Dental morphology and variation in theropod dinosaurs: Implications for the taxonomic identification of isolated teeth

Authors

  • Joshua B. Smith,

    Corresponding author
    1. Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, Pennsylvania
    • Department of Earth and Planetary Sciences, Washington University, 1 Brookings Drive, Campus Box 1169, St. Louis, MO 63130
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    • Fax: 314-935-7361

  • David R. Vann,

    1. Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, Pennsylvania
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  • Peter Dodson

    1. Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, Pennsylvania
    2. Department of Animal Biology, School of Veterinary Medicine, University of Pennsylvania, Pennsylvania
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Abstract

Isolated theropod teeth are common Mesozoic fossils and would be an important data source for paleoecology biogeography if they could be reliably identified as having come from particular taxa. However, obtaining identifications is confounded by a paucity of easily identifiable characters. Here we discuss a quantitative methodology designed to provide defensible identifications of isolated teeth using Tyrannosaurus as a comparison taxon. We created a standard data set based as much as possible on teeth of known taxonomic affinity against which to compare isolated crowns. Tooth morphology was described using measured variables describing crown length, base length and width, and derived variables related to basal shape, squatness, mesial curve shape, apex location with respect to base, and denticle size. Crown curves were described by fitting the power function Y = a + bX0.5 to coordinate data collected from lateral-view images of mesial curve profiles. The b value from these analyses provides a measure of curvature. Discriminant analyses compared isolated teeth of various taxonomic affinities against the standard. The analyses classified known Tyrannosaurus teeth with Tyrannosaurus and separated most teeth known not to be Tyrannosaurus from Tyrannosaurus. They had trouble correctly classifying teeth that were very similar to Tyrannosaurus and for which there were few data in the standard. However, the results indicate that expanding the standard should facilitate the identification of numerous types of isolated theropod teeth. © 2005 Wiley-Liss, Inc.

One of the first steps in studying interactions among ancient organisms and their environments is identifying the taxa that comprised the ecosystem. Regrettably, this task can be quite complicated. For vertebrates, the difficulties in obtaining taxonomic identifications for isolated bones, and in some cases partial skeletons, have plagued researchers since the infancy of paleontology. The difficulties stem from a lack of recognized characters in many elements, degradation and loss of anatomical data through taphonomic processes, and the fact that within-taxon variation is poorly understood for most bones of most taxa. These issues confound study into most questions regarding ancient vertebrates, but the situation is acute where bone beds or attempts to generate paleopopulation census data are concerned (e.g., Dodson, 1971; Behrensmeyer, 1975; Farlow, 1976; Badgley, 1986; Sander, 1992; Varricchio and Horner, 1993; Bilbey, 1999). As the time required to prepare and study skeletons is substantial and as discoveries of single bones far outnumber those of more easily identifiable associated individuals (Kirkland and Wolfe, 2001), it is disadvantageous to ignore issues regarding the taxonomy of isolated elements. Although one might argue that collection energies are put to better use by focusing on skeletons (see White et al., 1998), this approach can be restrictive when community-level questions are being asked (Brinkman, 1990). Moreover, the number of connections in the body that are easily severed during postmortem desiccation, transport, and burial (see Moore, 1985) will force vertebrate paleontology to remain largely “a game of parts.” It is thus beneficial to devote some energy toward finding better ways of extracting usable data from these parts.

Isolated teeth are common in Mesozoic rocks where tetrapod faunas were dominated by polyphyodont taxa that continually replaced their working dentitions (e.g., Estes, 1964; Dodson, 1983, 1987; Fiorillo, 1989; Evans and Milner, 1994; Hasegawa et al., 1995; Long and Murry, 1995; Ruiz-Omeñaca et al., 1996; Dong, 1997; Kellner and Mader, 1997; Chinnery et al., 1998; Tanimoto et al., 1998; Larsson and Sidor, 1999; Lucas et al., 1999; Weishampel et al., 1999; Papazzoni, 2003). Theropod dinosaurs in particular had an almost continual supply of teeth that could be shed into the local environment. Their high incidence of discovery (Chandler, 1990; Currie et al., 1990; Erickson, 1995, 1996) and comparative ease of recovery suggest that these elements (favored here over, for example, ribs) are good candidates to examine with the aim of devising a reliable means of taxonomic identification. Moreover, being covered with enamel, the most resistant substance in the body (Shellis et al., 1998), teeth can survive extensive abrasion with much of their anatomical information intact (e.g., Argast et al., 1987; Teaford, 1988).

The ability to identify a theropod taxon based solely on tooth morphology is an intriguing possibility, with clear benefits if proven successful. Mammal teeth utilized in this way have become integral in reconstructing Mesozoic and Cenozoic biotas (e.g., Andrews and Nesbit Evans, 1983; Jenkins et al., 1983; Jacobs et al., 1988, 1989; Cifelli et al., 1989; Cifelli, 1993, 1999; Albright, 1996; Goin and Candela, 1996; Kappelman et al., 1996; Rich et al., 1997; Robinson and Williams, 1997; Kelly, 1998; Koenigswald et al., 1999; Krause, 2001). However, comparatively little work has been directed at assessing the feasibility of a similar role for theropod teeth. Indeed, although the groundwork has been established (e.g., Chandler, 1990; Currie et al., 1990; Farlow et al., 1991; Baszio, 1997; Buscalioni et al., 1997), a rigorous means of discriminating morphologies has yet to appear and identifications placed on theropod teeth are usually weak (e.g., Holtz et al., 2004: p. 78). Some features have been cited as diagnostic for certain taxa (Currie, 1987; Currie et al., 1990; Charig and Milner, 1997; Sereno et al., 1998), but overall, relatively few dental characters have been identified (Holtz, 1998). Assessing the taxonomic utility of theropod teeth is thus our goal here, since the lack of a solid understanding of this utility is not preventing teeth from being used to define taxa at various levels (e.g., Carpenter, 1982; Buffetaut and Ingavat, 1986; Okazaki, 1992; Nessov, 1995; Sankey, 2001).

If we are to identify unknown theropod teeth taxonomically, then we require a method of discriminating morphotypes and a standard of morphology against which to compare the isolated crowns. This standard must be based as much as possible on in situ teeth of known taxonomic affinity. “In situ” here means teeth located in the jaws of specimens whose taxonomy is agreed on (e.g., there is a consensus that AMNH 5027 is a specimen of Tyrannosaurus rex Osborn, 1905). Most theropod tooth research has been conducted on shed crowns assigned to taxonomic groups on the basis of a priori assumptions (essentially untested hypotheses) of their phylogenetic affinities. Of the morphologically oriented papers, only Currie et al. (1990) and Farlow et al. (1991) included in situ teeth in their analyses and such crowns made up very small portions of their data. Farlow et al. (1991) stated that they “did not know the species or even genera” of most of their teeth (p. 174) and that their conclusions should be regarded as approximations of the “true” results that would be obtained from examining teeth of known taxonomies (p. 165). We focused on in situ teeth of well-supported taxa (see Gauthier, 1986; Holtz, 1994a, 1994b, 1996, 1998; Sereno, 1999; Gauthier and de Quieroz, 2001; Norell et al., 2001). Qualitative discrimination of theropod tooth morphologies is difficult, so we relied on quantitative methods and utilized simple, easily reproducible metrics to help reduce measurement error (see Bailey and Byrnes, 1990), maximize repeatability among researchers (see Carrasco, 1999), facilitate the incorporation of published data into subsequent studies, and perhaps alleviate some of the resistance to morphometrics discussed by MacLeod (1999).

The measurements we discuss here are not intended to be necessarily congruent with evolutionary or developmental processes; our aim was not to describe evolutionary pathways. Rather, the goal was to discriminate morphotypes and correlate teeth of unknown affinity with known groups. Isolated teeth (e.g., Fiorillo and Currie, 1994; Zinke, 1998; Vickers-Rich et al., 1999; Fiorillo and Gangloff, 2000; Sankey et al., 2002; Buffetaut et al., 2004) and bones (e.g., Buffetaut, 1989; Russell, 1996; Brinkman et al., 1998; Calvo and Coria, 1998) are constantly being referred to taxa, including genera and species. Our intention was simply to try and develop a rigorous means by which to test some of these hypotheses of taxonomic referral.

Abbreviations

The following abbreviations are used.

Anatomical and morphometric abbreviations.

AFCCS, crown curve slope of the A face; AL, apical length; CA, crown angle; CA2, crown angle corrected for size; CBL, crown base length; CBR, crown base ratio; CBW, crown base width; CH, crown height; CHR, crown height ratio; DA, distal apical denticle density; DAVG, average distal denticle density; DAVG2, average distal denticle density corrected for size; DB, distal basal denticle density; DC, distal mid-crown denticle density; MA, mesial apical denticle density; MAVG, average mesial denticle density; MB, mesial basal denticle density; MC, mesial mid-crown denticle density.

Institutional abbreviations.

AMNH, American Museum of Natural History, New York, New York; BHI, Black Hills Institute of Geological Research, Hill City, South Dakota; BMNH, Natural History Museum, London, United Kingdom; CGM, Egyptian Geological Museum, Cairo, Egypt; CM, Carnegie Museum of Natural History, Pittsburgh, Pennsylvania; CMNH, Cleveland Museum of Natural History, Cleveland, Ohio; FMNH, Field Museum of Natural History, Chicago, Illinois; FUB, Freie Universität Berlin, Berlin, Germany; GIN, Geological Institute, Mongolian Academy of Sciences, Ulan Bataar, Mongolia; KUVP, University of Kansas Natural History Museum, Lawrence, Kansas; LACM, Los Angeles County Museum, Los Angeles, California; MBR, Museum für Naturkunde der Humboldt Universität, Berlin, Germany; MCZ, Museum of Comparative Zoology, Harvard University, Cambridge, Massachusetts; MOR, Museum of the Rockies, Bozeman, Montana; NCSM, North Carolina State Museum, Raleigh, North Carolina; NIGP, Nanjing Institute of Geology and Palaeontology, Nanjing, China; OMNH, Oklahoma Museum of Natural History, Norman, Oklahoma; ROM, Royal Ontario Museum, Toronto, Canada; SDSM, South Dakota School of Mines, Rapid City, South Dakota; SGM, Ministére de l'Energie et des Mines, Rabat, Morocco; SMU, Southern Methodist University, Dallas, Texas; UA, Université d'Antananarivo, Antananarivo, Madagascar; UC, Department of Anatomy and Organismal Biology, University of Chicago, Chicago, Illinois; UCMP, Museum of Paleontology, University of California at Berkeley, Berkeley, California; UMNH, Utah Museum of Natural History, Salt Lake City, Utah; UNO, Department of Geology and Geophysics, University of New Orleans, New Orleans, Louisiana; YPM, Peabody Museum of Natural History, Yale University, New Haven, Connecticut.

MATERIALS AND METHODS

Materials and General Procedure

The dentitions of a number of well-supported theropods were examined (phylogenetic hypotheses were not evaluated). The data set (hereafter, the standard) that served as our standard of comparison for taxonomically unknown isolated teeth was built on that developed by Smith (2002). It contains data from across the Theropoda, including Dilophosaurus Welles, 1970, Liliensternus Welles, 1984, Ceratosaurus dentisulcatus Madsen and Welles, 2000 [? = Ceratosaurus nasicornis Marsh, 1884], Masiakasaurus Sampson et al. 2001, “Indosuchus,” Majungatholus Sues and Taquet, 1979, Baryonyx Charig and Milner, 1986, Suchomimus Sereno et al., 1998, Allosaurus Marsh, 1877, Acrocanthosaurus Stovall and Langston, 1950, Carcharodontosaurus Stromer, 1931, Gorgosaurus Lambe, 1914; see Holtz, 2001; Currie, 2003; Currie et al., 2003, for discussion supporting the validity of Gorgosaurus contra Russell, 1970, Daspletosaurus Russell, 1970, T. rex, Troodon Leidy, 1856, Saurornithoides junior Barsbold, 1974, Bambiraptor Burnham et al., 2000, Deinonychus Ostrom, 1969a, Dromaeosaurus Matthew and Brown, 1922, and Velociraptor Osborn, 1924 (Appendix A). A number of taxonomically unknown isolated teeth were selected to be compared against the standard as a test of the methodology discussed below (Appendix B). Where possible, the standard is comprised of in situ teeth. However, in cases where isolated crowns comprise a significant percentage of the known dental record of a taxon and it is very likely that they are from the taxon to which they are referred (e.g., Masiakasaurus), some shed teeth have been used. For example, the maxillary teeth of SGM Din-1 constitute the known record of in situ teeth for Carcharodontosaurus. However, two well-preserved isolated crowns were recovered with the specimen that are virtually identical to the in situ dentition and, although unknowns, are almost certainly Carcharodontosaurus teeth. These specimens were included.

Teeth were photographed, measured, and described. Variables used here are summarized in Figure 1A and B. Measurements were made with Chicago electronic calipers and on digital images using SigmaScan (SPSS Science, 1999). Denticle counts were taken with a Hensoldt-Wetzlar 8× hand lens containing a reticle calibrated in mm and using light microscopy in the laboratory. Measurement repeatability (see Smith, 2002) was assessed using percent measurement error (% ME) sensu Bailey and Byrnes (1990). An assessment of tooth maturity was made to try and exclude partially erupted crowns from the analyses. Notation and orientation nomenclature (Fig. 1C and D) follow Smith (2002) and Smith and Dodson (2003).

Figure 1.

Theropod dental anatomy and variables used in this study. A: Saurornitholestes Sues, 1978 crown in lateral view showing CH (measured from apex to the base of the enamel); CBL (measured along line segment AB at the base of the enamel), mesial apical (MA), mesial mid-crown (MC), and mesial basal (MB) denticle densities (measured along the length of the mesial carina); distal apical (DA), distal mid-crown (DC), and distal basal (DB) denticle densities (measured along the length of the distal carina); and the trace of the mesial curvature profile from which crown curve slope of the A face (AFCCS) is calculated. B: The crown in A in basal view showing CBL and crown base width (CBW, measured perpendicular to CBL). Crown in A after Currie et al. (1990). LM1 = left upper first molar. C: Labial view of Ld13 of T. rex (BHI 3033), showing general theropod tooth anatomy (inset shows tooth in occlusal view; the mesial carina is labeled). Since the crown and base meet at the cervix, in those teeth where the base is present, the crown base and cervix coincide. D: Schematic human dental arcade, in palatal view, showing mesial, distal, labial, and lingual directions (after Smith and Dodson, 2003). [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Analytical Methods

The enamel-covered surfaces of theropod teeth (Fig. 1C) are referred to as crowns (as opposed to bases, which are roughly analogous to mammalian roots; see Peyer, 1968). Crowns typically have simple forms containing few homologous points that can serve as morphometric landmarks (Smith, 1990; Cifelli, 1996). Indeed, there are only about 10 repeatable and reproducible measured or derived variables that can easily be obtained from a theropod tooth, and these are more analogous points than homologous landmarks (as stated above, this is not a crippling issue for this type of study, as we are not directly discussing evolutionary processes). Most quantitative theropod tooth studies have used roughly the same variables (e.g., Farlow and Brinkman, 1987; Chandler, 1990; Currie et al., 1990; Farlow et al., 1991; Rauhut and Werner, 1995; Brinkman et al., 1998; Holtz et al., 1998; Sankey et al., 2002), but the derivation of these metrics has not been standardized, nor always discussed (Hurum and Sabath, 2003). Numerical data have even been taken from composite drawings (Henderson, 1998). If quantitative studies are to be repeatable and reproducible, then the variables used need to be explicitly defined. The metrics used here are defined or discussed below, but they are done only with respect to the Theropoda; some adjustments can be expected for the dental arcades of other groups.

Size and shape.

We must first establish a baseline to which all measurements will be related. If the cross-section of a theropod crown at the base of the enamel is represented as an oval outline (defined as the crown base curve; Fig. 2A), then a Point A may be defined as the point to which all other points are related. Conceptually, A can be thought of as sitting at the origin of a Cartesian coordinate system. With respect to dental orientation, for most teeth A is the most mesial point on the outline (Fig. 2B). However, in the mesialmost teeth of some taxa, the crown basal long axis is oriented in the labiolingual direction (e.g., T.rex; Fig. 3). In these cases, A is the most labial point on the curve (some mammals possess similar morphologies; see Hillson, 1986). With A defined, Point B may be defined as the furthest point on the crown base curve from A, such that the resulting Line Segment AB describes the long axis of the curve and thus the crown basal long axis (Fig. 2B and C). As B is generally located at the most distal point on the curve, AB typically follows the mesiodistal axis of the crown base (except when AB is labiolingual; Fig. 3). With A at the origin, AB is located on the X-axis in the XY plane (Fig. 2D, which is rotated 90° from convention). The variable conceptually represented by AB, when measured on a crown, is defined here as the Crown Base Length (CBL). CBL, roughly equivalent to the fore-aft basal length (FABL) of some authors (see Farlow et al., 1989, 1991; Smith and Dodson, 2003), is the reference variable for this work. Because in some taxa (e.g., T.rex) the mesial face is shorter than the distal face (i.e., the enamel extends further basally on the distal side than it does on the mesial side), we measure CBL in a horizontal plane at the level where the distal carina intersects the base of the crown enamel, ∼ B (note: occasionally, the distal carina extends several mm beyond the bottom of the crown base; in these teeth, CBL is measured at B and not at the end of the carinae). Orthogonal to AB, at the point of maximum extent of the crown basal short axis, another line segment, CD, can be constructed (Fig. 2D). The variable measured on a crown that is conceptualized by CD is defined here as the Crown Base Width (CBW). The CBW is usually measured perpendicular to the CBL and is oriented roughly labiolingually, with C located on the lingual side of the crown and D situated on the labial side.

Figure 2.

Derivation of crown base length (CBL) and crown base width (CBW). A: Photo trace of a T. rex left maxillary crown base (MOR 008); the trace represents the crown base curve (note: this is a view of the base of a left maxillary tooth in occlusal view; as illustrated, labial is to the left). B: The crown base curve in A with cardinal points A and B established. C: The derivation of CBL, which is measured between points A and B, with A at the origin of a Cartesian coordinate system for reference. D: The derivation of CBW (the line between points C and D defines a line segment CD, which describes the maximum distance orthogonal to AB; this distance, measured on a tooth, is the crown base width).

