Dinosaurian and mammalian predators compared

Theropod dinosaurs were, and mammalian carnivores are, the top predators within their respective communities. Beyond that, they seem distinct, differing markedly in body form and ancestry. Nevertheless, some of the same processes that shape mammalian predators and their communities likely were important to dinosaurian predators as well. To explore this, we compared the predatory adaptations of theropod dinosaurs and mammalian carnivores, focusing primarily on aspects of their feeding morphology (skulls, jaws, and teeth). We also examined suites of sympatric species (i.e., ecological guilds) of predatory theropods and mammals, emphasizing species richness and the distribution of body sizes within guilds. The morphological comparisons indicate reduced trophic diversity among theropods relative to carnivorans, as most or all theropods with teeth appear to have been hypercarnivorous. There are no clear analogs of felids, canids, and hyaenids among theropods. Interestingly, theropods parallel canids more so than felids in cranial proportions, and all theropods appear to have had weaker jaws than carnivorans. Given the apparent trophic similarity of theropods and their large body sizes, it was surprising to find that species richness of theropod guilds was as great as or exceeded that observed among mammalian carnivore guilds. Separation by body size appears to be slightly greater among sympatric theropods than carnivorans, but the magnitude of size difference between species is not constant in either group. We suggest that, as in modern carnivoran guilds, smaller theropod species might have adapted to the threats posed by much larger species (e.g., tyrannosaurs) by hunting in groups, feeding rapidly, and avoiding encounters whenever possible. This would have favored improved hunting skills and associated adaptations such as agility, speed, intelligence, and increased sensory awareness.


Introduction
Tyrannosaurus rex and the lion, Panthera leo, would seem to have little in common other than both being the largest carnivores in their respective ecosystems. Among their many dif ferences, X rex was a five-ton biped with re duced forelimbs and multiple serrated teeth; the other, a 100-kg quadruped with muscular, clawed forelimbs and teeth specialized for distinct functions, such as killing or slicing.
Nevertheless, there is reason to believe that some of the same processes that shape mam malian predators and their communities were important to dinosaurian predators as well.
Interspecific competition, for example, ap pears to play a significant role in determining the abundance and distribution of many large extant carnivores. For instance, by choosing to hunt at a different place or time, coyotes avoid wolves, cheetahs avoid lions, and leopards avoid tigers (Van Valkenburgh 2001). Associ ated with these behavioral differences are morphological differences that can be ex-plained as adaptations to minimize competi tion. Thus sympatric large carnivores usually differ in body size, dental morphology, or skeletal anatomy (see Eaton 1979;Van Valken burgh 1985Dayan et al. 1990Dayan et al. , 1992. It might be expected that sympatric theropods diverged in a similar fashion if they faced comparable pressures from interspecific com petition. In this paper, we first review the relevant lit erature on mammalian carnivores to establish the background against which theropods will be viewed. We then compare some of the pred atory adaptations of theropod dinosaurs and mammalian carnivores, focusing primarily on aspects of their feeding morphology (skulls, jaws, and teeth). This is followed by an ex amination of suites of sympatric species (i.e., ecological guilds) of predatory theropods and mammals, emphasizing species richness and the distribution of body sizes within guilds.
The results presented here are not meant to be conclusive, as they are based on a limited sam-pie of mammals and theropods. Moreover, the gulf between carnivoran morphology and theropod morphology is large and this makes quantitative comparisons difficult. For exam ple, theropods differ from carnivorans in limb stance (biped vs. quadruped), masticatory musculature, tooth replacement, and skull construction. Nevertheless, similar biomechanical and ecological constraints are ex pected to have been important to both kinds of predators. This paper is intended as no more than a preliminary exploration of tro phic divergence among coexisting theropods, and it is our hope that it will inspire further, more-detailed studies.

The Guild of Large, Predatory Mammals
The ecological concept of guild was first de fined by Root (1967: p. 335) as "a group of spe cies that exploit the same class of environmen tal resources in a similar way." As such, spe cies within a guild are expected to compete more intensely with each other than with those outside the guild. In theory, guilds are not limited by taxonomic boundaries; an ex tant predator guild could include reptiles, birds, and mammals, for example (see Jaksic et al. 1981). However, in practice, they often are so limited for various reasons, such as to maximize the potential role of competition or to facilitate the study (for review of the guild concept, see Simberloff and Dayan 1991).
