The Structural Rigidity of the Cranium of Australopithecus africanusImplications for Diet Dietary Adaptations and the Allometry of Feeding Biomechanics.код для вставкиСкачать
THE ANATOMICAL RECORD 293:583–593 (2010) The Structural Rigidity of the Cranium of Australopithecus africanus: Implications for Diet, Dietary Adaptations, and the Allometry of Feeding Biomechanics DAVID S. STRAIT,1* IAN R. GROSSE,2 PAUL C. DECHOW,3 AMANDA L. SMITH,1 QIAN WANG,4 GERHARD W. WEBER,5 SIMON NEUBAUER,6 DENNIS E. SLICE,7 JANINE CHALK,8 BRIAN G. RICHMOND,8 PETER W. LUCAS,8 MARK A. SPENCER,9 CAITLIN SCHREIN,9 BARTH W. WRIGHT,10 CRAIG BYRON,11 AND CALLUM F. ROSS12 1 Department of Anthropology, University at Albany, Albany, New York 2 Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, Massachusetts 3 Department of Biomedical Sciences, Texas A&M Health Science Center, Baylor College of Dentistry, Dallas, Texas 4 Division of Basic Medical Sciences, Mercer University School of Medicine, Macon, Georgia 5 Department of Anthropology, University of Vienna, Vienna, Austria 6 Department of Human Evolution, Max-Planck-Institute for Evolutionary Anthropology, Leipzig, Germany 7 Department of Scientiﬁc Computing, Florida State University, Tallahassee, Florida 8 Department of Anthropology, Center for the Advanced Study of Hominid Paleobiology, The George Washington University, Washington, District of Columbia 9 School of Human Evolution and Social Change, Institute of Human Origins, Arizona State University, Tempe, Arizona 10 Department of Anatomy, Kansas City University of Medicine and Biosciences, Kansas City, Missouri 11 Department of Biology, Mercer University, Macon, Georgia 12 Department of Organismal Biology and Anatomy, University of Chicago, Chicago, Illinois ABSTRACT Australopithecus africanus is an early hominin (i.e., human relative) believed to exhibit stress-reducing adaptations in its craniofacial skeleton that may be related to the consumption of resistant food items using its premolar teeth. Finite element analyses simulating molar and premolar biting were used to test the hypothesis that the cranium of A. africanus is structurally more rigid than that of Macaca fascicularis, an Old World monkey that lacks derived australopith facial features. Previously generated ﬁnite element models of crania of these species were subjected to isometrically scaled loads, permitting a direct comparison of strain magnitudes. Moreover, strain energy (SE) in the models was compared after results were scaled to account for differences in bone volume and muscle forces. Results indicate that strains in certain skeletal regions below Grant sponsor: National Science Foundation (Physical Anthropology HOMINID Program); Grant numbers: NSF BCS 0725219, 0725183, 0725147, 0725141, 0725136, 0725126; 0725122; 0725078; Grant sponsor: EU FP6 Marie Curie Actions (EVAN); Grant number: MRTN-CT -2005-019564. *Correspondence to: David S. Strait, Department of Anthropology, University at Albany, 1400 Washington Avenue, Albany, NY 12222. Fax: (518) 442-5710. E-mail: firstname.lastname@example.org C 2010 WILEY-LISS, INC. V Received 7 January 2010; Accepted 11 January 2010 DOI 10.1002/ar.21122 Published online in Wiley InterScience (www.interscience.wiley. com). 584 STRAIT ET AL. the orbits are higher in M. fascicularis than in A. africanus. Moreover, although premolar bites produce von Mises strains in the rostrum that are elevated relative to those produced by molar biting in both species, rostral strains are much higher in the macaque than in the australopith. These data suggest that at least the midface of A. africanus is more rigid than that of M. fascicularis. Comparisons of SE reveal that the A. africanus cranium is, overall, more rigid than that of M. fascicularis during premolar biting. This is consistent with the hypothesis that this hominin may have periodically consumed large, hard food items. However, the SE data suggest that the A. africanus cranium is marginally less rigid than that of the macaque during molar biting. It is hypothesized that the SE results are being inﬂuenced by the allometric scaling of cranial cortical C 2010 Wiley-Liss, Inc. bone thickness. Anat Rec, 293:583–593, 2010. V Key words: ﬁnite element analysis; skull; hominin; human evolution; diet; strain; bone INTRODUCTION Strain, a measure of deformation, is a useful parameter for estimating bone deformation patterns and the response of bone to external loads (e.g., Bouvier and Hylander, 1981; Hylander, 1977, 1984; Hylander et al., 1991; Hylander and Johnson, 1997). However, there are nonetheless challenges inherent in using strain to assess the overall structural performance of skeletal objects of complex geometry. A major issue is that strain gauge measurements record local deformations at particular sites on an object (i.e., as recorded from a strain gage), but in an irregular structure (like a skull) there can be regions exhibiting very high and also very low strains (e.g., Hylander et al., 1991; Ross, 2001; Ross and Metzger, 2004), making it difﬁcult to characterize the rigidity of the entire object from gage data. This problem becomes more acute when comparing objects of different shape (e.g., skulls of different species). Even if those objects are subjected to equivalent loads, the patterning of local strains may be difﬁcult to interpret, particularly if different regions exhibit elevated (or reduced) strains in the different structures (e.g., Skull X exhibits higher strains than Skull Y in Region A but lower strains in Region B). To facilitate comparisons between whole objects (rather than simply parts of objects), Dumont et al. (2009) suggested using strain energy (SE) as a measure of overall structural performance (see also Farke, 2008) for a slightly different use of SE. SE is equivalent to the work done on an object by external forces, and thus encapsulates the net effect of deformations across an entire structure. Dumont et al. (2009) further laid the theoretical foundations for controlling and quantifying the effects of size on SE metrics. Here, we use SE to evaluate the structural performance of the skulls of two primate species, Macaca fascicularis (an Old World monkey) and Australopithecus africanus [an extinct hominin (human relative)]. Strait et al. (2009) recently used ﬁnite element analysis (FEA) to compare feeding biomechanics in these two species. Their analysis incorporated information about muscle architecture, muscle activity patterns, bone material properties, and in vivo bone strain collected in living primates (Richmond et al., 2005; Ross et al., 2005; Strait et al., 2005, 2007, 2008, 2009). They tested the hypothesis that certain derived facial features in A. africanus were adaptations that structurally reinforced the face against loads imposed by premolar biting (Rak, 1983). That hypothesis predicts that strain in the anterior face will be elevated during premolar biting, and that the derived traits (particularly, the position of the root of the zygomatic arch and the presence of a pillar of bone running along the nasal margin) will affect either the nature or magnitude of the strains recorded there. Results were consistent with both predictions insofar as both von Mises strain and strain energy density (SED) in the anterior face were elevated in both models during premolar biting (as opposed to biting on the molars alone or all of the cheek teeth at once), but that the nature of the deformations of the two models were different; minimum principal strain (compression) was much higher than maximum principal