Biting mechanics and niche separation in a specialized clade of primate seed predators

We analyzed feeding biomechanics in pitheciine monkeys (Pithecia, Chiropotes, Cacajao), a clade that specializes on hard-husked unripe fruit (sclerocarpy) and resistant seeds (seed predation). We tested the hypothesis that pitheciine crania are well-suited to generate and withstand forceful canine and molar biting, with the prediction that they generate bite forces more efficiently and better resist masticatory strains than the closely-related Callicebus, which does not specialize on unripe fruits and/or seeds. We also tested the hypothesis that Callicebus-Pithecia-Chiropotes-Cacajao represent a morphocline of increasing sclerocarpic specialization with respect to biting leverage and craniofacial strength, consistent with anterior dental morphology. We found that pitheciines have higher biting leverage than Callicebus and are generally more resistant to masticatory strain. However, Cacajao was found to experience high strain magnitudes in some facial regions. We therefore found limited support for the morphocline hypothesis, at least with respect to the mechanical performance metrics examined here. Biting leverage in Cacajao was nearly identical (or slightly less than) in Chiropotes and strain magnitudes during canine biting were more likely to follow a Cacajao-Chiropotes-Pithecia trend of increasing strength, in contrast to the proposed morphocline. These results could indicate that bite force efficiency and derived anterior teeth were selected for in pitheciines at the expense of increased strain magnitudes. However, our results for Cacajao potentially reflect reduced feeding competition offered by allopatry with other pitheciines, which allows Cacajao species to choose from a wider variety of fruits at various stages of ripeness, leading to reduction in the selection for robust facial features. We also found that feeding biomechanics in sympatric Pithecia and Chiropotes are consistent with data on food structural properties and observations of dietary niche separation, with the former being well-suited for the regular molar crushing of hard seeds and the latter better adapted for breaching hard fruits.

Introduction research should be to gain a broader understanding of the application of modeling techniques to the study of craniofacial biomechanics and diet in living primates (e.g., [55][56][57][58]).
We examine feeding biomechanics in the Pitheciinae (Pithecia, Chiropotes, Cacajao) relative to the only other member of the Pitheciidae, Callicebus. Simulations of forceful canine biting (as when breaching an unripe fruit) and molar biting (as when crushing a resistant seed) were performed using FEA. Previous analyses of biting mechanics in pitheciines [21,31,48] have relied on photographs and 2D estimates of lever/load arms, using methods that consider only the anterior-most cranial attachment of each muscle [59]. Our 3D analysis of feeding biomechanics considers entire muscle origins, as well as the orientation of muscle vectors. FEA also facilitates comparisons of structural strength. Specifically, we test the hypothesis (Hypothesis 1) that pitheciines are well-suited to generate and withstand forceful canine and molar biting, with the prediction that pitheciine species will exhibit greater bite force leverage and capacity to resist masticatory strain relative to Callicebus. We further test the hypothesis (Hypothesis 2) that Callicebus-Pithecia-Chiropotes-Cacajao represent a morphocline of increasing sclerocarpic specialization [10], with the prediction that these species will follow a trend of increasing bite force leverage and craniofacial strength. Smith et al. [57] show that intraspecific differences in craniofacial shape can result in high levels of variation in strain magnitudes during feeding, but that the distribution of strain concentrations is relatively conserved within species. To partially account for cranial shape variation within each of Callicebus, Pithecia, Chiropotes, and Cacajao, we collected 3D landmark data using Checkpoint software (Stratovan) from a sample of 21 pitheciid (i.e., Callicebinae + Pitheciinae) specimens (Table 1) surface-rendered using CT image stacks available on the Morpho-Source (www.morphosource.org), DigiMorph (www.digimorph.org), and Primate Research Institute (dmm.pri.kyoto-u.ac.j) databases. Only fully adult specimens preserving the mandible and free of damage (i.e., suitable for FEA) were included in this shape analysis. A formalinfixed cadaveric head of a male Chiropotes satanas (courtesy of J. Fleagle, Stony Brook University) was also included in the sample. This specimen was also used to collect jaw adductor muscle forces (see below).

