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Dental morphology and variation in theropod dinosaursImplications for the taxonomic identification of isolated teeth.

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THE ANATOMICAL RECORD PART A 285A:699 –736 (2005)
Dental Morphology and Variation in
Theropod Dinosaurs: Implications for
the Taxonomic Identification of
Isolated Teeth
JOSHUA B. SMITH, 1* DAVID R. VANN, 1 AND PETER DODSON1,2
Department of Earth and Environmental Science, University of Pennsylvania,
Philadelphia, Pennsylvania
2
Department of Animal Biology, School of Veterinary Medicine, University of
Pennsylvania, Pennsylvania
1
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. 娀 2005 Wiley-Liss, Inc. © 2005 Wiley-Liss, Inc.
Key words: dinosauria; theropoda; teeth; morphometrics; taxonomy; discriminant analysis
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 withintaxon 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).
©
2005 WILEY-LISS, INC.
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.
Grant sponsor: Washington University.
*Correspondence to: Joshua B. Smith, Department of Earth
and Planetary Sciences, Washington University, 1 Brookings
Drive, Campus Box 1169, St. Louis, MO 63130. Fax: 314-9357361. E-mail: smithjb@wustl.edu
Received 28 November 2004; Accepted 11 March 2005
DOI 10.1002/ar.a.20206
Published online 28 June 2005 in Wiley InterScience
(www.interscience.wiley.com).
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SMITH ET AL.
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 communitylevel 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 Tyrannosau-
rus 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,
IDENTIFYING ISOLATED THEROPOD TEETH
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.
701
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 HensoldtWetzlar 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).
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
702
SMITH ET AL.
Fig. 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.]
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.
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 Segment EF 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 Segment GH (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 Segment GB, 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 Segment AG) 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).
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 ␪). This angle ␪ (Fig. 4B) forms a
IDENTIFYING ISOLATED THEROPOD TEETH
703
Fig. 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.
Fig. 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).
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 cos␪,
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
冉
␪ ⫽ arcos
a2 ⫹ b2 ⫺ c2
2ab
冊
(1)
where ␪ ⫽ 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°).
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 Martı́nez 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
704
SMITH ET AL.
Fig. 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 (␪) is the crown angle (CA).
tion 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 A–D. 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.
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
Y ⫽ a ⫹ b 冑X
Fig. 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.
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 informa-
(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.
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
Fig. 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.
Fig. 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).
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SMITH ET AL.
Fig. 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.]
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).
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.
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). MidCrown Serration Density is the number of denticles per
IDENTIFYING ISOLATED THEROPOD TEETH
707
Fig. 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.
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
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SMITH ET AL.
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,
TABLE 1. Factor scores from the PCA*
Un-rotated
CBL
CBW
CH
AL
DAVG
CBR
CHR
CA
Orthogonal
Factor 1
Factor 2
Factor 1
Factor 2
0.972
0.984
0.982
0.978
⫺0.749
0.484
0.373
0.804
⫺0.164
⫺0.013
0.008
⫺0.017
0.332
0.569
0.811
⫺0.185
0.966
0.924
0.914
0.919
⫺0.818
0.249
0.059
0.817
0.194
0.340
0.359
0.334
0.042
0.704
0.891
0.115
*Factors (unrotated and the orthogonal solution) from the
variable PCA run on the 20 taxa comprising the theropod
standard.
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.
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:
S t ⫽ C t ⫹ W t1 ⫻ X 1 ⫹ W t2 ⫻ X 2 ⫹ . . .Wt n ⫻ X n,
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 LawleyHotelling 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
IDENTIFYING ISOLATED THEROPOD TEETH
709
Fig. 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.
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.
With 20 taxa and 8 variables, the discriminant analysis
produced 8 functions (Wilks’ lambda ⫽ 0.001 and 0.008 for
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SMITH ET AL.
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.
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.
DISCUSSION
Discrimination of Taxa
Fig. 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).
TABLE 2. Two-way analysis of variance among 20
theropod taxa and eight variables
Taxon
Variable
Residual
Total
Sum of
squares
Degree of
freedom
F-ratio
P
238782.81
1368089.24
475295.84
2086090.34
19
8
74.76
803.07
⬍0.001
⬍0.001
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
IDENTIFYING ISOLATED THEROPOD TEETH
711
Fig. 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.
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
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SMITH ET AL.
Fig. 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.
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.
713
IDENTIFYING ISOLATED THEROPOD TEETH
TABLE 3. Results of discriminant analysis on the standard data set
Nonstandardized
CBL
CBW
CH
AL
DAVG2
CBR
CHR
CA2
Constant
Dilophosaurus centroid
Liliensternus centroid
Ceratosaurus centroid
Masiakasaurus centroid
Indosuchus centroid
Majungatholus centroid
Baryonyx centroid
Suchomimus centroid
Allosaurus centroid
Acrocanthosaurus centroid
Carcharodontosaurus centroid
Gorgosaurus centroid
Daspletosaurus centroid
Tyrannosaurus centroid
Troodon centroid
Saurornithoides centroid
Bambiraptor centroid
Deinonychus centroid
Dromaeosaurus centroid
Velociraptor centroid
Classification
Function 1
Function 2
Function 1
Function 2
0.4453
⫺0.2081
⫺0.0397
⫺0.0103
1.1473
8.7256
⫺1.8661
2.2982
⫺6.7971
⫺1.0356
⫺3.0792
0.3470
⫺3.7436
⫺0.3998
⫺2.1411
⫺0.3508
⫺1.5147
⫺1.5765
1.0179
4.2821
⫺0.3736
⫺0.6282
3.3157
⫺4.5619
⫺4.0698
⫺6.3839
⫺3.6365
⫺3.0496
⫺5.0189
0.0616
⫺0.1269
⫺0.0049
⫺0.0104
10.5915
7.4781
3.2197
⫺2.8480
⫺9.5931
1.0798
0.9615
⫺1.3986
0.3764
⫺1.4835
⫺1.8717
9.6063
9.7350
0.3676
2.4134
0.0520
0.4552
0.5854
⫺0.6887
⫺5.0159
⫺4.9561
0.6537
⫺0.8525
0.1030
0.7682
11.7777
⫺7.1133
⫺3.6043
0.0621
84.4489
199.9437
109.8312
⫺50.7103
⫺189.4743
8.6310
⫺6.0298
⫺2.1816
⫺0.2558
93.2269
177.2429
84.4083
⫺48.6647
⫺123.7134
Fig. 14. Plot of the scores for factors 1 and 2 of the discriminant analysis including 20 theropod taxa
comprising the standard.
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
714
SMITH ET AL.
TABLE 4. Classification matrix for the discriminant analysis using 20 taxa comprising the standard data set*
Taxon Dil Lili Cer Masi Indo Maj Bary Such Allo Acro Carc Gorg Dasp Trex Troo Saur Bamb Dein Drom Vel Total
Dil
Lili
Cer
Masi
Indo
Maj
Bary
Such
Allo
Acro
Carc
Gorg
Dasp
Trex
Troo
Saur
Bamb
Dein
Drom
Vel
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
25
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
22
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
25
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
113
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13
4
7
10
10
6
26
8
4
22
26
6
14
7
115
6
8
10
11
11
13
Taxon Dil Lili Cer Masi Indo Maj Bary Such Allo Acro Carc Gorg Dasp Trex Troo Saur Bamb Dein Drom Vel %
Dil
100 0
0
0
0
Lili
0 85.7
0
0
0
Cer
0 0 100
0
0
Masi
0 0
0 100
0
Indo
0 0
0
0 100
Maj
0 0
0
0
0
Bary
0 0
0
0
0
Such
0 0
0
0
0
Allo
0 0
0
0
0
Acro
0 0
0
0
0
Carc
0 0
0
0
0
Gorg
0 0
0
0
0
Dasp
0 0
0
0
0
Trex
0 0
0
0
1.7
Troo
0 0
0
0
0
Saur
0 0
0
0
0
Bamb
0 0
0
0
0
Dein
0 0
0
0
0
Drom
0 0
0
0
0
Vel
0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
96.2
0
0
100
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0
0
0
0
0 0
0
0
0
0 0
0
0
0
0 0
0
0
0
0 0
0
0
0
0 0
0
0
0
0 0
0
0
0
100 0
0
0
0
0 100
0
0
0
0 0 96.2
0
3.9
0 0
0
100
0
0 14.3 0
0 85.7
0 0
0
0
0
0 0
0
0
0
0 0
0
0
0
0 0
0
0
0
0 0
0
0
0
0 0
0
0
0
0 0
0
0
0
0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3.9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
100
0
0
0
0 98.3 0
0
0
0 100
0
0
0
0
100
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 14.3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
100
0
0
0
0 100
0
0
0
0
100
0
0
0
0 100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
*97.8% of original group cases correctly classified.
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 pre-
clude 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.
715
IDENTIFYING ISOLATED THEROPOD TEETH
TABLE 5. Results of tests of taxonomic classification hypotheses for isolated theropod teeth in groups 1/4
using stepwise discriminant function analyses*
Group
Specimen
Taxon 1
Taxon 2
D2
1
1
1
1
1
2
2
2
2
2
3
3
3
3
3
4
4
4
4
4
AMNH 5027 mx1
BH1 3033 d6
FMNH PR2081 mx3
MOR 555 mx9
SDSM 12047 d4
FMNH PR2081
SDSM 12047a
SDSM 12047b
UCMP 131583
UNO 1234
BMNH R332
UMNH VP6368
MOR 693
YPM 5278
AMNH 5456
SMU 74646
FUB PB Ther1
YPM 54461
CM 30749
CGM 81136
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
cf. Tyrannosaurus
cf. Tyrannosaurus
cf. Tyrannosaurus
cf. Tyrannosaurus
cf. Tyrannosaurus
Megalosaurus
Marshosaurus
cf. Allosaurus
cf. Deinonychus
cf. Dromaeosaurus
cf. Acrocanthosaurus
cf. allosaurid
cf. tyrannosaurid
cf. tyrannosaurid
cf. Carcharodontosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Gorgosaurus
Allosaurus
Allosaurus
Deinonychus
Deinonychus
Acrocanthosaurus
Ceratosaurus
Majungatholus
Gorgosaurus
Tyrannosaurus
8.39
10.33
17.28
3.81
7.83
5.16
21.48
3.53
3.01
4.36
3.46
27.17
12.30
43.97
44.03
8.99
26.64
15.27
1.84
20.85
P
0.396
0.243
0.027
0.874
0.451
0.740
0.006
0.897
0.934
0.823
0.902
0.001
0.138
⬍0.0001
⬍0.0001
0.343
0.001
0.054
0.986
0.008
%
97.8
96.6
97.8
97.8
97.5
96.9
97.5
97.2
97.8
97.2
97.5
97.5
97.2
97.5
97.2
97.2
97.5
97.5
97.5
97.8
*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.
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,
716
SMITH ET AL.
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 mediumsized 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
IDENTIFYING ISOLATED THEROPOD TEETH
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.
ACKNOWLEDGMENTS
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.).
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722
SMITH ET AL.
