Theropod dinosaurs were the major terrestrial predators for most of the Mesozoic. Because of their large size and structural features, there is immense interest in the feeding dynamics of these animals. Therefore, theropod functional morphology in the context of feeding behavior has been investigated from many perspectives. Modeling cranial structuring, musculature, and kinesis has given insight into the skull's resistance to stress, potential bite force, and niche partitioning among species (Busbey, 1995; Henderson, 1998, 2002; Mazzetta et al., 1998; Molnar, 1998; Rayfield et al, 2001, 2007; Rayfield, 2004). Forelimb structure indicates a range of ability for securing prey with the manus (Holtz, 2002; Ostrom, 1969; Sereno, 1993; Tykoski and Rowe, 2004). Hind limb structure, as well as general size and body dimensions, is correlated with the theropod running speed (Farlow et al., 1995; Fastovsky and Smith, 2004; Larson, 1997; Seller and Manning, 2007), leading to several conclusions about the hunting and/or scavenging abilities (Horner and Lessem, 1993; Horner 1994). Although dentition is most definitely involved in food processing, and most likely acquisition, significantly less research has been done concerning the morphology of theropod teeth from a functional perspective.
This may be due to the unique dental morphotype of theropods. The majority of theropod dinosaurs possess ziphodont dentition, which is characterized by laterally compressed, curved, serrated teeth (Langston, 1975; Prasad and Lapparent de Broin, 2002). The degree of curvature and flattening can vary greatly (i.e., tyrannosaurids have lost much of their lateral compression), but all appear to possess serrations. These serrations, referred to as denticles, rest on carinae located along the margins of the tooth. The majority of carnivorous archosaurs throughout the Mesozoic era possessed ziphodonty (Benton, 2004). These include theropods, crurotarsians, and basal archosaurs (Benton, 2004; Farlow et al., 1991; Holtz, 2004; Senter, 2003; Smith et al., 2005). Within modern archosaurs though (i.e., crocodylians) it has been replaced by undenticulated, conical teeth. Ziphodonty has also convergently appeared in other tetrapod clades, including Permian pelycosaurs such as Dimetrodon (Farlow et al., 1991). Ziphodonty only occurs at present in certain members of the squamate family Varanidae (Auffenberg, 1981; Molnar, 2004).
Several comparative morphometric studies have been conducted on the diversity of theropod teeth, but most of these have focused primarily on the description and/or taxonomic identification of isolated teeth (Carr and Williamson, 2004; Currie et al., 1990; Molnar, 1998; Sadlier and Chapman, 1999; Sankey et al., 2002; Smith 2005, 2007; Smith et al., 2005; Samman et al., 2005). Consequently, there has been little analysis of dental function. Chandler (1990) suggested that theropod teeth are designed to cut by a combination of puncturing and drawing through flesh; the primary substrate modified by theropods. Farlow et al., (1991) depict these teeth as multipurpose implements, used for killing, cutting, and crushing bone. Because of increased tooth width and bending resistance, bone crushing may have been possible in larger taxa such as tyrannosaurids (Meers, 2003). Henderson (1998, 2002) used tooth lengths, heights, and orientations in addition to theropod skull measures to determine relative skull strengths and potential niche partitioning among theropods. Sadlier and Chapman (2002) used geometric morphometrics to determine that tooth shape reflects the variability in force applied to different tooth positions within individuals.
To gain better insight into the function of theropod teeth, researchers have also investigated the morphology and behavior of living ziphodont varanid analogues, especially the Komodo monitor, Varanus komodoensis. Studies of V. komodoensis indicate a unique feeding methodology associated with ziphodonty (Auffenberg, 1979, 1981; D'Amore and Blumenschine, in press), and cranio-dental similarities between theropods and V. komodoensis suggest similar food processing methods (Busbey, 1995; Carpenter, 1998; Molnar and Farlow, 1990; Paul, 1988; Rayfield et al., 2001).
Denticles are assumed to be a crucial component in theropod tooth function, yet few studies have described their functional value. In a study of the teeth of elasmobranch sharks, Frazzetta (1988) proposed that the serrated edges allow a blade to move through a substrate with less force than a smooth blade would require. As the serrations are drawn across this substrate they bind to a small portion of it and tear it, a mechanism described as “grip and rip” (Abler, 1992, p 178). Less force is needed to draw the serrated surface across the substrate because friction is reduced. Serrations are functionally analogous to denticles, so that a denticulated shark tooth would theoretically move into and through flesh more efficiently than one with smooth edges.
Abler (1992) simulated denticulated tooth performance in tyrannosaurids by using tooth casts and actual metal blades to determine the force needed to modify flesh. His results suggest that tyrannosaurids did not use their denticles to cut through meat by widening the size of a wound, as do sharks. Instead, tyrannosaurids used their teeth to “puncture and grip,” and denticles facilitated this (Abler, 1992, p 179).
Based on these results, it would seem to be advantageous to have denticulated carinae along the portions of the tooth margins that contact the substrate. Several authors have noted that the entire margin may not be denticulated. This is especially true for the mesial, or leading edge, of a tooth crown (Fig. 1). Chandler (1990, p 38) stated that mesial denticles near the base “become so small that they often appear to merge to form an unserrated keel.” Currie et al. (1990) report that mesial denticles in dromaeosaurids occur on less than half the length of the margin. Molnar and Carpenter (1989) note a similar condition in tyrannosaurids (see also Carr and Williamson, 2004). Abler (1992) states that in tyrannosaurids the mesial denticulation “tends to end where the tooth meets it maximum width.” Smith (2005) reported that the denticulated mesial carina terminates above the tooth base, but distal denticulation extends to the base in tyrannosaurids. Smith also noted a trend of decreasing mesial denticulation as each tooth moves closer to the hinge in position. The distance from the base of the mesial carina to the base of the tooth crown shows significant variance (Samman et al., 2005).