Selection of specimens for FEA
The landmark configuration included 51 fixed landmarks and 365 sliding semilandmarks along 22 curves (Table 2). Semilandmarks were permitted to slide along homologous curves based on minimized bending energy and were thus also considered homologous [62]. Shape coordinates of the landmarks were subjected to Generalized Procrustes Analysis (GPA) to ensure that shape was the only variable among specimens by translating the centers of the models to the same origin, scaling them to a common size, and rotating them to a best-fit using a least-squares calculation [63,64]. The Procrustes coordinates were then analyzed using Principal Component Analysis (PCA) using the R [65] "Geomorph" package [66]. The purpose of this analysis was to account for variation within each of the four groups examined, so we performed separate PCAs for each group and chose the two specimens with the most positive (PC1+) and most negative (PC1-) principal component scores along the first axis (Fig 1). These specimens were then used to build eight finite element models (FEMs). It should be noted that our analysis of intraspecific shape variation used in choosing specimens for FEA is limited by small sample sizes and that we have not comprehensively assessed shape variation in these species. It is therefore possible that our biting simulations do not capture the full range of mechanical variation within pitheciids. However, high levels of intraspecific shape variation are not always associated with high levels of mechanical variation [67] and it is not uncommon for studies such as the present one to include single specimens per species (e.g., [53,55,68]), due to the time-consuming nature of model construction. Nonetheless, we have attempted to account for intraspecific shape variation by including the two most distinct crania per group from among the previously-scanned specimens available to us.

Finite element model construction
CT data on the eight specimens chosen for analysis were used to generate solid (volumetric) meshes using a combination of thresholding in Mimics v 18.0 (Materialise, Ann Arbor, MI, USA), surface editing in Geomagic Studio 2014 (Research Triangle Park, NC, USA), and solidmeshing in 3-Matic v 10.0 (Materialise, Ann Arbor, MI, USA), largely following the methods outlined by Smith et al. [7,57]. Differences in scan resolution and therefore the quality of the models were reduced before solid-meshing by first re-meshing the surfaces using a target polygon edge length of 0.5 mm. This resulted in solid models of similar mesh density (between 1,236,492 in the smaller Callicebus and up to 2,055,744 elements in Cacajao). We created separate volumes of 4-noded tetrahedral (tet4) elements for each of the teeth, with each tooth consisting of one volume for the pulp cavity nested within a volume for the dental tissue (dentine + enamel). A periodontal ligament (PDL) was also included for each tooth by creating thin volumes (0.2 mm [69]) between the alveoli and tooth roots. Trabecular density in the species included in our sample was low, so we chose not to model whole volumes of trabeculae nested within the cortical bone volume (e.g., [7,54,57,67]). However, we did model trabecular vacuities in the maxillary and zygomatic regions, as opposed to modeling these areas as solid bone. Solid models were imported as Nastran (NAS) files into Strand7 (Strand7 Pty Ltd, NSW, Sydney, Australia) FEA software. The separate volumes for bone, teeth, and PDL were "zipped" to form a contiguous mesh. An enamel "cap" was also created during this stage by selecting surface elements on the tooth crowns and assigning them to their own group and set of properties. As discussed below, our comparisons of craniofacial stiffness (strength) focus on shape-related mechanical differences, so we assigned all models the same set of homogeneous and isotropic properties from the literature (Table 3). Muscle forces were also scaled as to remove the effects of size from the mechanical results (see below).

Muscle forces and constraints
Jaw adductor muscle forces were applied to each FEM for the temporalis, masseter, and medial pterygoid under the assumption that the chewing muscles were acting at peak activity levels on both sides of the cranium. These loads allow an estimate of the maximum bite force potential. As noted above, our comparisons focus on differences in mechanical performance that are purely the result of differences in shape. We removed the effects of size from the strain results by scaling forces based on differences in model volume [74]. The model of a male Chiropotes (PC1-) was chosen as the "baseline" for muscle force scaling. Baseline forces applied to this model were collected from a formalin-fixed cadaveric head of a male Chiropotes satanas, which was also included in the shape analysis described above.
