Finite element analysis of ursid cranial mechanics and the prediction of feeding behaviour in the extinct giant Agriotherium africanum



Stephen Wroe, Computational Biomechanics Research Group, School of Biological, Earth and Environmental Sciences, University of New South Wales, Kensington, NSW 2052, Australia. Tel: +61 2 9385 3866; Fax: +61 2 9385 2202.



Historically, predicting ursid feeding behaviour on the basis of morphometric and mechanical analyses has proven difficult. Here, we apply three-dimensional finite element analysis to models representing five extant and one fossil species of bear. The ability to generate high bite forces, and for the skull to sustain them, is present in both the giant panda and the gigantic extinct Agriotherium africanum. Bite forces for A. africanum are the highest predicted for any mammalian carnivore. Our findings do not resolve whether A. africanum was more likely a predator on, or scavenger of, large terrestrial vertebrates, but show that its skull was well-adapted to resist the forces generated in either activity. The possibility that A. africanum was adapted to process tough vegetation is discounted. Results suggest that the polar bear is less well-adapted to dispatch large prey than all but one of the five other species considered.


The identification of relationships between form and function in mammalian carnivores has been the subject of numerous morphometric and biomechanical studies (Radinsky, 1981a,1981b; Van Valkenburgh, 1985; Werdelin, 1986; Thomason, 1991; Therrien, 2005; McHenry et al., 2007; Wroe et al., 2007; Wroe & Milne, 2007; Wroe, 2008; Wroe, Lowry & Anton, 2008; Slater & van Valkenburgh, 2009; Goswami, Milne & Wroe, 2010). The results of such analyses have been useful to both evolutionary biologists and palaeontologists seeking to predict behaviour in fossil species. Correlations have been established between skull shape, mechanical behaviour and diet in many mammalian carnivore taxa. However, among these, extant bears (Ursidae) have been perhaps the most intractable (Radinsky, 1981b; Slater et al., 2010).

Some relationships remain uncertain among bears, but Ursidae is clearly a relatively young family that diverged from dog or dog-like caniform ancestors around 23–24 million years ago [McLellan & Reiner, 1994; Krause et al., 2008; and see Supplementary Information (SI) Fig S1]. Despite this recent origin, living ursids span a very wide range of feeding ecologies, from specialized herbivory to hypercarnivory, making the failure to find strong correlations between common mechanical or morphometric indicators and diet in bears surprising (Radinsky, 1981b; Sacco & Van Valkenburgh, 2004). For example, among carnivorans in general, a relatively short skull is often associated with active predation and carnivory, yet these are particularly well-developed features in the most herbivorous of bears, the giant panda, Ailuropoda melanoleuca. Similarly, bite force adjusted for body mass, which correlates with relative prey size for many extant carnivorans (Wroe, McHenry & Thomason, 2005), is also highest among this specialized herbivore. At the other end of the extant ursid feeding spectrum, results from a recent finite element analysis (FEA) suggest that the cranium of the most carnivorous living ursid, the polar bear, Ursinus maritimus, shows no special adaptations to a meat-eating habitus relative to its more herbivorous close relative, the brown bear, Ursus arctos (Slater et al., 2010).

As noted previously (Wroe et al., 2005; McHenry et al., 2007; Wroe et al., 2008), if other aspects of anatomy for a species under consideration differ markedly from those of related taxa, then bite force alone may prove a poor predictor. High bite forces in the giant panda likely represent a unique adaptation to specialized bamboo feeding. Tooth, mandibular and masticatory muscle anatomy in this species have all been considered both highly specialized within the family and consistent with increased herbivory on tough plant material (Davis, 1964; Endo et al., 2003).

In recent years, some progress has been achieved in the identification of craniodental features related to herbivory in living ursids using a morphometric approach (Sacco and Van Valkenburgh, 2004; Christiansen, 2008; Figueirido et al., 2010). Two-dimensional (2D) analyses of bite mechanics and mandibular force profiles have also identified features considered consistent with specialized herbivory in the giant panda (Christiansen, 2007). It has been concluded that the giant panda was the only specialized extant ursid in terms of craniodental morphology and bite force (Christiansen, 2007).

Regarding fossil ursids, the feeding ecology of short-faced bears, which include the largest known species, remains particularly contentious. Although arguments based on both morphology and isotopic data have been mounted for increased reliance on large vertebrates as food (hunted and/or scavenged) in a number of short-faced bear species (Hendey, 1980; Mattson, 1998; Sorkin, 2006; Soibelzon & Schubert, 2011), there remains little clear evidence from analyses of skull mechanics identifying specializations for carnivory.