Large, predatory mammals form a guild in which competition is expected to be relatively intense. Their shared food resources, prey, are often difficult and dangerous to kill, and con sequently carcass theft (kleptoparasitism) is a worthwhile alternative to hunting. Carcass theft involves confrontation between individ uals, which can be dangerous given that the participants are armed with teeth and jaws, and in some cases, claws, designed to kill. Moreover, given the species' predatory abili ties, interspecific competition can be manifest as intraguild predation (Polis and Holt 1992). If competition among carnivores is as intense as predicted, then adaptations to minimize dangerous encounters and escape predation are expected in less dominant members of the guild.
Two recent reviews of the published litera ture on interspecific interactions among ex tant large carnivores found ample evidence of carcass theft, intraguild predation, and inter specific avoidance in tropical and temperate ecosystems (Palomares and Caro 1999;Van Valkenburgh 2001). Four key points are sum marized here. First, most interspecific inter actions between predators occur as contests for the possession of a kill and these contests can be frequent. For example, in areas of high spotted hyena density, African wild dogs lost 60-86% of their kills to hyenas (Kruuk 1972;Fanshawe and Fitzgibbon 1993). As is true of carcass theft, the motivation for intraguild predation appears to be hunger in many in stances. However, equally or more often, the victim is not eaten and the likely motivation is to remove a competitor who might also prey on young. Second, body size is the usual de terminant of rank within the guild; larger spe cies tend to dominate smaller ones (e.g., lion over hyena in Africa or wolf over coyote in North America). Third, the body size rule can be overturned by the smaller species acting as a group (e.g., hyenas vs. lions; African wild dogs vs. hyenas). Fourth, intraguild predation and kleptoparasitism occur in both forested and open environments. Although these types of interaction have been observed less fre quently in forested environments, the behav ior of some species strongly suggests that they have had a significant impact. For example, leopards avoid areas where tigers are com mon (Seidensticker 1976;Seidensticker et al. 1990), and do not cache their kills in trees where tigers and dholes are absent (Muckenhirn and Eisenberg 1973).
Previous work on morphological diver gence among sympatric large carnivores sub stantiates the importance of interspecific com petition over evolutionary timescales. In a se ries of papers, Van Valkenburgh (1985 explored morphological separa tion among large carnivores in past and pre sent communities. Comparisons of dental and inferred dietary differences among sympatric predators from extinct and living communi ties revealed repeated patterns of divergence within guilds into meat specialists (e.g., felids, extinct nimravids), bone crackers (e.g., hyaenids, borophagine canids), and omnivores (e.g., coyotes, early amphicyonids). Within dietary types, coexisting species were likely to differ in body size or locomotor adaptations. Larger predators are capable of taking larger prey, thus effecting some dietary separation. Differ ences in locomotory abilities (such as climb ing, endurance running) can also reduce over lap in prey choice through differences in hab itat preference. Perhaps more importantly, they can allow one predator to escape from another, such as when leopards climb to avoid more-terrestrial lions, hyenas, and wild dogs (Van Valkenburgh 1985).
Further evidence of the potential role of in terspecific competition in shaping the mor phology of sympatric carnivores comes from the work of Dayan and colleagues (Dayan et al. 1989a(Dayan et al. ,b, 1990(Dayan et al. , 1992Dayan and Simberloff 1994). In studies of several suites of sympatric species, including mustelids, canids, and fe lids, they found evidence of remarkably even size separation between species in various fea tures, such as canine tooth length (felids) or lower molar length (canids, mustelids). They argue that such even size separation does not occur by chance and is better explained as di vergence due to competition for food. Simi larly, Kiltie (1988) found that differences in jaw length among sympatric neotropical cats were fairly constant and suggested that this reflected differences in maximum jaw gape and thus prey size.
This discussion of ecological separation and morphological divergence among sympatric mammalian carnivores was intended to en gage the reader in considering how theropods might have coexisted. Among living carnivor ans, almost all species larger than about 21 kg take prey much larger than themselves, whereas smaller species feed mostly on prey that is 45% or less of their body weight (Carbone et al. 1999). Using an energetic model, Carbone et al. (1999) argued that it becomes increasingly difficult to subsist on small prey items as predator body mass increases be cause of limitations on intake rate and forag ing time. Thus because of their large body size, most theropods probably hunted prey as large or larger than themselves. Given this, we expect that carcass theft was worthwhile and battles over kills occurred. Moreover, larger theropods likely preyed on smaller ones and may have even eaten juveniles of their own species. Consequently, we might expect to find predatory adaptations, as well as adap tations to interspecific competition and intraguild predation, among sympatric carnivo rous theropods that are similar to those of sympatric mammalian carnivores.