This study proposes a model that explains the variability in denticulation in functional terms. The model predicts that denticulated carinae will only exist in areas that make frequent contact with the substrate during typical feeding behaviors. These denticles will modify the substrate they contact, assisting the tooth in processing food. Conversely, areas with little contact with the substrate will lack denticles.
The amount of contact any portion of a tooth has with the substrate is based on the direction the tooth moves relative to the substrate. Rieppel (1979, p 812) describes this tooth movement or “line of action” for Varanus salvator. The orientation and curvature of the line of action of any tooth depends on its position relative to the hinge or hinges that the host bone rotates around, and the necessity that the apex of the tooth makes contact with the substrate. The apex has the smallest volume, focusing the force onto a smaller area and increasing the likelihood of puncturing the substrate (see also Chandler, 1990; Frazzetta, 1988; Lucifora et al., 2002). This results in axial loading of the tooth, which increases efficiency and reduces the chance of breakage.
As a tooth moves along its defined line of action, the degree of contact with the substrate will vary across the tooth's area. Opposite to the line of action is an area of the tooth that may not contact the substrate; this area is defined here as the tooth's “dead-space” (Fig. 2). This condition is considered analogous to the “trailing surface” of mammal molars (Evans and Sanson, 2003). This model predicts that because the dead-space does not make contact with unmodified substrate, it should have no denticles. The purpose of this study is to test this model of theropod tooth function by comparing the extent on denticulation with the dead-space. Theropod teeth are photographed and analyzed using both Euclidean and geometric morphometrics, focusing mainly on apex characters and denticulation. The line of action is determined based on the apex morphology, and a dead-space is proposed for each tooth. This dead-space is then compared to the degree of denticulation. If denticulation does reflect the extent of contact between a given tooth and the substrate, I hypothesize that the height of the dead space will correlate with the degree of denticulation. Conversely, the null hypothesis states that there is no meaningful relationship between the dead-space and the extent of denticulation. This is also examined in relationship to tooth position in the dental arcade, as well as the clade of the theropod it came from.
MATERIALS AND METHODS
Sampling and Photography
Data were collected on a total of 235 teeth of theropod dinosaurs. Sixty-eight of these were in situ and the rest were isolated. Teeth with extensive damage and those obscured by matrix were not included. Partial data were collected on specimens with limited damage and/or incomplete carinae. The best represented clade was Dromaeosauridae (N = 81), followed by Tyrannosauridae (N = 64), Abelisauridae (N = 26), Dryptosaurus (N = 17), Troodontidae (N = 12), and Allosauridae (N = 6). Previous researchers have identified the phylogenetic affinity of 209 teeth, and this was used to assign each tooth to a specific clade. The only deviation from this was that 10 isolated teeth considered “dromaeosaurid” were instead included in the troodontid clade. These were reclassified based on their distinctively large denticles, which are characteristic of Troodontidae (Holtz et al., 1998; Makovicky and Norell, 2004). Twenty-nine isolated teeth were placed in an “unknown” group. All abelisaurid teeth were taken from a cast of one individual in which no denticles could be observed, and most allosaurid teeth had damaged mesial carinae. Consequently, the majority of teeth with denticulation values available are members of Coelurosauria from the Cretaceous of North America. Tooth position is also considered for all in situ teeth available. The in situ sample is represented only by Abeliesauridae, Allosauridae, Dromaeosauridae, and Tyrannosauridae. Certain teeth were eliminated because the host bone was so damaged that the absolute position was impossible to determine. Teeth were sampled from the collections of the American Museum of Natural History (AMNH) in New York, NY and the Smithsonian Institution National Museum of Natural History (USNM) in Washington, D.C. In addition, casts of in situ teeth of two specimens from the Field Museum of Natural History (FMNH) in Chicago, IL are also used.
Because there is no standardized nomenclature for the description of ziphodont teeth (Sweetman, 2004), the nomenclature used here is proposed by Smith and Dodson (2003; Fig. 1); mesial, towards the premaxillary and mandibular symphyses; distal, away from the premaxillary and mandibular symphyses; lingual, towards the tongue; labial, towards the lips; apical, towards the tip of the tooth/the apex; basal, towards the base of the tooth/where the tooth meets the host bone; carina, the denticulated region of the mesial/distal margin; the substrate, the material that the tooth modifies. The direction of tooth movement through the substrate is defined by the leading margin. For example, a tooth that is “drawn distally” is describing the host bone moving the tooth so that it is leading with the distal margin. This is movement relative to the substrate, and not the movement of the tooth relative to any other skeletal elements.
When measuring unworn, in situ teeth, the position of the denticles was first quantified. The extent of the denticulated carinae was noted for both the mesial and distal margins of all teeth. The basal-most denticle on each carina, referred to here as the terminal denticle (TD; mesial [MTD] and distal [DTD]), was located and marked using a 16× hand lens. Marks were made on the tooth's labial surface directly under the TD using a grease pencil. Although wear is apparent on many specimens, the diaphysis (Abler, 1992) of a worn denticle is usually still visible. Theropod denticles run from the TD all the way to the apex, shrinking in size at close proximity to the apex. This was found to be the case in the majority of the sample (for exceptions see Smith, 2007). Therefore, marking the apical-most denticle was not necessary. Teeth possessing no denticles are described as having a “nondenticulate” carina. Fifteen specimens had nondenticulated mesial carinae, while all teeth were distally denticulated.
