THE ANATOMICAL RECORD 292:1352–1369 (2009) Jaw Mechanics in Basal Ceratopsia (Ornithischia, Dinosauria) KYO TANOUE,1* BARBARA S. GRANDSTAFF,2 HAI-LU YOU,3 4 AND PETER DODSON 1 Canadian Museum of Nature, Ottawa, Ontario, Canada 2 School of Veterinary Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 3 Institute of Geology, Chinese Academy of Geological Sciences, Beijing, People’s Republic of China 4 School of Veterinary Medicine and Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, Pennsylvania ABSTRACT Ceratopsian dinosaurs were a dominant group of herbivores in Cretaceous terrestrial ecosystems. We hypothesize that an understanding of the feeding system will provide important insight into the evolutionary success of these animals. The mandibular mechanics of eight genera of basal ceratopsians was examined to understand the variability in shape of the jaws and the early evolution of the masticatory system in Ceratopsia. Data were collected on lever arms, cranial angles and tooth row lengths. The results indicate that psittacosaurids had higher leverage at the beak and in the rostral part of the tooth row than basal neoceratopsians, but lower leverage in the caudal part of the tooth row. Although the vertebrate mandible is generally considered as a third-class lever, that of basal neoceratopsians acted as a second-class lever at the caudal part of the tooth row, as is also true in ceratopsids. When total input force from the mandibular adductor muscles on both sides of the skull is considered, the largest bite force in basal ceratopsian tooth rows was exerted in the caudal part of the tooth row at the caudal extremity of the zone with near-maximum input force. Medially positioned teeth generate higher leverage than laterally positioned teeth. The largest bite force in all basal ceratopsians is smaller than the maximum input force, a limit imposed by the morphology of the basal ceratopsian masticatory system. In ceratopsids, caudal extension of the tooth row resulted in a much larger bite force, even exceeding the maximum input force. Anat Rec, C 2009 Wiley-Liss, Inc. 292:1352–1369, 2009. V Key words: basal Ceratopsia; masticatory system; mandibular mechanics; leverage; bite force Grant sponsors: Summer Research Stipends in Paleontology, University of Pennsylvania; School of Arts and Sciences Dissertation Research Fellowship, University of Pennsylvania; The Jurassic Foundation Research Grant; Government of Canada Post-Doctoral Research Fellowship; The Basic Outlay of Scientiﬁc Research Work from Ministry of Science and Technology; Hundred Talents Project of Ministry of Land and Resources of China; Narayan Avadhani, School of Veterinary Medicine, University of Pennsylvania. Grant sponsor: National Natural Science Foundation of China; Grant number: 40672007. C 2009 WILEY-LISS, INC. V *Correspondence to: Kyo Tanoue, Canadian Museum of Nature, PO Box 3443, Station ‘D’, Ottawa, Canada ON K1P 6P4. Fax: 1-613-364-4022. E-mail: firstname.lastname@example.org Received 9 June 2009; Accepted 9 June 2009 DOI 10.1002/ar.20979 Published online in Wiley InterScience (www.interscience.wiley. com). JAW MECHANICS IN BASAL CERATOPSIA 1353 Fig. 1. Cladogram of the Ceratopsia compiled from You et al. (2003, 2005), Chinnery (2004), Makovicky and Norell (2006), and Xu et al. (2006). Schematic diagrams of the lateral views of mandibles are shown for Chaoyangsaurus, Psittacosaurus (Psittacosauridae), Auroraceratops (basal Neoceratopsia), and Triceratops (Ceratopsidae). The outline of Triceratops mandible is modiﬁed after Hatcher et al. (1907). INTRODUCTION Lindgren et al., 2007). The abundance of some basal ceratopsian genera (such as Psittacosaurus and Protoceratops) and richness of ceratopsids indicate that ceratopsians, as a group, were ecologically successful (Dodson, 1990; Dodson and Currie, 1990; Sereno, 1990; Dodson et al., 2004). Understanding of the effectiveness of the masticatory apparatus may help to explain how ceratopsians evolved to become a dominant group of herbivorous dinosaurs. However, only a few biomechanical analyses of ceratopsian masticatory apparatus have been carried out. Ostrom’s (1964, 1966) two-dimensional analyses of the mandibular levers of ceratopsians showed a progressive improvement of leverage within Ceratopsia. Norman and Weishampel’s (1991) model of jaw mechanics in Psittacosaurus, in which they suggested propalinal motion of the mandible, was limited by the general lack of biological and anatomical knowledge of the clade due to the incompleteness and poor preparation of the specimens then available. Since 1997, discoveries of superbly preserved skulls of basal Ceratopsia, including those of Archaeoceratops (Dong and Azuma, 1997; You et al., in press), Zuniceratops (Wolfe and Kirkland, 1998), Chaoyangsaurus (Zhao et al., 1999), Liaoceratops (Xu et al., 2002), Ceratopsia was one of the dominant herbivorous dinosaur clades in Cretaceous terrestrial ecosystems of Asia and western North America (Dodson et al., 2004; You and Dodson, 2004). Among ceratopsians, the Ceratopsidae is the most derived clade (Fig. 1). It is composed of large bodied (4–8 m in length) genera, known for their horns and well-developed frills on the skull (Dodson and Currie, 1990; Dodson et al., 2004). Ceratopsids were dominant in Late Cretaceous terrestrial ecosystems in western North America. Basal Ceratopsia include Psittacosauridae, basal Neoceratopsia, and a few basal-most genera (Zhao et al., 1999; You and Dodson, 2004; Xu et al., 2006; Zhao et al., 2006). They are generally much smaller than ceratopsids, typically 1–3 m in length. Their skulls generally lack horns, and frills are either undeveloped or poorly developed. Basal ceratopsians have been found in Oxfordian to Campanian deposits of Asia, and Turonian to Maastrichtian deposits in North America (Dodson and Currie, 1990; Wolfe and Kirkland, 1998; You and Dodson, 2004; Xu et al., 2006). Discoveries of European specimens from the early Campanian were reported recently (Godefroit and Lambert, 2007; 1354 TANOUE ET AL. TABLE 1. Measurements of various parameters of the mandibular lever in different ceratopsian specimens Leverage Taxon Ceratopsia Chaoyangsaurus youngi Psittacosauridae Hongshanosaurus houi P. mongoliensis P. major Neoceratopsia Archaeoceratops oshimai Archaeoceratops yujingziensis Auroraceratops rugosus Leptoceratops gracilis Liaoceratops yanzigouensis Protoceratops andrewsi Ceratopsidae Chasmosaurus belli Styracosaurus albertensis Caudal end of tooth row Tooth row/jaw length 0.51 0.94 0.40 0.45 0.40 0.48 0.44 0.39 0.53 0.52 0.53 0.58 0.49 0.85 0.86 0.83 1.03 0.80 0.31 0.30 0.33 0.33 0.31 31 33 41 42 48 40 34 32 42 34 40 32 29 0.28 0.33 <0.35 0.36 0.33 0.25 0.27 0.32 0.37 0.40 0.33 – 0.27 0.39 0.47 <0.53 0.51 0.48 0.41 0.46 0.41 0.43 0.51 0.50 0.48 0.41 0.94 1.07 1.14 1.21 1.23 1.48 1.60 0.97 1.00 1.19 1.11 1.07 0.95 0.43 0.40 – 0.41 0.42 0.44 0.41 0.45 0.49 0.44 0.46 – 0.37 54 57 55 0.32 – – 0.57 0.53 0.51 4.06 3.57 3.26 0.49 – – Specimen number Side Input lever angle Beak tip IGCAGS V371 r 13 0.45 IVPP V12617 IVPP V12617 AMNH6254 CAGS-IG-VD-004 CAGS-IG-VD-004 lf r lfa lf r 26 21 31 25 31 IVPP V11114 IVPP V11114 CAGS-IG-VD-003 IG-2004-VD-001 IG-2004-VD-001 CMN8889 CMN8889 IVPP V12738 IVPP V12633 IVPP V12633 AMNH6460 HMNH MPC-D100/530 HMNH MPC-D100/530 lf r r lf r lf r r lf r r lf r CMN2245 CMN344 