Figure 3.

Positional variation of theropod crown long-axis orientations. A: Photo trace of the lateral margin of the left maxilla and Lmx7 and 8 of T. rex (AMNH 5027), in occlusal view, illustrating the mesiodistal orientation of the crown long axes. B: Photo trace of the premaxilla of AMNH 5027 (teeth are schematic) in palatal view showing the labiolingual orientations of the crown long axes. Cardinal points A, B, C, and D as discussed in the text.

With a Plane ABCD defined on the crown, the direction along the Z-axis can be addressed. There exists a Point E on the crown at the maximum distance from ABCD (Fig. 4A). A line perpendicular to AB extended from E to ABCD will intersect AB at Point F. This Line SegmentEF represents a measure of the height of the crown. Unfortunately, E is very difficult to identify accurately on specimens, especially in large crowns where the apex does not form a distinct point but is rather a larger area (e.g., tyrannosaurids). Line segment EF is thus difficult to measure directly on specimens and as such it is easier to identify the point at the tip that is the farthest straight-line distance from A, which is Point G (Fig. 4B). A perpendicular line extended from G to ABCD at Point H will also produce a measure of crown height, along Line SegmentGH (E and G are often equivalent within the margins of repeatability; see Smith, 2002). H, however, is no easier to locate on a crown than is F. It is far easier to determine the distance between G and B, which also generates a measure of total crown length along the z-axis. This distance, along Line SegmentGB, is defined here as the Crown Height (CH). In practice, B is the point farthest from A on the crown base curve and G is the point farthest from A on the apex. These various measures of total length along the z-axis produce slightly different lengths, but the differences are trivial and are unimportant as long as CH is always measured consistently. The distance between A and G (Line SegmentAG) is simple to determine (Fig. 4B), giving us a variable that is similar to Chandler's (1990) “total length of the mesial serrated row.” The length of AG is defined here as the crown's Apical Length (AL).

Figure 4.

The left fourth dentary tooth of T. rex (BHI 3033) in lingual view, showing the derivation of crown height, apical length, and crown angle. A: Point E is the farthest point on the crown, in the z direction, from plane ABCD; this can be expressed by dropping a perpendicular from E to ABCD at F. The resulting line segment EF (in blue) provides one measure of total crown height. B: Point G is the farthest straight-line distance from point A. A perpendicular dropped from G to the base of the crown at H provides another measure of total crown length (in green). Because of the difficulty in accurately locating F or H on a crown, it is easier in practice to measure line segment GB rather than either line segment EF or GH. As such, line segment GB (in red) is defined as the crown height (CH). Line segment AG, measured on the tooth, is the apical length (AL), and angle AGB (θ) is the crown angle (CA).

The above metrics are the principal variables that we will use to describe crown shape and size in three dimensions. From these variables, several others can be derived. For example, AG (the apical length) creates an angle with ABCD (Angle GAB, or θ). This angle θ (Fig. 4B) forms a variable that is defined here as the Crown Angle (CA). The crown angle can be calculated using the law of cosines: C2 = a2 + b2 − 2ab cosθ, where a = line segment AB (CBL), b = line segment AG (AL), and c = line segment GB (CH).

Substituting and solving for a, b, and c yields

equation image(1)

where θ = CA. Theropod teeth are roughly conical structures and in a cone, the apex is easily identified; however, few theropod crowns are truly conical. Rather, most exhibit some degree of apex displacement away from where they would be located in a true cone (Fig. 5). The CA provides a measure of this displacement; the values change as the location of the apex changes with respect to the intersection of AB and CD (the Crown Base Center). If the apex is located close to the crown base center, the crown angle is large (e.g., ∼ 85°). If the apex has been displaced toward B, the CA value will be smaller (e.g., ∼ 45°).

Figure 5.

Apex displacement and crown curvature. A: An idealized cone, with a centrally located apex. B: The seventh left dentary tooth of T. rex (BHI 3033) in labial view. Note that the apex of Ld7 is displaced to such a degree that it is actually located slightly beyond B.

The ratio of CBW to CBL is a derived variable that is a measure of how elliptical or circular the crown base curve is (it is similar to the common term “lateral compression”). Some authors (e.g., Mathur and Srivastava, 1987; Harris, 1998; Carr, 1999; Currie and Carpenter, 2000) have used CBW:CBL in their discussions, but it has yet to be defined and its variation and distribution have not been assessed. We define CBW:CBL here as the Crown Base Ratio (CBR). CBR values range from 1 to 0 as the base shape changes from circular (a circle has a value of 1) to increasingly bladelike structures. Most theropods have mesial crowns that are slightly more circular and distal crowns that are slightly more bladelike. The ratio of CH to CBL produces a variable that is a measure of how stretched or squat a crown is. A similar parameter was used, but not defined, by Martínez et al. (1993) and Lamanna et al. (2002). It is defined here as the Crown Height Ratio (CHR). Taller crowns have larger CHR values and more squat teeth have smaller values. In general, this trend correlates with the overall crown size.

Crown curvature.

Curvature (usually of the mesial surface) is often mentioned in descriptions (e.g., Sampson et al., 1998; Azuma and Currie, 2000). However, aside from brief notes that this feature is variable (e.g., Mathur and Srivastava, 1987; Baszio, 1997), no rigorous attempt has been made to describe it. Sankey et al. (2002) utilized a variable that attempted to measure the distance between the distal face of a crown and the line made by their measure of crown height (Fig. 3) (Sankey et al., 2002). However, we have serious concerns about the repeatability of this metric and did not utilize it in this study.

Although CA defined above provides an indirect measure of curvature, it is advantageous to examine information held in the curves themselves (as was attempted by Sankey et al., 2002). First, however, the concept of curvature itself must be addressed. In doing so, we must refer to the specific faces of a theropod tooth that correspond to the locations of points AD. In most theropod crowns, the A, B, C, and D faces are the mesial, distal, lingual, and labial faces, respectively (Figs. 1 and 6A). As we saw in deriving CA, most crowns can be roughly described as cones whose apices have been translated toward B, such that in many cases they are located beyond B. Crown curvature relates to the fact that the A and B faces often form roughly parallel offset curves that are concave toward the caudal end of the skull (Fig. 6A). In a side view of the C or D (usually lingual or labial) face, the mesial and distal faces form the curved edges of the face (Fig. 6B and C). As all four faces are curved surfaces that are concave toward the crown base center, the curved edges of the labial or lingual faces formed by their intersection with the mesial or distal faces will appear, in lateral view, as distinct lines (in both conical and bladelike teeth). These linear expressions of the intersections between the mesial and distal faces with the sides are defined here as Curvature Profiles. In lateral view, the profiles of the mesial and distal faces show in 2D the curved nature in 3D of these surfaces.

Figure 6.

The curved A and B faces of theropod crowns. A: The mesial right dentary of Daspletosaurus (MOR 590) in lateral view showing the curved profiles of Rd2 and 3 (convex toward the rostral end of the skull). B: The right dentary of Gorgosaurus (ROM 1247) in medial view showing Rd6-11 in lingual view illustrating points A, B, and C and their corresponding faces (the D face is facing the page, directly opposite the C face). C: Schematic cross-section of ROM 1247 Rd6 in occlusal view, with points A, B, C, and D and the mesial face labeled. In cross-section, at any point basoapically on the crown, the A, B, C, and D faces are curved surfaces that are concave toward the crown base center. In a lateral view of the C face, the intersection between the A and C faces forms a distinct curved line that is concave toward the caudal end of the skull. Lines tracing these curved face intersections are the curvature profiles.

If curvature profile shapes vary by position or by taxon, then a line tracing one of these profiles will show similar variation (Fig. 7). As we can mathematically describe the shape of any line (see Anton, 1988), it should follow that we can devise functions to describe the lines that are the curvature profiles. The functions should be different as the lines are different, facilitating their comparison (see Rohlf, 1992). There are a number of practical ways to describe lines (e.g., Lohmann and Schweitzer, 1990; Rohlf, 1990), but because they are simply a series of n adjacent points, one effective method is to fit a curve to the points forming the line (see Rohlf, 1990, and references therein for discussion). The A face profiles of theropod crowns usually follow the general form of a power curve. From this family of curves, after a number of trials, we chose

equation image(2)

which provides a consistent and satisfactory fit to the profiles of the A faces of most theropods. The variable b describes the slope of the profile and represents a measure of the curvature of the crown face. It will be used to represent A face profile shapes.

Figure 7.

Variation in theropod A and B face curvature profiles. Lateral views and A and B face curvature profiles (scaled to A) of (A) T. rex Lmx7 (MOR 555), (B) Dromaeosaurus Ld5 (AMNH 5356), (C) Deinonychus Ld1 (YPM 5232), (D) T. rex Rd10 (BHI 3033), and (E) Majungatholus Lmx6 (FMNH PR2100).

We collected x, y data from curvature profiles by utilizing images of the teeth taken in lateral view. As it is often impossible to tell definitely if an isolated crown is from the left maxilla or the right dentary, we treat all crowns here as if oriented (e.g., while being held by researcher) such that the A face is facing toward the person, and the apex is pointing up. The sides are thus referred to as the left and right sides, respectively (nomenclature regarding the labial and lingual surfaces is meaningless for most isolated teeth). The long axis of a theropod crown is often substantially longer than the short axis and, as such, for most teeth, if the specimen is held in constant orientation with respect to a camera lens, the line of sight from the lens can usually be directed at an approximately analogous point (on the C or D face) on each crown examined. Using image-analysis software such as SigmaScan (SPSS Science, 1999), the profile is traced on an overlay of the digital image, oriented so that the base is horizontal and the A face is left (Fig. 8). Crown base orientations of in situ teeth vary by tooth position and taxon and it is important to ensure that the orientation is kept consistent between specimens (e.g., horizontal). The software converts the traced line into x, y coordinate data. Thirty data points were collected from each profile (by experimentation, 30 points represent a practical upper limit for images of small crowns, e.g., dromaeosaurids, taken with 50–80 mm lenses and scanned at 300 dpi). To help account for variations in camera angle, hand wobble, and cursor placement, each curve was digitized five times from five separate photographs of the tooth. Thus, 150 points were collected from each profile in groups of 30. The data from each analysis were then normalized to 1 (by dividing the data set by the range of x values), permitting comparisons among teeth of varying sizes. Function 2 was then fit to the data using nonlinear regression. The b value generated by function 2 is defined here as the A Face Crown Curve Slope (AFCCS). Crown curve slope of the A face values represents the mean b value from five replicate profile analyses. In general, smaller AFCCS values indicate greater curvature (e.g., in T. rex, d02 has an AFCCS value of 2.7, whereas the value for d12, with a more strongly curved apical mesial face profile, is 1.5).

Figure 8.

Collection of crown curve slope data. Schematic representation of the process of digitizing crown curves (black line) to collect x, y data (red dots) from which AFCCS values are generated. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Denticles.

In many theropods, the enamel ridges on the crowns (the carinae) are composed of a line of enamel bumps that are referred to as both denticles and serrations (see Abler, 1992). Notice of serrations has been taken since the earliest works on these animals (Buckland, 1824), and possession of carinae with denticles is considered to be the plesiomorphic theropod condition (see Gauthier, 1986; Holtz and Osmólska, 2004). It is a feature that, while not structurally uniform across taxa, theropods share with other dinosaurs (e.g., prosauropods, heterodontosaurids, and ankylosaurids), lower vertebrates (e.g., varanoids, sharks), and mammals (see Simpson, 1933; Thulborn, 1970, 1974; Martin, 1980; Carroll, 1988; Chandler, 1990; Coombs, 1990; Abler, 1992). Serration sizes have been qualitatively observed to vary among genera (e.g., Currie et al., 1990; Farlow et al., 1991; Abler, 1992; Fiorillo and Currie, 1994; Rauhut and Werner, 1995) and have long been quantified using the average number of denticles per unit distance (e.g., Ostrom, 1969b). This variable was named Serration Density by Farlow and Brinkman (1987). Theropod crowns range in size from about 3–8 mm in CH in small taxa like Coelophysis Cope, 1889 to ∼ 120 mm in very large T. rex teeth (Fig. 9A). As such, the unit of distance over which denticles are counted is either about 2 (for small crowns) or 5 (for large crowns) mm, using a CBL of 7 mm as the demarcation between the two classes after Farlow et al. (1991). As most data are not in the very small size range (see Rosenberg, 1995), 5 mm is the common unit of distance (see Currie et al., 1990; Farlow et al., 1991). However, the point on the carina where the measurements are taken has not been standardized in the literature. It is hoped that most workers have followed Farlow and Brinkman (1987) and Farlow et al. (1991) and have made counts as close to the mid-crown point on the carinae as possible, but this is generally not specified. Denticle widths and heights have been directly measured in an ambitious attempt to assess denticle size (see Sankey et al., 2002). These direct measurements are preferable to the cruder method of counting denticles per unit distance. However, to assess denticle size variation for in situ teeth using this method is prohibitively difficult in terms of logistics. The specimen in question or casts of the teeth must be observed using light microscopy. As most jaws of even moderately large theropods cannot be manipulated under a dissecting microscope to the degree necessary to measure denticle base lengths and heights, casts must be made of every tooth on every specimen of interest. This casting process and the resulting hundreds of denticles on each tooth that must then be measured is obviously a daunting task, but more problematic is the fact that many museums will understandably not allow fragile theropod dentitions to be cast. As such, in the interests of making progress in a timely fashion, we have elected at this time to assess denticle size and spacing by counts as we slowly tackle the logistics of amassing a data set of direct denticle measurements.

Figure 9.

Plots of CBL versus CH (A), CBL versus DAVG (B), CBL versus CA (C), and CBL versus CBW (D) for the 20 theropod taxa comprising the standard data set.

Chandler (1990), Farlow et al. (1991), and Smith (2002) independently noticed that denticle size can vary within individual carinae (e.g., T. rex premaxillary denticles are larger in the mid-crown than near the bases or tips). To account for this variation, Chandler (1990) measured mesial and distal serration densities for the basal, middle, and apical thirds of the carinae, a strategy we followed (Fig. 1), making the counts as close to the carinae bases, apices, and midpoints as possible. Basal Serration Density is the number of denticles per unit distance on the mesial and distal carinae, counted apically as close to the carinae bases as possible (MB and DB, respectively). Mid-Crown Serration Density is the number of denticles per unit distance in the middle of the mesial and distal carinae (MC and DC). Apical Serration Density is the number of mesial and distal denticles per unit distance counted basally from the most apical possible points of the carinae [MA and DA; Chandler (1990) used MT and DT, for mesial tip and distal tip]. As there are few published data on theropod serration densities that account for intracarina variation (see Chandler, 1990), it is useful to calculate Average Mesial and Distal Serration Densities (MAVG, DAVG) from the basal, mid-crown, and apical densities. We used MAVG and DAVG to examine denticle size and spacing variation within and among taxa. All serration counts are reported as the number of denticles per 5 mm (e.g., 10/5 mm). For very small crowns [e.g., Compsognathus Wagner, 1861 or Coelophysis], the carinae may be less than 5 mm long or the crowns may be so strongly curved as to make a 5 mm count impractical (see Currie et al., 1990). In such cases, we followed Farlow et al. (1991) and made counts over 2 mm, and then adjusted them to 5 mm to compare among taxa and facilitate the use of published data. As discussed by Farlow et al. (1991), prorating 1–2 mm counts to 5 mm can exaggerate counting errors, so the data must be collected with care. When only very small crowns are being compared, denticle data could be based solely on 2 mm counts. In some teeth, the carinae are short enough that the counted carina segments will overlap.

Serration densities are not uncommon in theropod descriptions (e.g., Allain and Taquet, 2000; Azuma and Currie, 2000; Hutt et al., 2001; Allain, 2002) and Rauhut and Werner (1995) considered the taxonomic utility of denticle size. They noticed that denticle sizes as generally measured overlapped between taxa and attempted to improve the situation by devising an independent index of size. They calculated a ratio of mesial to distal serration density, a parameter that had been previously examined in some detail, but not defined, by Chandler (1990). Rauhut and Werner's (1995) index is a ratio of MAVG to DAVG as defined in the broad sense, noting again that no controls exist on exactly where along the carinae denticle counts are taken. We discuss DSDI, the Denticle Size Density Index (after Rauhut and Werner, 1995), as a ratio of MAVG to DAVG as defined above. Smith (2002) explored calculating a DSDI value for the basal, mid-crown, and apical segments of the carinae but concluded that doing so offered little useful information.

Analyses.

Statistical analyses were generated using SPSS, SigmaStat (SPSS Science, 1997), and StatView (SAS Institute, 1999); results were illustrated using SigmaPlot. Smith (2002) found that biogeography (see Carrasco, 2000a, 2000b; Lieberman et al., 2002) appears to have no significant effect on dental variation in theropods (the effect of biogeography on the data was thus omitted here), but tooth position does have an effect. Heterodont taxa such as T. rex, Troodon, or Masiakasaurus are influenced by positional variation, but Smith (2002) found that positional effects on some other theropods (e.g., Dromaeosaurus, Allosaurus) are also significant, although these effects do not generally preclude comparisons between taxa.

We employed analysis of variance (ANOVA) (see Sokal and Rolf, 1995) to see if the variable taxon could account for a significant proportion of the variability observed in the data used here. The results were examined for significance using Fisher's PLSD (see Sokal and Rolf, 1995). StatView modifies Fisher's PLSD to permit the comparison of unequal sample sizes. However, since the probability of a type I error increases when sample sizes are not equal, we also used the more conservative Tukey-Kramer test (Kramer, 1956), which controls for overall error but detects fewer significant differences than some other tests. The Games-Howell test (Games and Howell, 1976) was not employed because it requires an n of at least 6 in each cell examined, a situation that will not always be possible in studies of fossil vertebrate teeth.