Digital photographs of all teeth were taken from the labial perspective (Fig. 3). For the majority of tooth length, the opposing carinae run parallel to one another along their respective sides. The camera was positioned perpendicular to a plane connecting the two carinae. In many teeth, the mesial carina curves lingually before terminating. In such cases, the camera was positioned in reference to only the portion of the carina occurring apical to this lingual curving. For teeth with no carinae at all, the camera was simply positioned perpendicular to the long axis of the tooth.
Coordinates were digitized from tooth photographs using TpsDig 2.10 (Rohlf, 2006). Each tooth had a total of 62 assigned coordinates from which all data were extrapolated (Fig. 3). Ziphodont teeth have very few distinct morphological features making it difficult to produce “true” landmarks, or coordinates that denote discrete homologous anatomical loci (Zelditch et al., 2004). Coordinates were placed at the pencil mark at the MTD and DTD, indicating the extent of denticulation. These may be considered optimal, or Type 1, landmarks because they are denoted by distinct morphological structures that are locally defined (Bookstein, 1991, 1997; Zelditch et al., 2004).
Another coordinate is placed at the tooth crown apex (CA). Finding a repeatable method for identifying the apex has proven difficult in the past, because the apex is often rounded and may occupy a large area (Smith et al., 2005). Many studies do not detail how the apex is identified (Henderson, 2002; Molnar, 1998; Rieppel, 1979; Sankey et al., 2002) and others derive tooth heights instead of apex positions (Farlow et al., 1991; Smith et al., 2005; Smith, 2005, 2007). I defined the apex as the point along the tooth where the most acute angle is formed and the two carinae meet. This angle was approximated qualitatively. Because this was defined by a maximum of curvature and not a morphological structure, it is a Type 2 landmark. Regardless, this landmark is essential in defining to the tooth's puncturing ability and line of action.
The establishment of a tooth base is necessary to measure the relative position of the apex and denticles. Therefore, two more coordinates were placed at the base of the tooth (Fig. 3). This is the basal most point where the tooth's mesial and distal margins meet the host bone, and may be defined as Type 1 landmarks because they define a “discrete juxtaposition of tissues” (Zelditch et al., 2004, p 31). This method can result in a portion of the tooth's dimensions represented by exposed roots, especially in tyrannosaurids. This is functionally significant because although the root probably was covered by tissue and did not make direct contact with the substrate, its height in relationship to the host bone will dictate aspects of its interaction with the substrate. Therefore, the exclusion of the root would artificially “shorten” the tooth relative to those with more embedded roots.
Fifty-six semilandmarks function to outline the mesial and distal margins of the tooth (Fig.3). These do not demarcate morphological characters (Zelditch et al., 2004). The margin is defined here as the “outline” of the tooth from the base landmark to the apex on a given side. Chainman3D (Sheets, 2005a) converted random points plotted along each margin into 30 equidistant semilandmarks, dividing up each margin into 29 equal increments. The first and last semilandmarks are equivalent to the CA and basal landmark, and are not considered further. Previous researchers have also used 30 coordinates to represent the mesial margin (Smith et al., 2005). The general shape of the margin is conserved in most teeth, but the resolution is also low enough that slight inconsistencies are not represented. Because an analysis of general tooth shape morphometrics is beyond the scope of this study, no direct data are taken from semilandmarks.
Chainman3D also converts all the landmarks and semilandmarks into a two point registration (Zelditch et al., 2004). This process converts the distance between two arbitrary coordinates to 1 unit (Bookstein coordinate), thus scaling the remainder of the points. For the two points the basal-most landmarks were chosen, positioning them along the x-axis.
Transferring the Bookstein coordinates to an Excel spreadsheet allows for easy calculations for all teeth simultaneously. Using a two point registration eliminates size as a factor, and using the base of the tooth is the most appropriate region to standardize because it is often considered the standard metric for tooth size (Farlow et al., 1991; Holtz et al., 1998; Sankey et al., 2002; Smith et al., 2005).
The Line of Action and the Dead Space
The line of action is crucial in the determination of a tooth's dead-space. Based on axial loading (see INTRODUCTION), I hypothesize that the apex indicates the direction in which the tooth must move when initially contacting the substrate. Although this aspect of the line of action can be accounted for, the rotation of the host bone cannot. Factors that contribute to this, such as cranial kinesis, tooth position, and distance from the hinge(s) (Rieppel, 1979) are unavailable for most teeth. Because of the exclusion of rotation, the line of action is based solely on the orientation of the apex resulting in a straight line.
The line of action is determined similarly to Rieppel (1979) by deriving a “tangential line.” This is a straight line drawn through the apex, and is determined by tooth morphology (Fig.3). First, two points on each of the margins are selected. On the distal margin, this point is the tenth semilandmark from the apex. On the mesial margin, the landmark closest to the length between the apex and the distal margin's tenth landmark was used. This results in both margins having points that are a similar length from the apex. A tangential line is then formed connecting CA with the midpoint of these two points. This is the line of action. Arbitrarily choosing these particular semilandmarks results in less than the apical third of the tooth influencing the line. This eliminates compounding factors, such as how elongate the body of the tooth is, that can reduce the line of action if more of the tooth is included.