CMN344 r lf r Rostral end of tooth row AMNH, American Museum of Natural History, New York, USA; CAGS, IG, IGCAGS, Institute of Geology, Chinese Academy of Geological Sciences, Beijing, China; HMNH, Hayashibara Museum of Natural History, Okayama, Japan; IVPP, Institute of Vertebrate Paleontology and Paleoanthropology, Academia Sinica, Beijing, China; CMN, Canadian Museum of Nature, Ottawa, Canada; PKUP, Peking University Paleontological Collections, Beijing, China. a Measured from the cast. Lengths are in millimeters and angles in degrees. Jaw length refers to the distance between the rostral end of the predentary and the center of the glenoid. lf, left mandible; r, right mandible. Hongshanosaurus (You et al., 2003), Magnirostris (You and Dong, 2003), Prenoceratops (Chinnery, 2004), Auroraceratops (You et al., 2005), Yinlong (Xu et al., 2006), Xuanhuaceratops (Zhao et al., 2006), Yamaceratops (Makovicky and Norell, 2006), and Cerasinops (Chinnery and Horner, 2007) make it possible to study the early evolution of the ceratopsian masticatory apparatus. However, articulated skulls and mandibles of type specimens are seldom separated when they are ﬁrst described. Further preparation of the specimens, especially involving the detachment and removal of mandibles from the skulls, has revealed new information that was not accessible in the initial studies. The effectiveness of a masticatory system, which can be examined biomechanically, determines the diversity of food accessible to an animal. Analysis of mandibular mechanics in basal Ceratopsia is necessary to understand the early evolution of the ceratopsian masticatory system. Mandibular mechanics should explain not only the establishment of the ceratopsid masticatory apparatus, but also the variation within basal Ceratopsia, which is evident from differences in mandibular morphology between psittacosaurids and basal neoceratopsians. In this study, jaw mechanics in basal ceratopsians is examined in greater detail than has been possible before. MATERIALS AND METHODS Materials Nineteen mandibular rami of eight basal ceratopsian genera were observed and measured (Table 1). Representative jaws for basal-most ceratopsians, psittacosaurids, basal neoceratopsians, and ceratopsids are shown in Fig. 2. In this study, Chaoyangsaurus (Fig. 2A,B) represents the basal-most Ceratopsia. One Chaoyangsaurus jaw was measured. Psittacosaurus (Fig. 2C,D) and Hongshanosaurus comprise the Psittacosauridae. Five psittacosaurid jaws are included in this study. Archaeoceratops (Fig. 2E,F), Auroraceratops, Leptoceratops, Liaoceratops, and Protoceratops represent the basal Neoceratopsia. Thirteen mandibular rami of basal neoceratopsians were measured. Three rami of mandibles belonging to two ceratopsid genera, Chasmosaurus (Fig. 2G,H) and Styracosaurus, were included for comparison with basal ceratopsians. Parameters used in the study (input lever length, tooth dimension, tooth row length and lengths from the glenoid to various bite points) were measured directly from the specimens. Mandibular Adductor Musculature M. adductor mandibulae externus (MAME), M. adductor mandibulae internus including M. pseudotemporalis JAW MECHANICS IN BASAL CERATOPSIA 1355 TABLE 2. Anatomical and mechanical abbreviations A B B1, B2, B3 Be G G0, G1 Gl, Gr Jl, Jr Jr1 Jr2 K lf MAME MAMP MPsT MPT P Pe PeG Fig. 2. Mandibles of representative ceratopsians. (A, B) Chaoyangsaurus youngi (IGCAGS V371) in dorsal (A) and right lateral (B) views. (C, D) Psittacosaurus major (CAGS-IG-VD-004) in dorsal (C) and left medial (D) views. (E, F) Archaeoceratops oshimai (IVPP V11114) in dorsal (E) and right medial (F, reﬂected) views. (G, H) Chasmosaurus belli (CMN 2245) in dorsal (G) and right lateral (H) views. Scale bars: 5 cm. (MPsT), and M. pterygoideus (MPT), and M. adductor mandibulae posterior (MAMP) are the major components of mandibular adductor musculature in ceratopsians (Table 2; Fig. 3; Haas, 1955; Ostrom, 1964). Based on Haas (1955), Ostrom (1964), and dissection of Alligator mississippiensis, the origins, insertions, and orientations of the action of these muscles in basal ceratopsians are postulated as follows: (1) MAME originates in the region of the supratemporal fenestra and inserts on the apex of the coronoid process. The line of action is directed caudodorsally. Haas (1955) and Ostrom (1964) assumed the origin of M. adductor mandibulae externus medialis and profundus to be on the dorsal surface of the frill. In Dodson (1996), the origin was restricted to the base of the frill. Both suggested origins lie caudodorsal to the mandibular insertion, and both interpretations therefore support a caudodorsal orientation for the line of action of MAME. (2) MPsT originates in the postorbital region on the lateral surface of the laterosphenoid and inserts on the rostral part of the apex of the coronoid process. The line of action is nearly vertical. (3) The origin of MPT is on the mandibular process of the pterygoid, and r R0, R2 y I II III Apex of coronoid process Bite point at tooth apex Bite points Effective bite point; point B projected onto a line at the level of the tooth bases Center of glenoid Effective fulcrums in the levers PR0G0 and B1R0G1, respectively Centers of left and right glenoid, respectively Positions where the resultant vectors for left and right mandibular adductor muscles, respectively, intersect the level of the tooth row Original position where the resultant vector for right mandibular adductor muscles intersect the level of the tooth row as assumed in this study Caudally shifted point of application of the resultant input vector due to steeper inclination of the vector Point where line GlR0 and GrR0 intersects line GrP and GlP, respectively Left mandible M. adductor mandibulae externus M. adductor mandibulae posterior M. pseudotemporalis M. pterygoideus Rostral end of the predentary Point P projected onto a line at the level of the tooth bases; the effective rostral end of the jaw The line from the glenoid to a point directly below the tip of the jaw Right mandible Positions of resultant vectors for the muscle forces from both sides of the mandible Angle of the input lever arm relative to the ramus of the mandible in degrees Region I of the mandible Region II of the mandible Region III of the mandible insertion is on the ventrolateral, ventral, and ventromedial surfaces of the caudalmost part of the mandible. The orientation of the MPT axis is rostrodorsal. In crocodilians (such as A. mississippiensis) there is a large anterior part of MPT, M. pterygoideus anterior, which was reduced or entirely absent in ceratopsians because no anatomical space for the muscle is available in this group. (4) The origin of MAMP is on the rostral surface of the quadrate, and its insertion is along and within the Meckelian fossa. The axis of MAMP is directed caudodorsally. MAME is the largest jaw adductor muscle in ceratopsians. The dominant direction of pull on the mandible of basal ceratopsians by the combined actions of all mandibular adductor muscles is caudodorsal. Electromyographic, cinematographic, and cineﬂuoroscopic studies of mastication pattern in extant reptiles such as tuatara (Gorniak et al., 1982) and A. mississippiensis (Busbey, 1989) have recorded that that jaw adductors act differently during bite cycles. This cannot be determined in fossil taxa and is ignored in this study. 