Taxonomically known and unknown teeth were compared against the standard data set to evaluate the robustness of this methodology in predicting the taxonomy of isolated crowns. The hypotheses were tested on the basis of morphological congruence between a test case tooth and a given taxon in the standard. As such, teeth of given taxonomic affinities (e.g., T. rex) would be expected to correlate more closely with that taxon than with all other taxa in the standard (i.e., Allosaurus crowns should not classify as T. rex). As group membership in the standard data set was determined a priori (we presumed robust taxonomic assignments for the specimens in the standard), stepwise discriminant function analyses (DFA) were employed to assess how effective the metrics discussed above were in correlating individual teeth with taxa (prediction of taxonomically unknown cases to specified group membership). Hypotheses of test case congruence with specific taxa were tested using squared Mahalanobis distances (D2) between the test cases and the centroids of the genus groups. AFCCS, MAVG, and DSDI were not used in the analyses (mesial denticles and mesial curvature profiles are often poorly preserved and including these variables significantly reduced the size of the data set). Raw data were used for CBL, CBW, CH, AL, CBR, and CHR. To remove size as a confounding variable (see Marko and Jackson, 2001) for DAVG and CA, which are not size metrics but which are affected by tooth size (Fig. 9B and C), the data were log-transformed and a principal components analysis (PCA) using orthogonal rotation and Varimax transformation (see SAS Institute, 1999) was run using AL, CA, CBL, CBR, CBW, CH, CHR, and DAVG (Table 1, Fig. 10). The log-transformed data were then regressed on the orthogonal scores for the first principal component, which accounted for 67.7% of the observed variation (Fig. 11; Appendix C); the residuals from these regressions for DAVG and CA produced variables that were corrected to remove size (CA2, DAVG2); these variables were then used in the DFA.

Table 1. Factor scores from the PCA*
 Un-rotatedOrthogonal
Factor 1Factor 2Factor 1Factor 2
  • *

    Factors (unrotated and the orthogonal solution) from the variable PCA run on the 20 taxa comprising the theropod standard.

CBL0.972−0.1640.9660.194
CBW0.984−0.0130.9240.340
CH0.9820.0080.9140.359
AL0.978−0.0170.9190.334
DAVG−0.7490.332−0.8180.042
CBR0.4840.5690.2490.704
CHR0.3730.8110.0590.891
CA0.804−0.1850.8170.115
Figure 10.

Plots of (A) the unrotated factors and the orthogonal solution and (B) the orthogonal scores generated by a PCA of the 20 theropod taxa comprising the standard using CBL, CBW, CH, AL, DAVG, CBR, CHR, and CA.

Figure 11.

Plots of log-transformed DAVG (A) and CA (B) data regressed against the factor scores for principal component 1, the residuals of which generate size-corrected versions of these variables (DAVG2 and CA2).

The DFA used multivariate analysis of variance (MANOVA) to determine significant differences between the various genera in the standard and then classified each data case to the genus group it is most similar to and calculated a canonical vector that maximizes the variation in the data (this is analogous to PCA; see Schulte-Hostedde and Millar, 2000). The mean values of the variables for each taxon as well as the weight values and constants were used to generate the classification scores using functions in the form:

equation image

where St is the classification score for a given taxon, Ct is a constant for that taxon, 1, 2, … n represent the variables used in the analysis, W represents the weight for a given variable, and X represents the value of a given variable. Wilks's lambda, Pillai's trace, and the Lawley-Hotelling trace were used to examine the significance of the discriminant functions. Wilks's lambda was also employed to examine the significance of the contributions of the independent variables.

We did not generate size-corrected variables from the log-transformed data for CBL, CBW, CH, AL, CBR, and CHR to use in the analyses in place of raw data as we did for DAVG and CA. Although this is a good strategy when the goal is to explore variance in shape (see Kowalewski et al., 1997; Marko and Jackson, 2001) and caveats to allometric effects are acknowledged, size remains an important factor in the study of theropod teeth, at least at this early stage before there is a solid understanding of ontogeny in theropod dentitions. As such, we have chosen not to remove size effects from the analyses. The strategy could well change as the research evolves and we begin to address ontogenetic issues.

Four groups of isolated teeth were examined (see Appendix B). The teeth in the first group are in situ T. rex crowns that were removed from the data set and tested against it. Each tooth in group 1 was extracted from the data set and a PCA was run to calculate DAVG2 and CA2 values. The DAVG2 and CA2 values were then used in the DFA. As the crowns in group 1 are T. rex teeth, they should absolutely correlate more strongly with T. rex than with any other taxon. Group 2 is comprised of unknowns that are almost certainly T. rex crowns. They were discovered with T. rex elements or in T. rex-bearing strata and qualitatively resemble T. rex teeth. FMNH PR2081 was found during the preparation of the skeleton. The SDSM teeth were found during excavation of the specimen. UCMP 131583 comes from a partial maxilla that is almost certainly T. rex (Molnar, 1991) and UNO 1234 comes from strata in which T. rex is the only very large predator (see Van Valkenburgh and Molnar, 2002). These teeth should all correlate more closely with T. rex than with any other taxon. The teeth in group 3 are almost certainly not T. rex. They are either known to be other genera or are unknowns from strata that make a T. rex affinity extremely unlikely. They are all morphologically dissimilar from T. rex and should not correlate most closely with it. Group 4 contains two types of data cases. SMU 74646, FUB PB Ther1, and CGM 81119 are not T. rex but are closer in size and shape to it than are the teeth in group 3. These crowns should not correlate most closely with T. rex. CM 47530 and YPM 54461 are unknowns from T. rex-bearing strata but have morphologies that are distinct from known T. rex teeth. As YPM 54461 and CM 30749 come from units in which T. rex is the only large predator, it is quite possible that they are juveniles of this taxon. As such, we might suspect that the observed differences in morphology are the result of ontogenetic variation. Regardless, these specimens are distinct from the T. rex teeth in the standard and should not be classified as T. rex.

RESULTS

Discrimination of Taxa

The ANOVA results (Table 2, Figs. 12 and 13) indicate that the variables “taxon” and “variable” are significant factors (P < 0.001 for both) in explaining the observed variability in the data. As is reasonable given their size, T. rex and Carcharodontosaurus teeth are significantly larger in CBL than any of the other theropods. It has been reported (e.g., Farlow et al., 1991; Baszio, 1997; Brinkman et al., 1998) that base width scales with base length in assemblages of isolated teeth; the in situ teeth here behave similarly (Fig. 9D). Regardless, Carcharodontosaurus and T. rex possess very large teeth. T. rex has significantly wider teeth than any other taxon. Except for CBW, the size variables separate the taxa in the standard into large theropods and small theropods, but there is little resolution within the groups. There is a strong correlation between crown size and curvature (expressed in apex displacement). The CA data for medium and large theropods reflect tall moderately curved crowns. The small theropods possess substantially more strongly curved teeth than the larger animals (Fig. 9C). Indeed, Bambiraptor, the smallest theropod examined, has the most strongly curved teeth. Between-taxon variation in CBR and CHR is substantially less than it is for any of the size variables, CA, or DAVG. DAVG values scale with tooth size and fall into two loose groups of larger and smaller theropods. However, there is no major distinction between very large theropods such as Carcharodontosaurus and moderately large forms such as Majungatholus.

Table 2. Two-way analysis of variance among 20 theropod taxa and eight variables
 Sum of squaresDegree of freedomF-ratioP
Taxon238782.811974.76<0.001
Variable1368089.248803.07<0.001
Residual475295.84   
Total2086090.34   
Figure 12.

Between-taxon comparisons of the size variables used in the two-way ANOVA. A: CBL. B: CBW. C: CH. D: AL. Error bars = ± 1 standard deviation.

Figure 13.

Between-taxon comparisons of the shape and denticle size variables used in the two-way ANOVA. A: CBR. B: CHR. C: CA. D: DAVG. Error bars = ± 1 standard deviation.

With 20 taxa and 8 variables, the discriminant analysis produced 8 functions (Wilks' lambda = 0.001 and 0.008 for the first and second functions; P < 0.0001 at both) and delineated the dental morphospace occupied by the included taxa according to the variables used (Table 3, Fig. 14). More than 97% of the specimens were correctly classified in a jackknifed analysis (Table 4). The Dilophosaurus, Ceratosaurus, Masiakasaurus, “Indosuchus,” Baryonyx, Suchomimus, Allosaurus, Carcharodontosaurus, Daspletosaurus, Troodon, Saurornithoides, Bambiraptor, Deinonychus, Dromaeosaurus, and Velociraptor teeth were classified 100% correctly. The analysis had the most difficulty classifying Liliensternus (85.7%) and Gorgosaurus (85.7% correct). Two Gorgosaurus teeth were assigned to Allosaurus and the misclassified Liliensternus tooth was assigned to Deinonychus. The remaining taxa were correctly classified more than 95% of the time.

Table 3. Results of discriminant analysis on the standard data set
 NonstandardizedClassification
Function 1Function 2Function 1Function 2
CBL0.44530.061611.77778.6310
CBW−0.2081−0.1269−7.1133−6.0298
CH−0.0397−0.0049−3.6043−2.1816
AL−0.0103−0.01040.0621−0.2558
DAVG21.147310.591584.448993.2269
CBR8.72567.4781199.9437177.2429
CHR−1.86613.2197109.831284.4083
CA22.2982−2.8480−50.7103−48.6647
Constant−6.7971−9.5931−189.4743−123.7134
Dilophosaurus centroid−1.03561.0798  
Liliensternus centroid−3.07920.9615  
Ceratosaurus centroid0.3470−1.3986  
Masiakasaurus centroid−3.74360.3764  
Indosuchus centroid−0.3998−1.4835  
Majungatholus centroid−2.1411−1.8717  
Baryonyx centroid−0.35089.6063  
Suchomimus centroid−1.51479.7350  
Allosaurus centroid−1.57650.3676  
Acrocanthosaurus centroid1.01792.4134  
Carcharodontosaurus centroid4.28210.0520  
Gorgosaurus centroid−0.37360.4552  
Daspletosaurus centroid−0.62820.5854  
Tyrannosaurus centroid3.3157−0.6887  
Troodon centroid−4.5619−5.0159  
Saurornithoides centroid−4.0698−4.9561  
Bambiraptor centroid−6.38390.6537  
Deinonychus centroid−3.6365−0.8525  
Dromaeosaurus centroid−3.04960.1030  
Velociraptor centroid−5.01890.7682  
Figure 14.

Plot of the scores for factors 1 and 2 of the discriminant analysis including 20 theropod taxa comprising the standard.

Table 4. Classification matrix for the discriminant analysis using 20 taxa comprising the standard data set*
TaxonDilLiliCerMasiIndoMajBarySuchAlloAcroCarcGorgDaspTrexTrooSaurBambDeinDromVelTotal
  • *

    97.8% of original group cases correctly classified.

Dil400000000000000000004
Lili060000000000000001007
Cer00100000000000000000010
Masi00010000000000000000010
Indo000060000000000000006
Maj00000250000000010000026
Bary000000800000000000008
Such000000040000000000004
Allo00000000220000000000022
Acro00000000025010000000026
Carc000000000060000000006
Gorg00000000200120000000014
Dasp000000000000700000007
Trex0000200000000113000000115
Troo000000000000006000006
Saur000000000000000800008
Bamb00000000000000001000010
Dein00000000000000000110011
Drom00000000000000000011011
Vel00000000000000000001313
TaxonDilLiliCerMasiIndoMajBarySuchAlloAcroCarcGorgDaspTrexTrooSaurBambDeinDromVel%
Dil1000000000000000000000100
Lili085.700000000000000014.300100
Cer0010000000000000000000100
Masi0001000000000000000000100
Indo0000100000000000000000100
Maj0000096.2000000003.900000100
Bary0000001000000000000000100
Such0000000100000000000000100
Allo0000000010000000000000100
Acro00000000096.203.900000000100
Carc0000000000100000000000100
Gorg0000000014.30085.700000000100
Dasp0000000000001000000000100
Trex00001.70000000098.3000000100
Troo0000000000000010000000100
Saur0000000000000001000000100
Bamb0000000000000000100000100
Dein0000000000000000010000100
Drom0000000000000000001000100
Vel0000000000000000000100100

Identification of Isolated Teeth

Application of the discriminant functions for classifying the test cases with known theropod taxa assigned all of the teeth in group 1 to T. rex (Table 5). The analyses in group 1 were all very strong, correctly classifying more than 96% of the teeth in the data set. Indeed, all of the analyses correctly assigned more than 96% of the specimens to their respective genera. In group 1, the crown that was most closely correlated with the centroid for T. rex was mx9 of MOR 555. The teeth that were the most poorly correlated with the T. rex centroid were d6 of BHI 3033 and mx3 of FMNH PR2081. In group 2, the DFA correlated all of the test cases with T. rex. The results for group 2 were robust; the most weakly correlated crown was SDSM 12047a at 21.48 D2, which is on the edge of being significantly distant from the centroid. The most strongly correlated tooth was UCMP 131583, at 3.01 D2. In group 3, the DFA was successful in not correlating any of the test cases with T. rex (Table 5). The results for group 4 were mixed. The DFA assigned CM 30749 to Gorgosaurus, FUB PB Ther1 to Ceratosaurus, and SMU 74646 to Acrocanthosaurus, which are all reasonable results. However, YPM 54461 was incorrectly classified as Majungatholus and CGM 81119 was incorrectly assigned to T. rex.

Table 5. Results of tests of taxonomic classification hypotheses for isolated theropod teeth in groups 1/4 using stepwise discriminant function analyses*
GroupSpecimenTaxon 1Taxon 2D2P%
  • *

    The taxon 1 column is the a priori taxonomic identification hypothesis for the specimen in question. The taxon 2 column is the classification returned by the analysis. The D2, p, and % columns indicate the number of squared Mahalanobis distance units returned by the analyses between the test case and the centroid of the genus group in the taxon 2 column, the significance of the result, and the percentage of the total dataset correctly classified by the analysis, respectively.

1AMNH 5027 mx1TyrannosaurusTyrannosaurus8.390.39697.8
1BH1 3033 d6TyrannosaurusTyrannosaurus10.330.24396.6
1FMNH PR2081 mx3TyrannosaurusTyrannosaurus17.280.02797.8
1MOR 555 mx9TyrannosaurusTyrannosaurus3.810.87497.8
1SDSM 12047 d4TyrannosaurusTyrannosaurus7.830.45197.5
2FMNH PR2081cf. TyrannosaurusTyrannosaurus5.160.74096.9
2SDSM 12047acf. TyrannosaurusTyrannosaurus21.480.00697.5
2SDSM 12047bcf. TyrannosaurusTyrannosaurus3.530.89797.2
2UCMP 131583cf. TyrannosaurusTyrannosaurus3.010.93497.8
2UNO 1234cf. TyrannosaurusTyrannosaurus4.360.82397.2
3BMNH R332MegalosaurusGorgosaurus3.460.90297.5
3UMNH VP6368MarshosaurusAllosaurus27.170.00197.5
3MOR 693cf. AllosaurusAllosaurus12.300.13897.2
3YPM 5278cf. DeinonychusDeinonychus43.97<0.000197.5
3AMNH 5456cf. DromaeosaurusDeinonychus44.03<0.000197.2
4SMU 74646cf. AcrocanthosaurusAcrocanthosaurus8.990.34397.2
4FUB PB Ther1cf. allosauridCeratosaurus26.640.00197.5
4YPM 54461cf. tyrannosauridMajungatholus15.270.05497.5
4CM 30749cf. tyrannosauridGorgosaurus1.840.98697.5
4CGM 81136cf. CarcharodontosaurusTyrannosaurus20.850.00897.8

DISCUSSION

Discrimination of Taxa

The results of the two-way ANOVA (Figs. 12 and 13) support the hypothesis that dental characters may have discrimination potential for theropods. T. rex and Carcharodontosaurus would be expected to have very large teeth given the size of these animals (they are among the largest known Mesozoic predators; see Sereno et al., 1996). Indeed, the teeth of these genera are generally so much larger than the teeth of other theropods in terms of CBL and CBW that these measurements alone might be useful in rejecting possible identifications for isolated crowns (Fig. 9D). Baszio (1997) felt that the very large size of tyrannosaurid teeth was sufficient to help identify them. The base lengths of even small T. rex crowns are significantly larger than the teeth of all but the largest theropods. The teeth of Carcharodontosaurus, however (and presumably Giganotosaurus) (Coria and Salgado, 1995), are larger than those of T. rex in terms of CBL, CH, and AL, and the apparent lack of heterodonty in Carcharodontosaurus (currently based on very few data) suggests that CH or AL might be synapomorphic for carcharodontosaurids. Along these lines, T. rex appears to have the widest crown bases of the entire known Theropoda and CBW might well be an autapomorphy of this genus (Smith, 2005). Daspletosaurus and Gorgosaurus, which are themselves very large predators, have on average smaller dentitions in terms of CH and AL than do the largest theropods. The position of Majungatholus is expected given its size (Sampson et al., 1998) and the brachydont nature of abelisaurids (Lamanna et al., 2002). The Allosaurus data, however, are curious. While the CBL and CBW data seem consistent with the size of the animal, the teeth are not as tall as expected. It is possible that further work will demonstrate that CH and AL have some systematic utility for Allosaurus: the taxon possesses a short dentition for its size (several truly huge Allosaurus specimens are known) (Madsen, 1976a). The teeth of Dromaeosaurus and Deinonychus are not much larger than those of Velociraptor. However, Deinonychus and Dromaeosaurus possess significantly more conical crowns (reflected in the CA data) with more centrally positioned apices. Although Velociraptor has a smaller dentition, mistakenly identifying a Velociraptor tooth as either Dromaeosaurus or Deinonychus is not impossible when issues of age and biogeography are disregarded. The results obtained here suggest that that CA might help discriminate some dromaeosaurids.

The DFA classification matrix (Table 4) is encouraging and suggests that the methods offered here permit successful discriminations of theropod genera. Even given the fairly small data set we used, 15 of the 20 taxa examined were correctly classified in 100% of the cases. Of the five remaining genera, three were correctly classified in more than 95% of the cases.

It is a pleasant surprise that T. rex and Masiakasaurus, the most heterodont dentitions in the analysis, were correctly classified for 98.3% and 100% of the cases. Given the degree of variation that occurs within the dentitions of these taxa, one could expect that a discriminant analysis, which is designed to emphasize the differences between data cases of different groups, would have high rates of misclassification for specimens in these groups. Indeed, that the two T. rex misclassifications occurred with “Indosuchus,” which is a significantly more basal theropod than a tyrannosaurid, speaks to the high degree of heterodonty in Tyrannosaurus.

