Functional Geometric MorphometricAnalysis of Masticatory SystemOntogeny in Papionin Primates

MICHELLE SINGLETON*Department of Anatomy, Chicago College of Osteopathic Medicine,

Midwestern University, Downers Grove, Illinois

ABSTRACTThe three-dimensional configuration of the primate masticatory sys-

tem is constrained by the need to maximize bite forces while avoiding dis-traction of the temporomandibular joint (TMJ). Within these bounds,shape variation has predictable effects on functional capacities such asmechanical advantage and gape. In this study, geometric morphometricanalysis is used to investigate the ontogeny of masticatory function inpapionin monkeys and test the hypothesis that biomechanical constraintsdetermine the location of molar eruption. This “constrained eruptionhypothesis” predicts that the distalmost molar (DMX) will occupy a con-sistent location anterior to the TMJ and that jaw adductor muscles willmaintain consistent positions relative to both DMX and TMJ. Craniomet-ric landmarks were digitized on cross-sectional ontogenetic series of ninepapionin species. Form-space PCA of Procrustes residuals, visualizationof Bookstein shape coordinates, and nonparametric ANOVA were used toidentify ontogenetic shape trends and test for significant ontogeneticchanges in relative landmark positions. In most taxa, DMX maintains aconsistent position relative to the TMJ while the anterior dentitionmigrates anteriorly. Where significant intraspecific ontogenetic differen-ces occur, they involve anterior migration of DMX in later dental stages,likely due to late adolescent growth of the posterior palate. Attachmentsof the anterior temporalis and deep masseter also maintain consistentpositions relative to the TMJ; however, the superficial masseter migratesanteriorly throughout ontogeny. All muscle attachments migrate laterallyrelative to the TMJ, reflecting positive scaling of adductor PCSA. Overall,results support the constrained eruption hypothesis and suggest mecha-nisms by which functional capacity is maintained during ontogeny. AnatRec, 298:48–63, 2015. VC 2014 Wiley Periodicals, Inc.

Key words: masticatory system ontogeny; constrained levermodel; dental eruption; papionin primates; func-tional geometric morphometrics

The primate masticatory apparatus is a complexthree-dimensional (3D) system whose configuration isconstrained by the need to generate adequate bite forceswhile dissipating or avoiding potentially harmful forceswithin the cranium (Hylander, 1979, 1985; Sakka, 1985;Ravosa, 1996a; Hylander and Johnson, 1997; Spencer,1999; Lieberman, 2011; Greaves, 2012). Within therange of mechanically viable cranial shapes, variation in

*Correspondence to: Michelle Singleton, Department ofAnatomy, Midwestern University, 555 31st Street, Downers Grove,IL 60515. Fax: 630-515-7199. E-mail: msingl@midwestern.edu

Received 3 October 2014; Accepted 11 October 2014.

DOI 10.1002/ar.23068Published online in Wiley Online Library (wileyonlinelibrary.com).

THE ANATOMICAL RECORD 298:48–63 (2015)

VVC 2014 WILEY PERIODICALS, INC.

the 3D geometry of the masticatory configuration haspredictable effects on functional capacities such asmechanical advantage and gape (Hylander, 1985; Ravosa,1990; Spencer, 1999; Greaves, 2012). Masticatory varia-tion has most often been studied using traditional mor-phometric variables (interlandmark distances, angles,etc.) analyzed within the framework of classic allometricand biomechanical models (Huxley, 1932; Gould, 1966;Greaves, 1974; Hylander and Bays, 1979; Lucas, 1981,1982; Smith, 1984; Bouvier, 1986a,b; Ravosa, 1990;Greaves, 1995; Ant�on, 1996; Ravosa, 1996a,b; Vinyardand Ravosa, 1998; Spencer, 1999; Vinyard, 2003; Perryet al., 2011; Greaves, 2012). The resulting atomization ofthe masticatory system is extremely effective for testingspecific, quantitative hypotheses concerning individualsystem components but sacrifices the spatial context ofthe configuration as a whole (Rohlf and Marcus, 1993).Given that “interpreting the relative functional abilitiesof forms across different-sized organisms...involves a com-parative assessment of proportionality,” i.e., shape (Vin-yard, 2008: 359), alternate approaches that preserveshape information are extremely desirable.