1356 TANOUE ET AL. Two-Dimensional Analysis of Mandibular Mechanics In the following two-dimensional analysis of the mandibular lever system the mandibular ramus is considered in lateral view. Only simple orthal jaw closing is considered. The vertebrate mandible generally operates as a third-class lever. The output force acts at the bite point on the beak or tooth row, and the input force at the insertion of the jaw closing muscles. Both are rostral to the glenoid, the fulcrum of the mandibular lever. Development of the lower jaw as a third class lever permits maximum depression (opening) of the jaw with a mini- Fig. 3. Diagram of lateral view of basal neoceratopsian Archaeoceratops skull with locations and actions of the mandibular adductor muscles represented by arrows. mum length of adductor muscle ﬁbers (Ostrom, 1964). In ceratopsids, however, the tooth row extends caudal to the coronoid process, and the caudal portion of the mandible therefore acts as a second-class lever (Fig. 2G; Ostrom, 1964, 1966). Figure 4 shows a schematic basal ceratopsian mandible in lateral view. G is the center of the glenoid and A the apex of the coronoid process. Thus the line GA is the input lever arm. In this study it is assumed that the input lever is perpendicular to the resultant vector of all jaw adductor muscles, indicated by an arrow in Fig. 4. The length of the output lever arm is the distance from the glenoid to the bite point along the line GPe, which is parallel to the long axis of the mandibular ramus. It is assumed that the resistant force at the bite point (bite force), provided by contact with the food, acts perpendicular to the long axis of the mandibular ramus. For example, if B is the bite point and Be is the effective bite point projected onto the mechanical axis of the jaw, the line GBe is the output lever arm. P is the beak tip, the rostral end of the predentary. The line GPe is the functional jaw length as well as the output lever arm when biting food at the tip of the beak. Friction is ignored in this analysis to simplify calculations. Any possible rostrocaudal movement of the mandible can also be ignored since only resistant force acting perpendicular to the long axis of the mandibular ramus is considered here. Measurements were made of the length of the input lever arm, and the angle between the input lever arm and the long axis of the mandibular ramus. The distances from the glenoid to the tip of the predentary and to the rostral and caudal ends of the tooth rows were measured. These represent the lengths of the output lever arms for bite points at three different points along the tooth row. The length of tooth row was also measured. In a mandibular lever system, ðTotal input forceÞ ðInput lever lengthÞ ¼ ðBite forceÞ ðOutput lever lengthÞ Fig. 4. Diagram of the mandibular lever of ceratopsians. The lateral view of the right mandible of Archaeoceratops is shown. The arrow pointing caudodorsally from the apex of the coronoid process is the resultant vector of the right jaw adductor musculature. JAW MECHANICS IN BASAL CERATOPSIA 1357 If the total input force exerted by the mandibular adductor muscles is set at 1 unit, bite force can be described by the ratio of input lever length to output lever length: Bite force ¼ Input lever length Output lever length for any given bite point along the jaw. To compare the mandibular mechanics of the different ceratopsian taxa, bite forces at the tip of the beak and at the rostral and caudal ends of the tooth row were calculated for each taxon included in the study. Three-Dimensional Analysis of Mandibular Mechanics Two-dimensional analysis is limited to consideration of forces acting on the working side of the head, on which an object is bitten, and ignores the effects of muscles on the balancing side of the head, the opposite side of the working side. During mastication, mandibular adductor muscles on both sides are active. Since both rami of the ceratopsian mandible are embraced ﬁrmly by the predentary, the input muscle force from the balancing side can be transmitted to the working side and will contribute to the total input forces acting on the working side. Greaves (1978) and Druzinsky and Greaves (1979) developed a method for three-dimensional analysis of mandibular mechanics that makes it possible to understand the total bite force produced by the combined activity of mandibular adductor muscles on both sides of the jaw. This three-dimensional model has been used to analyze bite forces in a wide variety of vertebrates (Druzinsky and Greaves, 1979; Spencer and Demes, 1993; Bryant and Russell, 1995; Greaves, 1978, 1988, 1995; Spencer, 1998, 1999). The models developed by Greaves (1978) and Druzinsky and Greaves (1979) are employed here. Figure 5A shows a dorsal view of the ceratopsian mandible. Gl and Gr are the centers of the left and right glenoid, respectively. P is the rostral end of the predentary. Vectors of the mandibular adductor muscle forces acting on the left and right mandibles intersect the level of the tooth rows at Jl and Jr, respectively. Only vertical components of the vectors are considered in this model. If the muscles on both sides produce equal forces, the resultant muscle force can be assumed to be acting at R0, the midpoint of a line connecting Jl and Jr. This model treats each tooth as a separate bite point, and assumes only one bite point is active at any one time. When the animal bites with the tip of the predentary (P) with the left and right jaw muscles supplying equal forces to the bite, the total resistance force at the glenoids can be represented by a force acting at an effective fulcrum G0 halfway between the glenoids, and the muscle forces can be assumed to act at R0. The lever PR0G0 can be regarded as a third-class lever with the fulcrum at G0. Moving the bite point caudally along the working side tooth row changes the location of the effective fulcrum, causing it to migrate toward the opposite (balancing side) glenoid. When the bite point is at B1 and both muscle forces are equal, G1 is the effective fulcrum needed to keep R0 on the output lever. As the bite point shifts caudally along the right tooth row, as shown in Fig. 5A, the Fig. 5. Diagram of the dorsal view of ceratopsian mandible. Archaeoceratops mandible is shown. effective fulcrum moves toward Gl. Since the effective fulcrum cannot be positioned lateral to the glenoid, any bite point caudal to the line GlK (K is the point where the line GlR0 intersects the line GrP). For instance, at 1358 TANOUE ET AL. B2, would be on a lever which does not incorporate R0. Instead, the resultant muscle force will shift laterally toward Jr, and will be located on the line GlB2 at R2, the point where GlB2 intersects the line JlJr. As the bite point shifts caudally and the resultant force input point shifts toward the working side, the force exerted by the balancing side decreases. Thus, when the bite point is at B2 the mandibular adductor muscles on the working side still exert maximum force, but the force produced by the muscles on the balancing side is reduced. The lateral shift in the effective force input point (from R0 to R2) is proportional to the reduction of input from the balancing side jaw adductor muscles. When the resultant input vector reaches Jr, effective muscle force input from the left side