It is not surprising that Gorgosaurus and Liliensternus were the most commonly misclassified groups, as both of these taxa were represented by small sample sizes of fairly simple teeth and visually discriminating Gorgosaurus and Daspletosaurus crowns is difficult. The statistics of small samples is a definite factor in these results as only one Liliensternus tooth was actually misclassified, weighting the results toward a more robust answer than might be expected with more data. For some taxa, however, this is a problem with no easy solution. For example, we already have data from almost every known in situ Carcharodontosaurus, Deinonychus, and Dromaeosaurus tooth. Indeed, even as the data set continues to be augmented with additional taxa and specimens, the number of teeth is likely to increase very slowly for some genera. For instance, although the Campanian (Late Cretaceous) dinosaur fauna of the western United States and Alberta is one of the best sampled in the world, Dromaeosaurus remains a very rare dinosaur (see Van Valkenburgh and Molnar, 2002; Farlow and Pianka, 2003) with in situ teeth currently limited to the holotype (AMNH 5356).

The misclassifications of Gorgosaurus with Allosaurus are significant. The results are suggestive that the teeth of Gorgosaurus are dissimilar from those of other tyrannosaurids as they are not being misclassified as T. rex or Daspletosaurus. This is heartening as Gorgosaurus and Daspletosaurus come from the same geographic area and formation (Farlow and Pianka, 2003). Perhaps these methods will be useful in rigorously testing taxonomic hypotheses of cf. Daspletosaurus and cf. Gorgosaurus crowns from the Western Interior region.

Identification of Isolated Teeth

Since all of the test cases in group 1 are known to be T. rex teeth, the classifications of these teeth have obvious implications for the use of the methods discussed here. It is thus fortunate that the DFA correctly assigned all of these teeth to T. rex. For the most part, the teeth are similar to the group centroid for T. rex, with D2 ranges of ∼ 4–17 (mean D2 for the group is 9.53). That there is substantial variation in the results is not surprising, given the heterodonty exhibited by T. rex (Smith, 2005). It was specifically because of this heterodonty that T. rex was selected as the taxon of comparison, the rationale being that if we can classify teeth of such a heterodont taxon, it should not be that difficult to classify other, more homodont dentitions.

It is likely that all of the specimens in group 2 are T. rex teeth. The cases were all classified as T. rex, and four of the five assignments are very robust. The mean distance from the T. rex centroid for group 2 is 7.51 D2, which is better than the mean obtained for group 1. The results are encouraging and indicate that the variables and methods discussed herein should permit correct classifications of unknown teeth for certain genus groups in the standard.

The differences in basal short-axis orientations in tyrannosaurid premaxillary teeth as compared to lateral crowns (e.g., Molnar and Carpenter, 1989; Molnar, 1991; Carr, 1999; Brochu, 2002; Currie, 2003) have led to the idea that it might be wise to compare the premaxillary set separately from the lateral dentitions for these theropods (see Currie et al., 1990; Farlow et al., 1991). We see no particular need to do this for most theropods (e.g., Allosaurus, Majungatholus) as the inclusion of highly derived tyrannosaurid premaxillary teeth does not appear to confound the analyses. However, it is certainly wise to keep track of such teeth in taxa with similarly derived premaxillary dentitions (e.g., Incisivosaurus Xu et al., 2002 during analyses so as not to confuse inherent variation with outliers.

In group 3, two of the teeth examined are known not to be Tyrannosaurus because they are teeth of other known taxa. The other three crowns, AMNH 5456, MOR 693, and YPM 5278, come from strata that should effectively preclude a T. rex assignment. The analyses correctly classified none of these test cases as T. rex (Table 5).

BMNH R332 is Rmx3 of the holotype of Megalosaurus hesperis Waldman, 1974 from the Jurassic of England. This tooth was classified as Gorgosaurus. The result is good in that the tooth was not assigned to T. rex, but the Gorgosaurus classification is puzzling. The BMNH R332 tooth is narrower (CBW = 11.79 mm) than Gorgosaurus (CBW = 12.87 mm), but not significantly so (P = 0.7818), and their morphologies are not that dissimilar. As such, in terms of morphology the Gorgosaurus classification makes some sense.

The UMNH VP6368 tooth is Rd4 of a specimen of Marshosaurus (Madsen, 1976a, 1976b) from the Upper Jurassic Morrison Formation of Utah. The DFA classified this tooth as Allosaurus. Marshosaurus and Allosaurus are both known from the same sequences and, in some cases, the same sites (Britt, 1991; Bilbey, 1999). It is possible that Marshosaurus might represent a juvenile morphotype of Allosaurus. The results here are intriguing given this hypothesis.

MOR 693 comes from the Upper Jurassic Morrison Formation in Montana and is labeled as Allosaurus fragilis. The crown is very similar to the in situ teeth of Allosaurus, and the DFA should not have classified this specimen as T. rex. The result was a good one. Not only was the tooth not classified as T. rex, it was assigned to Allosaurus, its predicted genus group, which is likely the correct one. Also, it did not fall significantly distant from the Allosaurus centroid. We are confident of the referral of this crown to Allosaurus.

YPM 5278 comes from the Lower Cretaceous Cloverly Formation (Yale quarry 64–65) from Carbon County, Montana. It was referred to Deinonychus by Ostrom (1969b; 1970) and is qualitatively extremely similar to the in situ teeth of Deinonychus and to isolated crowns thought to be Deinonychus (e.g., Brinkman et al., 1998). The DFA classified this tooth as Deinonychus. As with MOR 693, this is a good result, both because the crown was not classified as T. rex and because it was assigned to what is likely the correct genus group. Although YPM 5278 is significantly distant from the Deinonychus centroid (43.97 D2; P < 0.0001), this could be expected given the size of the current Deinonychus data set; the “true” dental morphospace occupied by the taxon is likely substantially larger than that currently demonstrated by the data at hand.

AMNH 5356 comes from the Late Cretaceous Dinosaur Park Formation in Alberta, Canada. It is cataloged with the type material of Dromaeosaurus and is likely a premaxillary tooth of that taxon. The DFA assigned this crown to Deinonychus (it is significantly distant from the Dromaeosaurus centroid at 44.03 D2), which is not a surprising result. Both of these taxa are represented by a small number of teeth in the standard and both have very similar dentitions. Moreover, the premaxillary condition for these animals is hardly represented in the standard. Classifying isolated premaxillary teeth of these taxa is likely to remain problematic until we have more data.

The results of the analyses of the group 4 teeth are mixed (Table 5). The SMU 74646 tooth comes from the Lower Cretaceous of Texas. It was recovered with a specimen of Acrocanthosaurus and was described and referred to that taxon by Harris (1998). It is quite likely an Acrocanthosaurus tooth and was classified as such by the DFA. This result, as with several in group 2, indicates that these methods, even with the current size of the standard, might have significant utility for testing specific affinity hypotheses for isolated crowns.

The FUB PB Ther1 tooth comes from a large theropod that lived in the Late Jurassic or earliest Cretaceous of what is now Portugal. It was described as Carnosauria indet. by Rauhut and Kriwet (1994). This crown superficially resembles the teeth of large tyrannosaurids. As such, because this tooth comes from a completely unknown animal that is not represented in the standard data set, the DFA's classification of it as Ceratosaurus is not unreasonable in terms of morphology. This result illustrates one of the issues related to describing isolated teeth from strata that have produced no viable candidate taxa against which to compare. The analyses cannot provide a genus-level classification for a tooth that came from a taxon for which there are no data in the standard. Regardless, however, a DFA will correlate a test case with one of the genus groups in the standard, presumably the group with which it is most morphologically congruent. Thus a given classification, even if it is not reasonable at the genus level, might have significance with respect to higher taxonomic levels. For example, Smith and Krause (2003) used the methods described herein to examine isolated teeth from the Late Cretaceous of India that had been referred to the Malagasy abelisaurid Majungatholus (see Mathur and Srivastava, 1987; Sampson et al., 1996, 1998). Although abelisaurids are certainly known from India (see Chatterjee, 1978; Lamanna et al., 2002; Wilson et al., 2003), most recent paleogeographic reconstructions postulate that India and Madagascar were separated by ∼ 80 Ma (see Krause et al., 1999). As such, the Majungatholus assignment for these specimens found by Smith and Krause (2003) is not particularly robust, but the abelisaurid classification that is implicit from their results makes sense. Analyzing any given isolated crown is thus potentially informative and interesting. That being said, however, the need for caution in analyzing “blind” teeth for which no provenance data are known about the data case should be obvious from this analysis. In such situations, something can perhaps be said about the morphological similarities of the isolated crown in question and specific clades of theropods, but it would probably be unwise to draw taxonomic conclusions from the results. The need for specimen context is likely always to remain important in these types of studies and should be included whenever possible as an additional line of evidence to support or refute a hypothesis about a given isolated tooth.

The CM 30749 and YPM 54461 specimens both come from Maastrichtian-aged (uppermost Cretaceous) rocks along the edge of the Western Interior Seaway in Montana and Wyoming (the Hell Creek and Lance formations). These teeth belong to large theropods and are labeled as tyrannosaurids in their respective collections, which are reasonable hypotheses. It seems odd given the diversity of predators in other Upper Cretaceous North American units (see Farlow and Pianka, 2003), but if problematic taxa are discounted, T. rex is the only very large predator definitively known from these sequences (Holtz, 1994a; Carr and Williamson, 2004). Teeth referred to a medium-sized tyrannosaur have been reported from the Lance Formation (Derstler, 1994). Given this, the Gorgosaurus classification for CM 30749 would seem to make sense. The classification of YPM 54461 as Majungatholus is puzzling, however, as the teeth of tyrannosaurids and abelisaurids are qualitatively quite dissimilar. YPM 54461 comes from a much smaller individual (in the size range of “Nanotyrannus”) than would be expected for Gorgosaurus or Daspleotosaurus, and as such is located within dental morphospace that is outside of the range occupied by the Tyrannosauridae according to the size and scope of the current data set. YPM 54461 might be a tooth of “Nanotyrannus” [the crown is similar to the descriptions of “Nanotyrannus” teeth offered by Bakker et al. (1988) or the “medium-sized tyrannosaur” discussed by Derstler (1994)]. “Nanotyrannus” might well represent a juvenile T. rex (see discussions in Carr, 1999; Brochu, 2002) and it is possible that YPM 54461 represents a juvenile T. rex crown. This would suggest that juvenile T. rex teeth have morphologies different enough from those of the adult animal to result in misclassifications. However, dental ontogeny in tyrannosaurids is very poorly understood (Smith, 2005), and contrary to Senter and Robins (2003), definitive juvenile T. rex dental material is almost completely lacking, so the hypothesis is currently impossible to test. The solution is obviously to incorporate juvenile dentitions into the standard data set used here. However, in order to do this, definitive teeth of juvenile theropods must be available. Such data are currently lacking for most theropods.

CGM 81136 comes from the Upper Cretaceous (Cenomanian) Bahariya Formation of Egypt. It was postulated by Smith et al. (2001b) to be a cf. Carcharodontosaurus tooth based on its size, shape, and location (the Bahariya Formation has produced Carcharodontosaurus material; see Stromer, 1931). Indeed, it qualitatively resembles cf. Carcharodontosaurus crowns from other places in Africa (Russell, 1996) as well as the only known in situ teeth for this taxon (see Sereno et al., 1996). We expected CGM 81136 to be classified as Carcharodontosaurus. The classification as T. rex is thus puzzling. The CH of CGM 81136 (64.12 mm) is slightly smaller than the mean for Carcharodontosaurus (78.39 mm; P = 0.4339) and is similar to the CH of T. rex (70.17 mm; P = 0.7568). The CBW of this crown (15.11 mm) is significantly less than the mean CBW for T. rex (26.12 mm; P = 0.0239), but is similar to that of Carcharodontosaurus (15.23 mm; P = 0.9807). As CGM 81136 is poorly preserved and only a small portion of the distal carina remains, an exploratory DFA was run in which denticle data were omitted. This analysis classified CGM 81136 as Acrocanthosaurus (18.4 D2; P = 0.010). It is possible that the results are real and that CGM 81136 did not come from the mouth of a Carcharodontosaurus. The hypothesized affinity for this specimen (see Smith et al., 2001b) was based on assumptions of the gross morphology of Carcharodontosaurus dentition but it is exactly these sorts of assignments for shed teeth that this article argues against. The Bahariya Formation preserves the remains of two other T. rex-sized theropods, Spinosaurus Stromer, 1915 and Bahariasaurus Stromer, 1934. CGM 81136 is very different in morphology from the teeth of any known spinosaurid (e.g., see Stromer, 1936; Kellner and Campos, 1996; Martill et al., 1996; Charig and Milner, 1997; Taquet and Russell, 1998; Sues et al., 2002). However, nothing is known about Bahariasaurus teeth. The type material was not dentigerous and was destroyed in WWII (Stromer, 1934, 1936) and no additional remains of this taxon have yet been described. The known material of Deltadromeus Sereno et al., 1996 shares characteristics with Bahariasaurus (Sereno et al., 1996; Rauhut, 2003), but there is no dental material known for this taxon. The phylogenetic relationships of both Deltadromeus and Bahariasaurus are poorly resolved at this time, but it is likely that these taxa are not closely allied with the Carcharodontosauridae (Sereno et al., 1996). Indeed, Deltadromeus has recently been reinterpreted as an abelisauroid (Sereno et al., 2004). It is thus possible, but probably unlikely, that CGM 81136 is a Bahariasaurus tooth. It is also possible that this specimen represents an as yet unknown theropod. Evidence of other predatory dinosaurs does exist in the Bahariya sequences (Stromer, 1934, 1936; Smith et al., 2001a), but as Carcharodontosaurus, Spinosaurus, and Bahariasaurus appear to have coexisted along the ancient Bahariya coastline (Smith et al., 2001b), the existence of a fourth genus of the same approximate size would seem very unlikely. The classification of CGM 81136 is thus probably a misclassification related either to the preservation of the specimen or the small amount of Carcharodontosaurus data that are available for comparison.

The results from the analyses involving groups 1 and 2 indicate that testing hypotheses of taxonomic classification for isolated cf. Tyrannosaurus teeth should be possible and that a decent degree of success should be expected. In particular, rigorous testing of published taxonomic hypotheses for isolated cf. Tyrannosaurus crowns (e.g., Carpenter and Young, 2002) can now begin. As data continue to be added to the standard, an additional step with T. rex will be to begin examinations of poorly preserved and partial teeth, which often comprise a significant portion of shed tooth assemblages (see Chandler, 1990).

The results obtained in this study indicate that, using the methods discussed above, it is possible to discriminate among theropod genera and to classify isolated teeth, often at the genus level, with numerical dental information. Here we have successfully correlated theropod teeth with genera using information taken from teeth of known taxonomic affinity. Even with the limited data set used here, the results were encouraging overall, suggesting that it should ultimately be possible to study even those taxa (the majority of theropods) for which there are only a limited number of teeth available. With the continuation of this work, we have reason to expect that it will be possible to sort out isolated tooth assemblages and identify unknown cases with a reasonable expectation of success. Ultimately it should be possible to utilize the vast theropod tooth data source, which has largely been ignored, to facilitate research into theropod systematics as well as into Mesozoic biogeography and paleoecology.

Acknowledgements

This article combines parts of two chapters of a PhD dissertation completed at the University of Pennsylvania by J.B.S. The research presented here has benefited strongly from discussions with R. Chapman, D. Krause, R. Sadleir, H.-D. Sues, S. Sampson, D, Krause, J. Farlow, P. Currie, G. Erickson, B. Grandstaff, T. Holtz, M. Lamanna, J.R. Smith, D. Chure, M. Norell, J.D. Harris, and A. Johnson. H.-D. Sues, H.-P. Schultze, D. Unwin, C. Herbel, S. Sampson, D. Krause, L. Murray, M. Norell, P. Sereno, D. Burnham, V. Schneider, C. Schaff, P. Barrett, P. Larson, B. Simpson, and J. Horner kindly provided specimen access. Supported by grants from the University of Pennsylvania Geobiology Fund, the Geological Society of America (grants 5936-96, 6139-97, 6329-98), the Dinosaur Society, and the Paleontological Society (to J.B.S.).

APPENDIX A

Table  . APPENDIX A. The theropod standard data set used in this article*
TaxonSpecimenSidePositionCBLCBWCHALCBRCHRCACA2MAMCMBDADCDBMAVGDAVGDAVG2
  • *

    Measured and derived variables as discussed in the text. For tooth positions where crowns were present on both sides of a skull, the values of the teeth were averaged into composite data cases. Values in bold were estimated using regression analysis.