APPENDIX A. The theropod standard data set used in this article*
Taxon
Dilophosaurus
Dilophosaurus
Dilophosaurus
Dilophosaurus
Liliensternus
Liliensternus
Liliensternus
Liliensternus
Liliensternus
Liliensternus
Liliensternus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Indosuchus
Indosuchus
Indosuchus
Indosuchus
Indosuchus
Indosuchus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Baryonyx
Baryonyx
Baryonyx
Baryonyx
Baryonyx
Baryonyx
Baryonyx
Baryonyx
Suchomimus
Suchomimus
Suchomimus
Suchomimus
Allosaurus
Allosaurus
Allosaurus
Specimen
UCMP 37303
UCMP 37303
UCMP 37303
UCMP 37303
MBR 21751.4
MBR 21751.3
MBR 21751.8
MBR 21751.8
MBR 21751.8
MBR 21751.8
MBR 21751.9
UMNHVP7819
UMNHVP7819
UMNHVP7819
UMNHVP7819
UMNHVP7819
UMNHVP5278
UMNHVP5278
UMNHVP5278
UMNHVP5278
UMNHVP5278
98312-1
95345-1
99016
95358
95244-1
98313-1
98203
93086-4
95435
96068-4
AMNH 1955
AMNH 1753
AMNH 1753
AMNH 1753
AMNH 1753
AMNH 1753
FMNHPR2008
UA 8716
UA 8716
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2278
FMNHPR2278
BMNH R9951
BMNH R9951
BMNH R9951a
BMNH R9951d
BMNH R9951e
BMNH R9951f
BMNH R9951h
BMNH R9951n
UC G89-5
UC G54-4
UC G48-9
UC G67-1
YPM1333
YPM1333
YPM1333
Side
Position
CBL
CBW
CH
AL
CBR
CHR
Right
Left
Left
Right
mx3
max
max
max
max
max
d01
d04
d15
d16
?d19
pm01
pm02
pm03
pm01
pm03
mx01
mx03
mx05
mx08
mx10
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
mx08
pm02
pm03
pm04
pm01
pm02
pm02
pm02
pm04
mx04
mx06
mx05
mx07
mx17
d01
d05
d07
d12
d13
d14
d15
d17
d02
d03
d04
d06
d10
d11
d15
d16
mx02
mx03
pm04
pm06
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
pm02
pm03
pm05
16.33
16.35
19.11
17.33
6.62
7.44
5.09
6.97
8.34
5.85
6.63
25.86
23.00
24.04
20.26
22.64
25.47
29.61
32.95
27.52
20.79
4.47
5.30
6.15
2.81
3.27
7.09
4.62
4.94
4.94
5.47
19.47
17.30
16.59
17.33
13.55
15.99
12.99
12.41
12.51
18.30
18.37
18.93
18.17
7.88
8.81
13.30
14.24
12.66
12.53
12.28
11.72
9.33
10.91
13.53
13.90
13.50
12.82
13.17
11.26
12.88
16.90
17.10
13.06
10.49
11.69
15.76
13.18
12.12
16.42
16.47
18.90
20.80
18.70
19.20
12.46
12.00
13.04
9.87
10.20
10.40
10.14
2.50
3.00
3.50
3.50
3.50
3.00
2.50
14.79
16.81
14.88
14.31
13.90
15.10
12.88
14.00
10.53
9.12
3.93
2.28
3.02
2.20
1.93
3.48
2.50
2.42
2.42
2.22
9.10
12.99
10.66
12.85
10.54
11.96
9.46
9.26
8.30
8.62
9.21
8.86
9.10
3.47
7.20
8.56
7.72
7.12
6.69
6.70
6.29
5.36
8.48
8.27
7.90
7.77
8.59
7.05
5.79
5.25
8.67
8.81
11.24
7.90
11.19
12.05
10.88
10.35
15.19
13.65
15.20
18.10
13.30
14.40
6.00
11.07
9.28
24.65
28.00
35.24
25.66
8.83
10.26
8.02
10.61
10.53
8.84
11.23
31.63
41.89
41.66
38.69
39.65
51.32
61.71
75.00
52.38
38.11
7.46
6.96
14.25
5.87
6.52
10.44
11.64
8.58
6.80
8.86
29.40
26.90
27.26
28.02
26.00
31.86
30.11
27.05
27.69
36.90
38.08
35.54
38.68
12.45
19.88
25.37
25.13
19.93
19.21
17.87
16.19
14.48
22.88
22.87
24.08
25.75
23.76
23.00
18.73
18.71
37.63
35.01
31.37
23.72
28.72
34.80
29.67
27.19
38.55
34.12
62.94
56.94
52.66
54.34
28.65
20.69
26.98
30.00
33.00
47.50
31.00
12.40
12.52
9.21
11.82
12.62
10.12
12.92
41.28
43.74
48.60
41.36
48.11
56.11
72.86
84.46
61.54
42.69
8.59
8.18
13.51
6.00
6.83
11.67
12.14
9.49
8.20
10.15
31.50
28.50
29.48
32.05
29.00
32.01
31.92
27.84
30.73
39.33
39.87
41.69
44.19
13.80
19.88
29.45
27.86
23.79
24.31
23.41
21.48
17.93
20.82
25.98
26.12
27.54
27.65
26.02
22.49
23.06
40.16
41.03
32.29
24.77
29.22
37.41
30.52
30.46
43.88
38.11
70.64
64.22
60.20
55.60
25.49
25.59
30.39
0.60
0.62
0.54
0.59
0.38
0.40
0.69
0.50
0.42
0.51
0.38
0.57
0.73
0.62
0.71
0.61
0.59
0.43
0.42
0.38
0.44
0.88
0.43
0.49
0.78
0.59
0.49
0.54
0.49
0.49
0.41
0.47
0.75
0.64
0.74
0.78
0.75
0.73
0.75
0.66
0.47
0.50
0.47
0.50
0.44
0.82
0.64
0.54
0.56
0.53
0.55
0.54
0.57
0.78
0.61
0.57
0.58
0.67
0.54
0.51
0.41
0.51
0.52
0.86
0.75
0.96
0.76
0.83
0.85
0.93
0.83
0.81
0.87
0.71
0.75
0.96
0.92
0.71
1.84
2.02
2.49
1.79
1.33
1.38
1.58
1.52
1.26
1.51
1.69
1.22
1.82
1.73
1.91
1.75
2.02
2.08
2.28
1.90
1.83
1.67
1.31
2.32
2.09
1.99
1.47
2.52
1.74
1.38
1.62
1.51
1.55
1.64
1.62
1.92
1.99
2.32
2.18
2.21
2.02
2.07
1.88
2.13
1.58
2.26
1.91
1.76
1.57
1.53
1.46
1.38
1.55
2.10
1.69
1.73
1.91
1.85
1.75
1.66
1.45
2.23
2.05
2.47
2.36
2.50
2.37
2.32
2.51
2.67
2.31
3.33
2.74
2.82
2.83
2.30
1.72
2.07
Left
Left
Left
Left
Right
Left
Left
Left
Right
Right
Left
Left
Left
Left
Left
Left
Left
Left
Left
Right
Right
Right
Right
Right
Left
Left
Right
Right
Right
Left
Left
Left
Left
Left
Left
Left
Left
Right
Right
Right
Right
Right
Right
Right
Right
Right
Right
Right
Right
Right
Right
Right
723
IDENTIFYING ISOLATED THEROPOD TEETH
CA
80.59
81.59
82.66
81.03
62.70
67.37
60.34
68.48
68.52
63.58
68.97
82.94
84.76
84.38
84.20
83.94
85.51
86.00
86.77
85.41
83.94
57.40
56.25
76.08
49.89
53.69
68.19
70.29
62.55
54.67
63.27
82.53
81.86
81.83
81.83
81.05
83.31
82.42
81.89
81.41
83.89
84.16
83.26
83.76
71.72
79.29
80.57
80.91
78.31
77.65
76.77
75.55
73.60
81.72
79.93
80.67
81.26
79.97
79.94
77.34
77.62
83.93
83.01
82.96
80.56
82.42
83.39
82.60
81.14
83.60
83.08
85.78
85.54
85.06
85.94
83.79
78.27
81.18
CA2
0.10
0.11
0.13
0.08
0.01
0.09
0.13
0.12
0.04
0.12
0.19
⫺0.13
0.00
0.00
0.04
⫺0.02
⫺0.06
⫺0.08
0.00
⫺0.01
0.02
0.06
0.01
0.32
0.17
0.17
0.10
0.29
0.14
⫺0.01
0.08
⫺0.01
0.04
0.05
0.02
0.09
0.08
0.17
0.15
0.15
0.04
0.05
0.02
0.04
0.08
0.19
0.09
0.06
0.04
0.03
0.02
0.01
0.06
0.15
0.05
0.06
0.09
0.10
0.06
0.07
0.02
0.10
0.07
0.34
0.35
0.36
0.30
0.32
0.34
0.32
0.29
0.30
0.25
0.29
0.28
0.22
0.09
0.15
MA
MC
MB
DA
35.0
30.0
30.0
25.0
25.0
30.0
35.0
9.0
12.0
10.0
12.0
13.0
11.0
11.0
9.5
12.0
12.5
17.0
30.0
22.5
25.0
25.0
40.0
35.0
27.5
8.0
14.0
9.0
9.0
11.0
12.8
14.0
12.0
17.0
30.0
25.0
12.0
13.0
13.0
16.0
20.0
17.0
30.0
27.5
7.5
7.0
12.0
9.0
8.8
9.8
12.0
13.0
12.5
12.0
14.0
26.0
27.5
17.5
30.0
16.0
20.0
22.5
26.3
10.0
11.5
10.0
30.0
25.0
16.7
16.0
22.5
23.8
20.0
12.3
9.0
10.0
9.0
10.5
8.3
9.0
14.0
9.0
11.0
10.5
11.5
13.0
13.0
14.0
14.0
10.0
10.0
13.0
11.0
12.0
12.0
13.0
13.0
12.0
12.0
8.0
8.0
11.0
10.0
10.0
8.5
9.5
10.0
9.7
12.0
9.0
11.0
11.0
12.0
11.7
12.0
12.8
15.0
8.0
9.5
9.5
9.5
10.8
11.0
11.5
12.2
10.0
12.0
12.0
9.5
9.0
15.7
15.0
16.0
10.7
10.0
12.0
11.0
14.5
10.7
11.0
11.0
16.0
13.0
14.0
13.5
16.0
10.5
10.0
10.0
13.0
16.0
14.0
15.0
15.0
12.7
13.5
13.0
10.0
9.0
8.0
8.5
11.0
8.8
11.0
10.0
10.0
9.5
9.5
13.0
10.0
11.5
10.0
13.0
12.0
13.0
14.0
14.0
10.0
10.5
11.5
11.0
12.0
10.5
12.0
13.2
12.0
11.6
11.8
11.8
12.6
10.0
10.0
10.0
9.8
13.7
15.7
11.9
11.0
12.0
11.0
8.8
DC
20.0
25.0
25.0
20.0
20.0
25.0
30.0
8.0
8.0
9.0
8.0
7.0
9.0
10.0
11.0
12.0
10.5
14.5
25.0
22.5
18.5
15.0
20.0
20.0
16.7
12.0
11.0
13.0
DB
MAVG
35.0
30.0
30.0
25.0
25.0
30.0
35.0
10.0
12.0
13.0
13.0
12.8
16.3
15.0
13.0
15.0
26.0
17.5
20.0
22.5
23.8
17.5
10.7
11.3
11.0
11.7
12.8
15.3
17.0
30.0
25.0
35.0
35.0
19.5
27.5
10.0
11.5
10.0
11.0
9.0
9.0
10.0
9.0
14.0
9.0
9.5
11.0
10.0
10.5
11.3
10.5
11.0
8.5
9.0
10.0
10.5
10.0
9.5
11.5
11.7
9.3
10.0
15.0
14.0
14.0
11.0
11.0
11.5
10.0
15.0
11.0
12.0
11.5
11.0
12.0
11.8
11.0
12.0
10.0
11.6
11.5
11.5
13.3
13.0
14.0
15.0
14.0
13.0
29.2
26.3
13.4
13.8
10.5
12.0
8.8
8.5
13.0
11.3
12.0
9.4
10.0
10.1
9.9
13.5
9.6
11.0
10.8
13.2
12.6
13.0
13.4
15.0
9.5
9.8
10.8
11.2
12.9
12.3
13.2
13.4
11.6
12.5
10.0
10.0
11.0
11.0
12.8
17.7
10.5
11.8
12.8
10.0
DAVG
DAVG2
15.0
14.0
15.0
14.0
20.0
25.0
25.0
20.0
20.0
25.0
30.0
8.5
9.0
11.3
10.0
9.5
6.3
7.3
13.4
13.2
11.8
14.5
25.7
22.5
32.0
30.0
19.5
18.8
21.3
22.5
18.1
11.5
12.0
11.5
10.0
10.0
9.3
12.5
10.9
12.0
10.0
10.0
10.3
9.5
14.0
10.0
11.0
10.8
11.3
11.5
12.0
11.8
12.3
9.5
10.4
11.0
11.0
11.8
11.0
12.5
13.3
11.8
11.5
35.0
35.0
35.0
35.0
35.0
35.0
35.0
35.0
27.5
27.0
35.0
29.0
11.0
11.3
13.6
0.10
0.03
0.09
0.07
0.17
0.38
0.18
0.14
0.24
0.26
0.46
⫺0.12
⫺0.21
0.02
⫺0.17
⫺0.14
⫺0.48
⫺0.29
0.22
0.19
0.02
⫺0.33
0.27
0.13
0.11
0.15
0.13
⫺0.13
0.05
0.12
0.10
0.01
⫺0.03
⫺0.07
⫺0.18
⫺0.29
⫺0.31
⫺0.15
⫺0.26
⫺0.18
⫺0.18
⫺0.18
⫺0.12
⫺0.23
⫺0.11
⫺0.45
⫺0.20
⫺0.17
⫺0.14
⫺0.12
⫺0.08
⫺0.10
⫺0.17
⫺0.41
⫺0.22
⫺0.16
⫺0.19
⫺0.15
⫺0.17
⫺0.10
0.03
⫺0.09
⫺0.08
0.66
0.61
0.62
0.72
0.68
0.63
0.70
0.73
0.52
0.57
0.76
0.60
⫺0.33
⫺0.21
⫺0.06
724
SMITH ET AL.
APPENDIX A (continued)
Taxon
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Carcharodontosaurus
Carcharodontosaurus
Carcharodontosaurus
Carcharodontosaurus
Carcharodontosaurus
Carcharodontosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Daspletosaurus
Daspletosaurus
Daspletosaurus
Daspletosaurus
Daspletosaurus
Daspletosaurus
Daspletosaurus
Specimen
Side
Position
CBL
CBW
CH
AL
CBR
CHR
SDSM25248
SDSM25248
UMNHVP9211
UMNHVP9211
UMNHVP9275
UMNHVP9273
UMNHVP9273
UMNHVP9218
UMNHVP9369
UMNHVP9365
UMNHVP1251
CM 21703
CM 21703
CM 21703
LACM 46030
LACM 46030
LACM 46030
LACM 46030
LACM 46030
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
SGM Din-1
SGM Din-1
SGM Din-1
SGM Din-1
SGM Din-1
SGM Din-1
ROM1247
ROM1247
ROM1247
ROM1247
ROM1247
ROM1247
ROM1247
ROM1247
ROM1247
ROM1247
ROM1247
BMNH R4863
BMNH R4863
BMNH R4863
AMNH5346
MOR590
MOR590
MOR590
MOR590
MOR590
MOR590
Left
Left
Left
Left
Right
Right
Right
Left
Right
Right
Right
Left
Left
Left
Comp.