strain (tension) in the rostrum of A. africanus, but these variables had similar magnitudes in M. fascicularis. Strait et al. (2009) suggested that premolar biting may have been an adaptively signiﬁcant behavior in A. africanus and that such bites may have been used during the ingestion of large, ‘‘hard’’ objects like nuts and seeds (such objects are more precisely described as being ‘‘stresslimited’’ insofar as they fracture under the application of high forces; Lucas, 2004). One counterintuitive aspect of Strait et al. (2009) results is that they observed that the A. africanus skull exhibited higher strain and SED density values than the M. fascicularis skull under all loading regimes. This might have been unexpected given that the former is hypothesized to possess derived stress-absorbing facial traits whereas the latter does not. However, as noted above, it is difﬁcult to directly compare entire skulls using localized strain values, and the comparison is further complicated by the fact that the two ﬁnite element models (FEMs) differed in size and were not subjected to equivalent loads. Here we use principles of isometric scaling to compare strain and SE in the two models. We hypothesize that, with appropriate size adjustment, the cranium of A. africanus is structurally more rigid than 585 CRANIAL RIGIDITY IN AUSTRALOPITHECUS that of M. fascicularis during feeding, particularly when biting on the premolars. TABLE 1. Muscle force magnitudes applied to the ﬁnite element models, in Newtons Muscle MATERIALS AND METHODS Finite Element Analysis FEA is an engineering technique used to examine how structures of complex design respond to external loads (e.g., Huiskes and Chao, 1983). In FEA, the structure of interest (e.g., a skull) is modeled as a mesh of simple bricks and tetrahedra (ﬁnite elements) joined at nodes, the elements are assigned material properties, certain nodes are constrained against motion, forces are applied, and displacements, stresses, and strains at each node and within each element are calculated. Recent advances in computer software and imaging technology have made it possible to capture and digitally reconstruct skeletal geometry with great precision, thereby facilitating the generation of detailed FEMs of bony structures, including nonhuman vertebrate crania (Dumont et al., 2005; Richmond et al., 2005; McHenry et al., 2007; Rayﬁeld, 2001, 2004, 2005a,b, 2007; Rayﬁeld et al., 2007; Wroe, 2007; Bourke et al., 2008; Farke, 2008; Moreno et al., 2008; Pierce et al., 2008; Rayﬁeld and Milner, 2008; Wroe et al., 2007, 2008; Kupczik et al., 2007, 2009; Moazen et al., 2008, 2009a,b; Strait et al., 2005, 2007, 2008, 2009). However, the incorporation of realistic muscle forces, bone material properties, modeling constraints, and experimental bone strain data are equally important components of FEA that are necessary to ensure biologically meaningful results (e.g., Richmond et al., 2005; Ross et al., 2005; Strait et al., 2005; Rayﬁeld, 2007). The methods used to create, load, constrain, and validate the M. fascicularis and A. africanus models have been described comprehensively elsewhere (Strait et al., 2005, 2007, 2008, 2009). Brieﬂy, in both models, computed tomography scans were used as the basis for creating solid models in a computer-assisted-design (CAD) software package. In the case of A. africanus, additional modeling steps were necessary to create a composite skull model consisting of parts of two fossil specimens and to reconstruct missing or distorted morphology. The solid models were converted into ﬁnite element meshes in commercially available FEA software. The M. fascicularis model contains 311,057 brick and tetrahedral elements, whereas the A. africanus model contains 778,586 elements. Although the element numbers differ dramatically, the macaque model was meshed here with midside nodes in facial regions, whereas the australopith model did not have midside nodes. As a result, the two models were meshed with similar numbers of nodes (337,073 vs. 303,312, respectively). As a test of mesh density, the macaque model was also analyzed without midside nodes, and during molar biting a mesh of 131,293 nodes produced only a 4% reduction in SE. This suggests that our models have sufﬁcient mesh density. In Strait et al. (2009), regions corresponding to different areas of cortical bone in the M. fascicularis model were assigned orthotropic material properties (elastic modulus, Poissons’ ratio, and shear modulus) using data collected from macaques by Wang and Dechow (2006) (see also Strait et al., 2005, 2007, 2008, 2009). These properties were not used by them (Strait et al., 2009) in the A. africanus model because preliminary analyses (Wang et al., 2006; Dechow, unpublished observations) Working-side Anterior temporalis Superﬁcial masseter Deep masseter Medial pterygoid Balancing side Anterior temporalis Superﬁcial masseter Deep masseter Medial pterygoid M. fascicularis A. africanus 36.6 70.6 22.6 34.8 105.0 202.7 64.8 99.9 15.1 34.7 8.2 6.9 43.5 99.5 23.6 19.8 suggest that the material properties of craniofacial bone in apes and humans differ subtly from those of Old World monkeys on a region-by-region basis. Instead, the A. africanus model was assigned isotropic material properties corresponding to the average of all of the regional material properties in M. fascicularis. These average values appear to be similar to the average values in apes and humans (Dechow, unpublished observations). Thus, in Strait et al. (2009), the models were assigned different sets of material properties and those differences have an effect on overall structural rigidity. Because the objective of this study is to focus more speciﬁcally on the mechanical consequences of shape differences between the two models, both were assigned the same set of isotropic properties, thereby eliminating any differences due to those variables. Trabecular bone was modeled as a volume (rather than as individual trabeculae) using material properties derived from Ashman et al. (1984). Force vectors corresponding to the right and left anterior temporalis, superﬁcial masseter, deep masseter, and medial pterygoid muscles were applied to nodes on the neurocranium, zygomatic arch, and lateral pterygoid plate. Vector orientations were determined by considering the relative origins and insertions of each muscle. Muscle force magnitudes (Table 1) in M. fascicularis were calculated using a combination of muscle physiologic cross-sectional area and electromyographic data (Ross et al., 2005; Strait et al., 2005, 2007, 2008, 2009). These muscle forces reﬂect the fact that during any given bite, the muscles act slightly out of phase to each other and thus are never all simultaneously acting at peak levels. Strait et al. (2009) applied muscle forces to the A. africanus model that were calculated using physiological cross-sectional area (PCSA) data gathered from Pan troglodytes, the common chimpanzee. However, in this study, a different set of forces was applied to the A. africanus model (see below). Moreover, to facilitate calculation of SE (see below), muscle forces were applied using a small number of vectors (20), which likely introduces some displacement artifacts into the FEA results. Constraints were applied to multiple nodes at the right and left articular eminences and either the left molars or left premolars. Muscle forces act to pull the skull models down onto the constrained nodes, generating reaction forces representing the joint forces at the temporomandibular joints and the bite force