DilophosaurusUCMP 37303Rightmx316.339.8724.6530.000.601.8480.590.10       15.00.10
DilophosaurusUCMP 37303Leftmax16.3510.2028.0033.000.622.0281.590.11       14.00.03
DilophosaurusUCMP 37303Leftmax19.1110.4035.2447.500.542.4982.660.13       15.00.09
DilophosaurusUCMP 37303Rightmax17.3310.1425.6631.000.591.7981.030.08       14.00.07
LiliensternusMBR 21751.4 max6.622.508.8312.400.381.3362.700.01 35.0  20.0 35.020.00.17
LiliensternusMBR 21751.3 max7.443.0010.2612.520.401.3867.370.09 30.0  25.0 30.025.00.38
LiliensternusMBR 21751.8Leftd015.093.508.029.210.691.5860.340.13 30.0  25.0 30.025.00.18
LiliensternusMBR 21751.8Leftd046.973.5010.6111.820.501.5268.480.12 25.0  20.0 25.020.00.14
LiliensternusMBR 21751.8Leftd158.343.5010.5312.620.421.2668.520.04 25.0  20.0 25.020.00.24
LiliensternusMBR 21751.8Leftd165.853.008.8410.120.511.5163.580.12 30.0  25.0 30.025.00.26
LiliensternusMBR 21751.9Right?d196.632.5011.2312.920.381.6968.970.19 35.0  30.0 35.030.00.46
CeratosaurusUMNHVP7819Leftpm0125.8614.7931.6341.280.571.2282.94−0.139.0  7.58.010.0 8.5−0.12
CeratosaurusUMNHVP7819Leftpm0223.0016.8141.8943.740.731.8284.760.0012.0  7.08.012.0 9.0−0.21
CeratosaurusUMNHVP7819Leftpm0324.0414.8841.6648.600.621.7384.380.0010.08.014.012.09.013.010.711.30.02
CeratosaurusUMNHVP7819Rightpm0120.2614.3138.6941.360.711.9184.200.0412.0  9.08.013.0 10.0−0.17
CeratosaurusUMNHVP7819Rightpm0322.6413.9039.6548.110.611.7583.94−0.0213.09.012.08.87.012.811.39.5−0.14
CeratosaurusUMNHVP5278Leftmx0125.4715.1051.3256.110.592.0285.51−0.0611.09.013.09.89.0 11.06.3−0.48
CeratosaurusUMNHVP5278Leftmx0329.6112.8861.7172.860.432.0886.00−0.0811.011.013.012.010.0 11.77.3−0.29
CeratosaurusUMNHVP5278Leftmx0532.9514.0075.0084.460.422.2886.770.009.512.816.013.011.016.312.813.40.22
CeratosaurusUMNHVP5278Leftmx0827.5210.5352.3861.540.381.9085.41−0.0112.014.020.012.512.015.015.313.20.19
CeratosaurusUMNHVP5278Leftmx1020.799.1238.1142.690.441.8383.940.0212.512.0 12.010.513.0 11.80.02
Masiakasaurus98312-1 Isolated4.473.937.468.590.881.6757.400.0617.017.017.014.014.515.017.014.5−0.33
Masiakasaurus95345-1 Isolated5.302.286.968.180.431.3156.250.0130.030.030.026.025.026.030.025.70.27
Masiakasaurus99016 Isolated6.153.0214.2513.510.492.3276.080.3222.525.027.527.522.517.525.022.50.13
Masiakasaurus95358 Isolated2.812.205.876.000.782.0949.890.17      35.032.00.11
Masiakasaurus95244-1 Isolated3.271.936.526.830.591.9953.690.17      35.030.00.15
Masiakasaurus98313-1 Isolated7.093.4810.4411.670.491.4768.190.1025.017.516.020.018.520.019.519.50.13
Masiakasaurus98203 Isolated4.622.5011.6412.140.542.5270.290.2925.030.0  15.022.527.518.8−0.13
Masiakasaurus93086-4 Isolated4.942.428.589.490.491.7462.550.1440.0  22.520.0  21.30.05
Masiakasaurus95435 Isolated4.942.426.808.200.491.3854.67−0.0135.022.530.023.820.023.829.222.50.12
Masiakasaurus96068-4 Isolated5.472.228.8610.150.411.6263.270.0827.526.325.020.016.717.526.318.10.10
IndosuchusAMNH 1955Leftmx0819.479.1029.4031.500.471.5182.53−0.01 10.016.7 12.0 13.411.50.01
IndosuchusAMNH 1753Leftpm0217.3012.9926.9028.500.751.5581.860.04 11.516.013.011.0 13.812.0−0.03
IndosuchusAMNH 1753Leftpm0316.5910.6627.2629.480.641.6481.830.0511.010.0 10.013.0 10.511.5−0.07
IndosuchusAMNH 1753Leftpm0417.3312.8528.0232.050.741.6281.830.02  12.09.0 10.012.010.0−0.18
IndosuchusAMNH 1753Rightpm0113.5510.5426.0029.000.781.9281.050.098.88.09.58.0  8.810.0−0.29
IndosuchusAMNH 1753Rightpm0215.9911.9631.8632.010.751.9983.310.08 8.09.08.510.0 8.59.3−0.31
MajungatholusFMNHPR2008Rightpm0212.999.4630.1131.920.732.3282.420.1712.311.015.711.011.515.013.012.5−0.15
MajungatholusUA 8716Rightpm0212.419.2627.0527.840.752.1881.890.159.010.015.08.810.014.011.310.9−0.26
MajungatholusUA 8716Rightpm0412.518.3027.6930.730.662.2181.410.1510.010.016.011.011.014.012.012.0−0.18
MajungatholusFMNHPR2100Leftmx0418.308.6236.9039.330.472.0283.890.049.08.510.710.09.011.09.410.0−0.18
MajungatholusFMNHPR2100Leftmx0618.379.2138.0839.870.502.0784.160.0510.59.510.010.09.011.010.010.0−0.18
MajungatholusFMNHPR2100Rightmx0518.938.8635.5441.690.471.8883.260.028.310.012.09.510.011.510.110.3−0.12
MajungatholusFMNHPR2100Rightmx0718.179.1038.6844.190.502.1383.760.049.09.711.09.59.010.09.99.5−0.23
MajungatholusFMNHPR2100Rightmx177.883.4712.4513.800.441.5871.720.0814.012.014.513.014.015.013.514.0−0.11
MajungatholusFMNHPR2100Leftd018.817.2019.8819.880.822.2679.290.199.09.010.710.09.011.09.610.0−0.45
MajungatholusFMNHPR2100Leftd0513.308.5625.3729.450.641.9180.570.0911.011.011.011.59.512.011.011.0−0.20
MajungatholusFMNHPR2100Leftd0714.247.7225.1327.860.541.7680.910.0610.511.011.010.011.011.510.810.8−0.17
MajungatholusFMNHPR2100Leftd1212.667.1219.9323.790.561.5778.310.0411.512.016.013.010.011.013.211.3−0.14
MajungatholusFMNHPR2100Leftd1312.536.6919.2124.310.531.5377.650.0313.011.713.012.010.512.012.611.5−0.12
MajungatholusFMNHPR2100Leftd1412.286.7017.8723.410.551.4676.770.0213.012.014.013.011.311.813.012.0−0.08
MajungatholusFMNHPR2100Leftd1511.726.2916.1921.480.541.3875.550.0114.012.813.514.010.511.013.411.8−0.10
MajungatholusFMNHPR2100Leftd179.335.3614.4817.930.571.5573.600.0614.015.016.014.011.012.015.012.3−0.17
MajungatholusFMNHPR2100Rightd0210.918.4822.8820.820.782.1081.720.1510.08.010.510.08.510.09.59.5−0.41
MajungatholusFMNHPR2100Rightd0313.538.2722.8725.980.611.6979.930.0510.09.510.010.59.011.69.810.4−0.22
MajungatholusFMNHPR2100Rightd0413.907.9024.0826.120.571.7380.670.0613.09.510.011.510.011.510.811.0−0.16
MajungatholusFMNHPR2100Rightd0613.507.7725.7527.540.581.9181.260.0911.09.513.011.010.511.511.211.0−0.19
MajungatholusFMNHPR2100Rightd1012.828.5923.7627.650.671.8579.970.1012.010.816.012.010.013.312.911.8−0.15
MajungatholusFMNHPR2100Rightd1113.177.0523.0026.020.541.7579.940.0612.011.014.010.59.513.012.311.0−0.17
MajungatholusFMNHPR2100Rightd1511.265.7918.7322.490.511.6677.340.0713.011.515.012.011.514.013.212.5−0.10
MajungatholusFMNHPR2100Rightd1612.885.2518.7123.060.411.4577.620.0213.012.215.013.211.715.013.413.30.03
MajungatholusFMNHPR2278Rightmx0216.908.6737.6340.160.512.2383.930.1012.010.012.712.09.314.011.611.8−0.09
MajungatholusFMNHPR2278Rightmx0317.108.8135.0141.030.522.0583.010.0712.012.013.511.610.013.012.511.5−0.08
BaryonyxBMNH R9951Rightpm0413.0611.2431.3732.290.862.4782.960.34       35.00.66
BaryonyxBMNH R9951Rightpm0610.497.9023.7224.770.752.3680.560.35       35.00.61
BaryonyxBMNH R9951a Isolated11.6911.1928.7229.220.962.5082.420.36       35.00.62
BaryonyxBMNH R9951d Isolated15.7612.0534.8037.410.762.3783.390.30       35.00.72
BaryonyxBMNH R9951e Isolated13.1810.8829.6730.520.832.3282.600.32       35.00.68
BaryonyxBMNH R9951f Isolated12.1210.3527.1930.460.852.5181.140.34       35.00.63
BaryonyxBMNH R9951h Isolated16.4215.1938.5543.880.932.6783.600.32       35.00.70
BaryonyxBMNH R9951n Isolated16.4713.6534.1238.110.832.3183.080.29       35.00.73
SuchomimusUC G89-5 Isolated18.9015.2062.9470.640.813.3385.780.30       27.50.52
SuchomimusUC G54-4 Isolated20.8018.1056.9464.220.872.7485.540.25       27.00.57
SuchomimusUC G48-9 Isolated18.7013.3052.6660.200.712.8285.060.29       35.00.76
SuchomimusUC G67-1 Isolated19.2014.4054.3455.600.752.8385.940.28       29.00.60
AllosaurusYPM1333Rightpm0212.466.0028.6525.490.962.3083.790.2211.810.09.811.910.011.010.511.0−0.33
AllosaurusYPM1333Rightpm0312.0011.0720.6925.590.921.7278.270.0911.810.013.711.010.012.811.811.3−0.21
AllosaurusYPM1333Rightpm0513.049.2826.9830.390.712.0781.180.1512.610.015.712.011.017.712.813.6−0.06
AllosaurusSDSM25248Leftpm0320.3612.2949.5754.000.602.4385.220.0810.09.011.010.09.012.010.010.3−0.17
AllosaurusSDSM25248Leftpm0516.018.2334.0539.740.512.1382.760.1113.016.024.014.012.515.017.713.80.04
AllosaurusUMNHVP9211Leftmx0414.997.3330.0237.510.492.0081.510.0814.011.515.012.010.015.013.512.3−0.06
AllosaurusUMNHVP9211Leftmx0615.227.0433.4837.900.462.2082.770.1315.011.015.015.011.019.013.715.00.09
AllosaurusUMNHVP9275Rightmx0712.087.4525.4330.530.622.1180.090.1818.014.021.017.017.518.017.717.50.14
AllosaurusUMNHVP9273Rightmx0714.067.5928.5032.120.542.0381.690.1415.013.520.016.014.018.516.216.20.13
AllosaurusUMNHVP9273Rightmx0614.787.2125.5229.820.491.7380.800.1016.012.522.018.015.018.016.817.00.22
AllosaurusUMNHVP9218Leftmx0117.3213.0338.2542.190.752.2183.830.1211.09.520.012.011.513.013.512.2−0.08
AllosaurusUMNHVP9369Rightd0611.778.2625.8029.100.702.1980.640.1916.018.020.015.013.518.018.015.50.01
AllosaurusUMNHVP9365Rightd0210.639.7724.6227.610.922.3280.130.1912.010.015.012.011.013.712.312.2−0.24
AllosaurusUMNHVP1251Rightpm0516.1013.8240.8540.610.862.5484.860.1911.010.014.012.011.017.511.713.5−0.06
AllosaurusCM 21703Leftpm0214.0512.5234.3134.820.892.4483.690.1611.010.011.09.010.011.010.710.0−0.33
AllosaurusCM 21703Leftpm0312.7910.5034.2036.530.822.6783.130.1711.09.511.59.510.010.010.79.8−0.38
AllosaurusCM 21703Leftpm0413.7310.6533.1935.510.782.4283.010.1511.510.512.79.511.011.011.610.5−0.29
AllosaurusLACM 46030Comp.pm0116.1015.3033.9036.690.952.1083.220.048.09.513.09.510.0 10.26.5−0.62
AllosaurusLACM 46030Comp.pm0216.0014.6033.8935.990.912.1283.330.128.09.312.59.810.312.89.910.9−0.20
AllosaurusLACM 46030Comp.pm0315.5014.9036.8138.300.962.3783.930.159.09.513.010.810.013.310.511.3−0.20
AllosaurusLACM 46030Comp.pm0416.3013.5037.6938.980.832.3284.130.139.39.812.510.310.013.010.511.1−0.19
AllosaurusLACM 46030Leftpm0517.5012.8038.8540.260.742.2384.310.1211.011.012.011.511.013.511.312.0−0.09
AcrocanthosaurusNCSM 14345Comp.pm0121.7016.2652.2355.150.752.4185.640.1314.415.117.912.714.118.815.815.20.14
AcrocanthosaurusNCSM 14345Comp.pm0326.8416.5672.3577.510.622.7186.730.1113.412.419.012.413.719.114.915.10.19
AcrocanthosaurusNCSM 14345Comp.mx0126.7317.5662.6071.290.662.3385.950.0813.512.019.613.614.218.215.015.30.23
AcrocanthosaurusNCSM 14345Comp.mx0235.2420.5979.2390.020.602.2286.780.0212.112.319.613.713.419.214.615.40.33
AcrocanthosaurusNCSM 14345Comp.mx0436.6020.6487.0997.500.562.3687.160.0312.212.116.213.013.619.513.515.40.33
AcrocanthosaurusNCSM 14345Comp.mx0542.0720.7493.08107.900.492.2187.35−0.0312.8 21.012.912.9  14.00.31
AcrocanthosaurusNCSM 14345Leftmx1322.4310.8733.7941.870.481.5183.110.00 15.0 14.016.0  15.00.27
AcrocanthosaurusNCSM 14345Comp.mx1417.118.5525.0332.120.501.4680.550.0218.0  15.3   15.00.20
AcrocanthosaurusNCSM 14345Rightmx0337.2121.4490.75101.460.582.4487.310.0312.111.016.811.715.317.813.314.90.30
AcrocanthosaurusNCSM 14345Rightmx0640.7917.8682.3090.250.442.0287.20−0.0412.813.018.012.312.020.014.614.80.37
AcrocanthosaurusNCSM 14345Rightmx0831.9416.7366.7876.590.522.0986.390.0011.3  12.114.9  13.50.21
AcrocanthosaurusNCSM 14345Rightmx0929.1114.4354.9764.000.501.8985.66−0.0113.0  13.3   13.30.20
AcrocanthosaurusNCSM 14345Rightmx1126.6411.7839.4046.470.441.4884.23−0.0416.015.0 13.8   14.00.27
AcrocanthosaurusNCSM 14345Leftd0114.4211.7729.4635.420.822.0481.530.1413.4  13.3   14.0−0.01
AcrocanthosaurusNCSM 14345Comp.d0223.9117.1058.5563.550.722.4485.950.11   12.513.018.0 14.50.14
AcrocanthosaurusNCSM 14345Leftd0329.6317.6372.2379.200.592.4486.700.0713.813.3 15.0   15.00.24
AcrocanthosaurusNCSM 14345Comp.d0429.1119.3370.6277.810.662.4286.570.0612.613.318.312.611.5 14.713.00.11
AcrocanthosaurusNCSM 14345Leftd0530.6018.7560.4868.810.611.9886.080.0213.3  13.013.018.3 14.80.27
AcrocanthosaurusNCSM 14345Comp.d0731.1017.1964.8576.070.552.0986.200.0113.515.918.312.016.513.015.913.80.22
AcrocanthosaurusNCSM 14345Leftd0826.0816.5843.0158.070.641.6584.240.0115.015.0 14.013.317.5 14.90.28
AcrocanthosaurusNCSM 14345Leftd1028.2614.3547.4755.540.511.6885.090.0114.017.0  14.521.0 16.00.36
AcrocanthosaurusNCSM 14345Leftd1224.9613.2238.9649.000.531.5683.93−0.0115.017.018.814.015.5 16.914.50.26
AcrocanthosaurusNCSM 14345Leftd1420.4211.4633.1338.860.561.6283.010.0413.010.0 14.015.0  14.50.19
AcrocanthosaurusNCSM 14345Leftd1715.379.1016.0422.610.591.0476.51−0.0412.5  13.016.7  15.00.22
AcrocanthosaurusNCSM 14345Rightd0528.9816.5468.1572.160.572.3586.660.0717.5  14.017.5  15.50.27
AcrocanthosaurusNCSM 14345Rightd0631.3516.7162.1572.970.531.9886.090.0212.014.019.016.312.819.515.016.20.37
CarcharodontosaurusSGM Din-1 Isolated41.5315.0980.6889.820.361.9487.12−0.0910.08.012.010.310.014.010.011.40.19
CarcharodontosaurusSGM Din-1Rightmx0341.4615.1571.0182.320.371.7186.73−0.1310.08.010.210.39.012.09.410.40.14
CarcharodontosaurusSGM Din-1Rightmx0541.0414.8873.9680.590.361.8086.95−0.129.27.710.010.09.011.29.010.10.10
CarcharodontosaurusSGM Din-1Rightmx0641.1714.8873.1779.510.361.7886.93−0.128.58.910.010.79.011.09.110.20.11
CarcharodontosaurusSGM Din-1Rightmx0839.9114.4973.9980.020.361.8586.95−0.119.08.09.010.08.211.88.710.00.08
CarcharodontosaurusSGM Din-1 Isolated46.6516.8897.55102.250.362.0987.72−0.128.08.011.69.59.011.09.29.80.08
GorgosaurusROM1247Rightd0212.4011.6025.5325.990.932.0681.520.16  15.012.811.012.0 11.9−0.20
GorgosaurusROM1247Rightd0317.8214.2542.2142.390.802.3784.950.1510.510.012.012.012.515.210.813.2−0.03
GorgosaurusROM1247Rightd0421.2810.7739.6845.910.511.8684.030.02 12.012.511.511.012.812.311.80.01
GorgosaurusROM1247Rightd0621.2412.8943.8453.440.612.0684.240.0611.011.012.712.512.014.711.613.10.07
GorgosaurusROM1247Rightd0819.9613.5643.3144.010.682.1785.020.11 10.511.512.014.014.211.013.40.05
GorgosaurusROM1247Rightd0917.817.6731.9132.750.431.7983.220.0512.012.0 12.012.512.012.012.10.00
GorgosaurusROM1247Rightd1118.4811.4137.0041.350.622.0083.660.08 10.014.313.013.0 12.213.00.03
GorgosaurusROM1247Rightd1317.729.2131.3041.500.521.7781.940.0610.0   15.0 10.015.00.17
GorgosaurusROM1247Rightd1513.698.8322.1924.900.651.6279.760.09    14.0  14.00.03
GorgosaurusROM1247Rightmx0426.4813.4054.8558.750.512.0785.860.019.09.010.012.011.511.08.711.50.03
GorgosaurusROM1247Rightmx0920.5510.5740.3136.920.511.9685.210.0612.012.514.012.011.0 12.811.5−0.04
GorgosaurusBMNH R4863Rightd0428.8319.8255.9959.020.691.9486.030.0112.011.015.012.010.012.512.711.50.04
GorgosaurusBMNH R4863Rightd0826.3717.7044.5751.280.671.6984.81−0.0114.013.014.013.010.012.013.711.70.06
GorgosaurusBMNH R4863Rightd1024.4718.4653.3757.270.752.1885.710.0613.010.013.012.010.014.012.012.00.01
DaspletosaurusAMNH5346Leftmx0227.0022.6374.7880.860.842.7786.790.0911.712.013.812.011.012.812.511.9−0.02
DaspletosaurusMOR590Rightd0218.0212.6836.4339.520.702.0283.710.1115.712.0  11.216.813.914.00.07
DaspletosaurusMOR590Rightd0322.8817.8152.6256.490.782.3085.620.0711.511.312.010.810.011.811.610.9−0.11
DaspletosaurusMOR590Rightd0522.8617.2854.5557.940.762.3985.800.0713.810.5 12.79.310.012.210.7−0.13
DaspletosaurusMOR590Rightd0722.5316.6349.5749.810.742.2085.700.0612.010.012.812.09.0 11.610.5−0.13
DaspletosaurusMOR590Rightd0822.3212.2946.7850.650.552.1085.090.0412.012.8 11.010.011.012.410.7−0.08
DaspletosaurusMOR590Rightd1019.1912.1734.9335.690.631.8283.820.0513.8  12.811.011.1 11.6−0.05
TyrannosaurusMOR 555Leftmx0742.8628.3572.6780.210.661.7086.90−0.098.811.112.09.011.013.710.611.20.17
TyrannosaurusMOR 555Leftmx0837.3422.8265.1170.530.611.7486.56−0.079.09.313.89.010.413.110.710.80.10
TyrannosaurusMOR 555Leftmx0933.7224.4455.1156.720.721.6386.09−0.057.88.814.08.610.813.710.211.00.08
TyrannosaurusMOR 008Leftd0346.0533.7891.0093.000.731.9887.62−0.10 8.012.0 7.011.010.09.0−0.04
TyrannosaurusMOR 008Leftd0539.2931.2578.0079.500.801.9987.23−0.07 9.0  9.0 9.09.0−0.09
TyrannosaurusMOR 008Comp.d0638.2327.0775.0076.500.711.9687.11−0.07 8.3  8.56.08.39.3−0.06
TyrannosaurusMOR 008Rightd0835.0026.6065.0067.000.761.8686.66−0.067.0   9.0 7.09.0−0.10
TyrannosaurusMOR 008Rightd1031.5021.0055.0056.500.671.7586.07−0.07 9.0  8.5 9.08.5−0.16
TyrannosaurusFMNH PR2081Leftpm0336.0624.0063.6571.970.671.7786.38−0.108.47.012.08.07.110.09.18.4−0.13
TyrannosaurusFMNH PR2081Leftmx0545.4632.6394.06108.360.722.0787.43−0.107.36.512.98.67.511.28.99.1−0.03
TyrannosaurusFMNH PR2081Leftmx0739.4127.1875.7586.340.691.9286.88−0.087.07.511.58.38.311.48.79.3−0.04
TyrannosaurusFMNH PR2081Leftmx0838.5626.2072.5583.440.681.8886.75−0.087.07.012.09.18.811.68.79.80.01