drops to zero and no longer contributes to mastication. At all points caudal to the line JlJr, for instance at B3 in Fig. 5A, only the muscle force from the right jaw adductors is applied, and leverage can be analyzed two-dimensionally. The zones of bite points lying rostral to K, between K and Jr, and caudal to Jr are termed Region I, II, and III, respectively, by Spencer and Demes (1993) and Spencer (1998). In Region I and the rostral part of Region II the jaw functions as a thirdclass lever; in the caudal part of Region II and in Region III it functions as a second-class lever. For this analysis the better-preserved side of the mandible was reﬂected about the midline to form a symmetrical reconstructed mandible, which minimizes taphonomic distortion. Complete reconstructed mandibles, including articulated left and right rami, were then analyzed three-dimensionally. The apices of teeth were selected as the bite points used to calculate the maximum bite force at each tooth position. The center of the tooth in occlusal view substituted for the apex if the apical portion of the crown is not preserved. The tip of the predentary was used as the predentary bite point. When the bite point is in Region I, mandibular adductor muscles on both sides can exert maximum input force. The total input force is set as 1 unit in this analysis, with half of the total input force being contributed by left adductors and half by right adductor muscles. Based on Druzinsky and Greaves (1979), at point B1: Bite force ¼ G1 R0 G1 B1 where G1 is the fulcrum for the lever arm passing through B1, R0 is the effective force application point, G1R0 is input lever arm length, and G1B1 is output lever arm length. This equation can be expanded to apply to Region II, where the working side can exert 0.5 units of muscle force, but the balancing side cannot exert the maximum input force, to give the following equation when the bite point is at B2: JrR2 GlR2 Bite force ¼ 0:5 1 þ JrR0 GlB2 where Jr is the working side muscle insertion point, Gl is the balancing side jaw joint, R0 is the effective force application point when input force from both sides is maximal, and R2 is the effective force application point when the bite point is at B2. The line JrR2 describes total muscle input at point R2 and the line JrR0 describes total muscle input at point R0. The ratio between the two gives effective muscle input from both sides when the input lever passes through R2. The line GlR2 is input lever arm length, and the line GlB2 is output lever arm length, when the bite point is at B2. The bite force in Region III was calculated as in two-dimensional analysis. However, since all of the muscle force being applied comes from the working side, the maximum input force available is 0.5 units. A striking contrast between psittacosaurids and some basal neoceratopsians lies in the geometry of the tooth row. The tooth row of psittacosaurids is nearly straight, but that of small basal neoceratopsians is concave laterally (Fig. 2C,E). To examine the possible effect on bite force produced by the curved tooth rows of Archaeoceratops oshimai (IVPP V11114), Auroraceratops (IG-2004VD-001), and Liaoceratops (IVPP V12738), the maximum bite force of the teeth of a hypothetical straight tooth row like that of psittacosaurids, lying on a line between the ﬁrst and the last teeth of the actual tooth row, was calculated. Bite forces produced along the hypothetical straight tooth row were then compared to bite forces generated on the actual curved tooth row (Fig. 5B). Each tooth in the hypothetical tooth row is placed the same distance from the glenoid as the corresponding tooth of the actual curved tooth row. Additionally, the bite force in mandibles with different angles between the two rami was examined because observed intermandibular angles vary among different species of psittacosaurids. Difference in intermandibular angle might affect the bite forces generated by the teeth by changing the distance from the tooth row to the midline of the mandibles, and it was desired to discover how much of an effect differences in the intermandibular angle might have on bite force. The left mandible of Psittacosaurus major (CAGS-IG-VD-004) was used for this analysis (Fig. 2C). If it is reﬂected onto the right side to form a symmetrical mandible, the angle between the mandibular rami is only 18 degrees. The holotype of P. major (LHPV1; Sereno et al., 2007) has an intermandibular angle of 30 degrees. In other Psittacosaurus species including P. sinensis (IVPP V738) and P. lujiatunensis (PKUP 1054), this angle reaches about 60 degrees. Differences in intermandibular angle could be an artifact of preservation, or could reﬂect real differences in skull morphology. Any real differences in this angle will affect the bite forces generated by the jaws. The bite force of hypothetical mandibles of P. major with intermandibular angles of 30 and 60 degrees, representing, respectively, the holotype mandible of P. major and the mandibles of other psittacosaurids with widelydiverging mandibles, were compared with that of the jaw of P. major (CAGS-IG-VD-004; Fig. 6A). RESULTS Two-Dimensional Analysis of Mandibular Mechanics Table 1 shows the calculated values of bite force relative to the input force at three points along the ceratopsian mandible. Bite force is represented in Table 1 by the ratio between input and output lever arm lengths. Average bite force at the rostral end of predentary and JAW MECHANICS IN BASAL CERATOPSIA 1359 Fig. 6. (A) Diagram of the dorsal views of the psittacosaurid mandibles. Reconstructed left mandible of Psittacosaurus major (CAGS-IGVD-004) in heavy line. Right mandible (dashed) is the reﬂected left mandible. The actual mandible has an intermandibular angle of 18 degrees. Hypothetical mandibles with intermandibular angles of 30 and 60 degrees, reﬂecting jaw angles of the type specimen of P. major (LHPV1) and other Psittacosaurus species with widely-diverging man- dibles, respectively, are shown with dotted lines. (B) Regions in the dentary tooth row of P. major (CAGS-IG-VD-004). (C) Regions in the dentary tooth row of hypothetical mandible reﬂecting the holotype of P. major (LHPV1). (D) Regions in the dentary tooth row of hypothetical mandible reﬂecting Psittacosaurus species with widely divergent mandibles. rostral and caudal ends of the tooth rows in Choayangsaurus (basal-most Ceratopsia), Psittacosauridae, basal Neoceratopsia, and Chasmosaurus (Ceratopsidae) are compared in Fig. 7. Leverage at the rostral ends of the predentary (the beak tip) and tooth row is greater in the ﬁve psittacosaurid jaws measured than at the same two points in the jaws of basal neoceratopsians. At the caudal end of the tooth row, in contrast, the leverage is greater in basal neoceratopsians than in psittacosaurids. With the exception of the left mandible of P. major, the output lever arm from the glenoid to the caudal end of the tooth row in psittacosaurids is longer than the input 1360 TANOUE ET AL. Fig. 7. Average bite force at the rostral end of predentary and rostral and caudal ends of tooth rows in Chaoyangsaurus (basal-most Ceratopsia), Psittacosauridae, basal Neoceratopsia, and Chasmosaurus (Ceratopsidae). Error bars indicate 95% conﬁdence intervals. See Table 1 for the bite force in each species. lever, and leverage at the caudal end of