A coordinate is then placed along the mesial margin in accordance to the line of action. This coordinate denotes the hypothetical terminal denticle (HTD), and is significant because it dictates the height of the dead-space as determined by the line of action. If the proposed model is correct, all of the tooth margin basal to this coordinate should have no denticles. The coordinates of all semilandmarks along the mesial margin are compared to points on the line of action function of equal x value, and the semilandmark that is farthest from that function becomes the HTD (Fig.3). Although not a “true” landmark by definition, this will be referred to as a landmark for the purposes of the model.
Last, the line of action as converted to an angular measure was derived. This is similar to curvature, recurvature, or pitch in previous studies because it dictates the angular orientation of the apex relative to the base. This has been described for theropods (Henderson, 2002; Molnar, 1998; Smith, 2005, 2007, Smith et al., 2005), varanids (Rieppel, 1979), and elasmobranch sharks (Lucifora et al., 2002). The angle of the line of action (LOA°) is the difference in degrees between the function derived earlier, and the two basal landmarks on the x-axis. Mathematically, this is the tangent of the CA y-value divided by the difference between CA x-value and the function's x-intercept. Because the LOA° is independent of denticle characters, it was calculated for all teeth sampled.
The percentage of mesial and distal denticulation was calculated for all teeth with denticulated carinae. The length of the denticulated carina is distance from the TD to the CA along the margin. This was then divided by the total length of the margin; the summation of the distance between the thirty adjacent coordinates along the margin. A hypothetical percentage of mesial denticulation was also calculated based on the position of the HTD in a similar manner.
The relative height of three landmarks is determined. The position of the MTD, DTD, and HTD is determined perpendicular to the base (similar to Samman et al., 2005). Because the two point registration positions the base on the x-axis, these data are simply the y-value for each landmark. MTD, DTD, and HTD are converted into percentages of the tooth height by dividing them by CA. In addition, DTD was subtracted from MTD to yield a value quantifying symmetry in TD height.
Basic statistics are performed on all angular and Euclidean variables. The number, average, median, and range are calculated for each value. Bivariate plots were constructed to compare height variables and the LOA°. Regressions lines are plotted, and r2 and P-values are calculated where appropriate. All plots have the different clades of theropod indicated. In situ teeth were plotted by position against the LOA° and certain linear variables. Percent denticulation was not used in any regression analyses because these data appear to be strongly influenced by tooth crown keeling.
Geometric Morphometric Analysis
Teeth complete enough to produce all six landmarks were entered into a landmark based morphometric analysis using a multivariate ordination technique (N = 175). The six landmarks were input into a principal component analysis using PCAGen6p (Sheets, 2005b). This program performs a generalized least squares Procrustes superimposition on the data, and calculates the partial warp scores for each landmark. From these partial warps, the factor loadings for both x and y values for each landmark are listed. These consist of Pearson's correlation coefficients and P-values, and are considered significant if they are above 0.4 and below 0.05, respectively. From this, a series of principal components was generated representing shape variances between the landmarks. Each tooth is assigned a component score along each principal component axis, and principal components were plotted against one another.
Methodological Modifications for Worn and/or Isolated Teeth
A naturally occurring TD tends to be smaller than the majority of the denticles, making it easily distinguishable. Many teeth had “abbreviated” carina where the basal-most denticle is the result of damage to the tooth, and under “natural” circumstances denticulation would extend basal to that denticle. Isolated teeth may have broken apical to the TD or the carina itself may be chipped or damaged. Teeth with abbreviated MTD were not sampled, but most teeth have abbreviated DTD. Because this abbreviation usually occurred at the base of the tooth, the basal-most distal denticle was always considered the DTD.
In a tooth with an apex that shows little damage or modification, the CA landmark is easily placed. However, many teeth sampled had either worn or broken apices (Fig. 4). A worn apex tends to be smooth and rounded, with no sharp or jagged edges. The worn area is also easily distinguished because it is polished and may be a different color than the rest of the tooth. A broken apex displays sharp edges where it was broken, with no polishing. Concerning worn apices, CA is placed approximately equidistant to the edges of the worn area. Teeth with broken apices were not sampled. I assume that there is only a slight deviation in overall shape between worn apices, whereas broken teeth can deviate greatly from the unmodified condition.
Because isolated teeth did not have the host bone available for reference, the basal landmarks are positioned at the mesial and distal most point where the tooth breaks. One cannot rule out the possibility that the base landmarks in isolated teeth may not always represent similar positions to in situ teeth, but instead represent artifacts of preservation. Although I found no way of safeguarding against this possibility, the methodology used here allows for the most repeatability and consistency in sampling due to a lack of discrete anatomical features. Past authors have used the extent of enamel to indicate these points (Chandler, 1990; Farlow et al., 1991; Sankey et al., 2002; Smith et al., 2005). In this sample, the enamel was indistinct or damaged in many specimens.
Simple Statistics and Regression Analysis
There is a large difference in the extent of denticulation between the mesial and distal carinae of a theropod tooth (Table 1). Median and average mesial denticulation is about 66%. Therefore, the basal one-third of the mesial margin possesses no denticles on average. Conversely, most teeth are denticulated along nearly the entire distal margin. Only 45 of the 174 teeth sampled had less than 90% distal denticulation. The majority of these teeth were tyrannosaurid or “unknown,” and appeared to have a noticeable amount of exposed root. Distal denticulation is also less variable than mesial. The relative heights of the MTD and DTD further support this. The MTD is found at average 44% of height from the base, but is still highly variable based range and standard deviation (Table 1). Again, the DTD has a noticeably smaller range than the MTD and is usually positioned close to the base.