In the present study, we address ursid cranial mechanics by applying three-dimensional (3D) FEA to six skulls representing five extant species. FEA is a promising approach in biological form–function studies, but its application has been somewhat limited by small datasets, which have typically included two or three species (McHenry et al., 2007; Wroe et al., 2007; Bourke et al., 2008; Wroe, 2008; Wroe et al., 2008; Slater & van Valkenburgh, 2009; Chamoli & Wroe, 2011).

The extant species modelled are as follows, including estimates of the percentage of vertebrate food comprising the diets of each [see Figueirido et al. (2010) and Mattson (1998)]: A. melanoleuca (giant panda) (0%); U. arctos (brown bear) (36%), Ursus americanus (black bear) (2%), Ursus maritimus (polar bear) (100%) and Ursus thibetanus (Asian bear) (2%).

In addition to finite element models (FEMs) of these extant taxa, we further reconstruct the skull of the fossil Agriotherium africanum (tribe Ursavini). Traditionally, it has been argued that the extinct giant short-faced bears, Agriotherium and Arctodus (tribe Tremarctini), were hypercarnivorous and more active predators on large terrestrial prey than any living bear, largely on the basis of craniodental morphology (Hendey, 1980). This is because both genera exhibit a range of independently evolved traits, including a short, broad skull, premasseteric fossa on the mandible and well-developed carnassial blades (Kurtén, 1967; Hendey, 1980; Sorkin, 2006). The relative importance of vertical shearing in the dentition is widely considered an important indicator of carnivory (Van Valkenburgh, 1989; Wroe, Brammal & Cooke, 1998) and a predaceous, felid-like feeding ecology for A. africanum has been hypothesized (Hendey, 1980).

More recently, however, it has been argued that Agriotherium and Arctodus were probably neither active predators of large prey nor hypercarnivores, although both likely consumed larger quantities of vertebrate prey than most living ursids in the form of carrion (Sorkin, 2006). A niche as scavengers of large vertebrate carcasses and predators of small prey supplemented with plant material has been proposed (Sorkin, 2006). Sorkin drew analogy with the living brown and striped hyaenas (Parahyaena brunnea and Hyaena hyaena) as opposed to large felids. The argument was based on a range of observations, including the high degree of wear on the carnassial teeth of a North American specimen of Agriotherium. Wear is far less pronounced in the specimen of A. africanum included in our analysis (Fig. 1), and it may be that proportions of killed to scavenged vertebrates varied considerably within the genus, or that our specimen is a younger individual. While recent studies by Figueirido & Palmqvist (2009) and Figueirido et al. (2010) support Sorkin's (2006) conclusion that Arctodus was more of an omnivore than a hypercarnivorous active predator, no further work in this regard had been carried out on Agriotherium.

Figure 1.

(a) Lower left carnassial blade of Agriotherium africanumSAM-PQL 45062 generated using computed tomography (CT) data. (b) Lower left carnassial blade of Canis lupus (grey wolf), C. lupus (TMMM-1709) CT.

Based on analyses of our FEMs, we ask a range of questions and test a number of predictions, some of which would not be possible with smaller datasets.

Where dental or craniomandibular morphology are consistent with increased herbivory in ursids, then a capacity to generate relatively high bite forces may indicate reliance on particularly tough foods as opposed to predation on relatively large prey.

  1. Is the skull of a near obligate herbivore such as the giant panda relatively better adapted to resist high reaction forces generated at the molars, where bamboo is primarily processed?

With respect to diet and ecology in the extinct A. africanum, we address the following:

  • 2.Regardless of whether A. africanum was a more regular predator of large prey or whether it consumed a high proportion of large vertebrate bones relative to extant species, if either interpretation is correct, then we would predict that this species was capable of generating relatively high bite forces and that its skull was well-adapted to sustain such forces.

In comparative FEA, single specimens are routinely used to represent entire species. An assumption here is that interspecific differences outweigh intraspecific ones. Our analyses include FEMs of two polar bears.

  • 3.We ask whether the mechanical behaviours of these two conspecifics are more similar to each other than to other species. Although our sample is tiny, it will nonetheless allow a limited first test of this assumption.