Materials and Methods
The Sample Our guilds of predatory dinosaurs were de fined to include all known theropods from a well-sampled geologic formation that could reasonably be assumed to have been sympat ric in time and space. We excluded from the guild edentulous theropods (ornithomimosaurs, oviraptors), small putatively edentu lous theropods (elmisaurids), and those with non-sectorial teeth (therizinosaurids) on the assumption that these taxa were not feeding regularly on large prey. Although we are un certain of their diets, the differences in their morphology from that of the presumably hypercarnivorous theropods do not suggest that they were exploiting "the same class of envi ronmental resources in a similar way" (Root 1967). We will, however, mention their occur rences. We also did not include crocodilian or avian species, but we do not consider them to have been major competitors of the large ter restrial theropods that form the focus of this analysis. Furthermore, although the teeth of many theropods, carnivorous "thecodonts/' ziphodont crocodilians, and varanoids, and even the canines of some sabercats are basi cally similar in form (Farlow et al. 1991), the teeth of other crocodilians-such as those found in the faunas we examine-seem to be different. Specifically, in this instance the croc odile teeth are unserrated and rounded in sec tion, not compressed as are most theropod teeth (Molnar personal observation). Vara noids are not included, both because of the scarcity of their fossils and because the plesiomorphic forms appear not to have been predators on relatively large prey (Losos and Greene 1988 Gittleman and Harvey 1982;Farlow 1993]), and so we assume that there was spatial over lap among them. The question of temporal overlap is discussed below in each of the paleoguild descriptions.

The Morrison
Guild.  true of the living animals, although it could reflect taphonomic bias. Allosaurus is the most common of the theropods, making up more than 60% of all theropod specimens (Foster and Chure 1998). The smaller forms are also rare as fossils. Of the moderately small forms, Elaphrosaurus sp. is represented by only very rare elements and Marshosaurus bicentesimus is also uncommon, although not as rare as Ela phrosaurus.
Likewise, the small forms are un common. Koparion douglassi, believed to be a primitive troodontid (Chure 1994), is known only from teeth, whereas Ornitholestes hermanni is represented by a single skeleton (and an additional manus), Coelurus fragilis by a single partial skeleton (and rare additional pieces), and Stokesaurus clevelandi by rare isolated piec es. To some extent this rarity is probably due to taphonomic bias, the more fragile bones of the smaller theropods being less likely to be preserved, but collecting bias and bias toward studying large specimens may also have been involved in the late nineteenth and early twen tieth centuries. Turner and Peterson (1999) divided the Morrison into four zones deposited over about 8 million years, from the Kimmeridgian into the basal Tithonian. Koparion is found only in zone 4 (the youngest) and all of the other spe cies are found in zones 2 and 3 (zone 1 yields only Allosaurus sp.  (Turner and Peterson 1999). Our focus is on zones 2, 3, and 4, and thus the time span represented is esti mated to be 2-4 Myr.
The Judith River Guild.-The Campanian Ju dith River Formation of the Montana-Alberta region has yielded a number of theropod taxa, some rather better known than others (see Dodson 1983). This unit dates to about 75 mil lion years ago, and seems to have been depos ited over a rather shorter period of time than the Morrison (Eberth et al. 1992). In the fauna, we recognize seven carnivorous theropods that probably took large prey and seven eden tulous theropods that were unlikely to have regularly hunted large prey (Table 1) Information on the stratigraphic occurrenc es of these taxa is less easily available than for the Morrison, but Dodson (1971) provided in formation for the outcrop of the Dinosaur Pro vincial Park in Alberta. Dromicieomimus was found higher in the section than Struthiomi mus, but as only a single specimen of each was recorded, this may not be significant. Caenag nathus occurred throughout the section, as did Albertosaurus libratus, but the single specimen of Daspletosaurus torosus was found near the bottom of the beds. Dodson suggested, be cause of their rarity, that the small theropods "habitually inhabited other environments in other areas" (p. 68), unlike Albertosaurus and the ornithomimosaurs.
The Nemegt Guild.-Similar information for the Nemegt Formation of Mongolia appears not to be readily available. The age is not ac curately known but is generally taken to be . An additional small species, Elmisaurus rarus, whose skull and teeth are unknown, is here assumed to have been edentulous based on its possible sister-taxon relationship to the Oviraptosauria (Currie 1990). Only T bataar, M. navojilovi, and G. bullatus are known from rea sonably complete or complete skeletons; the others are represented by less or much less complete rare material. Data from the Polish-Mongolian expeditions (Gradzinski et al. 1968;Gradzinski and Jerzykiewicz 1972) in dicate that Tyrannosaurus bataar and ornithomimid (presumably Gallimimus bullatus) re mains have a broad stratigraphic range through the beds.