Comp.
Comp.
Comp.
Left
Comp.
Comp.
Comp.
Comp.
Comp.
Comp.
Left
Comp.
Right
Right
Right
Right
Right
Left
Comp.
Left
Comp.
Left
Comp.
Left
Left
Left
Left
Left
Right
Right
pm03
pm05
mx04
mx06
mx07
mx07
mx06
mx01
d06
d02
pm05
pm02
pm03
pm04
pm01
pm02
pm03
pm04
pm05
pm01
pm03
mx01
mx02
mx04
mx05
mx13
mx14
mx03
mx06
mx08
mx09
mx11
d01
d02
d03
d04
d05
d07
d08
d10
d12
d14
d17
d05
d06
Isolated
mx03
mx05
mx06
mx08
Isolated
d02
d03
d04
d06
d08
d09
d11
d13
d15
mx04
mx09
d04
d08
d10
mx02
d02
d03
d05
d07
d08
d10
20.36
16.01
14.99
15.22
12.08
14.06
14.78
17.32
11.77
10.63
16.10
14.05
12.79
13.73
16.10
16.00
15.50
16.30
17.50
21.70
26.84
26.73
35.24
36.60
42.07
22.43
17.11
37.21
40.79
31.94
29.11
26.64
14.42
23.91
29.63
29.11
30.60
31.10
26.08
28.26
24.96
20.42
15.37
28.98
31.35
41.53
41.46
41.04
41.17
39.91
46.65
12.40
17.82
21.28
21.24
19.96
17.81
18.48
17.72
13.69
26.48
20.55
28.83
26.37
24.47
27.00
18.02
22.88
22.86
22.53
22.32
19.19
12.29
8.23
7.33
7.04
7.45
7.59
7.21
13.03
8.26
9.77
13.82
12.52
10.50
10.65
15.30
14.60
14.90
13.50
12.80
16.26
16.56
17.56
20.59
20.64
20.74
10.87
8.55
21.44
17.86
16.73
14.43
11.78
11.77
17.10
17.63
19.33
18.75
17.19
16.58
14.35
13.22
11.46
9.10
16.54
16.71
15.09
15.15
14.88
14.88
14.49
16.88
11.60
14.25
10.77
12.89
13.56
7.67
11.41
9.21
8.83
13.40
10.57
19.82
17.70
18.46
22.63
12.68
17.81
17.28
16.63
12.29
12.17
49.57
34.05
30.02
33.48
25.43
28.50
25.52
38.25
25.80
24.62
40.85
34.31
34.20
33.19
33.90
33.89
36.81
37.69
38.85
52.23
72.35
62.60
79.23
87.09
93.08
33.79
25.03
90.75
82.30
66.78
54.97
39.40
29.46
58.55
72.23
70.62
60.48
64.85
43.01
47.47
38.96
33.13
16.04
68.15
62.15
80.68
71.01
73.96
73.17
73.99
97.55
25.53
42.21
39.68
43.84
43.31
31.91
37.00
31.30
22.19
54.85
40.31
55.99
44.57
53.37
74.78
36.43
52.62
54.55
49.57
46.78
34.93
54.00
39.74
37.51
37.90
30.53
32.12
29.82
42.19
29.10
27.61
40.61
34.82
36.53
35.51
36.69
35.99
38.30
38.98
40.26
55.15
77.51
71.29
90.02
97.50
107.90
41.87
32.12
101.46
90.25
76.59
64.00
46.47
35.42
63.55
79.20
77.81
68.81
76.07
58.07
55.54
49.00
38.86
22.61
72.16
72.97
89.82
82.32
80.59
79.51
80.02
102.25
25.99
42.39
45.91
53.44
44.01
32.75
41.35
41.50
24.90
58.75
36.92
59.02
51.28
57.27
80.86
39.52
56.49
57.94
49.81
50.65
35.69
0.60
0.51
0.49
0.46
0.62
0.54
0.49
0.75
0.70
0.92
0.86
0.89
0.82
0.78
0.95
0.91
0.96
0.83
0.74
0.75
0.62
0.66
0.60
0.56
0.49
0.48
0.50
0.58
0.44
0.52
0.50
0.44
0.82
0.72
0.59
0.66
0.61
0.55
0.64
0.51
0.53
0.56
0.59
0.57
0.53
0.36
0.37
0.36
0.36
0.36
0.36
0.93
0.80
0.51
0.61
0.68
0.43
0.62
0.52
0.65
0.51
0.51
0.69
0.67
0.75
0.84
0.70
0.78
0.76
0.74
0.55
0.63
2.43
2.13
2.00
2.20
2.11
2.03
1.73
2.21
2.19
2.32
2.54
2.44
2.67
2.42
2.10
2.12
2.37
2.32
2.23
2.41
2.71
2.33
2.22
2.36
2.21
1.51
1.46
2.44
2.02
2.09
1.89
1.48
2.04
2.44
2.44
2.42
1.98
2.09
1.65
1.68
1.56
1.62
1.04
2.35
1.98
1.94
1.71
1.80
1.78
1.85
2.09
2.06
2.37
1.86
2.06
2.17
1.79
2.00
1.77
1.62
2.07
1.96
1.94
1.69
2.18
2.77
2.02
2.30
2.39
2.20
2.10
1.82
Right
Right
Right
Right
Right
Right
Right
Right
Right
Right
Right
Right
Right
Right
Right
Right
Right
Right
Left
Right
Right
Right
Right
Right
Right
725
IDENTIFYING ISOLATED THEROPOD TEETH
CA
85.22
82.76
81.51
82.77
80.09
81.69
80.80
83.83
80.64
80.13
84.86
83.69
83.13
83.01
83.22
83.33
83.93
84.13
84.31
85.64
86.73
85.95
86.78
87.16
87.35
83.11
80.55
87.31
87.20
86.39
85.66
84.23
81.53
85.95
86.70
86.57
86.08
86.20
84.24
85.09
83.93
83.01
76.51
86.66
86.09
87.12
86.73
86.95
86.93
86.95
87.72
81.52
84.95
84.03
84.24
85.02
83.22
83.66
81.94
79.76
85.86
85.21
86.03
84.81
85.71
86.79
83.71
85.62
85.80
85.70
85.09
83.82
CA2
MA
MC
MB
DA
DC
DB
MAVG
DAVG
DAVG2
0.08
0.11
0.08
0.13
0.18
0.14
0.10
0.12
0.19
0.19
0.19
0.16
0.17
0.15
0.04
0.12
0.15
0.13
0.12
0.13
0.11
0.08
0.02
0.03
⫺0.03
0.00
0.02
0.03
⫺0.04
0.00
⫺0.01
⫺0.04
0.14
0.11
0.07
0.06
0.02
0.01
0.01
0.01
⫺0.01
0.04
⫺0.04
0.07
0.02
⫺0.09
⫺0.13
⫺0.12
⫺0.12
⫺0.11
⫺0.12
0.16
0.15
0.02
0.06
0.11
0.05
0.08
0.06
0.09
0.01
0.06
0.01
⫺0.01
0.06
0.09
0.11
0.07
0.07
0.06
0.04
0.05
10.0
13.0
14.0
15.0
18.0
15.0
16.0
11.0
16.0
12.0
11.0
11.0
11.0
11.5
8.0
8.0
9.0
9.3
11.0
14.4
13.4
13.5
12.1
12.2
12.8
9.0
16.0
11.5
11.0
14.0
13.5
12.5
9.5
18.0
10.0
10.0
10.0
9.5
10.5
9.5
9.3
9.5
9.8
11.0
15.1
12.4
12.0
12.3
12.1
11.0
24.0
15.0
15.0
21.0
20.0
22.0
20.0
20.0
15.0
14.0
11.0
11.5
12.7
13.0
12.5
13.0
12.5
12.0
17.9
19.0
19.6
19.6
16.2
21.0
10.0
14.0
12.0
15.0
17.0
16.0
18.0
12.0
15.0
12.0
12.0
9.0
9.5
9.5
9.5
9.8
10.8
10.3
11.5
12.7
12.4
13.6
13.7
13.0
12.9
14.0
15.3
11.7
12.3
12.1
13.3
13.8
13.3
12.5
15.0
12.6
13.0
12.0
14.0
9.0
12.5
10.0
11.0
17.5
14.0
15.0
11.5
13.5
11.0
11.0
10.0
10.0
11.0
10.0
10.3
10.0
10.0
11.0
14.1
13.7
14.2
13.4
13.6
12.9
16.0
12.0
15.0
15.0
19.0
18.0
18.5
18.0
13.0
18.0
13.7
17.5
11.0
10.0
11.0
12.8
13.3
13.0
13.5
18.8
19.1
18.2
19.2
19.5
10.0
17.7
13.5
13.7
17.7
16.2
16.8
13.5
18.0
12.3
11.7
10.7
10.7
11.6
10.2
9.9
10.5
10.5
11.3
15.8
14.9
15.0
14.6
13.5
15.3
12.0
14.9
17.8
20.0
13.3
14.6
13.0
18.0
10.3
13.8
12.3
15.0
17.5
16.2
17.0
12.2
15.5
12.2
13.5
10.0
9.8
10.5
6.5
10.9
11.3
11.1
12.0
15.2
15.1
15.3
15.4
15.4
14.0
15.0
15.0
14.9
14.8
13.5
13.3
14.0
14.0
14.5
15.0
13.0
14.8
13.8
14.9
16.0
14.5
14.5
15.0
15.5
16.2
11.4
10.4
10.1
10.2
10.0
9.8
11.9
13.2
11.8
13.1
13.4
12.1
13.0
15.0
14.0
11.5
11.5
11.5
11.7
12.0
11.9
14.0
10.9
10.7
10.5
10.7
11.6
⫺0.17
0.04
⫺0.06
0.09
0.14
0.13
0.22
⫺0.08
0.01
⫺0.24
⫺0.06
⫺0.33
⫺0.38
⫺0.29
⫺0.62
⫺0.20
⫺0.20
⫺0.19
⫺0.09
0.14
0.19
0.23
0.33
0.33
0.31
0.27
0.20
0.30
0.37
0.21
0.20
0.27
⫺0.01
0.14
0.24
0.11
0.27
0.22
0.28
0.36
0.26
0.19
0.22
0.27
0.37
0.19
0.14
0.10
0.11
0.08
0.08
⫺0.20
⫺0.03
0.01
0.07
0.05
0.00
0.03
0.17
0.03
0.03
⫺0.04
0.04
0.06
0.01
⫺0.02
0.07
⫺0.11
⫺0.13
⫺0.13
⫺0.08
⫺0.05
15.0
18.0
12.1
12.8
11.3
13.0
16.0
13.4
13.8
12.6
13.3
13.5
15.0
14.0
15.0
13.0
12.5
17.5
12.0
10.0
10.0
9.2
8.5
9.0
8.0
10.5
11.0
12.0
11.0
13.0
16.8
18.0
15.0
13.3
13.3
18.3
15.9
15.0
17.0
17.0
10.0
18.3
14.0
8.0
8.0
7.7
8.9
8.0
8.0
19.0
12.0
10.2
10.0
10.0
9.0
11.6
15.0
12.0
12.5
12.7
11.5
10.0
12.0
11.0
10.5
12.0
10.0
18.8
14.3
14.0
14.0
13.0
14.0
16.3
10.3
10.3
10.0
10.7
10.0
9.5
12.8
12.0
11.5
12.5
12.0
12.0
13.0
10.0
14.0
15.0
14.0
13.0
13.8
12.0
12.0
12.0
13.0
12.0
12.0
12.0
10.8
12.7
12.0
11.0
12.8
10.0
9.0
12.0
12.0
14.0
13.0
11.7
15.7
11.5
13.8
12.0
12.0
13.8
9.0
12.5
11.0
13.0
10.0
12.0
12.0
11.3
10.5
10.0
12.8
12.8
11.5
13.0
16.5
13.3
14.5
15.5
15.0
16.7
17.5
12.8
10.0
9.0
9.0
9.0
8.2
9.0
11.0
12.5
11.0
12.0
14.0
12.5
13.0
15.0
14.0
11.5
11.0
10.0
10.0
10.0
11.0
11.2
10.0
9.3
9.0
10.0
11.0
14.7
18.3
13.0
17.5
21.0
15.9
16.9
19.5
14.0
12.0
11.2
11.0
11.8
11.0
12.0
15.2
12.8
14.7
14.2
12.0
11.0
12.5
12.0
14.0
12.8
16.8
11.8
10.0
11.0
11.1
15.0
10.0
9.4
9.0
9.1
8.7
9.2
10.8
12.3
11.6
11.0
12.0
12.2
10.0
8.7
12.8
12.7
13.7
12.0
12.5
13.9
11.6
12.2
11.6
12.4
726
SMITH ET AL.
APPENDIX A. (continued)
Taxon
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Specimen
Side
Position
CBL
CBW
CH
AL
CBR
CHR
MOR 555
MOR 555
MOR 555
MOR 008
MOR 008
MOR 008
MOR 008
MOR 008
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
Left
Left
Left
Left
Left
Comp.