Geometric morphometrics (GM), a well-developedbody of methods for the analysis of shape variation andcovariation, provides one such alternative (Bookstein,1984; Rohlf and Slice, 1990; Bookstein, 1991; Rohlf andMarcus, 1993; Dryden and Mardia, 1998; Adams et al.,2004; Mitteroecker and Gunz, 2009). Singleton (2005)demonstrated that GM analysis of the primate mastica-tory system yields functionally equivalent results todistance-based analyses while offering several potentialadvantages. Because GM analysis quantifies shape vari-ation of the masticatory system as a whole, it is an effi-cient means to map the morphospace of masticatorygeometries and correlate differences to developmentalstage, size, ecology, and phylogeny (Singleton, 2005;Stayton, 2005; Nicholson and Harvati, 2006; Herrelet al., 2007; Jones, 2008; Pierce et al., 2008; Figueiridoet al., 2009; Brusatte et al., 2011) Furthermore, directvisualization of shape trends in the original 3D objectspace facilitates functional interpretation and hypothesistesting relative to geometric predictions of biomechanicalmodels (Singleton, 2004). While not appropriate for allquestions, functional geometric morphometric analysis(FGM) can be an effective tool for evaluating the relativefunctional capacities of differing masticatory configura-tions within and between species as well as for testingfunctional hypotheses. In this study, FGM is used to testthe hypothesis that biomechanical constraints on theontogeny of the masticatory system dictate the locationof molariform tooth eruption.

Background

The constrained lever model, which posits that the 3Dgeometry of the mammalian masticatory system is con-strained to avoid production of harmful distractive forcesat the working-side temporomandibular joint (TMJ) dur-ing unilateral biting (Fig. 1), is a widely accepted theo-retical framework for comparative functional analysis ofthe primate masticatory system (Greaves, 1978, 1982;Spencer and Demes, 1993; Spencer, 1995b, 1999; Single-ton, 2004; Wright, 2005; Baab et al., 2010; Koyabu andEndo, 2010; Scott, 2010; Greaves, 2012). This model

classifies bite points by their location relative to theresultant vector of the jaw adductor muscles (Fig. 1a).Anterior bite points (Region I) are associated with trian-gles of support (Fig. 1b)—defined by the bite point andright and left TMJs—that intersect a midline resultantvector (R), permitting stable unilateral biting (Spencer,1999; Greaves, 2012). Posterior bite points (Region II)are associated with triangles of support that do notintersect R, necessitating a reduction in balancing-sidemuscle force to shift the vector toward the working sideand avoid TMJ distraction. Posterior to R (Region III),TMJ distraction is unavoidable and teeth are notexpected to occur. Whereas bite forces in Region Iincrease as the bite point shifts posteriorly, in Region II,decreased balancing-side muscle activity offsetsincreased mechanical advantage associated with moreposterior bite points (Spencer, 1999; Greaves, 2012). Asa result, bite forces peak at the Region I–Region IIboundary and either hold steady or decline slightly asbite points shift posteriorly within Region II (Spencer,1999; Thompson et al., 2003). Accordingly, Region II isexpected to coincide with the distribution of the“grinding teeth,” typically the molars and, in some spe-cies, premolars (Greaves, 1978; Spencer, 1999; Thomp-son et al., 2003; Greaves, 2012).

The distribution of Region II is determined primarilyby: (1) the mediolateral position of the TMJ; (2) themediolateral position of the tooth row; and (3) the antero-posterior (AP) location relative to the TMJ of the resul-tant’s intersection with the occlusal plane (Spencer andDemes, 1993; Spencer, 1995a, 1998). In primates, whoseTMJ is positioned superior to the occlusal plane, the ori-entation of the muscle resultant vector must also be con-sidered because elevation of the TMJ separates thetriangle of support from the occlusal plane (Fig. 1c). Ifthe resultant vector is perpendicular to the occlusalplane, this separation has no practical effect (Spencer,1999). But if the vector is oriented anteriorly, the inclinedtriangle results in anterior extension of Region II alongthe tooth row in proportion to both the degree of vectorinclination and TMJ height (Spencer, 1995b, 1999).