Materials and methods

Seven finite element models were assembled from computed tomography (CT) data representing five extant species (brown bear, Asian bear, black bear, polar bear and giant panda) and one fossil ursid A. africanum (SI Table S1). For extant taxa, preprocessing followed the previously published protocols (McHenry et al., 2007; Wroe et al., 2007; Moreno et al., 2008; Wroe, 2008; Degrange et al., 2010; Wroe et al., 2010).

The fossil skull (SAM-PQ 45062) that formed the basis of our A. africanum FEM (and see SI) is without obvious deformation but missing data comprise the majority of the left parietal, frontal bones and the palate. Virtual reconstruction to replace these missing data develops previously published protocols (Wroe et al., 2010). Preprocessing of the extant bear material also largely follows the published methodology (McHenry et al., 2007), but with the surface and solid meshes generated in Harpoon® (version 3.6, Sharc Pty Ltd., Manchester, UK). Each cranium comprised ∼1.5 million elements.

To reconstruct A. africanum, we first used Rhinoceros® (version 4, McNeal & Associates, Seattle, WA, USA) to mirror the right parietal and frontal bones. Then, a polar bear source mesh was warped to fit A. africanum in Landmark® (version 3.0, Institute for Data Analysis and Visualization, Davis, CA, USA). Six point primitives and 150 curved primitives were placed in Landmark on the interior and exterior surfaces of the source and target (A. africanum) meshes, allowing the polar bear cranium mesh to be warped to the same shape of A. africanum. A solid mesh was generated in Harpoon® from this complete surface mesh. For all subsequent analyses, FEA was performed using Strand7 (version 2.4.4, Company: Srand7 Pty Ltd., Sydney, Australia). To allow comparison between the extant species and the reconstructed fossil, models used a homogeneous, isotropic material property set, with solid elements representing bone assigned a Young's modulus of 13 000 MPa and a Poisson's ratio of 0.4.

Loadings comprised two intrinsic (bilateral biting at the canines and unilateral biting at the second molars) and two extrinsic load cases. These simulations were designed to approximate behaviours associated with killing and feeding (McHenry et al., 2007; Wroe, 2008). To examine the degree to which strain distributions and magnitudes varied between species-specific loadings, muscle forces for these intrinsic loads were determined on the basis of estimated cross-sectional areas (Thomason, 1991; Wroe et al., 2005) (see SI Table S2).

Bite forces and bite force quotients [i.e. bite forces adjusted for body mass (Wroe et al., 2005)] were derived from the unscaled FEMs (see Table 1). Body masses were estimated for each specimen using an equation presented for ursids based on skull length (Van Valkenburgh, 1990).

Table 1. Bite force and bite force quotient (BFQ)
SpeciesBody mass (kg)3D bite force canineBFQ canine (3D)
  1. 3D, three-dimensional.
Asian bear91.031217.39154
Black bear124.472016.94210
Brown bear213.682795.56207
Giant panda110.452603.47292
Polar bear SAM-ZM 35814187.271969.72159
Polar bear AM M42656226.552569.57184
Agriotherium africanum317.224566.14265

To compare mechanical performance between specimens, we scaled all FEMs to a uniform surface area (Dumont, Grosse & Slater, 2009). For intrinsic loads, we adjusted muscle recruitment to achieve a uniform bite force (Wroe et al., 2010). Two uniform extrinsic loads were also applied to the scaled models (lateral shake and pull back).

Statistical treatments largely concentrated on mandibular data because inspection of visual plots clearly showed higher and more variable strains in the mandibles. However, a two-way analysis of variance (ANOVA) also incorporated regions of the crania, which experienced high strain. Using code written in R (version 2.12.1) by H. Richards, for each simulation, mean von Mises (VM) ‘brick’ strain data were compiled (Table S3).

Two-factor without replication ANOVA at 1% level of significance (α = 0.01) was performed on the mean brick VM strain data for five different regions of the skull (left zygomatic arch, right zygomatic arch, rostrum, left dentary and right dentary) for the seven specimens included for the bilateral canine biting case. Once selected, regions were preset as groups containing a constant number of elements in Strand7 (version 2.4). The rostrum was defined as that part of the cranium anterior to the rim of the orbit, and the zygomatic arch was defined as that part of the jugal posterior to the anterior rim of the orbit and squamosal anterior to the glenoid fossa. P-values were used to test the null hypothesis that there was no statistically significant variation in the mean VM brick strain distribution across and within the species, and that any observed difference was because of the sampling error.