Mammalian
Guilds.-The three theropod guilds are compared with seven previously studied mammalian predator guilds. Four of these are extant: Serengeti (East Africa), Ma laysia, Chitawan (Nepal), and Yellowstone (North America). The remaining three are ex tinct North American guilds: (1) Orellan, 34-32 Ma; (2) Irvingtonian, 1.7-0.7 Ma; and (3) Rancholabrean, 0.7-0.01 Ma. The fossil guilds were included because it is clear that extant predator guilds are depauperate as a result of the late Pleistocene extinction event. More de tailed descriptions of these guilds, including taxonomic composition and environmental characteristics, are given by Van Valkenburgh (1985, 1989 and Van Valkenburgh and Hertel (1998). The guilds were defined to include all species larger than 7 kg that were predatory and potentially competed for food.

Data Analysis
Comparisons of predatory adaptations in theropods and mammalian carnivores were made using least-squares regression of log 10 transformed measurements, including skull length, snout width, tooth length, jaw depth, and jaw length. The data for the sampled mammals and theropods are derived from previous publications as noted in the text and relevant figure captions.
Species richness was estimated as the total number of species within each guild. Body size distributions within guilds were com pared by using Barton-David (B-D) statistics (Barton and David 1956;Simberloff and Boecklen 1981). B-D statistics test whether size differences between successively sized species are more similar than expected by chance. If they are, and if they approach some constant, the result is usually assumed to reflect char acter displacement (see Dayan et al. 1989a,b). To test for size ratio constancy, body mass es timates for each species within a guild were ordered from smallest to largest and log 10 transformed. The differences in log 10 trans formed mass values between successively sized species within a guild are the size ratio data. The B-D statistic used here, G, is the ratio of the smallest to the largest size ratio within each guild. Probability estimates for G-values are estimated as described in Barton and Da vid (1956).

Comparative Morphology
We begin our comparison of dinosaurian and mammalian predatory guilds with an ex amination of the array of predatory types ap parent in each group. As noted above, guilds of mammalian carnivorans (members of the order Carnivora) typically contain highly car nivorous species (e.g., felids, some canids), more omnivorous species (e.g., most canids, some ursids), and perhaps bone crackers (e.g., hyaenids). Can we find these same ecomorphs among dinosaurs in general and theropods in particular? Apparently not, in that the bonecrackers and probably the more omnivorous forms seem to be missing from dinosaur com munities. This claim is based on the relative lack of dental diversity among theropods. With the exception of theriznosaurids and edentulous species, all theropods considered here with known cranial material are relative ly similar in tooth form. Although the teeth may vary in size along the theropod tooth row, they all are shaped somewhat like the ca nine teeth of carnivorans and would have been of limited use for grinding plant matter or cracking large bones regularly (Farlow et al. 1991). It is clear that theropod teeth occa sionally contacted bone in killing and/or feeding as evidenced by various punctures and scores on the preserved bones of their prey and a large coprolite containing many bone fragments, but there is no evidence of significant gnawing (Currie and Jacob sen 1995; Erickson and Olson 1996;Chin et al. 1998). Moreover, a survey of tooth-damaged bone in six dinosaur localities found very little evidence of bone crushing, supporting the idea that habitual consumption of large bones was rare (Fiorillo 1991). These findings sug gest that all theropods with sectorial teeth were highly carnivorous (hypercarnivorous) and that ecological separation among coexist ing taxa would have depended on differences in habitat choice, prey size, or prey type. The diet of the edentulous forms is unclear, but a recent discovery of gastroliths in an undescribed Chinese ornithomimosaur may indi cate a herbivorous/granivorous diet for at least this species (Kobayashi et al. 1999). Pre vious work with stable nitrogen isotope anal ysis did not find a significant difference in val ues between North American ornithomimosaurs and clearly carnivorous theropods such as tyrannosaurids and dromaeosaurids (Ostrom et al. 1993). However, only two values were obtained, one similar to that for ceratopsians and the other greater than that of the dromaeosaurid examined. The ornithomimosaurs may have had a catholic diet, like living foxes or bears, or different species may have specialized in different foods, but they cer tainly do not appear to have been highly car nivorous.
In theropods, the absence of strongly heterodont dentitions such as are typical of om nivorous mammals might reflect the limited resources that were available. Omnivorous carnivorans rely fairly heavily on fruits for part or most of the year (Ewer 1973;Van Val kenburgh 1989), and fruits of significant size (>5 cm diameter) that likely depended on biotic dispersal were not common until the lat est Mesozoic (Tiffney 1984;Wing and Tiffney 1987). Among living carnivorans, the ability to crack bones allows access to marrow, in cluding fat deposits (see Haynes 1982). It is not clear that dinosaur bones, which are often pneumatic in saurischians, contained a highly nutritious marrow, and if not, the major ben efit of bone cracking would have been non existent. Thus, the limited carnivorous nature of theropod dental morphology is appropriate for the predominant food (dinosaurs) that was available to nonherbivorous species. Alterna tively, the lack of differentiation in theropod dentitions might reflect constraints on tooth form imposed by the nature of their develop ment. Theropod teeth are replaced multiple times over their life span and thus the tooth row always contains teeth of varying age and height. Consequently precise tooth-to-tooth occlusion between any pair of opposing upper and lower teeth is difficult to sustain, and thus the evolution of more complex teeth may not have been favored.