Right
Right
Left
Left
Left
Left
Right
Right
Right
Right
Right
Right
Comp.
Comp.
Left
Left
Left
Left
Left
Comp.
Comp.
Comp.
Comp.
Comp.
Comp.
Comp.
Comp.
Left
Right
Comp.
Comp.
Comp.
Comp.
Comp.
Comp.
Comp.
Comp.
Left
Right
Right
Right
Right
Comp.
Comp.
Right
Right
Comp.
Comp.
Right
Right
Comp.
Comp.
Comp.
Comp.
Comp.
Comp.
Right
Left
Left
Left
Left
Left
Comp.
Left
Comp.
Right
mx07
mx08
mx09
d03
d05
d06
d08
d10
pm03
mx05
mx07
mx08
mx01
mx02
mx03
mx10
mx11
mx12
d02
d12
d03
d05
d06
d08
d09
mx01
mx02
mx03
mx04
mx05
mx06
mx08
mx09
mx11
mx07
d01
d02
d03
d04
d06
d07
d09
d10
d13
d05
d08
d11
d12
pm01
pm03
pm02
pm04
pm01
pm03
pm02
pm04
mx01
mx03
mx05
mx06
mx07
mx08
mx11
mx04
mx01
mx02
mx03
mx04
mx08
mx10
mx11
mx06
42.86
37.34
33.72
46.05
39.29
38.23
35.00
31.50
36.06
45.46
39.41
38.56
44.86
47.69
46.74
35.65
27.86
18.96
40.76
26.47
52.07
48.74
40.21
34.49
34.69
45.88
51.98
48.63
49.71
48.15
38.48
29.25
32.08
21.25
40.19
26.23
40.66
46.20
46.28
37.65
33.38
30.62
28.05
15.01
45.89
33.12
23.64
18.52
27.38
34.87
31.75
30.05
29.84
30.94
29.93
31.86
38.89
41.46
48.60
38.37
40.01
37.54
25.92
50.01
49.49
36.77
47.17
46.68
43.60
42.51
30.97
48.00
28.35
22.82
24.44
33.78
31.25
27.07
26.60
21.00
24.00
32.63
27.18
26.20
32.60
37.58
37.21
23.48
18.18
13.20
24.51
19.13
32.67
33.94
27.37
25.71
24.51
34.97
34.23
33.03
29.58
31.47
27.20
19.01
21.86
14.57
23.64
18.32
26.36
32.70
31.88
27.74
23.15
21.42
20.44
9.22
32.17
24.75
16.61
13.56
14.27
21.75
18.04
19.03
16.45
19.46
16.94
21.18
31.57
30.59
31.17
24.42
25.31
26.05
16.46
33.93
34.82
28.68
32.77
36.68
27.50
26.68
20.17
33.14
72.67
65.11
55.11
91.00
78.00
75.00
65.00
55.00
63.65
94.06
75.75
72.55
91.12
105.26
108.82
61.04
45.96
29.72
75.03
44.29
87.42
88.87
78.09
66.25
63.57
93.68
102.21
115.30
103.42
94.89
73.70
48.55
55.34
31.96
66.28
45.17
71.99
94.97
89.01
62.01
50.54
46.83
41.56
15.85
77.74
54.12
30.34
21.91
44.22
58.66
50.14
52.80
42.55
45.42
43.64
54.62
85.47
103.98
102.44
77.64
79.70
82.14
37.57
104.06
100.89
81.60
117.06
108.53
87.85
91.27
51.14
105.46
80.21
70.53
56.72
93.00
79.50
76.50
67.00
56.50
71.97
108.36
86.34
83.44
101.55
117.64
122.99
71.65
49.90
32.17
81.29
47.71
95.97
93.94
84.19
74.66
66.84
98.79
108.00
118.82
110.83
99.43
79.43
56.35
56.57
32.14
69.94
46.31
78.02
96.00
90.85
66.10
53.48
50.62
45.04
17.41
78.96
56.48
33.09
24.25
50.21
60.01
56.28
53.94
50.21
58.26
54.33
60.01
93.14
109.25
104.79
88.33
84.23
84.04
42.72
115.51
103.67
88.33
120.69
116.36
105.70
103.51
57.92
116.94
0.66
0.61
0.72
0.73
0.80
0.71
0.76
0.67
0.67
0.72
0.69
0.68
0.73
0.79
0.80
0.66
0.65
0.70
0.60
0.72
0.63
0.70
0.68
0.75
0.71
0.76
0.66
0.68
0.59
0.65
0.71
0.63
0.68
0.69
0.59
0.70
0.65
0.72
0.69
0.74
0.69
0.70
0.73
0.61
0.70
0.75
0.70
0.73
0.52
0.62
0.57
0.63
0.56
0.63
0.57
0.66
0.81
0.74
0.61
0.62
0.58
0.69
0.64
0.68
0.70
0.78
0.69
0.79
0.63
0.63
0.65
0.69
1.70
1.74
1.63
1.98
1.99
1.96
1.86
1.75
1.77
2.07
1.92
1.88
2.03
2.21
2.33
1.71
1.65
1.57
1.84
1.67
1.68
1.82
1.94
1.92
1.83
2.04
1.97
2.37
2.08
1.97
1.92
1.64
1.73
1.50
1.65
1.72
1.77
1.91
1.94
1.48
1.51
1.53
1.48
1.06
1.69
1.63
1.28
1.18
1.62
1.68
1.58
1.76
1.42
1.47
1.46
1.71
2.20
2.52
2.05
1.99
2.06
2.19
1.45
2.08
2.04
2.22
2.48
2.33
2.01
2.15
1.64
2.20
727
IDENTIFYING ISOLATED THEROPOD TEETH
CA
86.90
86.56
86.09
87.62
87.23
87.11
86.66
86.07
86.38
87.43
86.88
86.75
87.43
87.73
87.76
86.16
85.15
82.55
87.00
84.98
87.43
87.51
87.10
86.47
86.53
87.62
87.81
88.09
87.81
87.67
86.93
85.01
86.11
83.34
86.70
85.22
86.89
86.89
87.56
86.44
85.65
85.29
84.71
76.45
87.25
85.98
82.84
80.12
84.85
86.33
85.51
85.92
84.59
84.83
84.70
85.87
87.28
87.81
87.87
86.99
87.32
87.35
84.05
87.75
87.84
87.16
88.11
87.88
87.18
87.37
85.40
87.76
CA2
MA
MC
MB
DA
DC
DB
MAVG
DAVG
DAVG2
⫺0.09
⫺0.07
⫺0.05
⫺0.10
⫺0.07
⫺0.07
⫺0.06
⫺0.07
⫺0.10
⫺0.10
⫺0.08
⫺0.08
⫺0.11
⫺0.11
⫺0.08
⫺0.08
⫺0.02
0.03
⫺0.11
⫺0.01
⫺0.17
⫺0.14
⫺0.08
⫺0.07
⫺0.04
⫺0.11
⫺0.16
⫺0.10
⫺0.12
⫺0.12
⫺0.07
⫺0.07
⫺0.04
0.02
⫺0.11
⫺0.03
⫺0.11
⫺0.15
⫺0.11
⫺0.13
⫺0.08
⫺0.07
⫺0.05
⫺0.02
⫺0.13
⫺0.04
⫺0.05
⫺0.01
⫺0.05
⫺0.06
⫺0.09
⫺0.04
⫺0.09
⫺0.09
⫺0.10
⫺0.06
⫺0.06
⫺0.04
⫺0.11
⫺0.08
⫺0.09
⫺0.05
⫺0.04
⫺0.13
⫺0.14
⫺0.05
⫺0.09
⫺0.09
⫺0.11
⫺0.09
⫺0.08
⫺0.11
8.8
9.0
7.8
11.1
9.3
8.8
8.0
9.0
8.3
12.0
13.8
14.0
12.0
9.0
9.0
8.6
11.0
10.4
10.8
7.0
9.0
8.5
9.0
8.5
7.1
7.5
8.3
8.8
7.0
7.0
7.0
9.0
10.0
12.0
7.0
10.5
6.5
7.0
9.0
8.0
9.0
7.7
7.2
8.2
8.0
7.0
4.5
10.2
9.9
14.0
9.0
8.9
8.2
7.0
7.7
8.0
9.4
9.2
10.4
15.7
7.0
10.0
10.9
14.0
9.9
9.8
8.5
8.7
9.6
9.5
8.0
8.9
8.4
7.8
7.5
7.4
7.4
8.3
10.5
8.0
6.5
7.0
7.5
6.7
8.0
7.8
8.5
7.0
13.7
13.1
13.7
11.0
10.6
10.7
10.2
10.0
9.0
8.3
7.0
9.0
9.1
8.9
8.7
8.7
7.1
8.5
8.8
8.4
10.7
10.9
9.3
10.0
8.5
8.1
9.7
9.0
10.1
8.4
8.3
8.3
7.9
9.6
8.4
10.3
10.2
13.4
10.6
9.6
8.4
8.0
7.6
8.1
9.5
9.2
10.5
14.4
8.3
10.3
11.9
13.7
10.6
10.8
9.6
9.7
10.0
10.0
9.2
9.7
7.7
8.1
8.8
9.2
9.3
9.3
10.2
7.8
9.0
7.5
8.5
8.5
8.8
9.0
8.6
11.2
10.8
11.0
9.0
9.0
9.3
9.0
8.5
8.4
9.1
9.3
9.8
8.0
8.0
8.6
9.8
11.8
11.7
8.6
11.1
8.6
8.3
9.3
8.7
10.9
8.1
7.3
7.7
8.8
8.5
9.6
9.4
10.6
13.2
9.9
9.4
8.6
7.2
8.7
8.7
9.9
9.7
11.0
15.7
9.0
11.3
11.6
14.0
11.0
10.6
9.2
10.1
10.4
10.5
9.3
10.0
8.5
9.0
9.2
8.9
8.8
9.1
11.7
7.8
7.2
8.3
7.5
8.1
8.7
8.5
9.3
8.0
0.17
0.10
0.08
⫺0.04
⫺0.09
⫺0.06
⫺0.10
⫺0.16
⫺0.13
⫺0.03
⫺0.04
0.01
⫺0.14
⫺0.14
⫺0.10
0.00
0.09
⫺0.02
⫺0.08
0.02
0.01
⫺0.06
⫺0.03
⫺0.14
0.06
⫺0.13
⫺0.17
⫺0.17
⫺0.02
⫺0.06
⫺0.02
⫺0.07
0.03
0.12
0.06
⫺0.12
⫺0.07
⫺0.21
⫺0.06
⫺0.05
0.01
⫺0.03
0.05
0.23
0.00
0.09
0.07
0.16
0.05
0.07
⫺0.05
⫺0.03
0.05
0.06
⫺0.04
⫺0.01
⫺0.16
⫺0.11
0.01
⫺0.07
⫺0.08
⫺0.10
0.09
⫺0.13
⫺0.20
⫺0.18
⫺0.22
⫺0.15
⫺0.06
⫺0.10
⫺0.07
⫺0.13
7.0
8.4
7.3
7.0
7.0
7.0
7.0
7.0
6.5
7.5
9.0
8.0
8.5
8.0
7.0
9.0
6.0
7.5
7.5
7.9
7.2
7.0
7.0
7.5
7.8
8.5
10.0
9.0
9.5
8.8
6.0
7.0
7.4
9.1
7.7
8.7
13.6
6.5
8.0
11.0
11.2
10.9
10.8
10.7
10.2
10.0
10.5
10.3
10.8
7.0
7.0
7.2
8.5
9.0
9.3
9.5
7.0
9.5
7.5
7.5
7.5
7.5
8.0
8.5
6.0
9.0
7.0
6.5
7.5
7.0
6.0
7.0
6.0
7.0
11.0
9.0
7.0
7.5
6.5
7.3
9.0
7.0
8.8
8.0
7.5
7.0
8.3
8.0
4.7
10.3
9.5
15.1
8.5
9.0
7.0
7.0
7.3
7.7
8.5
8.9
9.9
13.6
8.0
9.0
11.0
14.1
9.5
9.1
9.0
9.0
9.1
8.5
8.2
9.0
7.5
6.9
7.0
8.0
8.6
8.3
10.0
8.5
7.0
7.0
7.0
7.0
8.0
8.0
7.8
12.0
12.9
11.5
12.0
8.2
11.5
13.3
11.8
13.7
14.8
12.9
14.0
11.0
10.0
11.0
14.0
14.0
9.8
10.5
10.7
9.5
13.7
6.0
12.8
12.6
15.2
14.3
10.4
9.4
11.0
8.6
9.4
11.0
11.0
12.8
16.1
10.3
13.8
13.8
15.9
11.4
12.5
9.0
10.0
11.0
11.0
9.0
9.2
8.7
10.3
12.1
11.1
10.4
10.3
11.0
10.0
10.5
8.0
11.0
11.0
11.0
11.0
9.5
8.0
8.6
8.3
9.1
7.2
7.0
8.3
8.0
9.7
10.0
9.5
9.3
7.5
8.0
8.0
7.0
9.8
6.8
6.6
6.8
8.4
8.2
4.0
8.1
9.5
10.9
8.9
8.8
8.4
7.5
8.0
8.4
9.0
9.1
9.2
15.4
9.0
9.0
11.0
13.0
10.5
10.0
11.2
10.0
10.0
10.5
11.0
11.2
7.0
8.9
7.8
8.0
8.0
9.1
10.5
7.5
7.0
6.5
6.5
7.0
7.0
7.0
9.3
6.0
10.0
11.2
11.4
11.6
9.8
10.0
10.6
12.3
15.8
13.0
9.4
13.5
11.8
10.0
11.0
11.0
13.8
9.9
8.0
8.2
11.2
10.2
10.8
10.0
12.3
14.7
11.8
10.5
9.4
7.0
10.4
9.6
13.4
10.9
13.5
16.0
11.0
14.9
12.9
14.9
12.7
12.2
8.0
11.5
11.6
11.5
8.9
10.0
10.0
10.3
12.3
11.4
11.0
10.0
14.0
10.0
8.0
11.5
8.5
10.5
11.0
10.7
10.0
728
SMITH ET AL.