during either molar or premolar biting. The M. fascicularis model has previously been validated (Strait et al., 2005, 2008, 2009) against bone 586 STRAIT ET AL. TABLE 2. Surface areas and volumes of the ﬁnite element models Model M. fascicularis A. africanus tural rigidity in the A. africanus and M. fascicularis models. Surface area (mm2) Volume (mm3) 42,737 122,671 39,274 364,520 strain data collected during in vivo chewing experiments. Data on maximum shear strain, principal strain ratio, and the orientation of maximum principal strain were collected from nodes on the model corresponding to regions in which experimental data had also been gathered. For most regions and most strain measures, the FEA-generated data fell within the envelope of values derived from in vivo experiments, indicating that the macaque model deforms in a broadly realistic fashion. Calculation and Comparison of SE SE in each model is equal to the work done on the skulls by the muscle forces. This is calculated as onehalf of the sum of the dot products of the muscle force vectors and the displacements of the nodes at which the vectors are applied in the x-, y- and z-directions. Some FEA software packages calculate SE automatically as part of their standard output, but this was not the case with the software used here (Algor FEM Pro). Thus, displacements were extracted from the models and SE was calculated for each using a spreadsheet program. This process was simpliﬁed by having relatively few force vectors (and, hence, few nodes from which to collect displacements). The SE results from the two models cannot be directly compared because the models are at different scales. Comparison can occur only after the SE value of one model is adjusted to control for differences between the models in bone volume and force (note that ‘‘bone volume’’ excludes the air and soft-tissue ﬁlled cavities in the cranium; Table 2). In the case considered here, the raw SE value for M. fascicularis was compared to the scaled SE value for A. africanus. Following Dumont et al. (2009), the scaled SE value for A. africanus was calculated as: Scaled SEA ¼ ðVA = VM Þ1=3 ðFM = FA Þ2 SEA (1) where SEA, VA, and FA equal the SE of, the bone volume of, and the forces applied to the A. africanus model, respectively, and VM and FM represent the bone volume of and forces applied to the M. fascicularis model. Scaled SEA represents the SE that would have been observed in the A. africanus model if it possessed the same volume and was subjected to the same forces as the M. fascicularis model. As mentioned, SE is equivalent to work (one-half of force times displacement), and because the forces have been equalized, a comparison between scaled SEA and SEM (the SE of the macaque model) reﬂects the different displacements recorded in the two models at the nodes at which forces are applied. These displacements are themselves the products of the deformation of each model as a whole, meaning that the ratio scaled SEA/ SEM records the proportional difference in overall struc- Muscle Forces in the A. africanus Model Examination of Eq. (1) reveals that it has a very useful property. Namely, it allows the calculation of scaled SEA for any set of forces applied to the A. africanus and M. fascicularis models, so long as the ratio of the forces applied to the two models is known (Dumont et al., 2009). In other words, under such conditions, the magnitudes of the forces applied to the A. africanus model will not affect the value of scaled SEA. This may seem counterintuitive, but imagine a special case in which the macaque and A. africanus models retained their shapes but had the same bone volume (i.e., a very large macaque or a very small australopith). Because the ratio of volumes is equal to one, scaled SEA is purely a product of the squared ratio of the applied forces. If equivalent forces were applied to both models, then the ratio of forces would be equal to one, meaning that the raw SE values for the two models can be directly compared because scaled SEA would be equal to raw SEA. Now consider a case in which the forces applied to the A. africanus model were ﬁve times greater than those applied to the M. fascicularis model. The SE in the A. africanus model will be 25 times greater than that in the macaque model, because SE is equal to one-half the product of force and displacement, and in a linearly elastic model (as employed here) displacement varies in direct proportion to force. In other words, SE increases as a square of force because work is equal to the area underneath the force-displacement curve. Returning to Eq. (1), the raw value of SEA is multiplied by the square of the ratio of forces, which is now equal to 1/25. Thus, the increase in SEA caused by the greater forces is cancelled out by the decrease in the square of the force ratio, meaning that the value of scaled SEA remains unchanged. In theory, we could apply the same forces to the two models as were used by Strait et al. (2009), but this is problematic in practice because each of the A. africanus muscle forces differs distinctly from the corresponding macaque muscle forces (e.g., the force of the anterior temporalis in A. africanus is 10 times greater than that in M. fascicularis, but the force of the superﬁcial masseter is only approximately ﬁve times greater). This variation makes it difﬁcult to calculate the ratio of forces applied to the two models. Consequently, a new set of muscle forces was calculated and applied to the FEM of A. africanus. Given that any set of forces can be applied to the A. africanus model for the purpose of examining SE (so long as the ratio of those forces and the macaque forces are known), we chose to apply forces such that the differences in the stress states of the two models were purely a function of shape. Such forces facilitate the calculation of scaled SEA and are useful for comparing strains. Consider two objects of the same shape but different size, for example, a large and a small version of the macaque cranium. As shown by Dumont et al. (2009), if forces are applied to each cranium such that they maintain the same ratio of force to bone surface area, then they will be in the same stress state (recall that stress is equal to force divided by area), meaning that the strains observed in the two crania will be 587 CRANIAL RIGIDITY IN AUSTRALOPITHECUS identical. Note that in place of bone surface area, one may substitute bone volume to the two-thirds power. Now assume that the large macaque cranium has the same bone surface area as the A. africanus cranium. If the muscle forces applied to the large macaque were now applied to the australopith, then the differences between their stress states and resulting strains would be a result of shape rather than force. Moreover, recall that the large and small macaques have identical stress states. This means that the strains in the small macaque can be directly compared to those in A. africanus, and any differences can be attributed directly to the differences in the shapes of the crania [with the caveat that FEMs of the two crania must be constructed using similar assumptions regarding geometry (i.e., the presence or absence of particular cavities within the crania)]. Thus, in our FEAs, muscle force magnitudes in the A. africanus model were calculated by multiplying the macaque magnitudes by the ratio of the surface areas of the A. africanus and M. fascicularis models (Tables 1 and 2). This procedure also simpliﬁes the calculation of scaled SEA, because the ratio of areas in the two models can be substituted in place of FM/FA in Eq. (1). RESULTS Strain Strain maps of the FEAs are presented in Fig. 1. During molar biting, both the M. fascicularis and A. africanus models exhibit high von Mises strains in the working-side zygomatic root and arch and a complex and steep strain gradient in the working-side infraorbital region. Both models exhibit higher strains on the working- than on the balancing-side, and both show low strains along the supraorbital torus and the nasoalveolar region (below the nasal aperture). The models differ in that the macaque shows regions of moderately elevated von Mises strain on the working-side dorsal rostrum region (just below the inferior margins of the orbit), whereas the australopith shows elevated strains in the Fig. 1. Von Mises strain in the ﬁnite element models during molar and premolar biting. A: M. fascicularis model during molar biting. B: A. africanus model during molar biting. C: M. fascicularis model during premolar biting. D: A. africanus model during premolar biting. 