Table 1. Simple statistics for Euclidean and angular variables
Percentage distal denticulation
Percentage mesial denticulation
Percentage hypothetical denticulation
The angle of the line of action (LOA) is in degrees and the height of the tooth apex (CA) is in Bookstein coordinates. The mesial (MTD), distal (DTD), and hypothetical terminal denticle (HTD) heights are all percentages of the CA. The extent of denticulation is a percentage of the total margin length.
The height of the dead-space (HTD) is usually apical to the MTD. Its average relative height is 26% greater than the MTD. If the HTD dictated the extent of mesial denticulation instead of the MTD, the mesial margin would be around 22% less denticulated. Figure 5 displays the relative heights of these values plotted against one another. The vast majority of the teeth have a greater HTD than MTD, as indicated by their position above the threshold in a one to one ratio.
Tooth curvature is highly variable in theropods as indicated by LOA°. LOA° ranges from about 20° to over 112°. Teeth with LOA° values between 20° and 70° persist within most families (Fig. 6). It should be noted that taxa with ample sample size (Dromaeosauridae, Tyrannosauridae, Dryptosaurus) occupy the majority of the range of LOA° values. Larger taxa, such as tyrannosaurids, allosaurids, and abeilisaurids, are the only groups that show a noticeable number of teeth that exceed 70°.
Theropod teeth range in height from approximately one to four times their base size (Table 1). Heights are variable for all clades sampled, but tyrannosaurids are the only clade to have teeth greater than 2.5 times the base. Taller, thinner teeth relative to the base appear to exhibit less curvature. The height of the apex (CA) increases as LOA° decreases (Fig. 6). The larger teeth, especially those of tyrannosaurids, reflect this condition, but variability increases with increased LOA°.
LOA° shows a significant negative correlation with the relative heights of both the MTD and HTD, with r2 values above 0.33 (Fig. 6). As LOA° becomes less acute, these landmarks drift closer to the base. LOA° shows a very weak positive correlation with DTD as indicated by a very low r2. There is also an increase in tooth symmetry as the LOA° becomes less acute. The height of the mesial and distal terminal denticles converge as LOA° increases towards 90° (Fig. 7). All regressions have P-values less than 0.0001.
Tooth position correlates significantly with mesial denticulation and apex orientation (Fig. 8). All trends have r2 values of 0.3 or greater. These trends persisted for both the upper and lower tooth rows. Most teeth sampled have similar data for a given tooth position, as opposed to different specimens or families following different trajectories. LOA° negatively correlates with an increase in distal tooth position. MTD and HTD relative heights correlate positively with increasing distal tooth position, although few in situ teeth had an MTD available. There does not appear to be a meaningful correlation between tooth position and the DTD or CA (not shown). There appears to be a slight plateau effect as one moves distal in position along the upper tooth row that is not as evident in the lower tooth row. Only the regression produced between MDT and tooth position for the upper tooth row was not significant (P value > 0.05), and is likely due to the small sample size.
Troodontidae displays a unique “bimodal” mesial denticulation. Five of the twelve troodontid teeth have mesial margins that are almost fully denticulated, with the height of the MTD under 1% (Figs. 5 and 6). Conversely, the remainder of troodontid specimens have “nondenticulated” mesial margins, representing over half of all teeth with that condition in our sample. All others with this condition were “unknown.” Aside from these disparities, troodontids have almost fully denticulated distal margin, and HTD positioning and LOA° values do not appear to be dissimilar to other theropods (Fig. 6).
Principal Component Analysis
Four principal components were generated, accounting for over 94% of the overall variance for the six landmarks (Table 2). PC1 accounts for over 39% of the variance, and primarily defines the height of the tooth relative to the base (Fig. 9). Teeth with high scores on this component are differentiated from those with low ones by being tall and elongate. This is symbolized by a negative correlation between the x-value coefficients for landmarks on the mesial margins. Although size was factored out, it appears that larger teeth display higher scores. The sample above 0.1 units is mostly large tyrannosaurid teeth, and the stout dromaeosaurid and troodontid teeth are the most negatively positioned. PC1 may therefore be considered an indirect size component. PC2, representing 28.5% of the variance, primarily depicts an increase in mesial denticulation along the component (Fig. 9). MTD has large coefficients that only correlate with HTD significantly. This component shows that distance between the dead-space and mesial denticulation is not always uniform. Troodontids have the highest values with their uniquely well denticulated mesial carinae. All other clades appear evenly dispersed throughout. Tooth position does not correlate with either of these components. The line of action, as indicated by mesio-distal movement of the CA, does not appear to play a significant role in any of these components.
Table 2. Variances and eigenvalues (A) and factor loadings (B) for principal components (PC)
A. Variances and eigenvalues
Factor loadings consist of Pearson's correlation coefficients (above) and P-values (below) for both x and y coordinates for all landmarks.