Comparisons of the postcranial adaptations for hunting and killing in dinosaurs and car nivorans reveal few similarities. Among ex tant large carnivorans, there are short-dis tance ambush species (e.g., felids, some ur sids) that use their muscular forelimbs and clawed feet to grapple with prey while they administer a deadly bite. Alternatively, there are those that are incapable of grappling, and instead kill with jaws alone after a long-dis tance pursuit (e.g., canids, hyaenids). Two comparable types can be recognized among theropods, "head-hunters" and "grappler/ slashers." Presumably, the head-hunters were the allosaurs, later ceratosaurs, and tyrannosaurs, all relatively large species with reduced forelimbs and no evidence of enlarged pedal claws. These species killed through actions of their jaws and teeth with little or no assistance from their forelimbs. The best developed grappler/slashers were the dromaeosaurs, ag ile theropods of small to medium size with well-developed, clawed forelimbs and slash ing pedal claws. No doubt, these species used both hands and feet to produce mortal wounds, as felids will in some circumstances. Coelurosaurs and troodontids lacked the large, terrible claws of dromaeosaurs and can be considered less well equipped grapplers that almost always took prey smaller than themselves.
The two different killing styles in theropods are not so clearly associated with different hunting modes (ambush vs. long-distance pursuit) as they are in carnivorans. On the one hand, the light build of most of the grappler/ slashers suggests speed, and therefore the po tential for long-distance pursuit. Their mod erate size, however, would also have made them excellent ambush predators, as they could be concealed fairly easily in dense veg etation. On the other hand, many or all of the head-hunters were so large as to make am bush hunting seem ludicrous. What could a T. rex hide behind? Although dense vegetation might conceal a T. rex, could such a large an imal move through it quietly enough to stalk its prey? If ambush was not an option, then the tyrannosaurs must have overtaken their prey, although this was probably done with a fast walk rather than a run (Farlow et al. 1995;Carrano 1999;Hutchinson and Garcia 2002).
Although qualitative comparisons of the ropod and carnivoran adaptations can be stimulating, it is more satisfying to establish similarities in structure based on quantitative data. Fortunately, recent studies of the allom etry of teeth, jaws, and skulls of mammalian carnivores allow for some direct comparison of scaling relationships between mammalian and dinosaurian predators. The data present ed here are limited, in that only a subset of theropod diversity is represented and com parisons were constrained by the availability of similar data (e.g., measures of jaw depth or length) for both groups. Because we were in terested in examining sympatric suites of the- for canids, log 10 y = 1.85 + 0.332 (log 10 body mass), r 2 = 0.89, p < 0.001; for felids log 10 y = 1.8 + 0.273 (log 10 body mass), r 2 = 0.9, p < 0.001; for theropods, log 10 y = 1.92 + 0.314 (log 10 body mass), r 2 = 0.93, p < 0.001. Data for canids are from Van Valkenburgh and Koepfli (1993); data for felids are from Van Valkenburgh and Ruff (1987). Data for theropods are from Osborn (1916), Gilmore (1920Gilmore ( , 1946, Colbert (1962), Russell (1970), Barsbold (1974), Maleev (1974), Paul (1988), and Britt (1991). ropods, our sample is confined to 28 species from four formations, the Morrison (Late Ju rassic), Judith River (Late Cretaceous), Hell Creek (Late Cretaceous), and Nemegt (Late Cretaceous) ( Table 1). The Hell Creek assem blage was not included in our paleoguild com parisons because it has only three species as opposed to the 10-14 for the included assem blages, and this suggests that it is likely to be missing species that were present. In fact, one of the three species, Nanotyrannus lancensis, may be a juvenile T. rex (Carr 1999), leaving only two theropods in the Hell Creek. We in clude the Hell Creek species in the allometric analysis to expand the sample of theropods for comparison with mammals. An even larg er sample of theropod species might strength en our conclusions and we would like to ex pand the analysis in the future. Nevertheless, we feel that the 28 sampled species are broad ly representative of the diversity of theropod craniodental morphology.