588 STRAIT ET AL. TABLE 3. Strain energy recorded during ﬁnite element analyses, in Newton millimeters Variable M. fascicularis Strain energy (SEM) A. africanus Strain energy (SEA) Scaled SEA Ratio Scaled SEA/SEM FEA of molar biting FEA of premolar biting 3.56 4.65 14.55 3.71 16.03 4.09 1.04 0.88 postorbital bars and interorbital pillar (just above the inferior margins of the orbit). During premolar biting, many of the basic strain patterns seen during molar biting remain largely unchanged, but von Mises strains along the dorsal rostrum, nasal margin, and lateral rostrum are elevated in both species. However, the species differ in that the magnitude of those elevated strains are much higher in M. fascicularis than in A. africanus. Strain Energy Both FEMs exhibited higher SE during premolar than during molar loading (Table 3). In the macaque model, SE during premolar bites was 30.6% higher than during molar bites, whereas in the A. africanus model the difference was 10.2%. As SE increases, structural rigidity decreases, so these results indicate that premolar bites are associated with a mechanical cost (decreased rigidity resulting from increased deformations). However, the macaque incurs a greater cost than the australopith. When comparing SE in the macaque model to scaled SE in the A. africanus model, the A. africanus model exhibits values that are 4% higher than the macaque model during molar loading. During premolar loading, however, the A. africanus model had values that were 12% lower. Thus, compared to M. fascicularis, A. africanus is less rigid during molar biting and more rigid during premolar biting, but A. africanus shows a three times larger increase in relative rigidity under premolar loading than the relative decrease in rigidity under molar loading. DISCUSSION Structural Rigidity Certain aspects of the results are consistent with the hypothesis that the A. africanus cranium is more rigid than the M. fascicularis cranium. Under isometrically scaled loading conditions, the A. africanus model exhibited lower rostral strains during both types of biting, suggesting that at least this part of the face is more rigid in the australopith. High rostral rigidity may explain why strains in the postorbital bar and interorbital pillar are higher in this species: increased rostral rigidity in A. africanus may have the effect of passing strains from the mid to the upper face (see also Strait et al., 2007). Moreover, evidence that SE is lower in A. africanus than M. fascicularis during premolar biting is consistent with the hypothesis that aspects of facial form in A. africanus are adaptations to structurally reinforce the face against premolar-focused bites (Strait et al., 2009). Strait et al. (2009) have suggested that these bites may have been used to fracture the shells of large nuts and seeds that may have been critical resources during periods in which other, more preferred food items were unavailable (see below). In contrast, the hypothesis that the A. africanus facial skeleton is more rigid than that of M. fascicularis is not corroborated under molar loading. The australopith model is less rigid (i.e., has a higher SE) during molar loading than the macaque model. Moreover, in the absence of comparative data (e.g., FEMs of many macaque individuals) that would allow an assessment of whether the differences between the species are statistically signiﬁcant, the only deﬁnitive statement that can be made at present is that the relatively greater australopith rigidity under premolar loading is (three times) greater (12%) than the relative decrease in australopith rigidity (4%) under molar loading. The functional signiﬁcance of these differences in relative rigidity in the australopith and macaque models between molar and premolar biting can be appreciated when one considers the functional role of muscle recruitment during these two activities. The ability to generate powerful premolar bites on large, hard objects such as nuts determines whether an animal can access a food item. Thus, the goal of premolar biting plausibly requires recruitment of large amounts of muscle force. This is both required and facilitated by the geometry of the feeding system: that is, the load arm of the premolars is greater than that of the molars, but the jaw joints are more stable during premolar biting than during molar biting (Greaves, 1978; Spencer, 1998). In contrast, mastication along the molar toothrow acts on foods already acquired that are being processed for safe swallowing and is associated with recruitment of less muscle force than either incisor or premolar biting (Ross and Hylander, 2000; Ross, unpublished data on Cebus). Thus, the greater rigidity of the australopith facial skeleton under premolar biting is likely of greater functional importance than its decreased rigidity under molar loads. Moreover, a full interpretation of the SE results may require a consideration of the allometry of cranial architecture (see below). Differences in SE values in the A. africanus model and the M. fascicularis model, appropriately scaled to account for loading and volume differences, reﬂect the differences in the rigidity of the two skull systems under masticatory loading conditions. To assess and compare the rigidity of a particular anatomical region (i.e., the zygomatic arch) with the homologous region in another skull, one could compute the total SED of the region by integrating the SED ﬁeld provided by the ﬁnite element results over the volume of the anatomical region Vi. For four-noded tetrahedral elements, SED is constant over the element volume and, therefore, Z SEDðx; y; zÞdV ¼ SEVi ¼ Vi Mi X SEDe V e (2) e¼1 where SED (x,y,z) denotes the SED ﬁeld, SEDe and Ve are the SED and volume of element e, and the summation occurs over the Mi elements comprising the volume Vi. However, differences in performance due to shape only require accounting for volume and force differences 589 CRANIAL RIGIDITY IN AUSTRALOPITHECUS TABLE 4. Cortical bone thickness (mm) in cranial regions and body mass (kg) in selected primates Species Macaca mulattac Papio anubisc Pan troglodytesd Homo sapiensc Gorilla gorillae Vault thicknessa Torus and bar thicknessa Zygomatic thicknessa Alveolar thicknessa Muzzle thicknessa Mean male body massb Mean female body massb 2.06 1.86 1.97 2.49 1.65 2.81 1.83 2.18 2.43 2.40 1.84 1.65 1.76 2.20 2.50 1.88 1.26 1.66 1.98 2.39 1.75 1.52 1.84 1.48 2.91 6.99 23.0 59.7 57.4 169.3 4.94 13.3 45.8 49.7 75.7 a Values averaged across multiple drill sites in each