B. Factor loadings
Mesial terminal denticle (MTD)
Distal terminal denticle (DTD)
Hypothetical terminal denticle (HTD)
Representing over 17% of the variance, PC3 is the most biologically significant component for the purposes of this study (Table 2). It is highly correlated with the mesio-distal movement of the apex (Fig. 10). The coefficients of the apex and mesial basal landmark negatively correlate with the distal basal landmark, indicating that the apex rotates along the component. Teeth high on this axis are elongate with their apices in the center of the base, giving them a tall, straight appearance. Tooth shape, as well as the extent of denticulation, is symmetrical. As the component decreases the apex drifts distally, indicating a higher degree of curvature and consequently a more acute line of action. With this, MTD moves apically and the DTD moves basally, as indicated by negatively correlated coefficients for the y-values of these landmarks. There appears to be no distinction between clades based on this axis, which the exception of tyrannosaurids occurring solely above 0.15. The principal component value of these teeth also decreases and the position becomes more distal.
PC4 represents only about 9% of the variance, and displays a similar rotation of the apex along the component. In addition, this component accounts for variance in the distance between the DTD and the apex (Fig. 10). The DTD has the largest coefficients, and they are negatively correlated with the CA y-value. This value correlates with tooth curvature, and correlates well with in situ teeth similar to PC3. As the tooth becomes more curved, the overall size of the distal margin, as well as distal denticulation, decreases.
Denticulation and Substrate Modification
The mesial margin of a tooth is usually partially denticulated, whereas the distal margin is usually almost entirely denticulated. The height of the position where mesial denticulation terminates correlates with the distal curving of the tooth. Teeth with a high degree of curvature have the least denticulate mesial margins. As the tooth curvature decreases, mesial denticulation increases resulting in a straight, tall tooth with more symmetry between the two faces. Both Euclidean distances and a significant amount of principal component variance, especially PC3, support this.
The dimensions of the dead-space, as determined by the hypothesized line of action, do show a correlation with the extent of mesial denticulation. This indicates a degree of dependency between the two factors. Therefore, the null hypothesis that there is no relationship between these two variables is rejected. The height of the dead-space and the extent of mesial denticulation do not have similar dimensions though. They differ from one another in a consistent and predictable manner, with the height of the dead-space (HTD) almost always apical to the MTD. If function is still considered the major force driving the extent of tooth denticulation, then the mesial margin is “excessively” denticulated according to the model. The fact that the MTD is basal to where it is predicted to be indicates that more of the mesial margin is contacting and modifying the substrate than the dead-space predicts.
One explanation for the disparity between the dead-space and mesial denticulation is that the apex may not accurately determine the line of action. This would result in an inflated dead-space. LOA° correlated negatively with the height of the dead space, as symbolized by the HTD. One could argue that the line of action should be less acute, which would move the HTD basal and closer to the position of the MTD. I find this hypothesis unlikely for several reasons. If the line of action were less acute, the tooth would contact and puncture the substrate with the mesial carina first. Axial loading would not occur (Rieppel, 1979), decreasing the efficiency of the tooth and promoting tooth damage. This would be especially likely for large, potentially bone modifying theropods (Farlow et al., 1991; Meers, 2003). Also, teeth with very distally oriented apices would form another dead-space along the upper portion of distal carina: an area that is always denticulated.
A more likely explanation is based on the limitations of using fossils. Because there is little data on the tooth position in relation to any hinge(s), rotation was not factored in. During jaw adduction, rotation would result in a curved line of action (Rieppel, 1979) as opposed to the straight line proposed in this model (Fig. 11). By factoring in rotation, the tooth can still enter the substrate apex first, and then rotate along the hinge(s) so that more of the mesial carina comes in contact with the substrate. As inferred by this logic, the extent of mesial denticulation does predict the height of the dead-space. The disparity seen is because the model artificially inflates the dead-space height by having a straight line of action.
Regardless of the limitations of this model, the extent of denticulation in a theropod tooth is still determined by contact made with the substrate during movement in the direction of the line of action. Even with rotation factored in, a large portion of the mesial margin will avoid contact with the substrate in teeth with an acute line of action (Fig. 11). This produces a large dead-space, resulting in the mesial margin maintaining a relatively small degree of denticulation. As the apex becomes less curved, the line of action becomes less acute and the dead-space is reduced. This results in more of the mesial margin contacting the substrate, and consequently more denticulation. Eventually a tooth's apex becomes such that the line of action is perpendicular to the base. This results in similar degrees of contact with the substrate for both carinae, as reflected by symmetry in the amount of denticulation.
Because the angle at which the tooth moves through the substrate is very rarely over 90°, the majority of the distal carina always makes contact with the substrate under most circumstances. This results in the extensive denticulation seen, and its apparent independence from curvature. The exceptions within Tyrannosauridae are the result of these teeth having a noticeable amount of exposed roots, which would most likely not contact the substrate. This is supported by Smith (2005) in that the distal carina in tyrannosaurid teeth usually terminates in close proximity to the enamel base.
Serial Homology in Theropod Dentition
As reported by several previous researchers (Chandler, 1990; Colbert, 1989; Ostrom, 1969, 1978; Smith, 2005), a trend of gradually changing apex and denticulation characteristics is apparent in the in situ sample. Shimada (2002) describes this serial homology as shape heterodonty. For both the upper and lower tooth rows, apices become more curved at more distal positions. This correlates with decreased mesial denticulation and increased dead-space height. Clade membership does not play a significant factor in this, suggesting that the factors influencing heterodonty are consistent among most theropods. Dromaeosaurids appear to exhibit the greatest curvature for a given tooth position. This may be functional or allometric in nature, and the author is in the process of increasing the sample size so further conclusions can be made.
