ligaments
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Page 267: Figure 5.2. Phylogeny of the Therop
Page 278 and 279: Bock W.J. and von Wahlert G. Evolut
Page 280 and 281: Cume P.J. 1997. Theropoda. In: Fari
Page 282 and 283: Grenard S. 1991. Handbook of Alliga
Page 284 and 285: Liem K.F. and Osse J.W.M. 1975. Bio
Page 286 and 287: Richtsmeier J.T. and Cheverud J.M.
Page 290 and 291: Different variables in a PCA will h
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THE UNIVERSITY OF CALGARY Eric Snively A ... - Ohio University

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