Pairwise two-factor without replication ANOVA at 10% level of significance (α = 0.1) was also performed between polar bear SAM-ZM 35814, polar bear AM M42656 and other specimens to determine whether these were statistically more similar to each other than to the rest of the group.


Bite force

In absolute terms, bite force at the canines is greatest in A. africanum (4566 N) and least in the Asian bear (1217 N). Bite force adjusted for body mass (bite force quotient, BFQ) was much higher in A. africanum and the giant panda than in any other species/specimens (Table 1). Lowest values for BFQ were for the Asian bear and the polar bear.


For each model, we extracted mean VM brick strain data using Strand7 (version 2.4.4). The top 5% of data was disregarded because particularly high values present in restrained areas were clearly artefactual.

Intrinsic loads

Bilateral canine

From inspection of visual plots for scaled models with muscle recruitment adjusted to produce the same bite reaction force, the broad distributions of VM strain were similar across species for bilateral canine bites (Fig. 2). Mean brick VM strain in canine biting was lowest in A. africanum and the giant panda and highest in the polar bear specimens (SI Table S4).

Figure 2.

Scaled to surface area, bilateral canine bite: (a) Agriotherium africanum, (b) Asian bear, (c) black bear, (d) brown bear, (e) giant panda, (f) polar bear SAM – ZM 35814 and (g) polar bear AMM42656.

From two-factor ANOVA at 1% level of significance (α = 0.01) for a canine bite, P-values of 1.152 × 10−06 (across species) show significant mean VM brick strain variation between species.

P-values obtained from a two-factor ANOVA shows that at 10% level of significance (α = 0.1), P < α for all possible pairs of polar bears and other species, except between the two polar bear specimens (Table 2). This suggests that the mean VM brick strain distributions in the two polar bears are far more similar to each other than to any other specimen/species.

Table 2. P-values obtained from pairwise two-factor without replication analysis of variance on mean von Mises brick strain data for five regions in the skull under a bilateral canine load case
 Polar bear SAM-ZM 35814Polar bear AM M42654
  1. At 10% level of significance (α = 0.1), P < α for all possible pairs of polar bears and other species, except between the two polar bear specimens.
Asian bear0.0230.078
Black bear0.0330.030
Brown bear0.0720.088
Giant panda0.0130.014
Agriotherium africanum0.0090.0189
Polar bear SAM-ZM 35814X0.361
Polar bear AM M42654 X

Unilateral molar

Both peak and mean brick strains were lowest for A. africanum. The next lowest values were evident in the giant panda (SI Table S5), followed by the black bear, both polar bears and the Asian bear.

Extrinsic loads

Visual plots for extrinsic cases also showed similar broad distributions of VM strain across species (Fig. 3 and SI Fig. S2). However, again there were marked differences between species in plots for mean and maximum strain.

Figure 3.

Lateral shake loading case: (a) Agriotherium africanum, (b) Asian bear, (c) black bear, (d) brown bear, (e) giant panda, (f) polar bear SAM-ZM 35814 and (g) polar bear AMM42656.

Pull back

Maximal and mean brick VM strain was low in both A. africanum and the giant panda. For A. africanum, see SI Table S6. Overall rankings of performance based on mean VM brick strain data were similar to those calculated for intrinsic loadings.

Lateral shake

Similar relative rankings were also found under shake loading (Fig. 3) to that of the pull back loading case (SI Fig. S2). The giant panda had the lowest mean VM strain distribution, followed by A. africanum (SI Table S7).


At 4566 N, our 3D bilateral canine bite force estimate for A. africanum is the highest predicted for any mammal, being considerably greater than the equivalent for a very large male African lion (Panthera leo) (Wroe, 2008). A. africanum also had a very powerful bite for its size as indicated by a high BFQ value (Table 1).

Although our results are consistent with the suggestion that the giant panda is well-adapted to both generate and resist high bite reaction forces at the molars, they do not support the contention that it is better adapted to resist high reaction forces generated at the molars than at the canines. Only A. africanum shows lower mean and maximal VM strains under bilateral canine loading.