the tooth row is less than 1.0. In most basal neoceratopsians the length of this output lever is shorter than the input lever, and leverage at the caudal end of the tooth row is greater than 1.0. The leverage in Chaoyangsaurus, the basalmost ceratopsian studied, is similar to that of psittacosaurids. Measurements of ceratopsids, while few in number for this study, indicate higher leverage throughout the tooth row than in basal neoceratopsians. At the beak tip, the leverage of Chasmosaurus is lower than that of Chaoyangsaurus and psittacosaurids. The proportional lengths of tooth rows relative to the distances between the rostral end of predentary and the center of glenoid, referred to as jaw lengths in this study, differ among basal ceratopsians (Table 1). The tooth row in Chaoyangsaurus is relatively longer than that of psittacosaurids, but shorter than that of most basal neoceratopsians. The tooth row in psittacosaurids is very short. The tooth row in basal neoceratopsians is relatively longer than that of psittacosaurids. The tooth row is shorter relative to the jaw length in Protoceratops than in Chaoyangsaurus. Correspondingly, the postdentary length of the mandible is greater in psittacosaurids than in basal neoceratopsians, and the input lever arm is therefore longer in psittacosaurids. Three-Dimensional Analysis of Mandibular Mechanics Bite forces at each tooth position were calculated to provide a detailed picture of how bite force varies along the jaw in ceratopsians, and to test how reduced muscle input force effects the bite force in the caudal part of the jaw, where the balancing side muscle contribution to input force decreases. Table 3 shows bite force as a proportion of the combined input force from muscles on both sides of the head as calculated for each tooth position. The number of teeth falling into each of the three functional regions of the jaw varies among taxa. All teeth of Chaoyangsaurus and psittacosaurids lie in Regions I and II, with a majority of the teeth located in Region I. The teeth of basal neoceratopsians are distributed over all three regions, with more teeth located in Region I than in the other two regions. However, in Chasmosaurus (CMN 2245) the majority of the teeth (11 teeth, plus three additional tooth positions) are located in Region III because the toothless rostral part of the jaw is very elongated. Only three teeth are located in Region I, and seven in Region II. In basal ceratopsians, except for Protoceratops (AMNH 6460), the highest bite force is exerted in the caudal half of the tooth row, but not at the last tooth. In all basal ceratopsian specimens studied the teeth with the largest bite force are positioned at the boundary between Region I and II. In Chasmosaurus, the bite force increases caudally to a maximum at the fourth and ﬁfth teeth, which lie within Region II, then decreases caudally in the remainder of Region II. Bite force increases again in Region III, and is highest at the caudal end of the tooth row. Although the last three teeth are not preserved, the last two teeth analyzed exerted a bite force larger than the maximum input force. The bite force in the caudalmost region of the tooth row exceeds the highest bite force in Region II. Tooth size varies among ceratopsian species, and also varies along the tooth row of an individual animal. Differences in tooth size within a single tooth row might be related to the differences in bite force along the tooth row found using three-dimensional analysis. Calculated bite force at each tooth was compared with the size of that tooth to test whether there is any correlation between bite force and tooth size. The bite force and the product of labiolingual and mesiodistal diameters in occlusal view, as a proxy for tooth area, of the dentary teeth in Chaoyangsaurus (IGCAGS V371), Hongshanosaurus (IVPP V12617), P. major (CAGS-IG-VD-004), A. oshimai (IVPP V11114), and Liaoceratops (IVPP V12738) are plotted in Fig. 8. Bite force, tooth area in occlusal view, and the correlation coefﬁcient of the bite force and tooth area for teeth in Regions I and II in these ﬁve taxa are given in Table 4. The tooth area of Chaoyangsaurus (IGCAGS V371), Hongshanosaurus (IVPP V12617), A. oshimai (IVPP V11114), and Liaoceratops (IVPP V12738) is signiﬁcantly correlated with bite force (a ¼ 0.01 or 0.05). The tooth area of P. major (CAGS-IG-VD-004) is not as well correlated with bite force as in the other four genera (r ¼ 0.53; a ¼ 0.10). In Region III, bite force increases caudally even though the tooth diameters decrease in A. oshimai (IVPP V11114) and Liaoceratops, the only two of the ﬁve taxa tested which have teeth in Region III. Since the teeth of these ﬁve specimens are in the same size range, tooth area and bite force of the teeth in Regions I and II are plotted together in Fig. 9. The comparison of bite forces in the curved tooth row found in A. oshimai (IVPP V11114), Auroraceratops (IG2004-VD-001), and Liaoceratops (IVPP V12738) with bite force along a hypothetical straight tooth row positioned lateral to the actual tooth row, and anchored to the real tooth row at its rostral and caudal ends, is shown in Fig. 10. In Region I the curved tooth row has slightly greater leverage than the hypothetical straight tooth row, and in Region II the leverage is also better for the curved tooth 0.73 0.66 0.53 Region II Ceratopsidae 0.80 0.78 0.73 0.68 0.62 0.47 0.62 0.65 0.69 0.73 0.76 r 0.84 0.79 0.74 0.42 0.57 0.60 0.63 0.66 0.71 0.75 – lf 0.47 0.50 0.81 0.79 0.77 0.73 0.63 0.38 0.55 0.58 0.61 0.65 0.69 0.72 0.76 r 0.74 0.70 0.65 0.61 0.31 0.47 0.49 0.51 0.54 0.59 0.62 0.68 0.74 lf 0.40 0.44 0.47 0.82 0.79 0.75 0.67 0.42 0.56 0.58 0.60 0.62 0.65 0.69 0.73 0.78 r 0.41 0.45 – 0.52 0.78 0.77 0.71 0.63 0.43 0.68 0.71 0.74 – 0.81 r 0.47 0.50 0.53 0.57 0.61 0.66 0.72 0.83 0.92 1.03 1.14 – – – 0.82 0.82 0.77 0.77 – 0.67 0.62 0.43 0.75 0.77 0.80 r Psittacosaurus Archaeoceratops Hongshanosaurus major oshimai Auroraceratops Liaoceratops Protoceratops Chasmosaurus (IVPP V12617) (CAGS-IG-VD-004) (IVPP V11114) (IG-2004-VD-001) (IVPP V12738) (AMNH 6460) (CMN2245) Basal Neoeratopsia The bite force at the rostral end of the predentary is indicated by the top row in the table. The number of bite force values in each column represents the number of teeth in each region in that species. Region III 0.45 0.53 0.54 0.54 0.58 0.62 0.65 0.70 0.75 r Region I Side Chaoyangsaurus (IGCAGS V371) Psittacosauridae TABLE 3. Bite force relative to maximum input force at each tooth in the three regions of the jaw Basalmost Ceratopsia JAW MECHANICS IN BASAL CERATOPSIA 1361 1362 TANOUE ET AL. Fig. 8. Bite force and tooth area in occlusal view of the teeth of ﬁve basal ceratopsian specimens. Tooth area in mm2. rows. The difference is largest where medial deﬂection of the tooth row is greatest. In Region III the bite force is equal in both types of the tooth row, since balancing side muscles do not contribute to the bite and only the distance of the teeth from the glenoid along the mandibular ramus determines the leverage. Differences in bite force between medially and laterally positioned teeth at the same tooth position along the jaw can only be revealed by three-dimensional analysis. The analysis of bite force in P. major (CAGS-IG-VD004) mandibles with narrow and wide divergence produced results similar to those in the