region, following Wang et al. (2006). Data from Gordon (2006). c Thickness data from Wang et al. (2006). Values represent means of mixed-sex samples. d Thickness data from a single male chimpanzee. e Thickness data from a single female gorilla. b per Eq. (1) between the two volumetric regions being compared. The volumes are easily given by the sum of the element volumes for each region. Unfortunately, in a generally shaped three-dimensional (3D) region admitting a 3D stress ﬁeld contained within a larger structure, it is impossible to determine the ‘‘force" carried by this region. Thus, performances of anatomical regions based on SE will not allow a simple assessment of the mechanical impact of shape. Regardless, this could still be a useful performance measure (e.g., Farke, 2008), especially if the two systems are scaled to the same total volume and then subjected to the same total forces. Then, comparison of strain energies computed for homologous anatomical regions reﬂects a combination of shape differences and the relative way forces are transmitted through the structure. Allometry The muscle forces applied to the A. africanus model were calculated by ‘‘scaling-up" the M. fascicularis forces, according to the ratio of surface area in the two FEMs (i.e., by approximately a factor of 3). However, even though the muscle forces have been scaled isometrically, it is possible that cranial cortical bone thickness scales with negative allometry in primates, although more comparative data are needed to test this possibility. Table 4 summarizes cranial bone thickness and body mass data in ﬁve extant primates. Unfortunately, the thickness data for two species (Pan troglodytes, Gorilla gorilla) are preliminary insofar as they are derived from only one individual in each taxon. Moreover, the cortical thickness in our A. africanus model is only approximate (owing to the difﬁculty in discerning on computer topography scans the boundaries between cortical and matrixﬁlled trabecular regions), and thus is not presented. The incomplete nature of the data set therefore precludes formal regression analysis, but some general patterns are nonetheless discernable. For example, the very smallest species (M. mulatta) has moderately to very thick cortices. Furthermore, within each cranial region, the species with the thickest cortical bone exhibits values no more than 50% greater than those of the species with the thinnest cortical bone. In contrast, the species sampled here vary in body mass by more than an order of magnitude. Thus, even when taking into account the fact that thickness increases linearly while mass increases as a cube, it is clear that variation in bone thickness does not scale isometrically with bone mass and may well scale with negative allometry. Thickness contributes to bone cross-sectional area, which in turn inﬂuences stress, strain, and SE. Thus, larger primates may be predisposed to having less rigid crania, because they have proportionally thinner bones. In this context, the observation that the A. africanus model exhibits scaled SE within a few percentage points of the M. fascicularis model may be an indication of the fact that the A. africanus model, does, in fact, performs well in responding to feeding loads [although further study is needed to conﬁrm this (see below)]. Of course, thickness alone does not describe how bones deform in response to stress; variation in material properties is also critical. In this regard, a thin bone that is stiff may deform to the same degree as a thick bone that is more compliant (e.g., Wang et al., 2006). Yet, there may be a delicate balance between bone thickness and stiffness. There might be two different strategies for increasing bone or structural strength through either developing thicker yet less stiff or thinner yet denser bone, suggesting differences in bone adaptation to varying skeletal geometries and loading regimes at both phylogenetic and ontogenetic levels (Wang et al., unpublished observations). Thus, there could be regional differences in how cortical thickness and stiffness interact in macaques and australopiths, but this is difﬁcult to assess without better information about general evolutionary patterns of variation in cortical structure and material properties. Regardless, the data presented here are sufﬁcient to suggest that further investigation of the scaling of craniofacial bone thickness is warranted. The data presented here also explain why Strait et al. (2009) observed higher magnitude strains in A. africanus than in M. fascicularis. In this analysis, muscle forces in the former were equal to those in the latter scaled to approximately a factor of 3; however, in Strait et al. (2009), the forces of anterior temporalis and superﬁcial masseter in A. africanus were larger by factors of approximately 10 and 5, respectively. The reason for this is that A. africanus muscle forces were calculated using the PCSA of Pan troglodytes, and the PCSAs of these muscles in chimpanzees are much larger than they are in macaques. This is consistent with the suggestion of Anapol et al. (2008) that muscle PCSA scales with positive allometry in catarrhine primates. Thus, the scaling of PCSA may also be a factor to consider when assessing the structural performance of primate crania. The possibility that biomechanical variables like stress, strain, and SE may be inﬂuenced by the scaling of craniofacial bone thickness, and muscle PCSA is a hypothesis that can be tested by gathering more comparative data 590 STRAIT ET AL. on bone and muscle architecture, and by examining feeding biomechanics using FEA in a wide range of primates. If supported, the hypothesis has potentially far-reaching consequences. In particular, it implies that large primates are predisposed to have structurally less rigid crania in relation to the forces being applied to them. This, in turn, suggests that large species that consume resistant food items ought to be under particularly high selective pressure to evolve stress-reducing adaptations. Australopithecus africanus may be one such species. One way of testing this possibility is to compare A. africanus to other primates in the same general size range. In particular, FEAs comparing A. africanus and P. troglodytes should eliminate allometry as a confounding variable and allow a more complete test of the hypothesis that the cranium of A. africanus is structurally more rigid than those of primates lacking derived australopith facial features. Diet and Dietary Adaptations Strait et al. (2009) suggested that certain derived craniofacial features in A. africanus are adaptations for feeding on large, hard objects. This statement is not equivalent to one suggesting that such food items were frequently consumed by those hominins. The reason for this discrepancy is that there is a fundamental difference between reconstructing the diet of an extinct organism and explaining why some of its anatomical traits may have evolved. Although these goals are related, the methods frequently used to address these two questions are not equally well-suited to both. Two widely used methods of dietary reconstruction are isotopic analysis and dental microwear analysis. Dental microwear refers to the microscopic damage done to the surfaces of teeth by the foods (or other items) being consumed. Its principle strength is that it records direct information about the material properties of the objects being processed by the teeth (e.g., Scott et al., 2005; Ungar et al., 2008). Its principle weakness is that it is ephemeral; any