We microCT scanned the cadaveric specimen of Chiropotes at Penn State's Center for Quantitative Imaging and collected cross-sectional area (CSA) data on the temporalis and masseter muscles. The muscles on the left side of the head had been previously dissected, preserving an edge outlining the origin and insertion areas that helped with applying muscles to the FEMs. Much of the cervical region had also been dissected, with apparent damage to the pterygoid muscles. Before scanning, the skin and soft tissues overlying the temporalis and masseter muscles on the right side were freed, exposing the muscles. The masseter and temporalis Table 2. Landmarks and semilandmarks included in the shape analysis. Landmark definitions follow White et al. [60] and Baab [61]). For each plot, crania at the positive and negative ends of the PC1 and PC2 axes describe shape change along these axes, warped onto the specimen closest to the group centroid (i.e., shortest distance from group centroid). The specimens with the most positive and most negative principal component scores along PC1 were selected for use in FEA. In Callicebus, PC1 mainly captures variation in neurocranial height and length and facial length, with longer and lower crania with slightly longer faces toward negative scores. PC2 explains some differences in facial width and orbit, with wider faces toward minimum scores. In Pithecia, PC1 describes differences in facial and neurocranial width, with wider crania toward positive scores. PC2 reflects aspects of neurocranial and facial variation, with the neurocranium extended superoinferiorly and face extended inferoanteriorly toward positive scores. In Chiropotes, PC1 captures some differences in neurocranial shape and facial projection, with longer crania and faces toward positive scores. Faces are slightly wider toward positive scores along PC2. Cacajao is similar to Chiropotes, except that longer crania and face are found along the negative end of PC1. muscles, as well as the skull, were then segmented from the CT images and converted into a 3D surface model (Fig 2A) using Mimics software. CSAs were then calculated in Geomagic Studio at the thickest part of each muscle, perpendicular to the primary orientation of the muscle fibers. Our CSAs were very similar to physiological cross-sectional areas (PCSAs) reported by Anapol et al. [75] for both temporalis (4.21 cm 2 vs. 4.26 cm 2 ) and masseter (2.00 cm 2 vs. 2.08 cm 2 ). Therefore, we used the proportional relationship between the primary three jaw adductors of Chiropotes reported by Anapol et al. [75] to calculate a CSA for the medial pterygoid in our specimen (1.54 cm 2 ). CSAs were then used to calculate forces in Newtons (N) such that each cm 2 of muscle was equivalent to 30 N [76]. The "baseline" model of Chiropotes PC1was then assigned these unscaled forces, and the remaining models were applied total forces that were either scaled up or down based on differences in model volume to the two-thirds power (Table 4). This muscle force scaling procedure removes the effects of differences in model size on stress and strain from the mechanical results [74,77]. Although the FEMs were assigned comparable muscles forces by our scaling procedure, differences in jaw adductor muscle force ratios between species are likely to have an impact on mechanical performance. Notably, Anapol et al. [75] report a much greater temporalis/masseter PCSA ratio in Chiropotes (2.11) as compared to both Pithecia (1.23) and Callicebus (1.54). We measured a similarly high ratio in our cadaveric specimen (2.05). Anapol et al. [75] do not include Cacajao, but Cachel [78] reports an even larger temporalis/masseter ratio (2.87) based on dry weight measurements. Therefore, we performed a second batch (Batch 2) of biting simulations in order to account for differences in muscle force ratios by redistributing the total muscle forces in Callicebus, Pithecia, and Cacajao according to these data (see Table 4). Taylor et al. [79] also analyzed jaw muscle architecture in a sample of platyrrhines, including Callicebus and all three pitheciine genera. Their data show that the ratio of the temporalis and superficial part of the masseter was similarly high in Cacajao (2.30) and Chiropotes (2.14), as compared with the lower values in Pithecia (1.70) and Callicebus (1.60). However, the PCSA values reported by Taylor et al. [79] for pitheciids differ notably from those published in earlier studies. In particular, the PCSA values for the jaw adductors in Callicebus are around five times greater than those in Anapol et al. [75]. Additionally, Chiropotes and Pithecia have much more similarly-sized muscles in the Taylor et al. [79] study, with smaller values reported for Chiropotes and larger values for Pithecia. These discrepancies are likely the result of age-related muscle loss in the captive animals that were included in their sample, which the authors note with reference to their pitheciid sample, although it is unclear which specimens were affected by this. For these reasons, and because Taylor et al. [79] did not include deep masseter or medial pterygoid in their analysis, we did not incorporate these data into our study.
For all analyses, groups of plate elements representing each muscle's origin (Fig 2B and 2C) were created by tessellating the surface faces of tet4 elements and modeling them as 3D membrane (thickness = 0.0001 mm; E = 17.3 GPa; v = 0.28). These muscle origins were based on photographs taken during dissections of the Chiropotes specimen discussed above and four other specimens housed at Stony Brook University (two specimens each of Pithecia and Chiropotes), as well as published muscle maps [80]. Using Boneload [81], forces for each muscle plate group were then applied as tractions directed toward their respective insertions on the mandible. Insertion sites were defined using focal coordinates corresponding to the centroid of each muscles' insertion area, with the mandibles of all models set to the same gape angle of 12˚between the tips of the P 3 cusps (see Fig 2C). Adducting the mandible to this degree provided enough clearance for the canines in pitheciines so that they could be used in sclerocarpy, with a need for large gapes lessened by the lateral splay of the canines. This angle is also smaller than but near to the maximum gape angles used by Callicebus and Pithecia   1 FEMs of Callicebus, Pithecia, and Cacajao were run twice. The first batch (Batch 1) assigned models total muscle forces that were scaled from Chiropotes PC1-. For the second batch (Batch 2), total muscle forces were scaled following the same procedure, but forces were redistributed according to species-specific muscle force ratios [75,78]. See main text for further details. 2 Baseline FEM for muscle force scaling. https://doi.org/10.1371/journal.pone.0190689.t004 during ingestion in captive conditions [82]. During muscle loading, the models were oriented to a line best fit to the postcanine occlusal plane [83]. Models were subjected to separate trials of unilateral canine biting by constraining a single node from vertical displacement at the left canine tip. Molar biting was analyzed by constraining a single node in the center of the left M 2 . During each load case, a single node was also constrained against translation in all directions at the working-and balancing-side temporomandibular joint (TMJ), using the position of the condyles as a guide. These constraints create an axis of rotation around the TMJs, inducing deformation in the craniofacial skeleton and generating reaction forces at the constrained nodes upon the application of muscle forces.