While the positions of the tooth row and TMJ areeasily measured, the location and orientation of theadductor resultant force are difficult to quantify. Usinga geometric model, Greaves calculated the optimal vec-tor location as being 30% of jaw length anterior to theTMJ in the midline and hypothesized that this point—dubbed the “Greaves point” by Perry et al. (2011)—should fall immediately posterior to the tooth row(Greaves, 1978, 2012). However, subsequent estimateshave placed the resultant considerably posterior to thispoint (Spencer, 1999; Spencer and Schwartz, 2008;Perry et al., 2011; Schwartz, 2013). Spencer’s calcula-tions from bony landmarks located the vectors of indi-vidual adductor muscles between 40% (medialpterygoid) and 66% (anterior temporalis) of the perpen-dicular distance between the TMJ and the distal molar(DMX), with a mean vector location for anthropoids at60% of the TMJ-DMX distance in the occlusal plane(Spencer, 1999). Vector orientations, considered lessreliable by Spencer, ranged from 77.5� (superficialmasseter) to 91.9� (anterior temporalis), leading him toadopt a standard orientation of 80� (slightly anterior ofperpendicular) for purposes of analysis (Spencer, 1999).Similar calculations by Perry et al. (2011) yielded a

FUNCTIONAL GEOMETRIC ANALYSIS OF PAPIONIN MASTICATORY ONTOGENY 49

mean vector location for anthropoids at 22% of jawlength measured perpendicular to the resultant, i.e.,posterior to both the Greaves point and the most distalmolar, and a mean vector orientation of 91.93�.Although orientations were significantly more anteriorin folivores (mean 5 85.33�) than in frugivores (mean-5 93.75�), the authors concluded that a vertical vector(90�) is a reasonable approximation across anthropoids(Perry et al., 2011).

The failure of empirical measurements to supportGreaves’ optimized model of masticatory geometry ledSpencer to hypothesize that natural selection hasfavored a conservative masticatory configuration withsubstantial safety margins to accommodate the widerange of alternate resultant locations encountered acrossthe masticatory cycle and at varying degrees of gape(Spencer, 1998, 1999). As a corollary, Spencer andSchwartz have postulated that these same biomechani-cal constraints govern the ontogeny of the masticatorysystem and determine the timing of dental eruption(Spencer and Schwartz, 2008; Schwartz, 2013). Thishypothesis is supported by their finding that in Pan andmodern Homo, newly erupted deciduous and permanentmolars occupy a species-specific position anterior to theTMJ. Additionally, they found that the resultants ofindividual masticatory muscles consistently cross theocclusal plane at less than 75% of the distance from theTMJ to the most distal molariform tooth (Spencer andSchwartz, 2008; Schwartz, 2013). This stability of themasticatory configuration led the authors to concludethat there is a “biomechanically optimal location formolar eruption” anterior to the muscle resultant andthat successive molars erupt only when this position isvacated as a result of anterior facial growth (Schwartz,2013: S404). Noting that “the validity of this biomechan-ical model for modulating the timing of molar emergencehas not been fully established,” further studies in homi-noids are under way (Schwartz, 2013: S404), but an ear-lier study of mandibular molar initiation suggests thismay be a more general phenomenon (Boughner andDean, 2004). The 3D multivariate analysis of Boughnerand Dean (2004) found similar trajectories of mandibu-lar molar-row shape change in Pan and Papio, with theonly consistent difference between genera being aslightly greater space distal to newly initiated molars inPapio. These studies differ substantially in data andmethodology, but the findings of Boughner and Deansuggest that analysis of a taxonomically broader compar-ative sample could offer insights into the generality ofwhat will be termed here the “constrained eruptionhypothesis.”

Fig. 1. Constrained lever model of the masticatory system. A: Theconstrained lever model divides the jaw into regions defined by theirrelationship to the midline adductor resultant vector (R). B: Trianglesof support (TOS) for Region I bite points (e.g., light blue triangle) inter-sect R. Region II triangles of support (e.g., dark blue triangle) do not,necessitating a reduction in balancing-side muscle force to avoid TMJdistraction. Maximum bite forces occur at the Region I–Region IIboundary. C: Elevation of the TMJ above the occlusal plane potentiallyaffects the distribution of masticatory regions. If the resultant vector isvertically oriented (V), there is no effect; however, anteriorly orientedvectors (A) intersect the TOS (dotted line) farther anteriorly, shifting theRegion I–Region II boundary mesially. Illustrations adapted fromSpencer (1999).