given microwear feature may be replaced by another in a matter of days or weeks (Teaford and Oyen, 1989). In fossils, therefore, microwear is conservatively interpreted as recording information about diet only with respect to the days just before the individual in question died. Given this narrow time window, microwear preserved on any given tooth may not necessarily reﬂects the full dietary breadth of an individual or species. To compensate for this, large samples are needed to maximize the chances of adequately assessing diet, but in fossil species the potentially confounding impact of taphonomic bias should not be discounted. Isotopic analysis examines the chemical signal preserved in mineralized tissues that are left behind by the food items being consumed (e.g., Schoeninger, 1995). Strontium/calcium analysis (e.g., Sillen, 1992; Sillen et al., 1995) provides information about trophic level (e.g., carnivore, omnivore, and herbivore), but the method most widely applied to early hominins has been stable carbon isotope analysis (Lee-Thorp et al., 1994; Sponheimer and Lee-Thorp, 1999; Sponheimer et al., 2006; Van der Merwe et al., 2008), which records whether or not the individual in question consumed either plants that used the C3 or C4 photosynthetic pathways or the animals that ate those plants. The main strength of carbon isotope analysis is that it, too, pro- vides direct information about what was eaten. Moreover, the isotopic signal is not replaced; it is preserved in perpetuity once it has been established (although the signal can be impaired by diagenesis). A potential weakness is that it, like microwear analysis, provides information only about discrete time periods. Carbon isotope analyses of early hominins have typically been performed on dental enamel, and the isotopes record dietary information about the time during which the enamel was formed. Thus, the time frame of an analysis depends critically on the method used to collect the data. Data obtained from large enamel fragments contain dietary information averaged over weeks or months, whereas data obtained using laser ablation methods may provide information on the scale of days (e.g., Sponheimer et al., 2006). Of course, the ﬁne-grained time scale of the laser ablation method is also a strength insofar as it allows the assessment of seasonal ﬂuctuations in diet (Sponheimer et al., 2006). Regardless, both methods, when applied to primate teeth, only provide information about diet during the individual’s juvenile period. A second potential weakness of carbon isotope analysis is that if there is any mixture in the isotopic signal (i.e., an isotopic signature indicating the presence of both C3 and C4 foods), then it is impossible to exclude the possibility that any given food item was eaten. Dental microwear and isotopic analyses facilitate dietary reconstruction but do not directly explain adaptation. To do the latter, it is necessary to use functional morphology. Functional morphology (including biomechanics) examines how and why anatomical systems work (e.g., Bock and von Wahlert, 1965). Its primary strength is that it, among the three methods discussed here, is the only one that can provide information about why a given morphological trait may have evolved [especially when interpreted within a phylogenetic framework (e.g., Lauder, 1990)]. It is also the only one of the three that can potentially provide information on both shortand very long term time scales (e.g., bone remodeling vs. the inheritance of morphology, respectively), although it may be difﬁcult to disentangle these disparate sources of morphological change. The primary weakness of functional morphology is that it, in contrast to microwear and isotopic analysis, only provides indirect information about diet. In other words, it allows dietary inferences but does not record speciﬁc evidence of the foods that were eaten. Given the strengths and weaknesses of the three methods discussed above, what can be inferred about diet and dietary adaptations in A. africanus? This species evidently had an isotopically mixed diet (e.g., Sponheimer and Lee-Thorp, 1999). While informative, this information does not allow us to exclude any given food item from the diet. With respect to microwear (Scott et al., 2005; Ungar et al., 2008), A. africanus exhibits microwear fabrics that vary in anisotropy and have complexity values that are slightly higher than those of extant primate folivores. However, complexity in this species is, on average, lower in magnitude and less variable than that observed in extant primates said to ‘‘fall back" on hard food sources during time periods in which their preferred foods are unavailable. Scott et al. (2005) interpret these data to mean that this species fell back on tough vegetation and that hard objects comprised a comparatively minor proportion of the diet. 591 CRANIAL RIGIDITY IN AUSTRALOPITHECUS The dietary reconstruction of Scott et al. (2005) might be accurate [although the possibility that large, hard objects might not be detectable using microwear analysis (Lucas et al., 2008; Lawn and Lee, 2009) urges caution], but this is not equivalent to saying that hard objects were selectively unimportant dietary variables. Assessment of the latter possibility requires an evaluation of functional morphology. Results presented here and elsewhere (Strait et al., 2009) suggest that the facial skeleton of A. africanus is well-suited to withstand loads applied to the premolars. If derived facial traits in this species are adaptations to withstanding premolar bites, what types of food items might have been bitten? Assuming that dietary adaptations in A. africanus are related to the consumption of resistant food items, we can, as a heuristic device, classify food items into a few simple categories so as to facilitate discussion. Resistant foods can be separated into those that are ‘‘tough" or displacement-limited (foods that fail when subjected to high displacements; Lucas, 2004) and those that are ‘‘hard" or stress-limited (those that fail under the application of high forces; Lucas, 2004). Note that the terms ‘‘hard" and ‘‘tough" are imprecise in this context, because many stress-limited foods are, in fact, tough (insofar as tough is the opposite of brittle). Foods may also be classiﬁed as being either small (items that can be positioned anywhere in the oral cavity without ingestive preprocessing) or large (those that require ingestive preprocessing before they can be positioned on the molars). Given these categories, a functional assessment of early hominin dental topography argues strongly that displacement-limited foods were not selectively important components of the diet, regardless of how frequently such foods were consumed. ‘‘Gracile" australopiths, including A. africanus, exhibit reduced shearing crests on their molars relative to extant African apes (e.g., Ungar, 2004), suggesting that this reduction is, broadly speaking, phylogenetically derived. Hominin premolar occlusal topography has not been formally studied using advanced methods, but there is no reason to expect that the same results would not also be observed. Shearing crests are critical in primates for processing displacement-limited foods (e.g., Kay, 1977; Lucas, 2004), so it is very difﬁcult to argue that craniodental traits in A. africanus are adaptations for feeding on such foods because their teeth are evidently not especially well-designed for doing so. This conclusion applies even if ultimately it can be shown that occlusal topography in A. africanus