APPENDIX A. (continued)
Taxon
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Troodon
Troodon
Troodon
Troodon
Troodon
Troodon
Saurornithoides
Saurornithoides
Saurornithoides
Saurornithoides
Saurornithoides
Saurornithoides
Saurornithoides
Saurornithoides
Bambiraptor
Bambiraptor
Bambiraptor
Bambiraptor
Bambiraptor
Bambiraptor
Bambiraptor
Bambiraptor
Bambiraptor
Bambiraptor
Deinonychus
Deinonychus
Deinonychus
Deinonychus
Deinonychus
Deinonychus
Specimen
Side
Position
CBL
CBW
CH
AL
CBR
CHR
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
CM 9380
CM 9380
CM 9380
CM 9380
CM 9380
CM 9380
CM 9380
CM 9380
CM 9380
CM 9380
BMNH R5863
BMNH R5863
BMNH R5863
BMNH R5863
BMNH R5863
BMNH R5863
MOR 1125
LACM 150167
LACM 150167
LACM 150167
LACM 150167
LACM 23844
LACM 23844
LACM 23844
LACM 23844
LACM 23844
LACM 23844
LACM 23844
LACM 23844
LACM 23844
UCMP 118742
UCMP 118742
UCMP 118742
UCMP 118742
UCMP 118742
MOR 553
MOR 553
MOR 553
MOR 553
MOR 553
MOR 553
GIN100/1
GIN100/1
GIN100/1
GIN100/1
GIN100/1
GIN100/1
GIN100/1
GIN100/1
KUVP129737
KUVP129737
KUVP129737
KUVP129737
KUVP129737
KUVP129737
KUVP129737
KUVP129737
KUVP129737
KUVP129737
YPM523266-11
YPM523266-11
YPM523266-11
YPM5232612
YPM5232612
YPM5232557
Right
Left
Comp.
Comp.
Left
Comp.
Comp.
Right
Left
Left
Left
Comp.
Left
Right
Right
Right
Right
Right
Left
Left
Left
Left
Left
Left
Right
Left
Right
Right
Right
Right
Right
Right
Comp.
Left
Right
Comp.
Left
Left
Right
Right
Right
Right
Right
mx12
d04
d05
d06
d07
d08
d09
d03
d02
d04
d06
d07
d12
d01
d03
d05
d08
d10
d07
d08
d09
d11
d12
d13
mx10
mx06
d03
d04
d13
mx01
mx03
mx05
d02
d04
d05
d07
d08
d11
mx07
mx08
mx09
mx11
mx12
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
mx04
mx06
mx07
mx12
mx14
mx16
mx05
mx09
d06
d08
d09
d05
d07
mx04
mx06
mx09
Isolated
Isolated
d01
d12
d13
d14
d16
d07
22.50
44.90
42.37
40.22
39.10
34.77
30.92
46.11
42.34
51.10
46.93
41.69
21.50
25.56
48.46
47.34
39.08
30.20
40.46
38.87
32.59
30.49
23.98
18.37
34.20
42.10
38.10
42.10
16.20
46.00
54.50
47.80
38.80
47.10
47.60
37.20
41.20
20.00
45.40
42.00
41.30
28.80
19.10
4.92
6.22
6.00
5.60
5.20
4.45
3.58
3.66
4.31
3.80
4.09
3.76
2.98
4.09
2.37
2.34
2.08
2.37
2.47
2.61
2.35
2.54
3.22
2.15
5.07
7.07
6.76
6.74
5.35
7.15
12.83
32.89
28.11
28.37
26.46
25.60
20.59
30.97
30.87
38.04
35.35
31.29
16.32
18.09
37.48
37.21
28.71
23.90
28.55
33.12
26.99
22.12
16.12
10.35
21.30
25.80
23.90
28.90
11.00
33.70
34.40
32.60
27.40
35.10
33.90
27.10
28.50
15.90
35.00
30.50
33.50
19.00
14.00
2.43
2.95
3.03
2.71
2.33
1.62
2.68
2.69
2.45
2.48
2.51
2.26
2.50
2.61
1.41
1.41
1.40
1.61
1.24
1.41
1.20
0.99
1.37
1.57
3.00
3.20
2.93
2.80
2.41
3.23
32.08
105.61
96.28
82.23
74.66
68.24
55.57
99.03
86.64
92.07
82.01
70.93
34.05
35.01
97.52
96.12
68.04
51.94
76.12
65.23
56.60
45.63
32.38
22.51
60.68
88.82
73.35
76.02
17.75
79.09
117.1
100.5
68.93
87.99
96.94
60.98
85.30
21.78
83.09
71.36
72.95
48.26
27.02
7.22
9.61
9.39
8.47
7.84
7.25
5.01
5.51
5.61
6.45
6.40
6.23
4.28
6.33
5.33
5.01
4.82
4.91
5.58
5.99
5.86
4.62
5.66
4.03
8.85
10.07
9.56
9.14
6.53
11.01
39.31
115.88
98.90
93.04
80.16
75.89
63.53
109.10
87.83
104.05
87.03
78.07
37.10
40.02
102.32
100.54
72.00
62.75
86.28
79.88
62.74
52.60
37.07
26.85
68.00
92.44
86.70
87.89
19.90
88.18
138.90
110.90
77.65
107.40
102.20
71.93
96.94
27.29
94.84
78.29
88.32
54.52
34.25
8.66
10.25
10.36
8.94
9.74
7.36
6.92
7.79
7.37
8.47
7.16
7.97
5.25
6.57
7.28
6.53
5.25
6.83
6.39
7.13
6.86
5.14
6.95
4.39
10.37
12.31
12.29
11.78
8.35
13.50
0.57
0.73
0.66
0.71
0.68
0.74
0.67
0.67
0.73
0.74
0.75
0.75
0.76
0.71
0.77
0.79
0.73
0.79
0.71
0.85
0.83
0.73
0.67
0.56
0.62
0.61
0.63
0.69
0.68
0.73
0.63
0.68
0.73
0.74
0.71
0.76
0.69
0.79
0.77
0.73
0.81
0.66
0.73
0.49
0.47
0.51
0.48
0.45
0.36
0.75
0.74
0.57
0.65
0.61
0.60
0.84
0.64
0.60
0.60
0.67
0.68
0.50
0.54
0.51
0.39
0.43
0.73
0.59
0.45
0.43
0.42
0.46
0.45
1.43
2.35
2.28
2.04
1.91
1.96
1.80
2.15
2.05
1.80
1.75
1.70
1.58
1.37
2.01
2.03
1.74
1.72
1.88
1.68
1.74
1.50
1.35
1.23
1.77
2.11
1.93
1.81
1.09
1.92
2.55
2.32
1.96
2.28
2.15
1.50
2.35
1.36
2.09
1.87
2.14
1.89
1.79
1.47
1.55
1.57
1.51
1.51
1.63
1.40
1.51
1.30
1.70
1.57
1.66
1.44
1.55
2.25
2.14
2.32
2.07
2.27
2.30
2.49
1.82
1.76
1.87
1.74
1.42
1.41
1.36
1.23
1.54
Left
Left
Left
Left
Comp.
Comp.
Right
Right
Comp.
Comp.
Left
Right
Right
Left
Left
Left
Left
Left
Comp.
Right
Right
Right
729
IDENTIFYING ISOLATED THEROPOD TEETH
CA
82.87
87.75
87.72
87.11
86.99
86.59
85.81
87.64
87.52
87.49
87.31
86.82
83.47
83.66
87.73
87.70
86.76
85.41
86.93
86.35
85.99
85.05
83.16
80.21
86.22
87.51
86.7
86.91
77.86
87.12
87.87
87.68
86.50
87.22
87.70
86.05
87.20
80.06
87.19
86.85
86.71
85.27
81.45
56.53
66.58
65.53
63.39
58.81
59.04
34.94
39.64
45.04
48.08
52.26
47.35
21.14
53.46
22.10
20.95
31.88
11.89
39.74
41.83
39.80
30.01
41.88
10.74
62.34
66.71
65.04
64.12
53.03
68.35
CA2
MA
MC
MB
DA
DC
DB
MAVG
DAVG
DAVG2
⫺0.07
⫺0.09
⫺0.08
⫺0.09
⫺0.06
⫺0.06
⫺0.04
⫺0.12
⫺0.07
⫺0.14
⫺0.11
⫺0.10
0.02
⫺0.05
⫺0.09
⫺0.07
⫺0.05
⫺0.01
⫺0.10
⫺0.10
⫺0.05
⫺0.07
⫺0.05
⫺0.02
⫺0.07
⫺0.07
⫺0.07
⫺0.08
⫺0.01
⫺0.11
⫺0.10
⫺0.06
⫺0.06
⫺0.05
⫺0.10
⫺0.12
⫺0.04
0.00
⫺0.08
⫺0.09
⫺0.06
⫺0.01
0.05
⫺0.05
0.04
0.04
0.02
⫺0.02
0.01
⫺0.36
⫺0.28
⫺0.26
⫺0.08
⫺0.05
⫺0.10
⫺0.78
⫺0.06
⫺0.53
⫺0.59
⫺0.15
⫺1.03
⫺0.03
⫺0.01
⫺0.03
⫺0.29
⫺0.08
⫺1.12
0.13
0.05
0.07
0.03
⫺0.09
0.09
8.5
9.0
12.5
6.9
7.0
8.0
7.5
8.0
7.2
10.5
10.0
12.0
10.3
12.5
9.2
11.0
9.0
9.1
10.5
15.0
11.4
12.8
8.0
11.0
7.5
9.5
10.0
10.0
9.0
11.5
8.0
9.0
9.0
10.0
9.5
8.0
8.5
8.0
9
6.8
7.0
8.3
10.3
12.0
10.5
8.5
8.0
8.0
8.0
12.0
11.0
11.5
12.5
12.0
12.0
13.0
11.5
10.0
11.9
11.8
11.8
11.2
11.0
16.0
15.0
12.3
12.5
12.5
13.5
13.0
12.5
8.5
12.0
9.5
16.0
9.0
8.8
12.0
12.0
10.0
12.0
9.0
8.0
9.0
8.5
9.0
9.5
9.5
12.0
9.0
8.5
9.5
10.0
12.0
9.0
6.7
7.5
7.0
9.0
7.5
8.5
7.0
8.0
9.0
10.0
8.5
13.0
11.0
7.5
9.0
11.0
10.0
7.8
8.0
7.2
6.9
7.5
9.0
7.5
7.5
8.5
8.0
8.0
8.1
9.5
7.8
10.0
7.7
7.5
8.0
9.0
10.5
14.0
9.5
8.5
10.0
8.5
14.0
10.0
11.0
11.5
12.0
12.5
16.0
12.0
12.0
12.0
14.0
19.5
9.2
9.8
10.8
10.0
9.7
11.0
9.2
9.0
10.3
9.3
9.8
10.6
11.5
11.2
9.7
8.5
9.8
8.3
13
6.5
6.5
8.5
10.0
9.0
8.0
10.0
12.0
8.5
7.5
8.5
10.0
8.5
9.0
7
8.0
10
11.0
7.8
8.8
18.8
9.0
9.0
9.0
10.0
11.0
15.0
10.0
12.5
15.0
12.5
10.0
9.0
10.0
13.0
14.0
11.3
10.0
8.8
12.5
12.5
12.5
15.0
10.0
10.0
15.0
13.0
16.0
17.0
16.0
17.0
12.5
12.5
13.8
10.0
16.3
8.0
8.0
8.0
8.0
11.0
19.4
10.0
10.0
10.0
13.3
12.5
12.5
10.0
10.0
25.0
25.0
17.5
9.2
7.7
8.4
8.5
10.7
9.0
10.3
7.6
9.7
9.0
9.7
9.8
12.3
11.6
9.6
10.7
12.0
12.5
8.9
9.0
9.5
10.2
10.8
14.0
10.2
9.7
10.5
10.8
15.2
8.5
8.5
10.3
9.5
10.5
8.5
9.3
9.5
12.5
9.0
9.0
9.0
11.0
12.0
12.9
11.4
11.7
11.3
13.8
12.5
15.0
11.5
10.0
15.0
12.5
14.2
10.0
10.6
25.0
22.5
30.0
30.0
27.0
25.0
24.2
32.5
30.4
25.0
19.4
17.3
21.3
18.8
19.4
17.5
⫺0.13
⫺0.19
⫺0.14
⫺0.12
0.07
⫺0.11
⫺0.01
⫺0.18
⫺0.01
0.02
0.05
0.03
0.05
0.09
0.02
0.10
0.18
0.14
⫺0.06
⫺0.05
⫺0.07
0.01
0.02
0.18
0.02
0.00
0.06
0.12
0.21
⫺0.09
⫺0.09
0.05
⫺0.05
0.05
⫺0.09
0.00
⫺0.06
0.04
⫺0.07
⫺0.06
⫺0.10
0.00
⫺0.05
⫺0.33
⫺0.35
⫺0.35
⫺0.40
⫺0.26
⫺0.39
⫺0.42
⫺0.61
⫺0.61
⫺0.36
⫺0.46
⫺0.40
⫺0.92
⫺0.60
⫺0.29
⫺0.38
⫺0.12
⫺0.27
⫺0.09
⫺0.13
⫺0.21
0.07
0.16
⫺0.46
⫺0.03
0.05
0.21
0.11
0.04
0.05
9.0
8.5
8.5
9.0
9.0
10.0
8.0
9.0
9.5
7.5
11.0
9.0
7.0
8.0
8.0
10.0
10.0
10.0
12.5
12.5
20.0
10.0
10.0
10.0
12.5
12.0
12.5
12.5
10.0
20.0
30.0
35.0
30.0
30.0
25.0
24.2
32.5
23.7
17.7
22.3
20.0
24.3
20.5
17.5
17.2
17.5
16.3
17.8
17.5
17.5
24.0
32.0
35.0
33.8
32.3
24.8
29.5
27.5
29.5
29.0
28.5
30.0
28.5
29.8
8.4
8.3
9.1
8.2
9.3
8.5
12.5
11.8
25.0
32.5
25.0
25.0
27.5
23.8
20.3
17.5
24.8
28.4
30.8
30.4
30.3
29.0
730
SMITH ET AL.