Analysis of model output parameters
We compared mechanical performance in our FEMs using data on strain magnitudes and bite force leverage. Global von Mises strains were examined using color-coded strain maps, which provide information on both strain magnitude and the spatial patterning of strain concentrations. Strain data were also collected from each model at 20 sites across the craniofacial skeleton (see below). These locations include those used in previous analyses of primate feeding biomechanics (e.g., [56,57,84,85]). Data on reaction forces generated at the constrained teeth and two TMJs were recorded in Newtons (N). Reaction forces at the left canine and M 2 were recorded relative to the occlusal plane, while reaction forces at the left and right jaw joints were recorded and compared relative to a user-defined "triangle of support" Cartesian coordinate system, with one of three axes perpendicular to a reference plane defined by the "triangle of support" formed by the constrained nodes at the bite point and two articular eminences [7]. The efficiency of bite force production at a given bite point in each model was also compared using the mechanical advantage (MA), a measure of leverage, calculated as the ratio of bite force (output) to muscle force (input).

Results
Color maps of von Mises microstrain during the first set of canine and M 2 analyses (Batch 1, without species-specific muscle force ratios) are shown in Fig 3. During canine biting, large strain were generated along the working-side (left) nasal margin and infraorbital region of Callicebus. Strains are lower in the sakis and bearded sakis, but the uakaris experienced large strain magnitudes in the zygomatic and interorbital regions, as well as high strains along the nasal margin, corresponding to the canine root. Differences between taxa were less pronounced for M 2 biting, but the color maps indicate that strains were generally lowest in Chiropotes. Callicebus exhibits elevated strain concentrations in the working zygoma and at the medial infraorbital, but high strain magnitudes also occur in Cacajao surrounding the intersection of the temporal and frontal processes of the zygomatic (i.e., the jugal region), as well as in Pithecia near the lateral infraorbital superior to the working zygomatic root.
These results are supported by von Mises microstrain data collected from 20 craniofacial sites (Fig 4, Table 5). Of these 20 locations, peak strains during canine biting were highest in Callicebus at 12, with most of these well above and not overlapping with the ranges of other taxa. The working nasal margin of Callicebus (sites 10 and 12) experienced particularly high strain magnitudes. Cacajao experienced the highest strain at seven sites, notably the working infraorbital (site 14) and zygoma (site 16). Pithecia experienced the highest strain at only one site, the balancing-side dorsal orbital (site 3). However, strains were overall lowest in Pithecia (lowest at nine sites), followed by Chiropotes (lowest at six sites) during the canine bite. Only site 11 followed the predicted Callicebus-Pithecia-Chiropotes-Cacajao morphocline of increasing stiffness (i.e., decreasing strain), whereas site 18 experienced a reverse trend and 8 others (sites 1, 6,8,12,13,15,16,18) show a reverse trend within pitheciines (Cacajao-Chiropotes-Pithecia). For M 2 biting, strain magnitudes were greatest in Callicebus at 10 sites, while  Cacajao generated the highest strain at 7 sites. Although Chiropotes and Pithecia exhibited high stiffness across much of the face, three sites (sites 2, 14, 18) experienced high strain magnitudes. Overall, strain was lowest in Chiropotes during this load case.