This serial homology may be interpreted functionally. Rieppel (1979) proposes a mechanism for why tooth curvature is directly influenced by tooth position, and bases it on the distance from the cranial hinge(s); see also Sadlier and Chapman, 2002. Teeth positioned at different points along the jaw will vary in their distance from the hinge. In ziphodont carnivores the teeth tend to be somewhat similar in size, and the point at which the tooth strikes the substrate during rotation differs along the tooth row. A distal tooth will contact the substrate very early on during jaw adduction, whereas a mesial tooth will contact the substrate when the jaw is closer to being closed (Fig. 12). Unless it is dramatically shorter than its mesial counterparts, a distal tooth must be curved in order to avoid striking the substrate with the distal margin first. A mesial tooth's apex will strike when the jaw is further adducted. If the tooth is too curved, the mesial margin will make contact instead.
As jaw adduction occurs, all teeth located along the tooth row will be rotated around the hinge(s). Because of the elongate nature of the theropod rostrum, this rotation will occur along the plane parallel to the mesial and distal carinae for the majority of teeth (Fig. 12). The mesial-most teeth in the dental arcade are subjected to unique influences due to the morphology of the jaw. Because medial curvature occurs along the rostrum, the mesial-most dentary and premaxillary teeth instead rotate perpendicular to their mesial and distal margins. Hence from the labial perspective (from which all teeth were analyzed here), it would appear that these teeth move perpendicular to the base with little rotation at all. As expected, these teeth have apices oriented perpendicular to their base to allow for axial loading and very similar degrees of denticulation along both margins. The carinae can also be repositioned lingually in coelurosaurids, giving them a “D-shaped” cross-sectional appearance that has been noted by several authors (Molnar, 1978; Currie et al., 1990; Carr and Williamson, 2004; Smith, 2005). Also, the HTD and the MTD should not be dissimilar due to this lack of rotation (Fig. 11). It should be noted that our isolated sample lacks teeth with this distinct morphotype for dromaeosaurids, Dryptosaurus, and troodontids. This is most likely due to taphonomic or collecting bias against these teeth, and not that they do not occur.
As stated earlier, teeth have varied curvature because they are positioned along a hinge and are similar in size. Although size was not quantified here, theropod teeth do exhibit some variability in size [giving them shape size heterodonty according to Shimada (2002)]. The profile of the maxillary dentition has been compared to that of a “scalpel blade,” with teeth possessing the greatest heights located mid-way down the tooth row (Molnar and Farlow, 1990). This may be facilitated by an increase in exposed root (personal observation). If teeth become larger in more mesial positions, curvature does not need to be reduced because the point of contact between the apex and the substrate would be earlier during adduction. This is reflected in the plateauing in dental characters distally along the upper tooth row (Fig. 8), and may represent a trend towards increasing tooth size while maintaining curvature. The condition ceases mid-way along the dental arcade because large mesial teeth would not allow the jaws to close fully. Additional size data are needed to fully test this hypothesis.
Theropod Feeding Methodology
The orientation of theropod tooth apices can elaborate upon their feeding behavior. Many of the theropod teeth observed are strongly curved, some with less than a 30° LOA°. A bite with little additional movement would most likely not result in apical contact, so there must be an additional mechanism that allows for the curved teeth to achieve axial loading. Bakker (1998) and Rayfield et al. (2001) suggested that Allosaurus had a wide gape, and retractile forces during jaw adduction would allow for axial loading. Rieppel (1979) proposed a different mechanism for ziphodont varanids: cranial kinesis increases the number of hinges in the jaw mechanism, which allows for the tooth row to be abducted dramatically without an excessive gape. Both these mechanisms allow for the teeth to be drawn in the distally through the substrate.
An alternative mechanism to allow for the distal repositioning of the tooth is proposed here based on a modern ziphodont carnivore. Varanus komodoensis has highly curved teeth (Auffenberg, 1981). Although the skull is kinetic, this kinesis is not dramatic enough to reorient tooth apices to the extent Rieppel (1979) suggests (Auffenberg 1981; see also Burden, 1928; D'Amore and Blumenschine, in press). It also does not display a wide gape when defleshing. Instead, V. komodoensis rotates its rostrum both laterally (more specifically in the medial direction towards the mid-line of the rest of body) and caudally during adduction. Cranial structuring and the incorporation of postcranial musculature further assist in this process (Moreno et al., 2008). This “medial-caudal arc” not only forces the teeth into the substrate due to adduction, but also draws them a significant distance distally in relationship to where they started (D'Amore and Blumenschine, in press). This distal repositioning of the teeth during defleshing gives these teeth a very acute line of action when modifying the substrate.
Theropods may have used a method similar to that of V. komodoensis for defleshing based on both morphological and taphonomic similarities. There are striking similarities in both denticle properties and tooth shape between these two groups (Molnar and Farlow, 1990, Farlow et al., 1991). In addition, tooth mark similarities may also be used to support this model in Theropoda. Elongate, curved scores are typical feeding traces left by V. komodoensis (D'Amore and Blumenschine, in press). Theropods have been reported to produce elongate linear scores (Erickson and Olson, 1996; Jacobsen, 1995). This may indicate the distal drawing of teeth as well, although the technique may have differed due to rostral differences between these taxa.