APPENDIX A. (continued)
Taxon
Deinonychus
Deinonychus
Deinonychus
Deinonychus
Deinonychus
Deinonychus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Specimen
YPM5232557
YPM5232557
YPM5232557
YPM5232557
YPM5232557
MCZ8791
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH6515
AMNH6515
AMNH6515
AMNH6515
AMNH6515
AMNH6515
AMNH6515
Uncat. GIN
Uncat. GIN
Uncat. GIN
Uncat. GIN
Uncat. GIN
Uncat. GIN
Side
Right
Right
Right
Right
Right
Left
Comp.
Comp.
Left
Comp.
Right
Right
Left
Left
Left
Left
Left
Premax
Premax
Maxilla
Maxilla
Maxilla
Maxilla
Dentary
Maxilla
Maxilla
Maxilla
Maxilla
Maxilla
Maxilla
Position
CBL
CBW
CH
AL
CBR
CHR
d07
d08
d10
mx01
pm01
mx03
mx03
mx04
mx05
mx06
mx02
mx07
d02
d03
d04
d05
d08
pm01
pm03
mx02
mx04
mx06
mx08
d01
mx05
mx08
mx01
mx03
mx05
mx06
7.15
6.36
7.04
7.13
5.74
6.11
7.21
6.84
7.64
6.28
6.69
5.70
5.46
6.09
6.47
6.56
5.56
3.55
3.30
4.17
4.35
3.95
3.11
2.42
4.69
4.59
4.47
6.14
5.99
4.72
3.23
3.07
3.20
4.00
3.20
2.58
4.06
3.70
4.02
3.13
3.32
3.11
4.03
3.81
3.91
3.89
3.27
1.54
1.54
1.45
2.15
1.61
1.13
0.88
1.55
1.52
1.50
1.81
1.79
1.55
11.01
10.40
12.23
13.58
11.79
8.77
12.86
11.58
12.38
10.68
10.98
9.70
9.40
11.55
11.22
11.27
8.52
5.85
4.38
6.70
7.91
6.93
4.69
0.57
⫺0.13
⫺0.08
⫺0.02
⫺0.07
0.01
⫺0.02
13.50
12.10
14.17
16.14
10.80
13.70
15.80
13.97
16.37
12.40
12.89
11.00
10.50
12.34
13.10
12.99
10.70
6.79
5.88
8.42
9.54
9.09
0.80
1.17
1.98
2.00
2.79
2.46
2.40
2.01
0.45
0.48
0.45
0.56
0.56
0.42
0.56
0.54
0.53
0.50
0.50
0.55
0.74
0.63
0.60
0.59
0.59
0.43
0.47
0.35
0.49
0.41
0.26
0.48
0.42
0.44
0.62
0.40
0.40
0.43
1.54
1.64
1.74
1.90
2.05
1.44
1.79
1.69
1.62
1.70
1.64
1.70
1.72
1.90
1.73
1.72
1.53
1.65
1.33
1.61
1.82
1.75
1.51
1.76
2.01
2.02
1.70
1.60
1.66
1.44
*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.
731
IDENTIFYING ISOLATED THEROPOD TEETH
CA
68.35
67.24
70.57
71.87
73.56
60.88
70.76
69.08
69.92
67.66
68.39
65.64
64.99
70.23
68.66
68.96
61.27
46.51
23.87
51.72
57.85
51.05
35.07
13.62
64.86
63.35
57.08
64.98
64.66
52.81
CA2
0.09
0.11
0.13
0.17
0.26
0.02
0.15
0.13
0.12
0.16
0.12
0.16
0.19
0.19
0.15
0.15
0.06
⫺0.01
⫺0.59
0.02
0.15
0.04
⫺0.27
⫺0.95
0.19
0.19
0.11
0.11
0.13
⫺0.02
MA
27.5
20.0
27.3
22.0
18.8
28.0
18.8
21.5
21.5
MC
MB
28.5
28.5
27.5
25.0
28.0
13.8
16.0
17.5
18.8
17.5
15.0
13.8
17.0
17.0
17.0
30.0
30.0
37.5
37.5
40.0
29.8
15.0
15.0
15.8
8.8
15.0
17.5
17.5
DA
DC
DB
MAVG
DAVG
DAVG2
17.5
17.5
15.0
20.0
15.0
27.0
18.0
17.5
15.0
20.0
17.3
17.0
20.0
17.5
20.0
17.5
17.5
17.5
17.5
29.0
29.0
27.5
26.3
17.5
17.5
16.8
17.5
17.5
20.4
18.2
17.5
19.2
22.1
17.9
22.5
25.0
17.1
18.2
18.2
17.5
30.0
30.0
29.2
30.0
28.3
28.8
31.1
21.3
23.4
25.0
22.5
26.7
25.0
0.05
⫺0.01
⫺0.01
0.00
⫺0.08
0.14
0.04
0.01
0.13
0.17
0.03
0.15
0.19
⫺0.08
0.01
0.01
⫺0.06
0.20
0.09
0.27
0.28
0.20
0.12
⫺0.15
0.03
0.10
0.13
0.20
0.33
0.20
22.5
20.7
20.0
15.0
15.0
25.0
21.3
18.0
18.0
25.0
30.0
30.0
27.5
25.0
27.5
32.2
21.3
22.5
25.0
20.0
25.0
15.0
17.5
17.5
17.5
35.0
30.0
25.0
30.0
30.0
17.5
16.8
19.5
15.0
17.5
15.0
16.3
22.5
15.0
19.0
19.0
35.0
25.0
25.0
20.0
22.5
22.5
35.0
27.5
28.4
16.9
15.7
17.1
20.7
17.1
17.5
16.3
13.8
17.8
17.8
17.0
30.0
30.0
37.5
37.5
40.0
APPENDIX B. Data for the test case teeth used in this article*
Specimen
CBL
CBW
CH
AL
CBR
CHR
CA
CA2
MA
MC
MB
DA
DC
DB DAVG DAVG2
Fun.1
Fun.2
AMNH 5027 mx1
BHI 3033 d6
FMNH PR2081 mx3
MOR 555 mx9
SDSM 12047 d4
FMNH PR2081
SDSM 12047a
SDSM 12047b
UCMP 131583
UNO 1234
BMNH R332
UMNH VP6368
MOR 693
YPM 5278
AMNH 5456
SMU 74646
FUB PB Ther1
YPM 54461
CM 30749
CGM 81136
38.89
37.65
46.74
33.72
44.90
34.34
41.42
35.35
39.31
23.42
20.90
9.23
17.84
8.86
6.24
32.30
32.00
13.78
20.02
31.58
31.57
27.74
37.21
24.44
32.89
26.17
19.82
22.28
28.96
15.40
11.80
5.77
9.41
4.57
4.36
19.00
17.03
8.12
12.14
15.11
85.47
62.01
108.82
55.11
105.61
70.64
76.78
63.79
65.45
35.16
38.92
19.46
40.90
15.04
13.08
83.91
71.02
26.93
39.38
64.12
93.14
66.10
122.99
56.72
115.88
74.78
90.13
66.12
71.21
42.06
45.56
23.12
42.40
18.00
14.31
87.73
77.97
30.30
45.79
66.63
0.81
0.74
0.80
0.72
0.73
0.76
0.48
0.63
0.74
0.66
0.56
0.62
0.53
0.52
0.70
0.59
0.53
0.59
0.61
0.48
2.20
1.48
2.33
1.63
2.35
2.06
1.86
1.80
1.67
1.50
1.86
2.11
2.29
1.69
2.10
2.60
2.22
1.95
1.97
1.50
87.28
86.44
87.76
86.09
87.75
86.83
86.88
86.59
86.59
83.47
83.87
77.10
84.58
74.11
72.00
87.30
86.69
81.27
83.88
83.47
⫺0.06
⫺0.13
⫺0.08
⫺0.05
⫺0.09
⫺0.03
⫺0.11
⫺0.06
⫺0.11
⫺0.03
0.03
0.19
0.15
0.15
0.22
0.06
⫺0.31
0.11
0.06
⫺0.03
7.0
7.4
7.0
7.8
7.5
7.7
6.0
8.8
8.7
9.4
13.3
14.0
8.0
9.0
7.0
9.0
9.0
11.5
16.0
13.0
28.0
15.0
14.0
6.0
11.8
11.0
9.0
8.0
10.0
9.0
10.0
10.5
15.0
14.0
32.5
13.0
10.0
7.0
11.9
8.5
11.0
13.0
9.5
11.0
13.0
13.0
20.0
22.0
35.0
19.0
19.0
13.0
18.5
14.0
7.0
8.4
8.3
8.6
7.5
8.0
9.0
9.5
11.0
9.5
10.0
15.0
13.0
18.8
17.5
15.0
7.0
13.0
10.5
8.4
8.0
7.0
10.8
6.7
9.0
9.0
9.0
8.0
10.0
11.0
16.0
15.0
17.5
16.0
11.0
8.0
12.9
12.0
10.0
9.6
10.6
13.7
9.0
12.5
11.0
13.0
9.1
13.0
15.0
20.0
22.0
21.3
17.0
17.0
13.7
13.0
15.0
⫺0.16
⫺0.05
⫺0.10
0.08
⫺0.19
⫺0.05
0.03
0.05
⫺0.01
⫺0.01
0.02
0.03
0.20
0.17
⫺0.11
0.21
⫺0.08
⫺0.06
0.02
⫺0.01
2.27
4.38
2.99
3.61
2.54
2.16
3.97
3.15
4.46
1.48
⫺0.40
⫺2.94
⫺1.98
⫺2.66
⫺3.01
0.08
0.61
⫺2.03
⫺0.63
1.18
⫺0.92
⫺1.67
⫺0.59
0.21
⫺1.47
⫺0.07
⫺0.67
⫺0.08
⫺0.81
⫺0.91
⫺0.17
1.12
2.68
0.85
0.21
3.46
⫺0.59
⫺0.45
0.38
⫺0.47
*Fun. 1 and 2 are the scores from discriminate functions 1 and 2. Other variables as in the text.
8.5
8.7
8.6
11.0
7.7
9.8
9.5
10.5
9.4
10.8
12.0
17.0
16.7
19.3
16.8
14.3
9.6
12.9
12.5
10.2
APPENDIX C. PCA Orthogonal scores and DFA function scores for the specimens in the standard data set.