TyrannosaurusFMNH PR2081Rightmx0144.8632.6091.12101.550.732.0387.43−0.117.06.08.27.27.09.87.18.0−0.14
TyrannosaurusFMNH PR2081Rightmx0247.6937.58105.26117.640.792.2187.73−0.117.07.011.57.07.010.08.58.0−0.14
TyrannosaurusFMNH PR2081Rightmx0346.7437.21108.82122.990.802.3387.76−0.087.06.013.38.37.010.68.88.6−0.10
TyrannosaurusFMNH PR2081Rightmx1035.6523.4861.0471.650.661.7186.16−0.086.57.011.88.09.012.38.49.80.00
TyrannosaurusFMNH PR2081Rightmx1127.8618.1845.9649.900.651.6585.15−0.027.511.013.79.710.015.810.711.80.09
TyrannosaurusFMNH PR2081Rightmx1218.9613.2029.7232.170.701.5782.550.039.09.014.810.012.013.010.911.7−0.02
TyrannosaurusFMNH PR2081Comp.d0240.7624.5175.0381.290.601.8487.00−0.118.07.012.99.57.09.49.38.6−0.08
TyrannosaurusFMNH PR2081Comp.d1226.4719.1344.2947.710.721.6784.98−0.018.57.514.09.310.513.510.011.10.02
TyrannosaurusFMNH PR2081Leftd0352.0732.6787.4295.970.631.6887.43−0.178.06.511.07.56.511.88.58.60.01
TyrannosaurusFMNH PR2081Leftd0548.7433.9488.8793.940.701.8287.51−0.147.07.310.08.07.010.08.18.3−0.06
TyrannosaurusFMNH PR2081Leftd0640.2127.3778.0984.190.681.9487.10−0.089.09.011.08.09.011.09.79.3−0.03
TyrannosaurusFMNH PR2081Leftd0834.4925.7166.2574.660.751.9286.47−0.076.07.014.07.08.011.09.08.7−0.14
TyrannosaurusFMNH PR2081Leftd0934.6924.5163.5766.840.711.8386.53−0.047.58.814.09.89.013.810.110.90.06
TyrannosaurusBHI 3033Comp.mx0145.8834.9793.6898.790.762.0487.62−0.117.58.09.86.87.79.98.48.1−0.13
TyrannosaurusBHI 3033Comp.mx0251.9834.23102.21108.000.661.9787.81−0.167.97.510.56.67.28.08.37.3−0.17
TyrannosaurusBHI 3033Comp.mx0348.6333.03115.30118.820.682.3788.09−0.107.27.010.76.88.28.28.37.7−0.17
TyrannosaurusBHI 3033Comp.mx0449.7129.58103.42110.830.592.0887.81−0.127.08.39.58.48.011.27.98.8−0.02
TyrannosaurusBHI 3033Comp.mx0548.1531.4794.8999.430.651.9787.67−0.127.08.013.78.27.010.29.68.5−0.06
TyrannosaurusBHI 3033Comp.mx0638.4827.2073.7079.430.711.9286.93−0.077.54.76.04.04.510.88.49.6−0.02
TyrannosaurusBHI 3033Comp.mx0829.2519.0148.5556.350.631.6485.01−0.077.810.312.88.110.210.010.39.4−0.07
TyrannosaurusBHI 3033Comp.mx0932.0821.8655.3456.570.681.7386.11−0.048.59.512.69.59.912.310.210.60.03
TyrannosaurusBHI 3033Leftmx1121.2514.5731.9632.140.691.5083.340.0210.015.115.210.914.014.713.413.20.12
TyrannosaurusBHI 3033Rightmx0740.1923.6466.2869.940.591.6586.70−0.119.08.514.38.99.011.810.69.90.06
TyrannosaurusBHI 3033Comp.d0126.2318.3245.1746.310.701.7285.22−0.039.59.010.48.88.910.59.69.4−0.12
TyrannosaurusBHI 3033Comp.d0240.6626.3671.9978.020.651.7786.89−0.118.87.09.48.48.29.48.48.6−0.07
TyrannosaurusBHI 3033Comp.d0346.2032.7094.9796.000.721.9186.89−0.156.07.011.07.57.07.08.07.2−0.21
TyrannosaurusBHI 3033Comp.d0446.2831.8889.0190.850.691.9487.56−0.117.07.38.68.07.710.47.68.7−0.06
TyrannosaurusBHI 3033Comp.d0637.6527.7462.0166.100.741.4886.44−0.137.47.79.48.48.09.68.18.7−0.05
TyrannosaurusBHI 3033Comp.d0733.3823.1550.5453.480.691.5185.65−0.089.18.511.09.09.413.49.59.90.01
TyrannosaurusBHI 3033Comp.d0930.6221.4246.8350.620.701.5385.29−0.077.78.911.09.19.210.99.29.7−0.03
TyrannosaurusBHI 3033Comp.d1028.0520.4441.5645.040.731.4884.71−0.058.79.912.89.210.413.510.511.00.05
TyrannosaurusBHI 3033Leftd1315.019.2215.8517.410.611.0676.45−0.0213.613.616.115.415.716.014.415.70.23
TyrannosaurusBHI 3033Rightd0545.8932.1777.7478.960.701.6987.25−0.136.58.010.39.07.011.08.39.00.00
TyrannosaurusBHI 3033Rightd0833.1224.7554.1256.480.751.6385.98−0.048.09.013.89.010.014.910.311.30.09
TyrannosaurusBHI 3033Rightd1123.6416.6130.3433.090.701.2882.84−0.0511.011.013.811.010.912.911.911.60.07
TyrannosaurusBHI 3033Rightd1218.5213.5621.9124.250.731.1880.12−0.0111.214.115.913.014.014.913.714.00.16
TyrannosaurusBHI 3033Comp.pm0127.3814.2744.2250.210.521.6284.85−0.0510.99.511.410.59.912.710.611.00.05
TyrannosaurusBHI 3033Comp.pm0334.8721.7558.6660.010.621.6886.33−0.0610.89.112.510.09.812.210.810.60.07
TyrannosaurusBHI 3033Rightpm0231.7518.0450.1456.280.571.5885.51−0.0910.79.09.011.28.58.09.69.2−0.05
TyrannosaurusBHI 3033Rightpm0430.0519.0352.8053.940.631.7685.92−0.0410.29.010.010.08.711.59.710.1−0.03
TyrannosaurusAMNH 5027Comp.pm0129.8416.4542.5550.210.561.4284.59−0.0910.09.111.010.09.611.610.010.40.05
TyrannosaurusAMNH 5027Comp.pm0330.9419.4645.4258.260.631.4784.83−0.0910.58.511.010.59.511.510.010.50.06
TyrannosaurusAMNH 5027Rightpm0229.9316.9443.6454.330.571.4684.70−0.1010.38.29.011.08.08.99.29.3−0.04
TyrannosaurusAMNH 5027Rightpm0431.8621.1854.6260.010.661.7185.87−0.0610.89.09.211.28.910.09.710.0−0.01
TyrannosaurusAMNH 5027Comp.mx0138.8931.5785.4793.140.812.2087.28−0.067.07.58.77.08.410.07.78.5−0.16
TyrannosaurusAMNH 5027Comp.mx0341.4630.59103.98109.250.742.5287.81−0.047.06.910.38.97.810.38.19.0−0.11
TyrannosaurusAMNH 5027Comp.mx0548.6031.17102.44104.790.612.0587.87−0.117.27.012.17.87.512.38.89.20.01
TyrannosaurusAMNH 5027Comp.mx0638.3724.4277.6488.330.621.9986.99−0.088.58.011.18.07.411.49.28.9−0.07
TyrannosaurusAMNH 5027Comp.mx0740.0125.3179.7084.230.582.0687.32−0.099.08.610.48.07.411.09.38.8−0.08
TyrannosaurusAMNH 5027Comp.mx0837.5426.0582.1484.040.692.1987.35−0.059.38.310.39.18.310.09.39.1−0.10
TyrannosaurusAMNH 5027Rightmx1125.9216.4637.5742.720.641.4584.05−0.049.510.011.010.510.514.010.211.70.09
TyrannosaurusAMNH 5027Leftmx0450.0133.93104.06115.510.682.0887.75−0.137.08.510.07.58.010.07.87.8−0.13
TyrannosaurusSDSM 12047Leftmx0149.4934.82100.89103.670.702.0487.84−0.149.57.010.57.06.58.09.07.2−0.20
TyrannosaurusSDSM 12047Leftmx0236.7728.6881.6088.330.782.2287.16−0.057.57.08.06.57.011.57.58.3−0.18
TyrannosaurusSDSM 12047Leftmx0347.1732.77117.06120.690.692.4888.11−0.097.57.011.06.57.58.58.57.5−0.22
TyrannosaurusSDSM 12047Leftmx0446.6836.68108.53116.360.792.3387.88−0.097.57.011.07.06.710.58.58.1−0.15
TyrannosaurusSDSM 12047Comp.mx0843.6027.5087.85105.700.632.0187.18−0.117.58.011.07.08.011.08.88.7−0.06
TyrannosaurusSDSM 12047Leftmx1042.5126.6891.27103.510.632.1587.37−0.098.08.011.07.07.810.79.08.5−0.10
TyrannosaurusSDSM 12047Comp.mx1130.9720.1751.1457.920.651.6485.40−0.088.57.89.59.38.510.08.69.3−0.07
TyrannosaurusSDSM 12047Rightmx0648.0033.14105.46116.940.692.2087.76−0.116.0   7.0  8.0−0.13
TyrannosaurusSDSM 12047Rightmx1222.5012.8332.0839.310.571.4382.87−0.078.59.012.57.59.011.010.09.2−0.13
TyrannosaurusSDSM 12047Leftd0444.9032.89105.61115.880.732.3587.75−0.09   7.56.79.0 7.7−0.19
TyrannosaurusSDSM 12047Comp.d0542.3728.1196.2898.900.662.2887.72−0.087.86.910.58.57.59.18.48.4−0.14
TyrannosaurusSDSM 12047Comp.d0640.2228.3782.2393.040.712.0487.11−0.098.07.010.08.07.010.58.38.5−0.12
TyrannosaurusSDSM 12047Leftd0739.1026.4674.6680.160.681.9186.99−0.067.28.012.08.09.015.09.110.70.07
TyrannosaurusSDSM 12047Comp.d0834.7725.6068.2475.890.741.9686.59−0.066.97.510.38.17.511.48.29.0−0.11
TyrannosaurusSDSM 12047Comp.d0930.9220.5955.5763.530.671.8085.81−0.047.58.012.59.58.512.89.310.3−0.01
TyrannosaurusSDSM 12047Rightd0346.1130.9799.03109.100.672.1587.64−0.129.07.29.27.87.08.08.57.6−0.18
TyrannosaurusCM 9380Leftd0242.3430.8786.6487.830.732.0587.52−0.07   10.08.011.0 9.7−0.01
TyrannosaurusCM 9380Leftd0451.1038.0492.07104.050.741.8087.49−0.14    9.0  9.00.02
TyrannosaurusCM 9380Leftd0646.9335.3582.0187.030.751.7587.31−0.117.59.011.09.010.010.09.29.70.05
TyrannosaurusCM 9380Comp.d0741.6931.2970.9378.070.751.7086.82−0.109.59.011.58.88.511.99.89.80.03
TyrannosaurusCM 9380Leftd1221.5016.3234.0537.100.761.5883.470.0210.010.012.512.013.011.810.812.30.05
TyrannosaurusCM 9380Rightd0125.5618.0935.0140.020.711.3783.66−0.0510.09.512.012.011.011.810.011.60.09
TyrannosaurusCM 9380Rightd0348.4637.4897.52102.320.772.0187.73−0.099.08.012.010.07.511.29.79.60.02
TyrannosaurusCM 9380Rightd0547.3437.2196.12100.540.792.0387.70−0.0711.58.513.012.09.011.011.010.70.10
TyrannosaurusCM 9380Rightd0839.0828.7168.0472.000.731.7486.76−0.058.08.011.59.011.016.09.212.00.18
TyrannosaurusCM 9380Rightd1030.2023.9051.9462.750.791.7285.41−0.01 9 8.0  9.012.50.14
TyrannosaurusBMNH R5863Leftd0740.4628.5576.1286.280.711.8886.93−0.109.06.815.09.07.710.010.38.9−0.06
TyrannosaurusBMNH R5863Leftd0838.8733.1265.2379.880.851.6886.35−0.108.57.012.38.57.511.09.39.0−0.05
TyrannosaurusBMNH R5863Leftd0932.5926.9956.6062.740.831.7485.99−0.058.58.312.59.08.011.59.89.5−0.07
TyrannosaurusBMNH R5863Leftd1130.4922.1245.6352.600.731.5085.05−0.079.010.312.59.59.012.010.610.20.01
TyrannosaurusBMNH R5863Leftd1223.9816.1232.3837.070.671.3583.16−0.059.012.013.59.510.512.511.510.80.02
TyrannosaurusBMNH R5863Leftd1318.3710.3522.5126.850.561.2380.21−0.0210.010.513.012.014.016.011.214.00.18
TyrannosaurusMOR 1125Rightmx1034.2021.3060.6868.000.621.7786.22−0.078.08.512.59.09.512.09.710.20.02
TyrannosaurusLACM 150167Leftmx0642.1025.8088.8292.440.612.1187.51−0.079.08.08.58.58.512.08.59.70.00
TyrannosaurusLACM 150167Rightd0338.1023.9073.3586.700.631.9386.7−0.079.58.012.09.510.012.09.810.50.06
TyrannosaurusLACM 150167Rightd0442.1028.9076.0287.890.691.8186.91−0.087.58.09.510.08.514.08.310.80.12
TyrannosaurusLACM 150167Rightd1316.2011.0017.7519.900.681.0977.86−0.0111.012.016.012.014.019.51315.20.21
TyrannosaurusLACM 23844Rightmx0146.0033.7079.0988.180.731.9287.12−0.11       8.5−0.09
TyrannosaurusLACM 23844Rightmx0354.5034.40117.1138.900.632.5587.87−0.10 6.58.5 8.0  8.5−0.09
TyrannosaurusLACM 23844Rightmx0547.8032.60100.5110.900.682.3287.68−0.069.06.510.09.010.012.08.510.30.05
TyrannosaurusLACM 23844Comp.d0238.8027.4068.9377.650.731.9686.50−0.067.0      9.5−0.05
TyrannosaurusLACM 23844Leftd0447.1035.1087.99107.400.742.2887.22−0.05       10.50.05
TyrannosaurusLACM 23844Rightd0547.6033.9096.94102.200.712.1587.70−0.108.07.5 8.57107.88.5−0.09
TyrannosaurusLACM 23844Comp.d0737.2027.1060.9871.930.761.5086.05−0.128.08.510.09.08.011.08.89.30.00
TyrannosaurusLACM 23844Leftd0841.2028.5085.3096.940.692.3587.20−0.04       9.5−0.06
TyrannosaurusLACM 23844Leftd1120.0015.9021.7827.290.791.3680.060.00       12.50.04
TyrannosaurusUCMP 118742Rightmx0745.4035.0083.0994.840.772.0987.19−0.08   9.010.013.08.09.0−0.07
TyrannosaurusUCMP 118742Rightmx0842.0030.5071.3678.290.731.8786.85−0.09   9.09.016.08.09.0−0.06
TyrannosaurusUCMP 118742Rightmx0941.3033.5072.9588.320.812.1486.71−0.06   9.010.017.08.09.0−0.10
TyrannosaurusUCMP 118742Rightmx1128.8019.0048.2654.520.661.8985.27−0.01   10.013.016.08.011.00.00
TyrannosaurusUCMP 118742Rightmx1219.1014.0027.0234.250.731.7981.450.05   11.014.017.011.012.0−0.05
TroodonMOR 553 Isolated4.922.437.228.660.491.4756.53−0.05 20.018.815.011.312.519.412.9−0.33
TroodonMOR 553 Isolated6.222.959.6110.250.471.5566.580.0410.010.0  10.012.510.011.4−0.35
TroodonMOR 553 Isolated6.003.039.3910.360.511.5765.530.0410.010.010.012.58.813.810.011.7−0.35
TroodonMOR 553 Isolated5.602.718.478.940.481.5163.390.0210.010.0  12.510.010.011.3−0.40
TroodonMOR 553 Isolated5.202.337.849.740.451.5158.81−0.0212.512.515.012.512.516.313.313.8−0.26
TroodonMOR 553 Isolated4.451.627.257.360.361.6359.040.0112.5   12.5 12.512.5−0.39
SaurornithoidesGIN100/1Leftmx043.582.685.016.920.751.4034.94−0.36    15.0  15.0−0.42
SaurornithoidesGIN100/1Leftmx063.662.695.517.790.741.5139.64−0.28   12.010.012.5 11.5−0.61
SaurornithoidesGIN100/1Leftmx074.312.455.617.370.571.3045.04−0.26    10.0  10.0−0.61
SaurornithoidesGIN100/1Leftmx123.802.486.458.470.651.7048.08−0.08    15.0  15.0−0.36
SaurornithoidesGIN100/1Comp.mx144.092.516.407.160.611.5752.26−0.05   12.5   12.5−0.46
SaurornithoidesGIN100/1Comp.mx163.762.266.237.970.601.6647.35−0.10   12.512.517.5 14.2−0.40
SaurornithoidesGIN100/1Rightmx052.982.504.285.250.841.4421.14−0.78    10.0  10.0−0.92
SaurornithoidesGIN100/1Rightmx094.092.616.336.570.641.5553.46−0.06   10.010.011.8 10.6−0.60
BambiraptorKUVP129737Comp.d062.371.415.337.280.602.2522.10−0.53    25.025.0 25.0−0.29
BambiraptorKUVP129737Comp.d082.341.415.016.530.602.1420.95−0.59   20.025.0  22.5−0.38
BambiraptorKUVP129737Leftd092.081.404.825.250.672.3231.88−0.15   30.0   30.0−0.12
BambiraptorKUVP129737Rightd052.371.614.916.830.682.0711.89−1.03    30.0  30.0−0.27
BambiraptorKUVP129737Rightd072.471.245.586.390.502.2739.74−0.03   24.030.0  27.0−0.09
BambiraptorKUVP129737Leftmx042.611.415.997.130.542.3041.83−0.01    25.0  25.0−0.13
BambiraptorKUVP129737Leftmx062.351.205.866.860.512.4939.80−0.03    24.2  24.2−0.21
BambiraptorKUVP129737Leftmx092.540.994.625.140.391.8230.01−0.29    32.5  32.50.07
BambiraptorKUVP129737 Isolated3.221.375.666.950.431.7641.88−0.08   35.023.732.5 30.40.16
BambiraptorKUVP129737 Isolated2.151.574.034.390.731.8710.74−1.12     25.0 25.0−0.46
DeinonychusYPM523266-11Leftd015.073.008.8510.370.591.7462.340.13 24.8 17.717.225.024.819.4−0.03
DeinonychusYPM523266-11Leftd127.073.2010.0712.310.451.4266.710.0532.029.5 22.317.5 28.417.30.05
DeinonychusYPM523266-11Comp.d136.762.939.5612.290.431.4165.040.0735.027.530.020.016.327.530.821.30.21
DeinonychusYPM5232612Rightd146.742.809.1411.780.421.3664.120.0333.829.528.524.317.823.830.418.80.11
DeinonychusYPM5232612Rightd165.352.416.538.350.461.2353.03−0.0932.329.029.820.517.520.330.319.40.04
DeinonychusYPM5232557Rightd077.153.2311.0113.500.451.5468.350.09 28.5 17.517.517.529.017.50.05
DeinonychusYPM5232557Rightd077.153.2311.0113.500.451.5468.350.09 28.5 17.517.517.529.017.50.05
DeinonychusYPM5232557Rightd086.363.0710.4012.100.481.6467.240.11 28.5   17.529.017.5−0.01
DeinonychusYPM5232557Rightd107.043.2012.2314.170.451.7470.570.13 27.5 15.017.517.527.516.8−0.01
DeinonychusYPM5232557Rightmx017.134.0013.5816.140.561.9071.870.1727.525.0 20.015.0 26.317.50.00
DeinonychusYPM5232557Rightpm015.743.2011.7910.800.562.0573.560.2620.0  15.020.017.5 17.5−0.08
DeinonychusMCZ8791Leftmx036.112.588.7713.700.421.4460.880.0227.328.029.827.017.316.828.420.40.14
DromaeosaurusAMNH5356Comp.mx037.214.0612.8615.800.561.7970.760.1522.013.815.018.017.019.516.918.20.04
DromaeosaurusAMNH5356Comp.mx046.843.7011.5813.970.541.6969.080.13 16.015.0 20.015.015.717.50.01
DromaeosaurusAMNH5356Leftmx057.644.0212.3816.370.531.6269.920.1218.817.515.822.517.517.517.119.20.13
DromaeosaurusAMNH5356Comp.mx066.283.1310.6812.400.501.7067.660.1628.018.88.820.720.015.020.722.10.17
DromaeosaurusAMNH5356Rightmx026.693.3210.9812.890.501.6468.390.1218.817.515.020.017.516.317.117.90.03
DromaeosaurusAMNH5356Rightmx075.703.119.7011.000.551.7065.640.16  17.5  22.517.522.50.15
DromaeosaurusAMNH5356Leftd025.464.039.4010.500.741.7264.990.19 15.017.525.0  16.325.00.19
DromaeosaurusAMNH5356Leftd036.093.8111.5512.340.631.9070.230.19 13.8 21.315.015.013.817.1−0.08
DromaeosaurusAMNH5356Leftd046.473.9111.2213.100.601.7368.660.1521.517.015.018.017.519.017.818.20.01
DromaeosaurusAMNH5356Leftd056.563.8911.2712.990.591.7268.960.1521.517.015.018.017.519.017.818.20.01
DromaeosaurusAMNH5356Leftd085.563.278.5210.700.591.5361.270.06 17.0  17.5 17.017.5−0.06
VelociraptorAMNH6515Premaxpm013.551.545.856.790.431.6546.51−0.01 30.0 30.0  30.030.00.20
VelociraptorAMNH6515Premaxpm033.301.544.385.880.471.3323.87−0.59 30.0 30.0  30.030.00.09
VelociraptorAMNH6515Maxillamx024.171.456.708.420.351.6151.720.02  25.027.535.0  29.20.27
VelociraptorAMNH6515Maxillamx044.352.157.919.540.491.8257.850.15 37.5  30.0 37.530.00.28
VelociraptorAMNH6515Maxillamx063.951.616.939.090.411.7551.050.04 37.5 25.025.035.037.528.30.20
VelociraptorAMNH6515Maxillamx083.111.134.690.800.261.5135.07−0.27 40.0 27.530.0 40.028.80.12
VelociraptorAMNH6515Dentaryd012.420.880.571.170.481.7613.62−0.95   32.230.0  31.1−0.15
VelociraptorUncat. GINMaxillamx054.691.55−0.131.980.422.0164.860.19   21.3   21.30.03
VelociraptorUncat. GINMaxillamx084.591.52−0.082.000.442.0263.350.19   22.525.0  23.40.10
VelociraptorUncat. GINMaxillamx014.471.50−0.022.790.621.7057.080.11   25.0   25.00.13
VelociraptorUncat. GINMaxillamx036.141.81−0.072.460.401.6064.980.11   20.025.022.5 22.50.20
VelociraptorUncat. GINMaxillamx055.991.790.012.400.401.6664.660.13   25.020.035.0 26.70.33
VelociraptorUncat. GINMaxillamx064.721.55−0.022.010.431.4452.81−0.02    22.527.5 25.00.20