Data on bite force production and joint reaction forces are shown in Table 6. When not accounting for species-specific muscle force ratios (Batch 1), we found that the mechanical efficiency of canine biting increased from Callicebus to Pithecia to Chiropotes, but Cacajao exhibited the same efficiency as Chiropotes. A similar pattern describes second molar biting, except with higher MA in Chiropotes than Cacajao. As predicted by the constrained lever model of feeding biomechanics [86,87], canine biting generated strongly compressive reaction forces at both jaw joints. However, both models of Chiropotes and Cacajao, and to a much lesser extent one Pithecia model (PC1+), experienced distractive (tensile) reaction forces at the working jaw joint when biting at the molar. The redistribution of temporalis and masseter muscle forces in Callicebus, Pithecia, and Cacajao according to species-specific muscle force ratios (Batch 2) had a noticeable effect on the relative differences between models, but did not drastically alter the pattern observed in the Batch 1 results. In both Callicebus and Pithecia, strain was found to increase during both canine and M 2 biting, particularly in the zygoma and infraorbital regions, whereas strain in these areas experienced a slight decrease in Cacajao (Fig 5, Table 7). Of the 20 locations sampled, strains during canine biting were greatest in Callicebus at 13, with most of these well above and not overlapping with the ranges of other taxa. Cacajao experienced the highest strain at six sites, whereas Pithecia experienced the highest strain at only one site. Strains were overall lowest in Chiropotes (lowest at nine sites) and Pithecia (lowest at seven sites). As with the Batch 1 results, only site 11 followed the predicted Callicebus-Pithecia-Chiropotes-Cacajao trend of increasing stiffness (decreasing strain). Site 18 experienced a reverse trend and five others show a reverse pattern within pitheciines (Cacajao-Chiropotes-Pithecia). During M 2 biting, strain magnitudes were greatest in Callicebus at 12 sites, while Cacajao generated the highest strain at five sites. Although Chiropotes and Pithecia once again exhibited high stiffness across much of the face, three sites (sites 3, 14, 18) experienced high strain magnitudes. Overall, strain was lowest in Chiropotes during this load case. With respect to bite force, both canine and M 2 MA were found to increase in Callicebus and Pithecia, whereas MA slightly decreased in Cacajao when applying species-specific muscle force ratio data (see Table 6). Table 6. Bite force production. Bite force (BF), mechanical advantage (MA), working-side TMJ reaction force (WJRF), and balancing-side TMJ reaction force (BJRF) for canine and molar (M 2 ) biting. All forces are in Newtons (N), with positive values indicating compression and negative values indicating tension. The MA, a measure of biting leverage or efficiency, was calculated as the ratio of BF to total input muscle force.  Models are shown at roughly the same facial height (i.e., not to scale) to accentuate similarities and differences in strain distribution.

Discussion
We analyzed feeding biomechanics in pitheciine monkeys (Pithecia, Chiropotes, Cacajao), a clade that specializes on hard-husked unripe fruit (sclerocarpy) and mechanically resistant seeds (seed predation). We tested the hypothesis (Hypothesis 1) that pitheciine crania are wellsuited to generate and withstand forceful canine and molar biting, with the prediction that Pitheciine feeding biomechanics pitheciine species would generate bite forces more efficiently and would better resist masticatory strains relative to the closely-related Callicebus, which does not specialize on unripe fruits and/or seeds. We also tested the hypothesis (Hypothesis 2) that Callicebus-Pithecia-Chiropotes-Cacajao represent a morphocline of increasing sclerocarpic specialization with respect to bite force leverage and craniofacial strength, consistent with Kinzey's [10] proposed morphocline of anterior dental specialization. We found that pitheciines generate bite forces more efficiently than Callicebus, supporting the predictions of Hypothesis 1. All three pitheciine taxa, particularly Chiropotes and Cacajao, exhibited elevated mechanical advantage at both the canine and second molar bite points. This finding agrees with earlier studies of pitheciine feeding biomechanics using two-dimensional (2D) estimates of leverage and load arms [21,31,48], providing further evidence for the relationship between diet and bite force efficiency in primates that exploit foods that are hard or difficult to crack open (see also [88,89]).
We found that pitheciines experienced generally lower von Mises microstrain magnitudes than Callicebus, with the possible exception of Cacajao. During both biting simulations, Pithecia and Chiropotes generated the lowest strain at almost every sampled region. However, uakaris experienced the highest strain magnitudes at several craniofacial sites examined during both canine and molar biting, making them second to Callicebus in terms of craniofacial "weakness". Further, examination of von Mises strain during canine biting in Cacajao and Callicebus (see Fig 3) reveals regions of higher strain in the former around the jugal region and the interorbital/glabellar region. Therefore, Cacajao is arguably less strong than Callicebus depending on the region being compared. These results provide mixed support for Hypothesis 1.