is phylogenetically primitive. With the elimination of displacement-limited foods as selectively important variables, the remaining resistant foods are stress-limited. Small items seem unlikely to be sources of premolar bites, because such items can be easily positioned on the molars, where higher bite forces can typically be generated (Greaves, 1978; Smith, 1978; Spencer, 1998). By this logic, large, stress limited objects appear most likely to be the selectively important variables driving the evolution of derived facial form in A. africanus (and, possibly, other australopiths). Such food items include large nuts and seeds. After cracking the resistant outer shell with the premolars, the smaller, less resistant seed contents could have been removed manually and positioned on the molars for mastication. Dominy et al. (2008) have suggested that bulbs and corms are also hard objects that may have been selectively important for australopiths, but those foods are hard only in the sense that they are as stiff as seed kernels; they are orders of magnitude less stiff than many seed shells. The absence of a hard object microwear signal in A. africanus may be due to any of several factors: 1) large, hard objects may not induce microwear, as predicted by established principles of fracture mechanics (Lucas et al., 2008; Lawn and Lee, 2009), 2) none of the A. africanus specimens examined for microwear ate large, hard objects in the days or weeks before they died, or 3) A. africanus relied on large, hard objects less frequently than do extant primate hard object feeders (e.g., fall back episodes do not occur seasonally but rather are separated by several years). These possibilities can be evaluated through experimentation, increased sampling, and analysis of other types of evidence revealing how food items damage teeth (Lawn and Lee, 2009; Strait et al., 2009). A. africanus may have habitually eaten tough, displacement-limited vegetation, but the selective importance of those foods is likely to have been less than that of large, stress-limited foods. That a generalist species would eat considerable quantities of foods for whose consumption the species is not especially well-designed should not be surprising; generalist species do not have to do many things well, they merely have to do many things adequately. If they do something especially well, it should reﬂect a behavior upon which their survival periodically depends. The early hominin Paranthropus bosei provides a particularly apt example. Microwear data gathered from several specimens have been interpreted to suggest that hard objects were not habitually consumed by this species (Ungar et al., 2008). However, qualitatively different microwear data have just been presented for P. boisei from Konso, Ethiopia (Suwa et al., 2009) that may be consistent with hard object feeding. Given that dental topography in P. boisei is more bunodont than that of any other hominin, it would appear that members of this species in many Rift Valley localities were eating a fair amount of abrasive, possibly tough foods in spite of their dental topography. However, at other localities that exhibit different environmental conditions (as at Konso; Suwa et al., 1995), their teeth and faces were well-suited to cope with the challenges of consuming the hard foods upon which their survival may have depended. CONCLUSIONS FEA was used to compare the overall structural performance of the crania of M. fascicularis and A. africanus during feeding. Strain and SE data were consistent with the idea that the face of this australopith is structurally reinforced to withstand premolar loads. However, scaled SE in A. africanus was greater than that of M. fascicularis during molar biting, a result that was inconsistent with the hypothesis that the cranium of the former would be more rigid than that of the latter. A possible explanation of this ﬁnding is that the thickness of cranial bone may scale with negative allometry in primates. Additional data on bone thickness are needed to test this possibility, but, if true, an implication is that analyses of structural rigidity in primate crania will be easiest to interpret when comparing species within narrow size ranges. 592 STRAIT ET AL. ACKNOWLEDGMENTS The authors thank Francis Thackeray and Stephanie Potze from the Transvaal Museum, Northern Flagship Institution, Pretoria for access to fossils, and the staff of Selby Clark Clinic, Johannesburg, and the Little Company of Mary Hospital, Pretoria for the scanning of specimens. LITERATURE CITED Anapol F, Shahnoor N, Ross CF. 2008. Scaling of reduced physiologic cross-sectional area in primate muscles of mastication. In: Vinyard CJ, Ravosa MJ,Wall CE, editors. Primate craniofacial function and biology. New York: Springer. p 201–216. Ashman RB, Cowan SC, Van Buskirk WC, Rice JC. 1984. A continuous wave technique for measurement of the elastic properties of cortical bone. J Biomech 17:349–361. Bock WJ, von Wahlert G. 1965. Adaptation and the form-function complex. Evolution 19:269–299. Bourke J, Wroe S, Moreno K, McHenry C, Clausen P. 2008. Effects of gape and tooth position on bite force and skull stress in the dingo (Canis lupus dingo) using a 3-dimensional ﬁnite element approach. PLoS One 3:e2200. Bouvier M, Hylander WL. 1981. The inﬂuence of bone strain levels on levels of remodeling in primates. J Morphol 167:1–12. Dominy NJ, Vogel ER, Yeakel JD, Constantino P, Lucas PW. 2008. Mechanical properties of plant underground storage organs and implications for dietary models of early hominins. Evol Biol 35:159–175. Dumont ER, Grosse IR, Slater GJ. 2009. Requirements for comparing the performance of ﬁnite element models of biological structures. J Theor Biol 256:96–103. Dumont ER, Piccirillo J, Grosse IR. 2005. Finite-element analysis of biting behavior and bone stress in the facial skeletons of bats. Anat Rec 283A:319–330. Farke AA. 2008. Frontal sinuses and head-butting in goats: a ﬁnite element analysis. J Exp Biol 211:3085–3094. Gordon AD. 2006. Scaling of size and dimorphism in primates II: macroevolution. Int J Primatol 27:63–105. Greaves WS. 1978. The jaw lever system in ungulates: a new model. J Zool (London) 184:271–285. Huiskes R, Chao EYS. 1983. A survey of ﬁnite element analysis in orthopedic biomechanics: the ﬁrst decade. J Biomech 16:385–409. Hylander WL. 1977. In vivo bone strain in the mandible of Galago crassicaudatus. Am J Phys Anthropol 46:309–326. Hylander WL. 1984. Stress and strain in the mandibular symphysis of primates: a test of competing hypotheses. Am J Phys Anthropol 64:1–46. Hylander WL, Johnson KR. 1997. In vivo bone strain patterns in the zygomatic arch of macaques and the signiﬁcance of these patterns for functional interpretations of craniofacial form. Am J Phys Anthropol 120:203–232. Hylander WL, Picq PG, Johnson KR. 1991. Masticatory-stress hypotheses and the supraorbital region of primates. Am J Phys Anthropol 86:1–36. Kay RF. 1977. The evolution of molar occlusion in the Cercopithecidae and early catarrhines. Am J Phys Anthropol 46:327–352. Kupczik K, Dobson CA, Fagan MJ, Crompton RH, Oxnard CE, O’Higgins P. 2007. Assessing mechanical function of the zygomatic region in macaques: validation and sensitivity testing of ﬁnite element models. J Anat 210:41–53. Kupczik K, Dobson C, Phillips R, Oxnard C, Fagan M, O’Higgins P. 2009. Masticatory loading and bone adaptation in the supraorbital torus of developing macaques. Am J Phys Anthropol 139: 193–203. Lauder G. 1990. Functional morphology and systematics: studying functional patterns