Taxon
Dilophosaurus
Dilophosaurus
Dilophosaurus
Dilophosaurus
Liliensternus
Liliensternus
Liliensternus
Liliensternus
Liliensternus
Liliensternus
Liliensternus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Ceratosaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Masiakasaurus
Indosuchus
Indosuchus
Indosuchus
Indosuchus
Indosuchus
Indosuchus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Specimen
UCMP 37303
UCMP 37303
UCMP 37303
UCMP 37303
MBR 21751.4
MBR 21751.3
MBR 21751.8
MBR 21751.8
MBR 21751.8
MBR 21751.8
MBR 21751.9
UMNHVP7819
UMNHVP7819
UMNHVP7819
UMNHVP7819
UMNHVP7819
UMNHVP5278
UMNHVP5278
UMNHVP5278
UMNHVP5278
UMNHVP5278
98312-1
95345-1
99016
95358
95244-1
98313-1
98203
93086-4
95435
96068-4
AMNH 1955
AMNH 1753
AMNH 1753
AMNH 1753
AMNH 1753
AMNH 1753
FMNHPR2008
UA 8716
UA 8716
FMNHPR2100
FMNHPR2100
Side Position Orth.1 Orth.2 Fun.1 Fun.2
R
L
L
R
L
L
L
L
R
L
L
L
R
R
L
L
L
L
L
L
L
L
L
R
R
R
R
R
L
L
mx3
max
max
max
max
max
d01
d04
d15
d16
?d19
pm01
pm02
pm03
pm01
pm03
mx01
mx03
mx05
mx08
mx10
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
mx08
pm02
pm03
pm04
pm01
pm02
pm02
pm02
pm04
mx04
mx06
⫺0.13
⫺0.14
⫺0.15
⫺0.01
⫺0.81
⫺0.86
⫺1.46
⫺0.90
⫺0.58
⫺1.22
⫺1.16
0.95
0.50
0.48
0.31
0.54
0.80
0.90
0.58
0.57
0.37
⫺1.37
⫺1.27
⫺1.28
⫺2.45
⫺2.14
⫺0.85
⫺1.51
⫺1.36
⫺1.32
⫺1.07
0.42
0.16
0.16
0.26
⫺0.07
0.10
⫺0.33
⫺0.27
⫺0.28
0.28
0.26
⫺0.05
0.33
0.85
⫺0.25
⫺2.12
⫺1.74
⫺0.06
⫺1.02
⫺2.10
⫺0.87
⫺1.05
⫺1.93
0.10
⫺0.32
0.25
⫺0.39
⫺0.18
⫺0.64
⫺0.02
⫺0.95
⫺0.87
0.40
⫺1.74
0.50
1.41
0.56
⫺1.21
0.93
⫺0.56
⫺1.35
⫺1.32
⫺1.47
⫺0.29
⫺0.46
⫺0.27
0.45
0.47
1.12
0.86
0.72
⫺0.47
⫺0.23
⫺0.68
⫺1.12
⫺1.83
⫺0.51
⫺3.83
⫺3.06
⫺2.11
⫺2.99
⫺2.68
⫺3.04
⫺3.85
2.23
0.57
0.83
⫺0.22
0.20
⫺0.49
⫺0.10
0.83
0.53
⫺0.91
⫺1.71
⫺3.63
⫺4.55
⫺2.84
⫺4.08
⫺2.98
⫺5.30
⫺4.13
⫺3.62
⫺4.60
⫺0.26
0.56
⫺0.45
0.09
⫺1.21
⫺1.13
⫺2.26
⫺2.08
⫺2.58
⫺2.07
⫺2.05
0.93
0.77
2.24
0.38
⫺0.80
1.47
1.91
0.01
⫺0.08
1.34
2.89
⫺3.14
⫺1.86
⫺0.32
⫺1.20
⫺1.85
⫺4.71
⫺3.30
2.20
0.93
⫺0.73
⫺1.69
0.59
1.83
3.46
2.14
⫺0.26
0.19
⫺0.30
⫺0.31
⫺1.88
⫺1.54
⫺0.43
⫺1.18
⫺1.84
⫺1.81
⫺2.11
0.38
⫺1.03
⫺0.51
⫺2.10
⫺1.90
Taxon
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Majungatholus
Baryonyx
Baryonyx
Baryonyx
Baryonyx
Baryonyx
Baryonyx
Baryonyx
Baryonyx
Suchomimus
Suchomimus
Suchomimus
Suchomimus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Specimen
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2100
FMNHPR2278
FMNHPR2278
BMNH R9951
BMNH R9951
BMNH R9951a
BMNH R9951d
BMNH R9951e
BMNH R9951f
BMNH R9951h
BMNH R9951n
UC G89-5
UC G54-4
UC G48-9
UC G67-1
YPM1333
YPM1333
YPM1333
SDSM25248
SDSM25248
UMNHVP9211
UMNHVP9211
UMNHVP9275
UMNHVP9273
Side Position Orth.1 Orth.2 Fun.1 Fun.2
R
R
R
L
L
L
L
L
L
L
L
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
L
L
L
L
R
R
mx05
mx07
mx17
d01
d05
d07
d12
d13
d14
d15
d17
d02
d03
d04
d06
d10
d11
d15
d16
mx02
mx03
pm04
pm06
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
pm02
pm03
pm05
pm03
pm05
mx04
mx06
mx07
mx07
0.35
0.28
⫺0.55
⫺0.57
⫺0.09
0.06
⫺0.01
0.00
⫺0.02
⫺0.02
⫺0.35
⫺0.30
0.04
0.02
⫺0.06
⫺0.15
⫺0.01
⫺0.19
0.03
0.05
0.13
⫺1.02
⫺1.16
⫺1.14
⫺0.82
⫺0.96
⫺1.12
⫺0.90
⫺0.79
⫺0.91
⫺0.79
⫺0.68
⫺0.49
⫺0.49
⫺0.22
⫺0.30
0.20
⫺0.06
0.00
⫺0.15
⫺0.48
⫺0.26
⫺0.72
⫺0.15
⫺1.38
1.12
0.06
⫺0.62
⫺0.94
⫺1.14
⫺1.25
⫺1.49
⫺0.90
0.71
⫺0.53
⫺0.57
⫺0.20
0.08
⫺0.68
⫺0.88
⫺1.86
0.18
⫺0.13
2.30
1.81
2.57
1.90
1.96
2.33
2.77
1.98
2.77
1.99
3.17
2.61
1.57
0.51
0.70
0.82
0.10
⫺0.30
0.03
0.59
0.11
⫺1.57 ⫺1.93
⫺2.36 ⫺2.22
⫺3.69 ⫺2.72
⫺2.53 ⫺2.16
⫺1.94 ⫺1.68
⫺1.97 ⫺2.30
⫺1.78 ⫺2.42
⫺1.90 ⫺2.47
⫺1.67 ⫺2.20
⫺1.75 ⫺2.60
⫺2.45 ⫺2.59
⫺2.08 ⫺2.58
⫺1.63 ⫺2.62
⫺1.79 ⫺2.19
⫺2.26 ⫺1.97
⫺1.67 ⫺1.19
⫺2.23 ⫺2.44
⫺2.54 ⫺2.04
⫺2.21 ⫺1.82
⫺2.54 ⫺0.48
⫺2.10 ⫺0.88
⫺1.57 ⫺1.93
⫺2.36 ⫺2.22
⫺0.46
9.70
⫺1.30
8.41
⫺0.13
9.98
⫺0.30
9.47
⫺0.29
9.25
⫺0.68
9.52
⫺0.01 10.82
0.37
9.70
⫺2.69 10.05
⫺0.53
9.08
0.33
0.43
⫺0.05 ⫺0.69
⫺1.68
0.56
⫺2.11 ⫺0.37
⫺2.33
0.56
⫺2.58 ⫺0.84
⫺2.87
1.01
⫺2.27
2.11
⫺2.17
1.38
(continues)
APPENDIX C. PCA Orthogonal scores and DFA function scores for the specimens in the standard data set. (continued)
Taxon
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Allosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Acrocanthosaurus
Carcharodontosaurus
Carcharodontosaurus
Carcharodontosaurus
Carcharodontosaurus
Specimen
UMNHVP9273
UMNHVP9218
UMNHVP9369
UMNHVP9365
UMNHVP1251
CM 21703
CM 21703
CM 21703
LACM 46030
LACM 46030
LACM 46030
LACM 46030
LACM 46030
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
NCSM 14345
SGM Din-1
SGM Din-1
SGM Din-1
SGM Din-1
Side Position Orth.1 Orth.2 Fun.1 Fun.2
R
L
R
R
R
L
L
L
C
C
C
C
L
C
C
C
C
C
C
L
C
R
R
R
R
R
L
C
L
C
L
C
L
L
L
L
L
R
R
R
R
R
mx06
mx01
d06
d02
pm05
pm02
pm03
pm04
pm01
pm02
pm03
pm04
pm05
pm01
pm03
mx01
mx02
mx04
mx05
mx13
mx14
mx03
mx06
mx08
mx09
mx11
d01
d02
d03
d04
d05
d07
d08
d10
d12
d14
d17
d05
d06
Isolated
mx03
mx05
mx06
⫺0.13
⫺0.03
⫺0.50
⫺0.54
⫺0.28
⫺0.21
⫺0.30
⫺0.21
0.24
⫺0.07
⫺0.19
⫺0.09
⫺0.03
⫺0.02
0.15
0.22
0.50
0.51
0.75
0.40
0.18
0.51
0.77
0.56
0.56
0.62
⫺0.24
0.10
0.31
0.35
0.46
0.51
0.44
0.49
0.48
0.26
0.23
0.29
0.46
1.00
1.13
1.11
1.11
⫺0.68
1.03
0.95
1.62
1.88
1.64
1.79
1.32
1.01
1.23
1.78
1.37
0.99
1.48
1.50
1.09
0.73
0.83
0.25
⫺1.23
⫺1.30
0.99
⫺0.33
0.13
⫺0.39
⫺1.53
0.99
1.42
1.04
1.18
0.32
0.25
⫺0.27
⫺0.67
⫺0.91
⫺0.65
⫺2.15
0.82
0.07
⫺1.03
⫺1.53
⫺1.38
⫺1.44
⫺1.51
⫺1.13
⫺2.12
⫺1.50
⫺1.42
⫺1.67
⫺2.89
⫺2.31
⫺0.78
⫺0.37
⫺0.77
⫺1.26
⫺1.22
⫺0.64
⫺1.15
0.05
2.01
1.68
3.27
0.89
⫺0.36
1.54
3.85
1.43
1.34
1.90
⫺0.75
⫺0.60
0.12
0.06
1.84
1.34
1.86
2.07
1.51
0.37
0.66
0.28
1.89
3.98
4.70
4.25
4.40
1.26
0.75
1.56
0.68
2.48
⫺0.28
⫺0.46
⫺0.49
⫺3.87
0.21
1.13
0.36
0.60
3.36
3.83
3.38
3.64
3.79
2.99
1.15
0.39
3.73
3.10
2.02
1.34
0.92
1.52
3.11
3.43
2.37
2.67
2.20
2.09
2.53
1.34
0.97
0.10
3.45
3.33
0.96
⫺0.07
⫺0.28
⫺0.17
Taxon
Specimen
Carcharodontosaurus
Carcharodontosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Gorgosaurus
Daspletosaurus
Daspletosaurus
Daspletosaurus
Daspletosaurus
Daspletosaurus
Daspletosaurus
Daspletosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
SGM Din-1
SGM Din-1
ROM1247
ROM1247
ROM1247
ROM1247
ROM1247
ROM1247
ROM1247
ROM1247
ROM1247
ROM1247
ROM1247
BMNH R4863
BMNH R4863
BMNH R4863
AMNH5346
MOR590
MOR590
MOR590
MOR590
MOR590
MOR590
MOR 555
MOR 555
MOR 555
MOR 008
MOR 008
MOR 008
MOR 008
MOR 008
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
Side Position Orth.1 Orth.2 Fun.1 Fun.2
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
L
R
R
R
R
R
R
L
L
L
L
L
C
R
R
L
L
L
L
R
R
R
R
R
R
C
C
mx08
isolated
d02
d03
d04
d06
d08
d09
d11
d13
d15
mx04
mx09
d04
d08
d10
mx02
d02
d03
d05
d07
d08
d10
mx07
mx08
mx09
d03
d05
d06
d08
d10
pm03
mx05
mx07
mx08
mx01
mx02
mx03
mx10
mx11
mx12
d02
d12
1.07
1.14
⫺0.34
⫺0.12
0.36
0.21
0.05
0.23
0.09
0.10
⫺0.12
0.49
0.27
0.53
0.54
0.28
0.21
⫺0.02
0.24
0.24
0.27
0.36
0.22
0.98
0.88
0.77
1.04
0.88
0.88
0.84
0.84
1.09
1.02
0.94
0.91
1.09
1.08
0.98
0.91
0.59
0.27
1.06
0.55
⫺1.28
⫺0.84
1.21
1.46
⫺0.49
0.36
0.80
⫺1.00
0.26
⫺0.50
⫺0.40
⫺0.09
⫺0.29
0.36
⫺0.20
1.01
2.14
0.63
1.21
1.27
0.91
0.08
⫺0.10
⫺0.20
⫺0.31
⫺0.17
0.48
0.66
0.36
0.30
⫺0.27
⫺1.25
0.62
0.25
0.16
0.50
0.99
1.26
⫺0.27
⫺0.35
⫺0.43
⫺0.26
⫺0.10
3.74
4.62
⫺0.51
⫺1.07
⫺0.61
⫺0.65
⫺0.73
⫺1.54
⫺0.96
⫺0.92
⫺0.84
0.04
⫺0.91
1.53
1.72
0.21
⫺0.96
⫺0.57
⫺0.44
⫺0.81
⫺0.37
⫺0.91
⫺0.33
5.27
3.80
3.61
4.56
3.27
3.11
2.90
2.32
3.18
3.96
3.40
3.44
3.87
3.58
2.99
3.40
2.17
0.57
3.91
1.94
⫺0.35
0.23
0.37
1.95
⫺0.46
1.03
1.49
⫺1.12
0.57
0.98
⫺0.09
0.21
⫺0.66
0.62
0.21
1.26
2.66
1.48
0.62
0.54
⫺0.02
⫺0.66
⫺0.53
0.67
0.17
0.21
⫺0.71
⫺0.73
⫺0.69
⫺1.07
⫺2.01
⫺1.86
⫺0.54
⫺0.68
⫺0.32
⫺1.64
⫺1.37
⫺0.59
⫺0.71
0.31
⫺0.63
⫺1.46
⫺0.10
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
FMNH PR2081
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
BHI 3033
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
AMNH 5027
L
L
L
L
L
C
C
C
C
C
C
C
C
L
R
C
C
C
C
C
C
C
C
L
R
R
R
R
C
C
R
R
C
C
R
R
C
C
C
C
C
C
R
d03
d05
d06
d08
d09
mx01
mx02
mx03
mx04
mx05
mx06
mx08
mx09
mx11
mx07
d01
d02
d03
d04
d06
d07
d09
d10
d13
d05
d08
d11
d12
pm01
pm03
pm02
pm04
pm01
pm03
pm02
pm04
mx01
mx03
mx05
mx06
mx07
mx08
mx11
1.31
1.20
0.94
0.85
0.75
1.08
1.30
1.09
1.15
1.15
0.89
0.80
0.73
0.31
1.03
0.62
1.06
1.01
1.08
1.10
0.88
0.81
0.67
0.12
1.14
0.73
0.58
0.29
0.69
0.83
0.91
0.71
0.86
0.85
0.92
0.78
0.86
0.82
1.12
0.96
0.98
0.81
0.62
⫺0.49
0.03
0.26
0.37
0.19
0.63
0.12
0.91
0.20
0.18
0.30
⫺0.55
⫺0.14
⫺0.55
⫺0.65
⫺0.17
⫺0.22
0.21
0.27
⫺0.60
⫺0.62
⫺0.57
⫺0.54
⫺2.02
⫺0.20
⫺0.09
⫺1.14
⫺1.26
⫺0.97
⫺0.42
⫺0.94
⫺0.27
⫺1.32
⫺0.90
⫺1.24
⫺0.24
1.05
1.38
0.23
0.13
0.08
0.72
⫺0.90
7.10
5.64
3.54
2.43
3.06
4.06
5.59
3.25
4.95
4.98
3.34
2.00
2.82
1.40
4.70
1.48
4.20
4.39
4.83
4.38
3.74
3.05
2.87
0.78
5.71
3.55
2.44
1.86
1.64
3.49
2.76
2.10
2.91
3.16
2.65
2.66
2.27
1.56
4.45
2.65
2.65
2.13
2.24
⫺1.30
⫺1.49
⫺0.61
⫺1.32
0.34
⫺1.50
⫺2.40
⫺1.41
⫺0.70
⫺1.21
⫺0.44
⫺1.54
⫺0.22
0.49
⫺0.57
⫺1.47
⫺1.46
⫺2.56
⫺1.01
⫺1.67
⫺0.89
⫺1.16
⫺0.26
0.35
⫺1.04
0.42
⫺0.46
0.52
⫺0.67
⫺0.15
⫺1.70
⫺0.78
⫺1.05
⫺0.67
⫺1.88
⫺0.68
⫺0.92
⫺0.02
⫺0.60
⫺1.09
⫺1.26
⫺0.50
⫺0.23
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
AMNH 5027
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
SDSM 12047
CM 9380
CM 9380
CM 9380
CM 9380
CM 9380
CM 9380
CM 9380
CM 9380
CM 9380
CM 9380
BMNH R5863
BMNH R5863
BMNH R5863
BMNH R5863
BMNH R5863
BMNH R5863
MOR 1125
LACM 150167
LACM 150167
LACM 150167
LACM 150167
LACM 23844
LACM 23844
LACM 23844
LACM 23844
LACM 23844
Left
Left
Left
Left
Left
Comp.