comparison of curved and straight tooth rows in basal neoceratopsians (Fig. 11). As the intermandibular angle increases, boundaries among the three regions shift rostrally along the tooth row, incorporating more teeth in Region II. Because the position where the vector of input muscle force (Jl in Fig. 6B) intersects the jaw is ﬁxed, increases in intermandibular angle shift the line JlJr and the point R0 rostrally relative to the tooth row, so that the boundaries between regions (marked by the lines GrR0K and GrJl) pass through more rostral teeth as the intermandibular angle increases (Fig. 6B–D). In Region I, bite force is only slightly affected by changes in intermandibular angle. The bite force in Region II shows a clear association with jaw separation, and the difference is much larger and more consistent than that seen in Region I. In Region II, bite force decreases as the intermandibular angle increases. DISCUSSION Leverage To date, the oldest known basal ceratopsians are known only from Asia, as are the oldest and most basal neoceratopsians. In most basal neoceratopsians, the 6.2 4.9 7.4 15.2 19.0 24.2 26.2 23.8 18.9 8.3 0.70 0.75 0.73 0.66 0.53 Tooth area 0.53 0.54 0.54 0.58 0.62 Bite force Tooth areas are in mm2. Chaoyangsaurus r a 0.96 0.01 16.0 18.0 16.3 17.5 15.2 14.9 11.9 0.73 0.76 0.80 0.78 0.73 0.68 0.42 Hongshanosaurus r a 0.87 0.01 14.6 Tooth area 0.65 Bite force Right mandible Right mandible Correlation test results 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Tooth position r 0.53 0.84 0.79 0.74 0.57 0.60 0.63 0.66 0.71 0.75 a 0.1 20.7 21.6 13.7 14.1 16.6 17.5 19.8 23.6 20.3 Tooth area P. major Bite force Left mandible Psittacosaurus major (CAGS-IG-VD-004) Psittacosauridae Hongshanosaurus (IVPP V12617) Chaoyangsaurus (IGCAGS V371) Basalmost Ceratopsia r 0.65 0.58 0.61 0.65 0.69 0.72 0.76 0.81 0.79 0.77 0.73 0.43 0.47 a 0.05 4.9 11.4 15.2 18.4 13.9 25.9 18.0 21.6 29.0 8.9 17.9 15.1 Tooth area A. oshimai Bite force Right mandible Archaoeceratops oshimai (IVPP V11114) 6.8 4.3 6.5 8.4 16.3 18.7 24.1 18.3 22.9 29.4 23.0 17.6 10.4 6.9 Tooth area Liaoceratops r a 0.79 0.01 0.58 0.60 0.62 0.65 0.69 0.73 0.78 0.82 0.79 0.34 0.36 0.40 0.44 0.47 Bite force Right mandible Liaoceratops (IVPP V12738) Basal Neoceratopsia TABLE 4. Correlation of bite force with tooth area in occlusal view of the teeth in Region I and II of the ﬁve specimens shown in Figure 8 JAW MECHANICS IN BASAL CERATOPSIA 1363 1364 TANOUE ET AL. Fig. 9. Plot of bite force versus tooth area of the teeth in Regions I and II. Data for teeth of all ﬁve basal ceratopsian specimens shown in Fig. 8 are plotted together. Tooth area in mm2. Solid line, regression for the data (y ¼ 48.916.9, r2 ¼ 0.44); dashed lines, 95% conﬁdence band. mandible acted as a second-class lever in the caudal portion of the tooth row due to the geometry of the jaw (Table 1). If the vector of the input muscle force were steeper than is assumed in this study, the point of application of the resultant input vector would be shifted caudally (Fig. 12). As a result, the input lever arm would have been shorter, which reduces the leverage. Nevertheless, two-dimensional analysis shows that basal neoceratopsians could still produce a bite force nearly equal to the input muscle force at the caudal end of the tooth row even if the input vector was steeper than assumed in this study. Most basal neoceratopsian mandibles would be restricted to third-class lever action by this variation. Caudal displacement of the coronoid process in neoceratopsians shortens the input lever arm signiﬁcantly. At the same time, it increases the slope of the input lever arm. The angle of the input lever arm relative to the mandibular ramus in neoceratopsians, with the exceptions of Archaeoceratops and Protoceratops, is higher than the angles in Chaoyangsaurus and the psittacosaurids (Table 1). In ceratopsids, depression of the glenoid also affects jaw mechanics. The glenoid of Chaoyangsaurus is almost at the same level as the dentary tooth row in lateral or medial view (Fig. 2B). That of psittacosaurids and basal neoceratopsians lies slightly ventral to the level of the tooth row (Fig. 2D,F). The glenoid of the more derived ceratopsids, in contrast, is well below the level of the tooth row. Although the coronoid process is even more displaced in a caudal direction than is that of basal ceratopsians, the increased depression of the glenoid and increased height of the coronoid process lengthen the input lever arm to increase leverage in ceratopsids (Ostrom, 1964). Three-dimensional analysis of ceratopsian mandibles produced a pattern of bite forces along the jaw that differed from the steady increase in bite force caudally seen in the two-dimensional analysis. At the rostral end of the predentary the bite forces calculated using the three-dimensional method are generally higher than those calculated using the two-dimensional method. Bite forces calculated for the rostral ends of the tooth row are also generally higher using the three-dimensional method. However, in bite forces calculated for the caudal end of the tooth row using the three-dimensional method, calculations are much lower than expected from the two-dimensional analysis. The low caudal bite force results because input force in the caudal part of the jaw comes only from the working side adductor muscles, and is therefore only half of the total input force from both sides applied in Region I. Bite forces calculated using the three-dimensional method vary along the jaw because input forces decrease caudally in Region II, reaching a minimum value of 50% of the maximum input force at the caudal end of Region II. In contrast, bite forces calculated using two-dimensional analysis increase caudally because they depend only on the decreasing distance from the jaw hinge, while input force remains constant over the entire jaw length. Three-dimensional analysis shows that the largest bite force is exerted at or close to the Region I/Region II boundary, near the caudal end of the zone receiving maximum total input force from the muscles on both sides of the skull in basal ceratopsians (Table 3). Bite force never exceeds the maximum total input force in any of the basal ceratopsians analyzed, with the largest ratio of 0.84 relative to the maximum total input force being found in P. major. The bite force in Region III increases caudally. In basal neoceratopsians it remains smaller than the bite force in Region II throughout the entire length of Region III, which contains only two to four teeth. Even in basal neoceratopsians, however, the caudalmost Region III teeth exert a larger bite force than teeth in the rostral part of Region III. In Chasmosaurus, more than half of the teeth (14 of 24 teeth) lie within Region III. From the 18th tooth (the eighth tooth JAW MECHANICS IN BASAL CERATOPSIA 1365 Fig. 10. Comparison of bite forces at the teeth of the actual curved tooth row and a hypothetical straight tooth row for three basal neoceratopsians. in Region III) and the bite force in the caudal part of Region III exceeds that of Region II. The two most caudal teeth analyzed exert a bite force higher than the maximum total input force. Position and Shape of the Tooth Row The mandibles of ceratopsians are much wider than the labiolingual diameters of the teeth. The tooth rows of basal neoceratopsians lie