Relative Head Size.-Relative
head size varies among extant large carnivorans (Fig. 1). Felids have small heads relative to their body mass, both because their bodies tend to be fairly heavily muscled and because their skulls are 1 " * 1 1 1 1 1.5 2 2.5 3 3.5 LOG SKULL LENGTH FI GURE 2. Log 10 -Log 10 plot of maximum snout width (mm) against skull length (mm) for canids (solid squares, n = 33), felids (open circles, n = 18), and the ropods (triangles, dashed line, n = 10). Linear regres sion equations: for canids, log 10 y = -1.14 + 1.26 (log 10 skull length), r 2 = 0.92, p < 0.001; for felids log 10 y = -0.89 + 1.16, r 2 = 0.98; for theropods, log 10 y = -1.2 + 1.19 (log 10 skull length), r 2 = 0.74, p < 0.01. Data for ca nids are from Van Valkenburgh and Koepfli (1993); fe lids were measured for this paper. Data for theropods as in Figure 1. somewhat small. Canids on the other hand have relatively larger skulls and more slender bodies. The difference is most pronounced among species of large size and reflects killing behavior to some extent. Felids tend to kill with a single, strong bite to the neck or muz zle, whereas canids tend to use repeated, shal lower bites to subdue their prey. The short snout of felids enhances the leverage of their jaw muscles for a killing bite with the canines by reducing the moment arm of resistance of an anteriorly placed load (Biknevicius and Van Valkenburgh 1996). Theropods were pro portioned more like canids (Fig. 1). With the exception of the small coelurosaur Ornitholes tes hermanni, all sampled theropods have rel atively larger skulls than felids of similar body mass. Thus, we do not see a clear divi sion of theropods into the two alternative kill ing types that are apparent today. Rather, they all appear to have been built fairly similarly and there is little or no evidence of catlike the ropods in our sample. It would be interesting to be able to include more taxa, especially smaller species.
Skull Shape.-A comparison of skull shape among canids, felids, and theropods reveals additional similarities between canids and theropods (Fig. 2). Felids have broader snouts relative to skull length than either canids or theropods. Maximum muzzle width is posi tively allometric in all three groups, with larg er species exhibiting relatively broader muz zles. The smallest theropods for which we have data overlap canids on the plot of maxi mum snout width against skull length. The re lationship of snout width to skull length in theropods is close to isometry (1.19), but our sample size is quite small (n -10), and the 95% confidence interval for the slope is large (0.62-1.76). In canids, the broader muzzle of larger species was correlated with enlarged canine and incisor teeth and with diets that in clude relatively large prey (Van Valkenburgh and Koepfli 1993). For example, wolves, dholes, and African hunting dogs often take prey larger than themselves, whereas similarsized canids such as the maned wolf or Ethi opian wolf are more narrow-snouted and tend to hunt small prey (e.g., lagomorphs and ro dents). Theropods may have been similar, with the largest forms such as the tyrannosaurids tackling the most difficult prey. No tably, the large theropod Torvosaurus tanneri has a very narrow snout for its skull length (TTA in Fig. 2), suggesting it may have had a weaker bite and might have favored smaller prey than similar-sized tyrannosaurs.

Relative Tooth Size.-Because
of the absence of specific serial homology between the teeth of theropods and mammals, it is difficult to compare them in terms of relative tooth size. It is not clear whether one should compare theropod cheek teeth to the premolars or carnassials of carnivorans, for example. We chose the carnassials because they are usually the largest teeth in the jaw and function some what similarly in felids and canids. A com parison of the largest lower teeth of theropods with the lower carnassials of canids and felids reveals that the teeth of theropods are sub stantially shorter mesiodistally than those of canids and felids of similar jaw length (Fig. 3). The large carnosaurs and tyrannosaurs also appear to have shorter teeth than would be ex pected for a mammalian carnivore of their body size. This is not surprising given that theropod jaws contain many more teeth, all of more similar size, than do jaws of mammals. Although felids and canids appear to be sim ilar in tooth length/jaw length proportions, LOG JAW LENGTH FI GURE 3. Log 10 -Log 10 plot of the mesiodistal length of the longest lower tooth (mm) against maximum jaw length (mm) for canid (solid squares, n = 32), felid (open circles, n = 16), and theropod (triangles, n = 10) species. For canids and felids, the lower first molar was used. Linear regression equations: for canids and felids to gether, log 10 y = -0.93 + 1.05 (log 10 jaw length), r 2 = 0.85, p < 0.001; for theropods, log 10 y -1.94 + 1.25 (log 10 jaw length), r 2 = 0.77, p < 0.01. For data sources, see the slopes of the log-log regressions differ sig nificantly, with canids showing positive al lometry as opposed to near isometry in felids. Interestingly, theropods also show positive al lometry with larger species displaying even larger teeth (slope = 1.25). However, our sam ple size for theropods is small and the addi tion of more species could easily alter the ap parent positive relationship.