The relative differences between models did not change much with the inclusion of speciesspecific muscle force ratio data (i.e., Batch 2). However, bite force leverage and strain did increase to a small degree in both Callicebus and Pithecia, while these metrics were both found to decrease slightly in Cacajao (see Fig 5 and Tables 6 and 7). These changes are most apparent in the zygoma, particularly the superior root of the zygomatic arch, and infraorbital regions. In Callicebus and Pithecia, the observed changes reflect a decrease in the temporalis force and increase in the masseter muscle force, whereas forces in Cacajao were redistributed to have higher temporalis and lower masseter forces. These results support previous studies suggesting that inferior bending of the zygomatic arch under the pull of the masseter muscle force and the resulting frontal shearing of the infraorbital and zygoma are predominant loading regimes in primates [56], including humans [67,90,91]). The arch is potentially stabilized by the tensile strength of the temporalis fascia [92], which inserts onto its superior border. However, previous FEA studies of primate feeding that did not include the temporalis fascia (e.g., [56, [93][94][95] generated strains more similar in magnitude to those collected during in vivo bone strain experiments [84,85,96]. Therefore, we did not feel that it was necessary to include this structure in our FEMs. Given the results discussed above, we find limited support for of Hypothesis 2, that mechanical performance would follow Kinzey's [10] proposed Callicebus-Pithecia-Chiropotes-Cacajao morphocline of sclerocarpic specialization, developed on the basis of anterior dental specialization. Consistent with our muscle force scaling approach, absolute bite forces increased with increasing model size, a trend that follows the predicted morphocline (see Table 5). Size alone may therefore allow uakaris to access the hardest-husked fruits, although Taylor et al. [79] report PCSA values for Cacajao that are very similar to the data for Chiropotes published by Anapol et al. [75] (Taylor and colleagues report lower values for Chiropotes). However, as discussed above, Cacajao was found to exhibit canine biting leverage more or less identical to that in Chiropotes when not accounting for species-specific muscle force ratios (Batch 1), with our results supporting a Callicebus-Pithecia-Chiropotes/Cacajao gradient of increasing canine MA. When muscle forces were redistributed according to species-specific jaw adductor force ratios (Batch 2), canine and molar biting efficiency in Cacajao decreased and were found to overlap with Pithecia. With respect to strain magnitudes during canine biting, only one site (site 11) followed the expected trend for both Batch 1 and Batch 2. Cacajao was far from the strongest taxon examined, if not the weakest. Although Callicebus was weaker at more than half of the 20 sites examined, only five (Batch 1) or six (Batch 2) sites exhibited a Callicebus-Pithecia-Chiropotes trend of increasing stiffness. In fact, strains at the sample locations were overall lower in Pithecia than in Chiropotes during canine biting, in contrast to the proposed morphocline. This is further evidenced by comparing the average von Mises strains during canine biting from all 20 craniofacial sites using the data in Table 5. This comparison masks large differences in strain at particular facial sites (e.g., high strain at the nasal margin, site 12, of Callicebus), but nonetheless it reveals that Pithecia experienced the lowest average strain for both Batch 1 (227 με) and Batch 2 (255 με). However, Chiropotes experienced only slightly higher average strain magnitudes (266 με for both Batches). The average von Mises strain data also further demonstrate that the most highly strained taxa in our sample were Callicebus and Cacajao, which experienced remarkably similar average strain magnitudes of 336 με and 335 με, respectively, during Batch 1. The difference between these taxa was greater during Batch 2, with Callicebus experiencing a higher average strain value (376 με) than Cacajao (308 με).
Interestingly, a greater number of sites show a pattern within pitheciines (Cacajao-Chiropotes-Pithecia) during canine biting (8 for Batch 1 or 5 for Batch 2) that is the reverse of the predicted trend. This could indicate that increases in canine bite force leverage and enhancements in anterior dental specialization as proposed by Kinzey [10], including larger and more laterally splaying canines and procumbent incisors, were selected for at the expense of increased strain magnitudes in some regions of the face. These results provide some support for the conclusions of Ross and Iriarte-Diaz [49], who note that primate craniomandibular morphology "reflects trade-offs in primate feeding system design enforced by the multiple performance criteria that the feeding system must meet" (pg. 117). We suggest that pitheciine feeding biomechanics and dietary adaptation represent a functional compromise between anterior dental specialization, increased bite force leverage, and maintaining an appropriate safety factor with respect to bone strain and structural strength. Adaptations for increasing bite force leverage have also been shown to increase craniofacial strain magnitudes in australopiths, and certain facial buttressing features may have evolved to compensate for this reduced structural stiffness [52]. However, in pitheciines, elevated strains resulting from specialized sclerocarpy remain low relative to the strain magnitudes experienced by larger species (e.g., chimpanzees [57]), so may not require additional bony adaptations to mitigate their weakening effect.