medially on the jaw, while those of Chaoyangsaurus and psittacosaurids lie more laterally. Moreover, the tooth rows of basal neoceratopsians such as A. oshimai and Liaoceratops are often strongly curved; that is, they are labially concave (Fig. 2E). Comparison of bite strength between the curved tooth row and a hypothetical straight tooth row with its ends anchored at the ends of the real tooth row reveals the advantage associated with a medial shift of the tooth row (Fig. 10). The effect of mediolateral tooth position on bite force can be found only using the threedimensional method of analysis; it cannot be discovered using two-dimensional analysis, which considers only the distance from the glenoid along the mandibular ramus in calculations of bite force. Changes in the mediolateral position of the bite point in Region I do not change the leverage (Greaves, 2002). However, in Region II the leverage increases as a tooth shifts medially due to shortening of the output lever as pointed out in Greaves (2002). In Region III, the input force is ﬁxed at the 0.5 units contributed by the working-side mandibular adductors regardless of the mediolateral position of a tooth, and bite force is linked only to distance from the glenoid. Taken as a whole, a more medial position of the tooth row results in greater leverage than is produced by the laterally positioned tooth row, and curvature of the tooth row increases the leverage of the tooth row as a whole by increasing leverage of the teeth in Region II even without any increase in leverage for Regions I and III. The ceratopsian tooth row becomes greatly elongated relative to mandibular length in derived taxa. Medial displacement had to take place in order for the tooth row to extend caudal to the laterally-located coronoid process in ceratopsids. 1366 TANOUE ET AL. Fig. 11. Comparison of bite forces at the teeth of actual and hypothetical mandibles of P. major. See Fig. 6 for the caudal divergence of the rami. Fig. 12. Caudal shift of the point of application of the resultant input vector due to the change in slope of vector. The lateral view of the right mandible of Archaeoceratops is shown. The input vector used in this study is shown by the solid arrow. A steeper input vector is shown by a dashed arrow. Differences in the intermandibular angle, like those seen in psittacosaurids, may also have affected bite force. The three-dimensional comparison of mandibles with narrow and wide divergence angles also indicates the advantage of positioning the teeth closer to the midline (Fig. 11). In Region I, the teeth of widely diverging mandibles can produce bite forces slightly higher than those produced by the narrow jaws of the actual specimen due to the shorter distance of the teeth from the effective fulcrum G0 in the wider forms. However, the bite force is much higher in Region II of the narrowlydiverging jaws than in the widely divergent jaws due to JAW MECHANICS IN BASAL CERATOPSIA 1367 the shorter output lever arm lengths when the teeth lie closer to the midline. As a whole, P. major had a more efﬁcient masticatory apparatus than P. lujiatunensis and P. sinensis, which have widely-diverging mandibles. Another interesting characteristic of psittacosaurids is their very short tooth rows in comparison to jaw length, when compared to the basal-most ceratopsian Chaoyangsaurus and to basal neoceratopsians (Table 1). The tooth row in psittacosaurids occupies no more than one-third of the mandible. In basal neoceratopsians, such as Liaoceratops, it may occupy nearly one half of the jaw length. Psittacosaurus have been found with gastroliths (Osborn, 1923; Xu, 1997; Wings, 2007), and may have needed only a short tooth row for oral processing of food. The angle y between the input lever arm and the mandibular ramus is higher in neoceratopsians, with the exceptions of Archaeoceratops and Protoceratops, than in Chaoyangsaurus and the psittacosaurids. Slope of the input lever arm is linked to the vertical distance between the adductor muscle insertion and the teeth; increase in this angle means that the tooth row lies farther below the point where MAME and MPsT insert on the apex of the coronoid process in most basal neoceratopsians and ceratopsids than in Chaoyangsaurus, Archaeoceratops, Protoceratops, and the psittacosaurids. One possible result of an increase in y, and the consequent increase in vertical distance between the adductor muscle insertions and the tooth row, could be an increase in gape. Gape Input Force of Mandibular Adductor Muscles Gape refers to the distance between the upper and lower jaws when they are open, and is associated with the size of the largest food particles which can enter the mouth. In terms of bite force generated, it is mechanically more efﬁcient to have the jaw adductor muscle attachment far rostral to the jaw joint to lengthen the input lever as much as possible (Ostrom, 1964). This, however, results in reduction of the gape since the angle to which the jaw can open is limited by the length of the jaw adductor muscles. In ceratopsians the jaw adductors insert onto the coronoid process. The position of the coronoid process along the length of the jaw is correlated with beak morphology in basal ceratopsians. The dorsal margin of the predentary is nearly horizontal and the broadly squared off rostral tip is no higher than the dentary tooth row in psittacosaurids, whose coronoid process is positioned just caudal to the midlength of the mandible (Fig. 2D). This morphology limits intrusion of the beak tip into the mouth opening, and therefore allows maximizing the gape even with the relatively more limited degree of jaw depression permitted by the rostral extent of the jaw adductors in psittacosaurs. In contrast, the narrow, wedge-shaped predentary extends rostrodorsally in basal neoceratopsians, whose coronoid process is in the caudal third of the mandible (Fig. 2F). The predentary is especially long in relatively large forms such as Leptoceratops and Protoceratops, and extends dorsal to the dentary tooth row as it does in ceratopsids (Fig. 2H). An exception is Auroraceratops, whose predentary has a horizontal dorsal margin (You et al., 2005). The hooked beaks of neoceratopsians extend into the mouth opening, and these animals may have had a decreased gape compared to those forms with a horizontal dorsal margin of the predentary. At the same time, the caudal shift of the coronoid process permitted more madibular depression than in psittacosaurids. The difference in beak shape may reﬂect differences in diet between psittacosaurids and basal neoceratopsians. The narrow, pointed beaks of basal neoceratopsians might have been able to scrape off and penetrate hard plant materials including stems and large seeds, which were not available to the taxa with a broad, ﬂat beak morphology. On the other hand, the wide semicircular beaks of psittacosaurids might have been suitable for plucking more foliage, fruits, and possibly small seeds with each bite than the narrow neoceratopsian beaks, which suggest selective feeding. One way to increase the bite force is to increase the mass or the cross sectional area of the mandibular adductor muscles. The size of the mandibular adductor muscles and the magnitude of input muscle force were not considered in this study because it is difﬁcult to estimate the mass of