Relative Jaw Depth.-The ratio of jaw depth to length should be indicative of jaw strength during biting. Although it would be prefera ble also to include information on jaw width and cortical bone distribution internally as has been done for carnivorans (Biknevicius and Ruff 1992), few data are available for the ropods. When tetrapods bite an object, their jaws are loaded somewhat as beams with the jaw joint acting as a fulcrum. Bending strength is enhanced by deepening the jaw rel ative to its length, and consequently, carnivor ans such as the bone-cracking hyenas have rel atively deep jaws. Here we compare jaw depth taken midway along the tooth row of thero pods with previously published data on max imum depth in carnivorans (canids, felids, hyaenids). Maximum jaw depth in carnivor ans tends to occur posterior to the midpoint of the tooth row, near the carnassials. Al though it might have been preferable to com pare maximum jaw depth in both groups,
Despite the potential problems of compar ing non-analogous measures, a log-log regres sion of jaw depth on length for carnivorans and theropods reveals similar scaling relation ships, with both groups showing positive al lometry (slope = 1.12, theropods; 1.04 felids; 1.37, canids; Fig. 4). The slopes of the regres sion lines are not significantly different be tween theropods and felids (ANCOVA: p = 0.357), theropods and canids (ANCOVA: p = 0.137), or theropods against all 22 carnivoran species (ANCOVA: p = 0.894). Apparently, however, the jaws of theropods were relatively weaker for their length than those of carni vorans. The positive allometry in both groups suggests that larger species loaded their jaws more heavily, because deeper jaws are much stronger in resisting loads applied dorsoventrally, as during jaw closure. This component of jaw strength is largely dependent on jaw depth and increases approximately with the square of depth (see Biknevicius and Van Val kenburgh 1996 for details). As was the case for muzzle width, the positive allometry of jaw depth suggests that larger theropods killed prey that were very large relative to their own body size. Thus, the data presented here sug gest that the jaws of Tyrannosaurus rex were at least as strong as and probably relatively stronger than those of other carnosaurs, and do not support the idea that T. rex was a less capable killer and relied more on scavenging than other carnosaurs (see also Molnar 2000).
The fact that theropods appear to have had weaker jaws than similarly sized carnivorans might be explained by our choice of tooth row midpoint for the depth comparison. As noted above, the measure for carnivorans was taken posterior to the midpoint, and it is clear that theropod jaws do deepen behind the midpoint but beyond the end of the tooth row. To re solve this issue, it would be useful to compare jaw depth in carnivoran and theropod jaws at multiple positions in a more comprehensive analysis. In addition, it should be noted that theropod dentary bones are solid (Molnar 2000), whereas those of carnivorans have a medullary cavity. A solid dentary is some what stronger than a hollow one, but because strength in bending is enhanced more by in creasing overall diameter, the carnivorans probably retain the stronger jaws. In the two examples where theropods and carnivorans overlap in size (Ornitholestes hermanni and Dromaeosaurus albertensis), carnivorans have jaws that are approximately twice as deep. No tably, a recent finite element analysis of cra nial and bite strength in Allosaurus fragilis also found that this species had a relatively weaker bite than do carnivorans (Rayfield et al. 2001). Jaw depth is significantly correlated with typical prey size in a limited sample of ten species of canids and felids (Fig. 5). If this re gression is used to predict the typical prey of theropods, it produces overestimates, at least for those species that were much larger than any of the carnivorans used in the regression. For example, it predicts that Tyrannosaurus rex was usually killing prey that weighed 10 6 kg LLI N O O -2 1 .... , 1 1 1.5 2 2.5 LOG JAW DEPTH FI GURE 5. Log 10 -Log 10 plot of typical prey size (kg) against maximum jaw length (mm) for ten species each of canids and felids (solid circles). The linear regression equation derived from these data was used to estimate typical prey sizes of theropods (triangles) based on their estimated body masses. Linear regression equation for carnivorans (n = 10): log 10 y = -7.25 + 6.22 (log 10 jaw length), r 2 = 0.84, p < 0.001. Data for typical prey size of carnivorans are from Van Valkenburgh and Hertel (1998).
(one thousand tons), a size that exceeds the maximum weight estimates made for any di nosaur (Peczkis 1994). On the other hand, the prey size estimates for the three smaller the ropods, Ornitholestes, Saurornithoides, and Dro maeosaurus, might be reasonable, as they are much more similar in size to the mammalian carnivores used for the regression. It is diffi cult to assign much confidence to any of these estimates given the differences in body form between dinosaurs and carnivorans. However, it is likely that there was a positive relation ship between prey size and jaw depth in the ropods, and consequently, jaw depth might be useful in examining ecological separation among sympatric theropods. Unfortunately, we could not do so because of the absence of jaw depth data for many of our species.