Although the trend of increasingly more specialized anterior teeth in pitheciines might explain our strain results, these adaptations are unlikely to explain some of the unexpectedly high strains observed in our Cacajao FEMs. Notably, the zygomaticoalveolar crest (ZAC) of Cacajao is more curved than in either saki. A straighter and more steeply-inclined ZAC is thought to better resist masticatory stresses associated with masseteric contraction and the bite reaction force [1,52]. The more curved ZAC of Cacajao could therefore explain high strain magnitudes at the superior and inferior roots of the zygomatic arch. This potentially reflects a reduction in the need for regular de-husking of unripe fruits and reduced selection for maintaining robust facial features in Cacajao, perhaps offered by allopatry and relaxed feeding competition with other pitheciine species. However, it should be noted that Chiropotes also exhibited high strains at the inferior zygomatic root (site 18) during molar biting.
Uakaris are not broadly sympatric with either saki, so may not be limited to eating the hardest-husked fruits. Compared with Pithecia and Chiropotes, less work has been done on the mechanical properties of foods in the diets of Cacajao species, but many studies note that uakaris prefer fruits with hard husks (e.g., [27,28]). Indeed, Ayres [25] notes that the preference for hard fruits in both Chiropotes satanas and Cacajao calvus are likely to explain their mutual avoidance of each other. However, Barnett et al. [44] found that golden-backed uakaris at Jau National Park (Brazil) often feed on softer fruits when available. This suggests that the relative lack of competition may allow uakaris to choose from a wider variety of fruits and seeds at various stages of ripeness. Indeed, low occlusal complexity in Cacajao relative to other pitheciines might also reflect relaxed dietary resource competition, specifically a reduced reliance on leaves as a source of dietary fiber and/or greater access to fruit seeds with lower fracture toughness [22]. This form of competitive exclusion is strongest among primate taxa that exploit less readily available and less ubiquitous resources [97,98], such as unripe fruit seeds. Competition remains high between sympatric Pithecia and Chiropotes, driving dietary niche separation in these taxa characterized by intensified sclerocarpy in the latter [9,26,32], whereas Cacajao occupies a nearly competition-free ecological niche [43].
Although the craniofacial skeleton of Cacajao may be not be remarkably stiff, Norconk et al. [31] found that the mandible of Ca. melanocephalus was the second most "robust" species included in their platyrrhine sample, occupying an intermediate position between the slightly stronger Chiropotes satanas and slightly weaker Cebus (Sapajus) apella. Other studies find the mandible of Cacajao to be similarly robust [20]. Therefore, a hypothesis that has yet to be tested fully is that the mandible is more highly influenced by selection for increased strength in pitheciines, and perhaps across all primates [68]. Indeed, although cranial shape reflects a compromise between numerous integrated functions (e.g, cognition, respiration, feeding), perhaps masking a strong dietary signal in some primate groups (e.g., lemurs [99]), the mandible may be more closely linked to diet and feeding behavior, although evidence for this relationship also appears to be weak [49,100].
In addition to comparisons of the puncture resistance of fruits breached by Pithecia and Chiropotes, Norconk and colleagues [9,26,32] compared the crushing resistance of seeds eaten by these taxa and found that seeds masticated by Pithecia have significantly higher crushing resistance. In contrast to these ecological data, we found that Pithecia generated less efficient molar bite forces and experienced higher von Mises strain magnitudes than Chiropotes. This was in addition to Pithecia generating absolutely lower bite forces. However, unlike Pithecia, Chiropotes generated highly distractive (tensile) joint reaction forces at the working-side TMJ during molar biting (see Table 5). These distractive forces "pull" the working-side mandibular condyle from the articular eminence, increasing the risk of damaging the soft tissues of the joint capsule when biting forcefully on the back teeth [86,87]. Therefore, although Chiropotes is capable of generating high bite forces more efficiently at its distal molars than Pithecia, it is likely that they reduce tensile loading of the jaw joint by avoiding powerful molar biting behaviors. Instead, Chiropotes is more suited for the efficient grinding of softer seeds (from harder fruits), as suggested by the published crushing resistance data. In this scenario, high molar bite force efficiency is viewed as a byproduct of strong selection for increased anterior bite force efficiency.
Evidence in support of this hypothesis comes from Spencer's [47] study of pitheciine postcanine tooth root morphology. He found that, unlike Pithecia, Chiropotes exhibits a decrease in the number of molar tooth roots and a striking decrease in molar tooth root surface area in a gradient from M 1 to M 3 , suggesting that this finding reflects a decreased reliance on forceful biting at the distal molars. Ledogar [101] similarly found a significantly smaller M 3 occlusal surface area in Chiropotes than Pithecia when scaled to a geometric mean of skull size. Consistent with this observation, several studies have linked increased jaw adductor leverage with third molar reduction and agenesis [47,48,102]. With an anterior shift of the muscles, the third molar may fall within Region III of the tooth row [102]. Forceful biting in this region increases the chances of TMJ distraction by shifting the muscle resultant vector outside of the triangle of support formed by the mandibular condyles and the bite point [86]. Thus, the functional area of the postcanine tooth row is reduced and the expected result is a reduction of molar occlusal surface area, particularly the third molar, or even agenesis of this tooth. Third molar agenesis is common in modern humans [103], which has been linked to the combination of high bite force leverage and TMJ distraction found to also characterize human molar biting [67]. However, human bite force efficiency is the result of facial retraction, as opposed to an anterior migration of the masticatory muscles, and there are various non-masticatory hypotheses purporting to explain the evolution of facial flatness in humans [104].