muscles, or their effective cross sectional area, especially in fossil taxa. However, similar greatest bite forces relative to total input force in most basal ceratopsian genera examined here suggest that the magnitude of input forces differentiated the actual bite force among them. Studies on extant vertebrates involving actual measurements of bite force and resistance of their food prove that larger skull size is associated with a larger mass of mandibular adductor muscles, which produce higher bite forces (Kiltie, 1982; Herrel et al., 2002; van der Meij and Bout, 2008). The absolute skull size of large basal neoceratopsians such as Protoceratops, Leptoceratops, and Udanoceratops exceeds the size of the largest psittacosaurids, indicating larger mandibular adductor muscle mass in these basal neoceratopsians compared to psittacosaurids and smaller basal neoceratopsians (Kurzanov, 1992; You and Dodson, 2004; Sereno et al., 2007; You et al., 2008). Furthermore, the expanded dorsal margin of the coronoid process in Leptoceratops and ceratopsids implies the attachment of mandibular adductor muscles that were much larger than those of most basal ceratopsians. The larger absolute skull size of ceratopsids compared to basal ceratopsians means that ceratopsids would have had a larger mass of mandibular adductor muscles than did the smaller basal ceratopsians. This study shows that derived ceratopsians also had greater leverage than basal ceratopsians. These factors clearly indicate the evolution of a highly effective and powerful masticatory system in the Ceratopsidae. Potential Food for Basal Ceratopsians Basal ceratopsians date from the Late Jurassic to the end of the Cretaceous. Angiosperms, which have often been regarded as the most nutritious plants, did not constitute a signiﬁcant part of the Early Cretaceous ﬂora. They were the most taxonomically diverse plants in the Late Cretaceous, but they may not have been abundant even in the Late Cretaceous, with conifers and ferns providing the dominant vegetational cover (Wing et al., 1993; Tiffney, 1997; Barrett and Willis, 2001). Although 1368 TANOUE ET AL. pteridophytes and gymnosperms are often dismissed as having low nutrition quality, the foliage of Equisetum and some conifers and ferns has an energy content comparable to that of angiosperms when fermented (Hummel et al., 2006; Hummel et al., 2008). In fact, Equisetum yields more energy than angiosperms. Ginkgo foliage contains a high amount of protein (Hummel et al., 2008). The foliage of cycads is less nutritious than other plants mentioned above, but their stems store starch in the pith (Jones, 1993; Whitelock 2002). Palms, which emerged in the Late Cretaceous, may have contained starch in their stems as well (Daghlian, 1981; Crabtree, 1987; Wing et al., 1993; Pei-Lang et al., 2006). Palm stems, like cycads, would have been another source of starch for ceratopsians. The pre-angiosperm ﬂora would have provided enough nutrition for contemporary herbivores, even for sauropods (Hummel et al., 2008). Basal ceratopsians were obligatory browsers on low vegetation due to their small body size. They probably could reach no higher than 1.5 m above ground, even if a large bipedal basal ceratopsian stretched its neck upward or a large quadrupedal basal neoceratopsian could stand on its hindlimbs. All basal ceratopsians must have fed on foliage and fruits within this range. Availability of seeds depends on the bite force necessary to overcome their hardness. Large basal neoceratopsians could have consumed some seeds not available to smaller basal ceratopsians. Cycad phytoliths have been extracted from ceratopsid teeth, indicating that ceratopsids actually fed on cycads (Krauss, 2001). Ceratopsids probably could scrape off the outer layers of cycad stems to reach the starchy pith inside using their high bite force and hooked beaks. Large basal neoceratopsians may have been able to feed on the stem as well. Implications for Ceratopsian Evolution The mandibular mechanics of basal ceratopsians mainly from Asia was examined to understand the early evolution of the ceratopsian masticatory system. Complete mandiblular ramus is necessary for two-dimensional analysis and articulated left and right mandibular rami for three-dimensional analysis, but the preservation of North American specimens does not allow these analyses. Hence well-preserved Leptoceratops (CMN 8889) is the only North American basal ceratopsian specimen analyzed in this study. It is worth noting that in two-dimensional analysis, bite force is always greatest at the caudal end of the tooth row and lowest at the predentary in all taxa. In basal neoceratopsians bite force at the caudal end of the tooth row equals or slightly exceeds input force, and in ceratopsids bite force at the caudal end of the tooth row greatly exceeds the input muscle force. In psittacosaurs, however, the bite force at the caudal end of the tooth row may be less than the input force. Three-dimensional analysis shows that in basal ceratopsians the largest bite force is exerted near the caudal end of the zone receiving maximum total input force from the muscles on both sides of the skull, not at the caudal end of the tooth row. Leverage of the labially concave tooth rows of some basal neoceratopsians and of medially-positioned teeth in psittacosaurids with narrow intermandibular angles is higher than the leverage of teeth with more lateral positions due to the shorter output lever arm length in forms with medially- positioned teeth. Elongation and caudal extension of the tooth row took place in basal neoceratopsians and was associated with a caudal shift of the coronoid process, resulting in greater leverage at the caudal end of the tooth row (Tanoue et al., in press). Nevertheless, bite force in all basal ceratopsians examined does not ever greatly exceed total input force, which shows the limit of the basal ceratopsian masticatory apparatus. Within the Ceratopsia, it was only in ceratopsids that bite force greatly exceeded the total input force. The exceptionally high bite forces of ceratopsids were made possible by the caudal extension of the tooth row, reaching even caudal to the coronoid process. Ceratopsids also had larger mandibular adductor muscles than basal ceratopsians. These factors combined with rapidly-replaced dental batteries mean that ceratopsids had a much more effective masticatory system than basal ceratopsians. However, the early stages of medial displacement of the teeth and of caudal elongation of the tooth rows, both of which are characteristic of the derived ceratopsid masticatory apparatus, can be seen in basal neoceratopsians. This study also demonstrates that the early evolution of the ceratopsian masticatory system was not a monolithic march leading only to the ceratopsid form, but rather reﬂected diversity of feeding adaptations within the basal ceratopsians. ACKNOWLEDGMENTS The authors thank Carl Mehling (American Museum of Natural History), Kieran Shepherd and Margaret Feuerstack (Canadian Museum of Nature), Xing Xu (Institute of Vertebrate Paleontology and Paleoanthropology), Keqin Gao (Peking University), and Ken-ichi Ishii, Shigeru Suzuki, Mahito Watabe, and Yukihide Matsumoto (Hayashibara Museum of Natural History) for providing access to their collections. 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