in an historical context. Ann Rev Ecol Syst 21:317–340. Lawn B, Lee J. 2009. Analysis of fracture and deformation modes in teeth subjected to occlusal loading. Acta Biomater 5:2213–2221. Lee-Thorp JA, Van der Merwe NJ, Brian CK. 1994. Diet of Australopithecus robustus at Swartkrans from stable carbon isotopic analysis. J Hum Evol 27:361–372. Lucas P. 2004. Dental functional morphology: how teeth work. Cambridge: Cambridge University Press. Lucas PW, Constantino P, Wood B, Lawn B. 2008. Dental enamel as a dietary indicator in mammals. Bioessays 30:374–385. McHenry C, Wroe S, Clausen PD, Moreno K, Cunningham E. 2007. Supermodeled sabercat, predatory behavior in Smilodon fragilis revealed by high resolution 3D computer simulation. Proc Natl Acad Sci USA 104:16010–16015. Moazen M, Curtis N, Evans SE, O’Higgins P, Fagan MJ. 2008. Combined ﬁnite element analysis and multibody dynamics analysis of biting in a Uromastyx hardwickii lizard skull. J Anat 213:499–508. Moazen M, Curtis N, O’Higgins P, Evans SE, Fagan MJ. 2009b. Biomechanical assessment of evolutionary changes in the lepidosaurian skull. Proc Natl Acad Sci USA 106:8273–8277. Moazen M, Curtis N, O’Higgins P, Jones MEH, Evans SE, Fagan MJ. 2009a. Assessment of the role of sutures in the lizard skull: a computer modeling study. Proc R Soc B Biol Sci 276:39–46. Moreno K, Wroe S, Clausen P, McHenry C, D’Amore DC, Rayﬁeld EJ, Cunningham E. 2008. Cranial performance in the Komodo dragon (Varanus komodoensis) as revealed by high resolution 3-D ﬁnite element analysis. J Anat 212:736–746. Pierce SE, Angielczyk KD, Rayﬁeld EJ. 2008. Patterns of morphospace occupation and mechanical performance in extant crocodilian skulls: a combined geometric morphometric and ﬁnite element modeling approach. J Morphol 269:840–864. Rak Y. 1983. The australopithecine face. New York: Academic Press. Rayﬁeld EJ. 2001. Cranial design and function in a large theropod dinosaur. Nature 409:1033–1037. Rayﬁeld EJ. 2004. Cranial mechanics and feeding in Tyrannosaurus rex. Proc R Soc B 271:1451–1459. Rayﬁeld EJ. 2005a. Aspects of comparative cranial mechanics in the theropod dinosaurs Coelophysis, Allosaurus and Tyrannosaurus. Zool J Linn Soc 144:309–316. Rayﬁeld EJ. 2005b. Using ﬁnite-element analysis to investigate suture morphology: a case study using large carnivorous dinosaurs. Anat Rec 283A:349–365. Rayﬁeld EJ. 2007. Finite element analysis and understanding the biomechanics and evolution of living and fossil organisms. Annu Rev Earth Planet Sci 35:541–576. Rayﬁeld EJ, Milner AC. 2008. Establishing a framework for archosaur cranial mechanics. Paleobiology 34:494–515. Rayﬁeld EJ, Milner AC, Xuan VB, Young PG. 2007. Functional morphology of spinosaur ‘crocodile-mimic’ dinosaurs. J Vert Paleontol 27:892–901. Richmond BG, Wright BW, Grosse I, Dechow PC, Ross CF, Spencer MA, Strait DS. 2005. Finite element analysis in functional morphology. Anat Rec 283A:259–274. Ross CF. 2001. In vivo function of the craniofacial haft: the interorbital ‘‘pillar.’’ Am J Phys Anthropol 116:108–139. Ross CF, Hylander WL. 2000. Electromyography of the anterior temporalis and masseter muscles of owl monkeys (Aotus trivirgatus) and the function of the postorbital septum. Am J Phys Anthropol 112:455–468. Ross CF, Metzger KA. 2004. Bone strain gradients and optimization in vertebrate skulls. Ann Anat 186:387–396. Ross CF, Patel BA, Slice DE, Strait DS, Dechow PC, Richmond BG, Spencer MA. 2005. Modeling masticatory muscle force in ﬁniteelement analysis: sensitivity analysis using principal coordinates analysis. Anat Rec 283A:288–299. Schoeninger MJ. 1995. Stable isotope studies in human evolution. Evol Anthropol 4:83–98. Scott RS, Ungar PS, Bergstrom TS, Brown CA. 2005. Dental microwear texture analysis shows within-species diet variability in fossil hominins. Nature 436:693–695. Sillen A. 1992. Strontium-calcium ratios (Sr/Ca) of Australopithecus robustus and associated fauna from Swartkrans. J Hum Evol 23:495–516. CRANIAL RIGIDITY IN AUSTRALOPITHECUS Sillen A, Hall G, Armstrong R. 1995. Strontium calcium ratios (Sr/ Ca) and strontium isotopic ratios (86Sr/87Sr) of Australopithecus robustus and Homo sp. in Swartkrans. J Hum Evol 28:277–285. Smith RJ. 1978. Mandibular biomechanics and temporomandibular joint function in primates. Am J Phys Anthropol 49:341–350. Spencer MA. 1998. Force production in the primate masticatory system: electromyographic tests of biomechanical hypotheses. J Hum Evol 34:25–54. Sponheimer M, Lee-Thorp JA. 1999. Isotopic evidence for the diet of an early hominid, Australopithecus africanus. Science 283:368–370. Sponheimer M, Passey BH, DeRuiter DJ, Guatelli-Steinberg D, Cerling TE, Lee-Thorp JA. 2006. Isotopic evidence for dietary variability in the early hominin Paranthropus robustus. Science 314:980–982. Strait DS, Richmond BG, Spencer MA, Ross CF, Wood BA. 2007. Masticatory biomechanics and its relevance to early hominid phylogeny: an examination of palate thickness using ﬁnite element analysis. J Hum Evol 52:589–599. Strait DS, Wang Q, Dechow PC, Ross CF, Richmond BG, Spencer MA, Patel BA. 2005. Modeling elastic properties in ﬁnite element analysis: how much precision is needed to produce an accurate model? Anat Rec 283A:275–287. Strait DS, Weber GW, Neubauer S, Chalk J, Richmond BG, Lucas PW, Spencer MA, Schrein C, Wright BW, Ross CF, Dechow PC, Wang Q, Grosse I, Byron C, Wood BA, Lawn B, Constantino P, Slice DE, Smith AL. 2009. The feeding biomechanics and dietary ecology of Australopithecus africanus. Proc Natl Acad Sci USA 106:2124–2129. Strait DS, Wright BW, Richmond BG, Ross CF, Dechow PC, Spencer MA, Wang Q. 2008. Craniofacial strain patterns during premolar loading: implications for human evolution. In: Vinyard CJ, Ravosa MJ, Wall CE, editors. Primate craniofacial function and biology. New York: Springer. p 173–198. 593 Suwa G, Asfaw B, Beyene Y, White TD, Katoh S, Nagoka S, Nakaya H, Uzawa K, Renne P, WoldeGabriel W. 1995. The ﬁrst skull of Australopithecus boisei. Nature 389:489–492. Suwa G, Kono RT, Simpson SW, Asfaw B, Lovejoy CO, White TD. 2009. Paleobiological implications of the Ardipithecus ramidus dentition. Science 326:94–99. Teaford MF, Oyen OJ. 1989. In vivo and in vitro turnover in dental microwear. Am J Phys Anthropol 80:447–460. Ungar P. 2004. Dental topography and diets of Australopithecus afarensis and early Homo. J Hum Evol 46:605–622. Ungar PS, Grine FE, Teaford MF. 2008. Dental microwear and diet of the Plio-Pleistocene hominin Paranthropus boisei. PLOS One 3:e2044. Van der Merwe NJ, Masao FT, Bamford MK. 2008. Isotopic evidence for contrasting diets of early hominins Homo habilis and Australopithecus boisei of Tanzania. S Afr J Sci 104:153–155. Wang Q, Dechow PC. 2006. Elastic properties of external cortical bone in the craniofacial skeleton of the rhesus macaque. Am J Phys Anthropol 131:402–415. Wang Q, Strait DS, Dechow PC. 2006. A comparison of cortical elastic properties in the craniofacial skeletons of three primate species and its relevance to human evolution. J Hum Evol 51:375– 382. Wroe S. 2007. Cranial mechanics compared in extinct marsupial and extant African lions using a ﬁnite-element approach. J Zool 274:332–339. Wroe S, Huber DR, Lowry M, McHenry C, Moreno K, Clausen P, Ferrara P, Cunningham E, Dean MN, Summers AP. 2008. Threedimensional computer analysis of white shark jaw mechanics: how hard can a great white bite? J Zool 276:336–342. Wroe S, Moreno K, Clausen P, McHenry C, Curnoe D. 2007. Highresolution three-dimensional computer simulation of hominid cranial mechanics. Anat Rec 290:1248–1255.