Conclusion
We found that the feeding biomechanics of pitheciine monkeys (Pithecia, Chiropotes, Cacajao) are consistent with a diet that includes mechanically resistant foods (unripe fruits and seeds). During simulations of canine and second molar biting, pitheciines out-performed Callicebus with respect to the mechanical efficiency (leverage) of bite force production and resistance to masticatory strain. However, Cacajao was found to experience unexpectedly high facial strain magnitudes relative to the other pitheciines in some regions of the face. We therefore found limited support for the hypothesis that Callicebus-Pithecia-Chiropotes-Cacajao represent a morphocline of increasing sclerocarpic specialization [10], at least with respect to the mechanical performance metrics examined here. In fact, strain magnitudes during canine biting were more likely to follow a Cacajao-Chiropotes-Pithecia trend of increasing craniofacial strength, in contrast to the proposed morphocline. On the other hand, we found that Callicebus-Pithecia-Chiropotes/Cacajao represent a gradient of increasing canine MA, with leverage in Cacajao nearly identical to (or slightly less than) in Chiropotes. Together, these results could indicate that increased bite force efficiency and increasingly derived anterior dental morphology was selected for in pitheciines at the expense of higher craniofacial strain magnitudes. However, the unexpectedly weak facial skeleton of Cacajao potentially reflects reduced feeding competition with other pitheciines; this reduced competition allows uakaris to choose from a wider variety of fruits at various stages of ripeness, leading to reduction in the selection for robust facial features.
We also found that Pithecia and Chiropotes exhibit differences in biting performance that are consistent with food structural property data and previous observations of dietary niche separation between these sister taxa [9,26,32], supporting the hypothesis that sakis and bearded sakis are able to reduce competition and remain sympatric by specializing on fruits and seeds at different stages of ripeness. Consistent with data on fruit puncture resistance, we found that bite force production and efficiency during canine biting was greatest in Chiropotes. Biting leverage was also great at the molar in Chiropotes, but Pithecia was found to be better suited for the regular forceful crushing and grinding of seeds using the postcanine teeth, consistent with data on seed crushing resistance and molar root surface area.
Future studies investigating the dietary ecology of pitheciines should focus on the collection of mechanical properties of foods eaten by Cacajao. Although uakaris have traditionally been considered a flooded forest specialist (e.g., [42]), which has complicated attempts to study their dietary ecology, recent work indicates that not all species are restricted to such habitats. A recent review of all available information concerning the habitat of Ca. calvus ucayalii [105] concluded that this species is more flexible in habitat preference than previously thought and most frequently occupies non-flooded terra firme forests or mixed habitats. For example, uakaris at the Lago Preto Conservation Concession in Iquitos, Peru are commonly associated with terra firme forest [106], which offers high potential for a detailed study of Cacajao dietary ecology and the collection of food mechanical properties. Future work on feeding ecology in Cacajao and other pitheciines will also allow for more detailed collection of data on fruit size, gape, and paramasticatory feeding behaviors, such as when using the hands to pull fruits or when manipulating a fruit to avoid biting along its largest dimension [31]. One limitation of the current study is that our biting simulations have not taken the broad range of such behaviors into account.
Much-needed research exploring the relationship between primate food mechanical/structural properties and their ecological significance has been growing in recent years (e.g., [31,36,48,[107][108][109][110][111][112][113][114][115][116][117]). With respect to pitheciines, Norconk and colleagues [9,26,32] quantify fruit and seeds eaten by Pithecia and Chiropotes in terms of their puncture and crushing resistance (i.e., structural properties). Lucas [118] suggests that the mechanical properties E (Young's modulus, a measure of material stiffness) and R (fracture toughness, a measure of resistance to fracture propagation) more accurately describe food fragmentation during ingestion and mastication, and may have more of a direct influence on the evolution of the masticatory apparatus. Therefore, it is an appropriate question as to whether E and R explain niche partitioning in pitheciines equally well. Future work should focus on the incorporation of both structural and mechanical food properties into the analysis of craniofacial form in pitheciines.