Left
Comp.
Right
Right
Left
Comp.
Comp.
Left
Comp.
Comp.
Right
Left
Left
Left
Comp.
Left
Right
Right
Right
Right
Right
Left
Left
Left
Left
Left
Left
Right
Left
Right
Right
Right
Right
Right
Right
Comp.
Left
mx04
mx01
mx02
mx03
mx04
mx08
mx10
mx11
mx06
mx12
d04
d05
d06
d07
d08
d09
d03
d02
d04
d06
d07
d12
d01
d03
d05
d08
d10
d07
d08
d09
d11
d12
d13
mx10
mx06
d03
d04
d13
mx01
mx03
mx05
d02
d04
1.20
1.23
0.83
1.05
1.02
1.07
1.01
0.84
1.11
0.69
1.02
0.96
0.97
0.85
0.82
0.72
1.13
0.91
1.20
1.09
1.00
0.33
0.62
1.03
0.94
0.81
0.58
0.99
0.99
0.77
0.80
0.62
0.33
0.83
0.93
0.86
0.94
0.17
1.06
1.07
0.89
0.84
0.84
0.43
0.38
0.98
1.11
1.18
0.20
0.41
⫺0.51
0.68
⫺1.34
1.04
0.73
0.48
0.25
0.44
⫺0.05
0.50
0.63
0.19
0.13
0.02
⫺0.16
⫺0.87
0.71
0.83
0.16
0.30
0.20
0.20
0.27
⫺0.54
⫺1.08
⫺1.71
⫺0.25
0.36
0.12
0.10
⫺1.67
0.32
1.06
0.99
0.43
1.12
4.67 ⫺1.73
4.70 ⫺2.46
1.80 ⫺1.09
2.46 ⫺1.51
2.99 ⫺1.13
3.75 ⫺1.09
3.03 ⫺1.09
2.51 ⫺1.51
3.81 ⫺1.41
0.88 ⫺2.72
2.54 ⫺1.47
2.57 ⫺1.01
3.00 ⫺1.22
3.61
0.40
2.38 ⫺0.98
2.18 ⫺0.42
3.62 ⫺1.91
3.67 ⫺0.08
6.15 ⫺0.89
5.70 ⫺0.37
4.82 ⫺0.41
1.42
0.32
2.63 ⫺0.17
4.86 ⫺0.14
4.71
0.77
4.43
1.22
2.79
1.36
3.73 ⫺1.05
4.22 ⫺1.03
2.99 ⫺0.70
3.21 ⫺0.74
2.11 ⫺0.99
0.85 ⫺0.04
2.90 ⫺0.43
3.33 ⫺0.09
3.17
0.19
4.57
0.50
1.33
0.59
5.09 ⫺1.28
4.68 ⫺0.34
4.12
0.87
3.73 ⫺0.39
4.44
0.92
(continues)
APPENDIX C. PCA Orthogonal scores and DFA function scores for the specimens in the standard data set. (continued)
Taxon
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Tyrannosaurus
Troodon
Troodon
Troodon
Troodon
Troodon
Troodon
Saurornithoides
Saurornithoides
Saurornithoides
Saurornithoides
Saurornithoides
Saurornithoides
Saurornithoides
Saurornithoides
Bambiraptor
Bambiraptor
Bambiraptor
Bambiraptor
Bambiraptor
Bambiraptor
Bambiraptor
Bambiraptor
Bambiraptor
Bambiraptor
Deinonychus
Deinonychus
Deinonychus
Deinonychus
Deinonychus
Deinonychus
Deinonychus
Deinonychus
Deinonychus
Deinonychus
Specimen
LACM 23844
LACM 23844
LACM 23844
LACM 23844
UCMP 118742
UCMP 118742
UCMP 118742
UCMP 118742
UCMP 118742
MOR 553
MOR 553
MOR 553
MOR 553
MOR 553
MOR 553
GIN100/1
GIN100/1
GIN100/1
GIN100/1
GIN100/1
GIN100/1
GIN100/1
GIN100/1
KUVP129737
KUVP129737
KUVP129737
KUVP129737
KUVP129737
KUVP129737
KUVP129737
KUVP129737
KUVP129737
KUVP129737
YPM523266-11
YPM523266-11
YPM523266-11
YPM5232612
YPM5232612
YPM5232557
YPM5232557
YPM5232557
YPM5232557
YPM5232557
Side Position Orth.1 Orth.2 Fun.1 Fun.2
R
C
L
L
R
R
R
R
R
L
L
L
L
C
C
R
R
C
C
L
R
R
L
L
L
L
L
C
R
R
R
R
R
R
R
d05
d07
d08
d11
mx07
mx08
mx09
mx11
mx12
Isolated
Isolated
Isolated
Isolated
Isolated
Isolated
mx04
mx06
mx07
mx12
mx14
mx16
mx05
mx09
d06
d08
d09
d05
d07
mx04
mx06
mx09
Isolated
Isolated
d01
d12
d13
d14
d16
d07
d08
d10
mx01
pm01
1.05
1.04
0.79
0.25
0.95
0.97
0.84
0.54
0.10
⫺1.017
⫺0.69
⫺0.76
⫺0.79
⫺0.97
⫺1.08
⫺1.73
⫺1.51
⫺1.07
⫺1.56
⫺1.31
⫺1.52
⫺2.05
⫺1.21
⫺2.91
⫺2.88
⫺2.97
⫺3.41
⫺2.53
⫺2.42
⫺2.56
⫺2.62
⫺2.14
⫺3.46
⫺1.32
⫺0.74
⫺0.89
⫺0.80
⫺1.11
⫺0.76
⫺0.93
⫺0.82
⫺0.91
⫺1.17
0.69
⫺0.45
1.01
⫺0.63
0.79
0.23
0.97
0.14
0.18
⫺1.41
⫺1.41
⫺1.21
⫺1.45
⫺1.50
⫺1.76
⫺0.45
⫺0.39
⫺1.62
⫺0.13
⫺0.70
⫺0.44
⫺0.19
⫺0.76
1.21
1.00
1.54
1.49
0.70
0.86
1.02
⫺0.50
⫺0.55
1.19
⫺0.17
⫺1.57
⫺1.57
⫺1.88
⫺1.97
⫺1.28
⫺0.92
⫺0.86
⫺0.03
0.20
4.31
4.53
2.70
2.11
4.41
4.49
3.66
1.80
0.48
⫺4.41
⫺4.19
⫺4.06
⫺4.32
⫺4.61
⫺5.79
⫺3.41
⫺3.77
⫺4.45
⫺4.02
⫺4.04
⫺4.46
⫺4.45
⫺3.96
⫺6.87
⫺6.85
⫺5.34
⫺6.95
⫺6.25
⫺5.97
⫺6.80
⫺6.70
⫺5.50
⫺6.61
⫺3.45
⫺3.37
⫺3.38
⫺3.57
⫺3.72
⫺3.54
⫺3.74
⫺3.95
⫺3.42
⫺3.96
⫺0.95
⫺0.92
0.12
0.01
⫺0.59
⫺0.94
⫺0.55
0.04
⫺0.10
⫺4.75
⫺5.08
⫺4.78
⫺5.50
⫺4.16
⫺5.83
⫺3.09
⫺5.11
⫺7.00
⫺3.05
⫺4.87
⫺3.91
⫺6.45
⫺6.17
0.44
⫺0.67
1.88
2.13
0.53
0.38
0.03
0.70
1.05
0.07
⫺0.41
⫺1.43
0.06
⫺1.12
⫺1.57
⫺1.14
⫺1.27
⫺1.25
⫺0.06
⫺0.66
Taxon
Deinonychus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Dromaeosaurus
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Velociraptor
Specimen
MCZ8791
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH5356
AMNH6515
AMNH6515
AMNH6515
AMNH6515
AMNH6515
AMNH6515
AMNH6515
uncat. GIN
uncat. GIN
uncat. GIN
uncat. GIN
uncat. GIN
uncat. GIN
Side Position Orth.1 Orth.2 Fun.1 Fun.2
L
C
C
L
C
R
R
L
L
L
L
L
P
P
M
M
M
M
D
M
M
M
M
M
M
mx03
mx03
mx04
mx05
mx06
mx02
mx07
d02
d03
d04
d05
d08
pm01
pm03
mx02
mx04
mx06
mx08
d01
mx05
mx08
mx01
mx03
mx05
mx06
⫺0.96
⫺0.90
⫺0.89
⫺0.80
⫺1.11
⫺0.90
⫺1.25
⫺1.43
⫺1.09
⫺1.01
⫺0.99
⫺1.10
⫺1.96
⫺2.33
⫺1.66
⫺1.73
⫺1.77
⫺2.07
⫺3.18
⫺1.43
⫺1.52
⫺1.62
⫺1.06
⫺1.20
⫺1.42
⫺1.57
⫺0.22
⫺0.54
⫺0.70
⫺0.58
⫺0.83
⫺0.37
0.41
0.17
⫺0.18
⫺0.26
⫺0.70
⫺0.78
⫺1.20
⫺1.39
⫺0.17
⫺0.73
⫺2.22
0.08
⫺0.36
⫺0.22
0.02
⫺1.26
⫺1.04
⫺1.42
⫺3.90
⫺3.12
⫺3.27
⫺2.91
⫺3.47
⫺3.51
⫺3.29
⫺1.79
⫺3.20
⫺2.92
⫺2.94
⫺3.12
⫺4.93
⫺5.54
⫺5.20
⫺4.14
⫺5.14
⫺6.86
⫺7.62
⫺5.20
⫺5.05
⫺3.12
⫺4.11
⫺4.07
⫺4.27
⫺0.53
0.12
⫺0.64
0.32
0.78
⫺0.84
0.84
2.62
⫺0.49
⫺0.14
⫺0.18
⫺1.26
1.06
0.70
0.96
2.33
1.07
⫺0.72
0.67
⫺0.30
0.50
1.42
0.31
1.74
0.25
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