Results also suggest that the polar bear is not only less well-adapted to dispatch and eat large prey than the brown bear (Slater et al., 2010), but that it is among the poorest performers. Under almost all loadings, mean and maximal VM strain values between the two polar bear specimens are closer to each other than to any other species. This is supported by the results of pairwise two-factor ANOVA. Table 2 shows that at α = 0.1, P < α for all possible pairs of polar bears and other species, except between polar bear (SAM-ZM 35814) and polar bear (AM M42656), suggesting that the mean VM brick strain distributions in the two polar bears are statistically similar.

Our finding that the polar bear is arguably the poorest performer is surprising given its status as the only living hypercarnivorous ursid. Our results agree with a recent analysis. (Slater et al., 2010), which compared the mechanics of a polar bear cranium with those of a brown bear, from which polar bears have recently diverged (Lindqvist et al., 2010). We suggest that the skull biomechanics of the polar bear, which primarily ingests easily processed blubber (Perry, 1966), are consistent with predation upon relatively small prey. Moreover, its primary prey is semiaquatic and poorly equipped to resist capture on land.

Regarding diet in A. africanum, it was clearly capable of generating very high bite forces for its size, and its skull was well-adapted to resist both these and relatively high extrinsic loads, and these are features that would be expected in a species that regularly kills and/or scavenges on relatively large prey. However, our results also show that the exclusively herbivorous giant panda is similarly well-adapted to sustain relatively high loadings, indicating that ursid feeding behaviour cannot be predicted on the basis of our FEA alone. Many craniodental variables have been considered by previous authors. Relative grinding area (RGA) is perhaps the most reliable indicator of the relative importance of plant material in the diet, with low values correlating with decreased reliance on plants (Sacco & Van Valkenburgh, 2004). On this basis, it is unlikely that similarities in mechanical performance between the A. africanum and the giant panda are a consequence of similarities in diet. We calculate a value of 1.47 for RGA in our specimen of A. africanum, well below values for RGA evidenced in any living bears, the next lowest being 1.83 in the polar bear (Van Valkenburgh, 1989).

Relative carnassial blade length (RBL) has also been regarded as a strong indicator of the importance of vertebrate prey in carnivoran diets, and RBL in A. africanum is also considerably higher than in extant bears. However, among extant bears, the only hypercarnivore that has relatively short carnassial blades is the polar bear (Sacco & Van Valkenburgh, 2004), perhaps because it feeds mostly on blubber as opposed to meat or bone (Perry, 1966), as previously mentioned.

No living ursids occupy niche spaces similar to those previously hypothesized for A. africanum, that is either a hypercarnivorous active predator of relatively large terrestrial prey, or a scavenger of large terrestrial vertebrate carcasses that included less plant and non-vertebrate food than most living bears, but was nonetheless omnivorous. However, it is perhaps notable in this context that the brown bear is the next closest in overall mechanical performance to A. africanum aside from the giant panda. The brown bear is the only extant bear, which at least in part of its range, does include substantial quantities of large terrestrial vertebrate prey in its diet, killed and scavenged.

Our FEA-based results of skull mechanics do not conclusively resolve the question of dietary niche for A. africanum. However, our findings do strongly support the view that A. africanum was capable of delivering and sustaining extremely powerful bites.

As such, our findings suggest that both major competing hypotheses are tenable on the basis of cranial mechanics. A. africanum was more than capable of dispatching very large vertebrate prey, but this does not mean that it did. Likewise, in a role as scavenger on large vertebrate carcasses, A. africanum would have been well-equipped, with both a very high potential bite force and the craniomandibular strength to resist high reaction forces. A more detailed FEA of heterogeneous ursid models, including multi-property detail for dental morphology, may help resolve which of these two proposed roles are more likely.


This work was funded by an Australian Research Council Discovery Project grant (DP0986471) Discovery Project (DP0987985) and University of New South Wales Goldstar grants to S. W. We thank Sandy Ingelby (Australian Museum) for providing access to several specimens, and Eleanor Cunningham (Newcastle Mater Hospital) for CT scanning of these. The CT scanning of the IZIKO South African Museum specimens was funded by a Palaeontological Scientific Trust grant to P. D. S. and a National Research Foundation African Origins Platform grant (AOP/West Coast Fossil Park) to R. Smith (Iziko SA Museum). P. D. S. thanks Denise Hamerton for the loan of the Iziko South African Museum specimens and N. Peters (Groote Schuur Hospital) for CT scanning assistance. Thanks are due to H. Richards for assistance with writing code used to perform statistical analysis, and finally, we thank M. McCurry and C. Walmsley for providing insight into the methods of model preparation.