Species Richness.-The mammalian predator guilds include species whose diets range from omnivorous to hypercarnivorous and thus are not strictly comparable to the theropod guilds, which include putative hypercarnivores only. If the edentulous and presumably less carnivorous theropods are considered as part of the predator guild, then total species diversity is similar in both mammalian and theropod guilds (Fig. 6). The total number of species within the mammalian guilds ranges    (Fig. 6). This is somewhat sur prising for two reasons. First, as mentioned earlier, sympatric theropods appear more similar to one another than do sympatric hy percarnivorous mammals, and thus one would expect fewer species could coexist. Such a limit on co-occurrence is known to oc   (Van Valkenburgh and Koepfli 1993;Van Valken burgh and Hertel 1998), and thus ecological separation among sympatric hypercarnivores can be effected by differences in body size. As noted above, studies of modern carnivore guilds have documented remarkably even spacing between species in the size of certain features, such as jaw length or tooth size (e.g., Dayan et al. 1992;Kiltie 1988). We would have liked to do the same sorts of quantitative anal yses of the theropod guilds but the data are not sufficiently complete. Unfortunately, size ratio analyses are not useful when the same measurement is not available for all species within the guild. The only parameter for which we had nearly complete data was esti mated body mass, and it has not been ob served to show constant size ratios in modern carnivore guilds. Because the body mass data for theropods used here are estimates taken from the literature that were derived by dif ferent methods, our results must be viewed with caution.
For both carnivorans and theropods, size ratios were not constant within any guild, and B-D statistics indicate that the distribution of size ratios could be explained by chance (Table  2, Fig. 7). Unlike the mammal guilds, each of the three theropod guilds includes at least one pair or trio of very similarly sized species. It would be interesting to look for other evi dence of character divergence within these clusters, such as differences in locomotor or feeding adaptations, as is apparent among mammals. For example, the Serengeti includes three species of similar mass-leopard, chee tah, and spotted hyena. Each of these is quite distinct morphologically and behaviorally. The hyena exploits carcasses more fully than either cat because of its bone-cracking abili ties. The two cats separate by habitat and hunting style; the cheetah is a sprinter of more open country whereas the leopard is an ambusher that prefers gallery forest. By contrast, the trios and pairs of similar-sized theropods are not composed of combinations of head hunters and grappler/slashers. Instead, there is no overlap in size between these two; grap pler/ slashers always filled the low end of the size range.
The average difference between successive ly sized species among the seven mammalian predator guilds was 0.201 (n = 38, SD = 0.173) ( Table 2). The same value was larger (0.399; n = 19, SD = 0.348) for the three theropod guilds, and this difference was significant us ing a t-test (F = 8.275; p < 0.01), but not using a Mann-Whitney nonparametric test (p = 0.11). The nonparametric test is more appro priate given that ratio data are being com pared, but it is much more conservative. Given that the sample size for theropods is much less than that for the mammals, the lack of statis tical significance should not be considered as definitive. It does appear from examination of the distribution of body sizes within guilds that sympatric theropods tend to separate by size more than mammals (Fig. 7). This might reflect an increased pressure to segregate by size among theropods because of their overall similarity in body form. In addition, suites of sympatric theropods span a much greater range of body sizes than do those of mam mals; consequently, there is more room to spread out.
In sum, theropod guilds do not seem to demonstrate ecological separation as clearly as do the mammalian guilds. Size separation is apparent, but when there is overlap, it is not clear how the species differ along another di-l u -j y

S u m m a r y and C o n c l u s i o n s
O u r a d m i t t e d l y p r e l i m i n a r y l o o k at the structure of d i n o s a u r i a n a n d m a m m a l i a n predator guilds revealed s o m e i n t r i g u i n g re sults that d e s e r v e further investigation w i t h a n e x p a n d

A c k n o w l e d g m e n t s
We gratefully a c k n o w l e d g e t w o thoughtful a n o n y m o u s reviewers as well as S. W i n g , W. DiMichele, J. D o w n s , a n d G. E r i c k s o n for their helpful a n d insightful c o m m e n t s . We also t h a n k D. S i m b e r l o f f for a s s i s t a n c e w i t h the B a r t o n -D a v i d statistics.

Literature C i t e d
Anderson, J. E , A. Hall-Martin, and D. A. Russell. 1985. Longbone circumference and weight in m a m m a l s , birds and di nosaurs. Journal of Zoology 2 0 7 : 5 3 -6 1 .