APPENDIX B

Table  . APPENDIX B. Data for the test case teeth used in this article*
SpecimenCBLCBWCHALCBRCHRCACA2MAMCMBDADCDBDAVGDAVG2Fun.1Fun.2
  • *

    Fun. 1 and 2 are the scores from discriminate functions 1 and 2. Other variables as in the text.

AMNH 5027 mx138.8931.5785.4793.140.812.2087.28−0.067.07.58.77.08.410.08.5−0.162.27−0.92
BHI 3033 d637.6527.7462.0166.100.741.4886.44−0.137.47.79.48.48.09.68.7−0.054.38−1.67
FMNH PR2081 mx346.7437.21108.82122.990.802.3387.76−0.087.06.013.38.37.010.68.6−0.102.99−0.59
MOR 555 mx933.7224.4455.1156.720.721.6386.09−0.057.88.814.08.610.813.711.00.083.610.21
SDSM 12047 d444.9032.89105.61115.880.732.3587.75−0.09   7.56.79.07.7−0.192.54−1.47
FMNH PR208134.3426.1770.6474.780.762.0686.83−0.038.09.011.08.09.012.59.8−0.052.16−0.07
SDSM 12047a41.4219.8276.7890.130.481.8686.88−0.119.08.013.09.09.011.09.50.033.97−0.67
SDSM 12047b35.3522.2863.7966.120.631.8086.59−0.067.010.09.59.59.013.010.50.053.15−0.08
UCMP 13158339.3128.9665.4571.210.741.6786.59−0.119.09.011.011.08.09.19.4−0.014.46−0.81
UNO 123423.4215.4035.1642.060.661.5083.47−0.039.010.013.09.510.013.010.8−0.011.48−0.91
BMNH R33220.9011.8038.9245.560.561.8683.870.0311.510.513.010.011.015.012.00.02−0.40−0.17
UMNH VP63689.235.7719.4623.120.622.1177.100.1916.015.020.015.016.020.017.00.03−2.941.12
MOR 69317.849.4140.9042.400.532.2984.580.1513.014.022.013.015.022.016.70.20−1.982.68
YPM 52788.864.5715.0418.000.521.6974.110.1528.032.535.018.817.521.319.30.17−2.660.85
AMNH 54566.244.3613.0814.310.702.1072.000.2215.013.019.017.516.017.016.8−0.11−3.010.21
SMU 7464632.3019.0083.9187.730.592.6087.300.0614.010.019.015.011.017.014.30.210.083.46
FUB PB Ther132.0017.0371.0277.970.532.2286.69−0.316.07.013.07.08.013.79.6−0.080.61−0.59
YPM 5446113.788.1226.9330.300.591.9581.270.1111.811.918.513.012.913.012.9−0.06−2.03−0.45
CM 3074920.0212.1439.3845.790.611.9783.880.0611.08.514.010.512.015.012.50.02−0.630.38
CGM 8113631.5815.1164.1266.630.481.5083.47−0.03      10.2−0.011.18−0.47