This model also supports Abler's (1992) model of tooth use as well. Abler stated that in tyrannosaurids the denticles allow for the tooth to fully puncture the substrate, and the same basic principle apply here. Frazzetta (1988, p 95) describes modifying the substrate by puncturing as “puncture cutting.” These data suggest that teeth were drawn distally during feeding. Theropods therefore processed the substrate with what is essentially a distally oriented puncture cut. The extent of denticulation is directly related to the efficiency of this. Denticles still fundamentally function to assist in a puncture (Abler, 1992), but they assist in the distal repositioning of the tooth relative to its starting position during this puncture. The dead-space that is produced during this puncturing is what allows for the removal for flesh.
This behavioral model has been witnessed in V. komodoensis (D'Amore and Blumenschine, in press). This animal sections off portions of flesh by simultaneously puncturing and drawing teeth distally through the substrate. This process is repeated until a portion of the prey is removed. In addition, many authors have proposed defleshing models for Theropoda. These include the “puncture and pull” method of tyrannosaurids (Erickson and Olson, 1996; Molnar and Farlow, 1990; Rayfield, 2004), or the “slashing” method of Allosaurus and Ceratosaurus (Holtz, 2002; Rayfield, 2001; Snively and Russell, 2007). Jacobsen (1995, p 66) also asserted that theropods drew their teeth backwards through the substrate.
Although heterodonty is apparent in theropods, the morphometric variation observed does not suggest specialized functions of specific teeth. Tooth position relative to the hinge seems to be the only major factor influencing variability in denticulation and apex orientation. This suggests that most teeth modified the substrate through puncture cutting. This supports Farlow et al. (1991) in that theropod teeth were multipurpose general instruments. Several studies have suggested that theropod heterodonty indicates that certain teeth were specialized for certain aspects of hunting, killing, and defleshing (Molnar, 1998). Although this may have been the case, theropod teeth most likely achieved these variable tasks by universally modifying the substrate through puncture cutting.
Denticulation conforms to the model proposed here for all theropod clades sampled except Troodontidae. Other studies have noted the unique tooth morphology of troodontids, mostly focusing on the their significantly large denticles relative to their tooth size (Farlow et al., 1991; Holtz et al., 1998). These data show that this is coupled with a unique, bimodal extent of mesial denticulation. Theropods are believed to be primarily carnivorous (Van Valkenburgh and Molnar, 1998), and the morphological consistency seen across the majority of the clades sampled here suggests that they all used their teeth to puncture compliant, fleshy substrate. The exception of Troodontidae is most likely the consequence of differences in tooth use. Troodontid dentition is reminiscent of herbivorous lizards and ornithischians, indicating the incorporation of plant material into their diet (Holtz et al., 1998). The mechanical demands of tough, fibrous plant material are quite different from those from those imposed on the teeth of a flesh specialist. This would result in different selection pressures on the sizes of both denticles and carinae.
More work is needed to further test the validity of the model proposed here. It should be noted that tooth denticulation was analyzed solely from a labial, two-dimensional perspective. The mesial carina bends lingually in many theropod taxa (Farlow and Pianka, 2002; Smith, 2005), which may reflect a “screw-like” effect during puncture (Farlow, personal communication). Similar morphometric analyses should be conducted on teeth from other perspectives. Farlow et al. (1991, p 192) notes a “remarkable evolutionary convergence” in ziphodont teeth within and outside of Theropoda. Exceptions may exist, such as Majungasaurus (Smith, 2007). A larger, more taxon-specific sample would help determine if this trend is consistent across most theropods, and across most ziphodont taxa. Tooth wear and wear facets should be further investigated to shed light on tooth movement through the substrate. Chandler (1990) found there was more wear apparent on the tooth apex than on the carinae, further supporting that the apex is receiving the initial resistance from the substrate. There are also wear facets common on tyrannosaurid teeth, which may be due to wear from food items and occlusion with the opposing tooth row (Farlow and Brinkman, 1994; Schubert and Ungar, 1995). Although cranial kinesis is postulated for several theropods based on skull morphology (Bakker, 1986; Mazzetta et al., 1998; Versluys, 1910), it has never been rigorously tested. More information concerning this would help determine if cranial kinesis also contributed to the line of action as proposed by Rieppel (1979). The effect of the inclusion/exclusion of the tooth root should also be evaluated, as it had a noticeable influence on this study.
Modifying actual substrate with ziphodont teeth may also test this model. Following Abler (1992), experimental systems may be set up with artificial teeth to test whether apex orientation and denticle position affects the efficiency of a tooth puncture. The feeding behavior of modern ziphodont carnivores may also be quantitatively analyzed. Studies of V. komodoensis indicate a feeding method analogous to the model proposed here. Tracking the tooth and head movements of feeding individuals may allow researchers to quantify the direction of tooth movement through the substrate, rather than relying on speculation based on tooth morphology.
Marina Sereda assisted in all cataloging, photographing, and describing of all theropod teeth. H. David Sheets copied and mailed morphometric software, as well as gave input on software applications. Kathleen M. Scott, George R. McGhee, and Kathryn A. Weiss gave critical comments on this manuscript. Christine L. Chandler provided necessary literature. Helpful advice was given by Peter Dodson, Henry John-Alder, Robert J. Blumenschine, Peter J. Morin, Raymond R. Rogers, Rudyard Sadlier, and Joshua B. Smith. The American Museum, Field Museum, and National Museum of Natural History Curatorial Staff, allowed access to fossil tooth specimens. Antonietta Corvasce, Stephen Goldstein, and L. Graeme Spicer provided lodging. This research was funded by the Paul Bond Scholarship Fund awarded by the Delaware Valley Paleontological Society. The author is grateful for the help received from these sources.