APPENDIX C

Table  . APPENDIX C. PCA Orthogonal scores and DFA function scores for the specimens in the standard data set.
TaxonSpecimenSidePositionOrth.1Orth.2Fun.1Fun.2
DilophosaurusUCMP 37303Rmx3−0.13−0.05−0.680.93
DilophosaurusUCMP 37303Lmax−0.140.33−1.120.77
DilophosaurusUCMP 37303Lmax−0.150.85−1.832.24
DilophosaurusUCMP 37303Rmax−0.01−0.25−0.510.38
LiliensternusMBR 21751.4 max−0.81−2.12−3.83−0.80
LiliensternusMBR 21751.3 max−0.86−1.74−3.061.47
LiliensternusMBR 21751.8Ld01−1.46−0.06−2.111.91
LiliensternusMBR 21751.8Ld04−0.90−1.02−2.990.01
LiliensternusMBR 21751.8Ld15−0.58−2.10−2.68−0.08
LiliensternusMBR 21751.8Ld16−1.22−0.87−3.041.34
LiliensternusMBR 21751.9R?d19−1.16−1.05−3.852.89
CeratosaurusUMNHVP7819Lpm010.95−1.932.23−3.14
CeratosaurusUMNHVP7819Lpm020.500.100.57−1.86
CeratosaurusUMNHVP7819Lpm030.48−0.320.83−0.32
CeratosaurusUMNHVP7819Rpm010.310.25−0.22−1.20
CeratosaurusUMNHVP7819Rpm030.54−0.390.20−1.85
CeratosaurusUMNHVP5278Lmx010.80−0.18−0.49−4.71
CeratosaurusUMNHVP5278Lmx030.90−0.64−0.10−3.30
CeratosaurusUMNHVP5278Lmx050.58−0.020.832.20
CeratosaurusUMNHVP5278Lmx080.57−0.950.530.93
CeratosaurusUMNHVP5278Lmx100.37−0.87−0.91−0.73
Masiakasaurus98312-1 Isolated−1.370.40−1.71−1.69
Masiakasaurus95345-1 Isolated−1.27−1.74−3.630.59
Masiakasaurus99016 Isolated−1.280.50−4.551.83
Masiakasaurus95358 Isolated−2.451.41−2.843.46
Masiakasaurus95244-1 Isolated−2.140.56−4.082.14
Masiakasaurus98313-1 Isolated−0.85−1.21−2.98−0.26
Masiakasaurus98203 Isolated−1.510.93−5.300.19
Masiakasaurus93086-4 Isolated−1.36−0.56−4.13−0.30
Masiakasaurus95435 Isolated−1.32−1.35−3.62−0.31
Masiakasaurus96068-4 Isolated−1.07−1.32−4.60−1.88
IndosuchusAMNH 1955Lmx080.42−1.47−0.26−1.54
IndosuchusAMNH 1753Lpm020.16−0.290.56−0.43
IndosuchusAMNH 1753Lpm030.16−0.46−0.45−1.18
IndosuchusAMNH 1753Lpm040.26−0.270.09−1.84
IndosuchusAMNH 1753Rpm01−0.070.45−1.21−1.81
IndosuchusAMNH 1753Rpm020.100.47−1.13−2.11
MajungatholusFMNHPR2008Rpm02−0.331.12−2.260.38
MajungatholusUA 8716Rpm02−0.270.86−2.08−1.03
MajungatholusUA 8716Rpm04−0.280.72−2.58−0.51
MajungatholusFMNHPR2100Lmx040.28−0.47−2.07−2.10
MajungatholusFMNHPR2100Lmx060.26−0.23−2.05−1.90
MajungatholusFMNHPR2100Rmx050.35−0.72−1.57−1.93
MajungatholusFMNHPR2100Rmx070.28−0.15−2.36−2.22
MajungatholusFMNHPR2100Rmx17−0.55−1.38−3.69−2.72
MajungatholusFMNHPR2100Ld01−0.571.12−2.53−2.16
MajungatholusFMNHPR2100Ld05−0.090.06−1.94−1.68
MajungatholusFMNHPR2100Ld070.06−0.62−1.97−2.30
MajungatholusFMNHPR2100Ld12−0.01−0.94−1.78−2.42
MajungatholusFMNHPR2100Ld130.00−1.14−1.90−2.47
MajungatholusFMNHPR2100Ld14−0.02−1.25−1.67−2.20
MajungatholusFMNHPR2100Ld15−0.02−1.49−1.75−2.60
MajungatholusFMNHPR2100Ld17−0.35−0.90−2.45−2.59
MajungatholusFMNHPR2100Rd02−0.300.71−2.08−2.58
MajungatholusFMNHPR2100Rd030.04−0.53−1.63−2.62
MajungatholusFMNHPR2100Rd040.02−0.57−1.79−2.19
MajungatholusFMNHPR2100Rd06−0.06−0.20−2.26−1.97
MajungatholusFMNHPR2100Rd10−0.150.08−1.67−1.19
MajungatholusFMNHPR2100Rd11−0.01−0.68−2.23−2.44
MajungatholusFMNHPR2100Rd15−0.19−0.88−2.54−2.04
MajungatholusFMNHPR2100Rd160.03−1.86−2.21−1.82
MajungatholusFMNHPR2278Rmx020.050.18−2.54−0.48
MajungatholusFMNHPR2278Rmx030.13−0.13−2.10−0.88
BaryonyxBMNH R9951Rpm04−1.022.30−1.57−1.93
BaryonyxBMNH R9951Rpm06−1.161.81−2.36−2.22
BaryonyxBMNH R9951a Isolated−1.142.57−0.469.70
BaryonyxBMNH R9951d Isolated−0.821.90−1.308.41
BaryonyxBMNH R9951e Isolated−0.961.96−0.139.98
BaryonyxBMNH R9951f Isolated−1.122.33−0.309.47
BaryonyxBMNH R9951h Isolated−0.902.77−0.299.25
BaryonyxBMNH R9951n Isolated−0.791.98−0.689.52
SuchomimusUC G89-5 Isolated−0.912.77−0.0110.82
SuchomimusUC G54-4 Isolated−0.791.990.379.70
SuchomimusUC G48-9 Isolated−0.683.17−2.6910.05
SuchomimusUC G67-1 Isolated−0.492.61−0.539.08
AllosaurusYPM1333Rpm02−0.491.570.330.43
AllosaurusYPM1333Rpm03−0.220.51−0.05−0.69
AllosaurusYPM1333Rpm02−0.491.570.330.43
AllosaurusYPM1333Rpm05−0.300.70−1.680.56
AllosaurusSDSM25248Lpm030.200.82−2.11−0.37
AllosaurusSDSM25248Lpm05−0.060.10−2.330.56
AllosaurusUMNHVP9211Lmx040.00−0.30−2.58−0.84
AllosaurusUMNHVP9211Lmx06−0.150.03−2.871.01
AllosaurusUMNHVP9275Rmx07−0.480.59−2.272.11
AllosaurusUMNHVP9273Rmx07−0.260.11−2.171.38
AllosaurusUMNHVP9273Rmx06−0.13−0.68−1.511.26
AllosaurusUMNHVP9218Lmx01−0.031.03−1.130.75
AllosaurusUMNHVP9369Rd06−0.500.95−2.121.56
AllosaurusUMNHVP9365Rd02−0.541.62−1.500.68
AllosaurusUMNHVP1251Rpm05−0.281.88−1.422.48
AllosaurusCM 21703Lpm02−0.211.64−1.67−0.28
AllosaurusCM 21703Lpm03−0.301.79−2.89−0.46
AllosaurusCM 21703Lpm04−0.211.32−2.31−0.49
AllosaurusLACM 46030Cpm010.241.01−0.78−3.87
AllosaurusLACM 46030Cpm02−0.071.23−0.370.21
AllosaurusLACM 46030Cpm03−0.191.78−0.771.13
AllosaurusLACM 46030Cpm04−0.091.37−1.260.36
AllosaurusLACM 46030Lpm05−0.030.99−1.220.60
AcrocanthosaurusNCSM 14345Cpm01−0.021.48−0.643.36
AcrocanthosaurusNCSM 14345Cpm030.151.50−1.153.83
AcrocanthosaurusNCSM 14345Cmx010.221.090.053.38
AcrocanthosaurusNCSM 14345Cmx020.500.732.013.64
AcrocanthosaurusNCSM 14345Cmx040.510.831.683.79
AcrocanthosaurusNCSM 14345Cmx050.750.253.272.99
AcrocanthosaurusNCSM 14345Lmx130.40−1.230.891.15
AcrocanthosaurusNCSM 14345Cmx140.18−1.30−0.360.39
AcrocanthosaurusNCSM 14345Rmx030.510.991.543.73
AcrocanthosaurusNCSM 14345Rmx060.77−0.333.853.10
AcrocanthosaurusNCSM 14345Rmx080.560.131.432.02
AcrocanthosaurusNCSM 14345Rmx090.56−0.391.341.34
AcrocanthosaurusNCSM 14345Rmx110.62−1.531.900.92
AcrocanthosaurusNCSM 14345Ld01−0.240.99−0.751.52
AcrocanthosaurusNCSM 14345Cd020.101.42−0.603.11
AcrocanthosaurusNCSM 14345Ld030.311.040.123.43
AcrocanthosaurusNCSM 14345Cd040.351.180.062.37
AcrocanthosaurusNCSM 14345Ld050.460.321.842.67
AcrocanthosaurusNCSM 14345Cd070.510.251.342.20
AcrocanthosaurusNCSM 14345Ld080.44−0.271.862.09
AcrocanthosaurusNCSM 14345Ld100.49−0.672.072.53
AcrocanthosaurusNCSM 14345Ld120.48−0.911.511.34
AcrocanthosaurusNCSM 14345Ld140.26−0.650.370.97
AcrocanthosaurusNCSM 14345Ld170.23−2.150.660.10
AcrocanthosaurusNCSM 14345Rd050.290.820.283.45
AcrocanthosaurusNCSM 14345Rd060.460.071.893.33
CarcharodontosaurusSGM Din-1 Isolated1.00−1.033.980.96
CarcharodontosaurusSGM Din-1Rmx031.13−1.534.70−0.07
CarcharodontosaurusSGM Din-1Rmx051.11−1.384.25−0.28
CarcharodontosaurusSGM Din-1Rmx061.11−1.444.40−0.17
CarcharodontosaurusSGM Din-1Rmx081.07−1.283.74−0.35
CarcharodontosaurusSGM Din-1 isolated1.14−0.844.620.23
GorgosaurusROM1247Rd02−0.341.21−0.510.37
GorgosaurusROM1247Rd03−0.121.46−1.071.95
GorgosaurusROM1247Rd040.36−0.49−0.61−0.46
GorgosaurusROM1247Rd060.210.36−0.651.03
GorgosaurusROM1247Rd080.050.80−0.731.49
GorgosaurusROM1247Rd090.23−1.00−1.54−1.12
GorgosaurusROM1247Rd110.090.26−0.960.57
GorgosaurusROM1247Rd130.10−0.50−0.920.98
GorgosaurusROM1247Rd15−0.12−0.40−0.84−0.09
GorgosaurusROM1247Rmx040.49−0.090.040.21
GorgosaurusROM1247Rmx090.27−0.29−0.91−0.66
GorgosaurusBMNH R4863Rd040.530.361.530.62
GorgosaurusBMNH R4863Rd080.54−0.201.720.21
GorgosaurusBMNH R4863Rd100.281.010.211.26
DaspletosaurusAMNH5346Lmx020.212.14−0.962.66
DaspletosaurusMOR590Rd02−0.020.63−0.571.48
DaspletosaurusMOR590Rd030.241.21−0.440.62
DaspletosaurusMOR590Rd050.241.27−0.810.54
DaspletosaurusMOR590Rd070.270.91−0.37−0.02
DaspletosaurusMOR590Rd080.360.08−0.91−0.66
DaspletosaurusMOR590Rd100.22−0.10−0.33−0.53
TyrannosaurusMOR 555Lmx070.98−0.205.270.67
TyrannosaurusMOR 555Lmx080.88−0.313.800.17
TyrannosaurusMOR 555Lmx090.77−0.173.610.21
TyrannosaurusMOR 008Ld031.040.484.56−0.71
TyrannosaurusMOR 008Ld050.880.663.27−0.73
TyrannosaurusMOR 008Cd060.880.363.11−0.69
TyrannosaurusMOR 008Rd080.840.302.90−1.07
TyrannosaurusMOR 008Rd100.84−0.272.32−2.01
TyrannosaurusFMNH PR2081Lpm031.09−1.253.18−1.86
TyrannosaurusFMNH PR2081Lmx051.020.623.96−0.54
TyrannosaurusFMNH PR2081Lmx070.940.253.40−0.68
TyrannosaurusFMNH PR2081Lmx080.910.163.44−0.32
TyrannosaurusFMNH PR2081Rmx011.090.503.87−1.64
TyrannosaurusFMNH PR2081Rmx021.080.993.58−1.37
TyrannosaurusFMNH PR2081Rmx030.981.262.99−0.59
TyrannosaurusFMNH PR2081Rmx100.91−0.273.40−0.71
TyrannosaurusFMNH PR2081Rmx110.59−0.352.170.31
TyrannosaurusFMNH PR2081Rmx120.27−0.430.57−0.63
TyrannosaurusFMNH PR2081Cd021.06−0.263.91−1.46
TyrannosaurusFMNH PR2081Cd120.55−0.101.94−0.10
TyrannosaurusFMNH PR2081Ld031.31−0.497.10−1.30
TyrannosaurusFMNH PR2081Ld051.200.035.64−1.49
TyrannosaurusFMNH PR2081Ld060.940.263.54−0.61
TyrannosaurusFMNH PR2081Ld080.850.372.43−1.32
TyrannosaurusFMNH PR2081Ld090.750.193.060.34
TyrannosaurusBHI 3033Cmx011.080.634.06−1.50
TyrannosaurusBHI 3033Cmx021.300.125.59−2.40
TyrannosaurusBHI 3033Cmx031.090.913.25−1.41
TyrannosaurusBHI 3033Cmx041.150.204.95−0.70
TyrannosaurusBHI 3033Cmx051.150.184.98−1.21
TyrannosaurusBHI 3033Cmx060.890.303.34−0.44
TyrannosaurusBHI 3033Cmx080.80−0.552.00−1.54
TyrannosaurusBHI 3033Cmx090.73−0.142.82−0.22
TyrannosaurusBHI 3033Lmx110.31−0.551.400.49
TyrannosaurusBHI 3033Rmx071.03−0.654.70−0.57
TyrannosaurusBHI 3033Cd010.62−0.171.48−1.47
TyrannosaurusBHI 3033Cd021.06−0.224.20−1.46
TyrannosaurusBHI 3033Cd031.010.214.39−2.56
TyrannosaurusBHI 3033Cd041.080.274.83−1.01
TyrannosaurusBHI 3033Cd061.10−0.604.38−1.67
TyrannosaurusBHI 3033Cd070.88−0.623.74−0.89
TyrannosaurusBHI 3033Cd090.81−0.573.05−1.16
TyrannosaurusBHI 3033Cd100.67−0.542.87−0.26
TyrannosaurusBHI 3033Ld130.12−2.020.780.35
TyrannosaurusBHI 3033Rd051.14−0.205.71−1.04
TyrannosaurusBHI 3033Rd080.73−0.093.550.42
TyrannosaurusBHI 3033Rd110.58−1.142.44−0.46
TyrannosaurusBHI 3033Rd120.29−1.261.860.52
TyrannosaurusBHI 3033Cpm010.69−0.971.64−0.67
TyrannosaurusBHI 3033Cpm030.83−0.423.49−0.15
TyrannosaurusBHI 3033Rpm020.91−0.942.76−1.70
TyrannosaurusBHI 3033Rpm040.71−0.272.10−0.78
TyrannosaurusAMNH 5027Cpm010.86−1.322.91−1.05
TyrannosaurusAMNH 5027Cpm030.85−0.903.16−0.67
TyrannosaurusAMNH 5027Rpm020.92−1.242.65−1.88
TyrannosaurusAMNH 5027Rpm040.78−0.242.66−0.68
TyrannosaurusAMNH 5027Cmx010.861.052.27−0.92
TyrannosaurusAMNH 5027Cmx030.821.381.56−0.02
TyrannosaurusAMNH 5027Cmx051.120.234.45−0.60
TyrannosaurusAMNH 5027Cmx060.960.132.65−1.09
TyrannosaurusAMNH 5027Cmx070.980.082.65−1.26
TyrannosaurusAMNH 5027Cmx080.810.722.13−0.50
TyrannosaurusAMNH 5027Rmx110.62−0.902.24−0.23
TyrannosaurusAMNH 5027Leftmx041.200.434.67−1.73
TyrannosaurusSDSM 12047Leftmx011.230.384.70−2.46
TyrannosaurusSDSM 12047Leftmx020.830.981.80−1.09
TyrannosaurusSDSM 12047Leftmx031.051.112.46−1.51
TyrannosaurusSDSM 12047Leftmx041.021.182.99−1.13
TyrannosaurusSDSM 12047Comp.mx081.070.203.75−1.09
TyrannosaurusSDSM 12047Leftmx101.010.413.03−1.09
TyrannosaurusSDSM 12047Comp.mx110.84−0.512.51−1.51
TyrannosaurusSDSM 12047Rightmx061.110.683.81−1.41
TyrannosaurusSDSM 12047Rightmx120.69−1.340.88−2.72
TyrannosaurusSDSM 12047Leftd041.021.042.54−1.47
TyrannosaurusSDSM 12047Comp.d050.960.732.57−1.01
TyrannosaurusSDSM 12047Comp.d060.970.483.00−1.22
TyrannosaurusSDSM 12047Leftd070.850.253.610.40
TyrannosaurusSDSM 12047Comp.d080.820.442.38−0.98
TyrannosaurusSDSM 12047Comp.d090.72−0.052.18−0.42
TyrannosaurusSDSM 12047Rightd031.130.503.62−1.91
TyrannosaurusCM 9380Leftd020.910.633.67−0.08
TyrannosaurusCM 9380Leftd041.200.196.15−0.89
TyrannosaurusCM 9380Leftd061.090.135.70−0.37
TyrannosaurusCM 9380Comp.d071.000.024.82−0.41
TyrannosaurusCM 9380Leftd120.33−0.161.420.32
TyrannosaurusCM 9380Rightd010.62−0.872.63−0.17
TyrannosaurusCM 9380Rightd031.030.714.86−0.14
TyrannosaurusCM 9380Rightd050.940.834.710.77
TyrannosaurusCM 9380Rightd080.810.164.431.22
TyrannosaurusCM 9380Rightd100.580.302.791.36
TyrannosaurusBMNH R5863Leftd070.990.203.73−1.05
TyrannosaurusBMNH R5863Leftd080.990.204.22−1.03
TyrannosaurusBMNH R5863Leftd090.770.272.99−0.70
TyrannosaurusBMNH R5863Leftd110.80−0.543.21−0.74
TyrannosaurusBMNH R5863Leftd120.62−1.082.11−0.99
TyrannosaurusBMNH R5863Leftd130.33−1.710.85−0.04
TyrannosaurusMOR 1125Rightmx100.83−0.252.90−0.43
TyrannosaurusLACM 150167Leftmx060.930.363.33−0.09
TyrannosaurusLACM 150167Rightd030.860.123.170.19
TyrannosaurusLACM 150167Rightd040.940.104.570.50
TyrannosaurusLACM 150167Rightd130.17−1.671.330.59
TyrannosaurusLACM 23844Rightmx011.060.325.09−1.28
TyrannosaurusLACM 23844Rightmx031.071.064.68−0.34
TyrannosaurusLACM 23844Rightmx050.890.994.120.87
TyrannosaurusLACM 23844Comp.d020.840.433.73−0.39
TyrannosaurusLACM 23844Leftd040.841.124.440.92
TyrannosaurusLACM 23844Rd051.050.694.31−0.95
TyrannosaurusLACM 23844Cd071.04−0.454.53−0.92
TyrannosaurusLACM 23844Ld080.791.012.700.12
TyrannosaurusLACM 23844Ld110.25−0.632.110.01
TyrannosaurusUCMP 118742Rmx070.950.794.41−0.59
TyrannosaurusUCMP 118742Rmx080.970.234.49−0.94
TyrannosaurusUCMP 118742Rmx090.840.973.66−0.55
TyrannosaurusUCMP 118742Rmx110.540.141.800.04
TyrannosaurusUCMP 118742Rmx120.100.180.48−0.10
TroodonMOR 553 Isolated−1.017−1.41−4.41−4.75
TroodonMOR 553 Isolated−0.69−1.41−4.19−5.08
TroodonMOR 553 Isolated−0.76−1.21−4.06−4.78
TroodonMOR 553 Isolated−0.79−1.45−4.32−5.50
TroodonMOR 553 Isolated−0.97−1.50−4.61−4.16
TroodonMOR 553 Isolated−1.08−1.76−5.79−5.83
SaurornithoidesGIN100/1Lmx04−1.73−0.45−3.41−3.09
SaurornithoidesGIN100/1Lmx06−1.51−0.39−3.77−5.11
SaurornithoidesGIN100/1Lmx07−1.07−1.62−4.45−7.00
SaurornithoidesGIN100/1Lmx12−1.56−0.13−4.02−3.05
SaurornithoidesGIN100/1Cmx14−1.31−0.70−4.04−4.87
SaurornithoidesGIN100/1Cmx16−1.52−0.44−4.46−3.91
SaurornithoidesGIN100/1Rmx05−2.05−0.19−4.45−6.45
SaurornithoidesGIN100/1Rmx09−1.21−0.76−3.96−6.17
BambiraptorKUVP129737Cd06−2.911.21−6.870.44
BambiraptorKUVP129737Cd08−2.881.00−6.85−0.67
BambiraptorKUVP129737Ld09−2.971.54−5.341.88
BambiraptorKUVP129737Rd05−3.411.49−6.952.13
BambiraptorKUVP129737Rd07−2.530.70−6.250.53
BambiraptorKUVP129737Lmx04−2.420.86−5.970.38
BambiraptorKUVP129737Lmx06−2.561.02−6.800.03
BambiraptorKUVP129737Lmx09−2.62−0.50−6.700.70
BambiraptorKUVP129737 Isolated−2.14−0.55−5.501.05
BambiraptorKUVP129737 Isolated−3.461.19−6.610.07
DeinonychusYPM523266-11Ld01−1.32−0.17−3.45−0.41
DeinonychusYPM523266-11Ld12−0.74−1.57−3.37−1.43
DeinonychusYPM523266-11Cd13−0.89−1.57−3.380.06
DeinonychusYPM5232612Rd14−0.80−1.88−3.57−1.12
DeinonychusYPM5232612Rd16−1.11−1.97−3.72−1.57
DeinonychusYPM5232557Rd07−0.76−1.28−3.54−1.14
DeinonychusYPM5232557Rd08−0.93−0.92−3.74−1.27
DeinonychusYPM5232557Rd10−0.82−0.86−3.95−1.25
DeinonychusYPM5232557Rmx01−0.91−0.03−3.42−0.06
DeinonychusYPM5232557Rpm01−1.170.20−3.96−0.66
DeinonychusMCZ8791Lmx03−0.96−1.57−3.90−0.53
DromaeosaurusAMNH5356Cmx03−0.90−0.22−3.120.12
DromaeosaurusAMNH5356Cmx04−0.89−0.54−3.27−0.64
DromaeosaurusAMNH5356Lmx05−0.80−0.70−2.910.32
DromaeosaurusAMNH5356Cmx06−1.11−0.58−3.470.78
DromaeosaurusAMNH5356Rmx02−0.90−0.83−3.51−0.84
DromaeosaurusAMNH5356Rmx07−1.25−0.37−3.290.84
DromaeosaurusAMNH5356Ld02−1.430.41−1.792.62
DromaeosaurusAMNH5356Ld03−1.090.17−3.20−0.49
DromaeosaurusAMNH5356Ld04−1.01−0.18−2.92−0.14
DromaeosaurusAMNH5356Ld05−0.99−0.26−2.94−0.18
DromaeosaurusAMNH5356Ld08−1.10−0.70−3.12−1.26
VelociraptorAMNH6515Ppm01−1.96−0.78−4.931.06
VelociraptorAMNH6515Ppm03−2.33−1.20−5.540.70
VelociraptorAMNH6515Mmx02−1.66−1.39−5.200.96
VelociraptorAMNH6515Mmx04−1.73−0.17−4.142.33
VelociraptorAMNH6515Mmx06−1.77−0.73−5.141.07
VelociraptorAMNH6515Mmx08−2.07−2.22−6.86−0.72
VelociraptorAMNH6515Dd01−3.180.08−7.620.67
Velociraptoruncat. GINMmx05−1.43−0.36−5.20−0.30
Velociraptoruncat. GINMmx08−1.52−0.22−5.050.50
Velociraptoruncat. GINMmx01−1.620.02−3.121.42
Velociraptoruncat. GINMmx03−1.06−1.26−4.110.31
Velociraptoruncat. GINMmx05−1.20−1.04−4.071.74
Velociraptoruncat. GINMmx06−1.42−1.42−4.270.25

Ancillary