50 SINGLETON

Objectives

The Old World monkey tribe Papionini is an appropri-ate test group for Spencer and Schwartz’s hypothesis.Papionins are a diverse radiation encompassing a broadrange of cranial sizes and facial forms (Kuhn, 1967; Hill,1974; Delson, 1975a,b; Szalay and Delson, 1979; Strasserand Delson, 1987; Groves, 2001). Differences in faciallength, projection, and orientation are well representedamong its member species (Fig. 2), and prior studieshave documented significant relationships between facialvariation and masticatory function in the context of eco-morphological divergence between small- and large-bodied species (Jolly, 1970; Delson, 1975b; Szalay andDelson, 1979; Cheverud, 1989; Ravosa, 1990; Jablonski,1993; Profant and Shea, 1994; Ravosa and Shea, 1994;Profant, 1995; Ravosa, 1996a; Vinyard and Ravosa,1998; Ravosa and Profant, 2000; Collard and O’Higgins,2001; O’Higgins and Collard, 2002; Singleton, 2002;Leigh et al., 2003; Singleton, 2004, 2005; Leigh andBernstein, 2006; Daegling and McGraw, 2007; Leigh,2007; Daegling et al., 2011). Using papionins as a testgroup, this study applies geometric morphometric meth-ods to test the functional hypothesis that dental eruptionin primates is governed by biomechanical constraints onthe masticatory system that require successive molari-form teeth to erupt at a consistent location relative to

the temporomandibular joint. If this hypothesis is cor-rect, the mean position of DMX relative to the TMJshould remain constant across ontogenetic stages. Addi-tionally, it is expected that the average location of theadductor resultant vector, calculated according toSpencer’s formulation as 60% of the TMJ-DMX distance,should remain constant through ontogeny. It is alsoexpected that the attachments of the masseter and tem-poralis muscles will maintain a constant location rela-tive to the TMJ.

MATERIALS AND METHODS

Data Collection and Processing

The study sample comprised 268 juvenile and adultcrania representing mixed-sex, cross-sectional ontoge-netic series for nine papionin taxa; specimens were pre-dominantly wild-collected and of known provenience(Table 1). Specimens were assigned to dental stages(dp4–M3) on the basis of eruption of the nominal toothto full occlusion. These categories encompass somewithin-stage ontogenetic variation in relative tooth posi-tion; however, the small number of juveniles withactively erupting molars made finer-grained categoriesimpractical. As the sex of juvenile specimens is generallyunknown, no effort was made to control for the sex

Fig. 2. Cranial form variation in papionin monkeys. Members of the catarrhine tribe Papionini exhibitsignificant variation in cranial size and shape. Interspecific differences in facial length, projection, and ori-entation reflect phylogeny, masticatory adaptation, and allometric scaling, among other influences. Cranialimages to common scale; Theropithecus and Rungwecebus are not shown.

FUNCTIONAL GEOMETRIC ANALYSIS OF PAPIONIN MASTICATORY ONTOGENY 51

composition of the juvenile sample; most adult sampleswere roughly balanced. The use here of mixed-sex sam-ples is supported both by past findings that facial shapedimorphism in papionins is minimal prior to adolescenceand by the absence of consistent sex-based differences inthe timing of postcanine dental eruption in cercopithe-cines generally (Cheverud, 1981; Oyen, 1984; Phillips-Conroy and Jolly, 1988; O’Higgins and Collard, 2002;Bolter and Zihlman, 2003).

Three-dimensional craniometric landmarks were col-lected from each specimen using a Microscribe 3DXVR

contact digitizer. Twenty-seven landmarks (Fig. 3,Table 2) were chosen to register the locations of func-tionally significant features as well as to capture theoverall geometry of the masticatory system. Parasagittallandmarks were recorded bilaterally. Following an initial

Procrustes superimposition (Gower, 1975; Rohlf andSlice, 1990), the resulting configurations were symme-trized using reflected relabeling with averaging (Mardiaet al., 2000; Mitteroecker and Gunz, 2009). Symmetriza-tion served two purposes: (1) estimation of missing bilat-eral landmarks by substitution of the reflected antimericcoordinates; and (2) elimination of developmental “noise”in the form of fluctuating and/or developmental asymme-try (Mardia et al., 2000; Mitteroecker and Gunz, 2009).Where unpaired (midsagittal) landmarks were missing,thin-plate spline (TPS) estimation was used to imputetheir coordinates (Gunz et al., 2009; Mitteroecker andGunz, 2009). Missing values for each such specimenwere calculated using a TPS interpolation between thatspecimen and the mean landmark configuration corre-sponding to its species and dental stage (Gunz et al.,

TABLE 1. Study sample by dental stage

dp4 M1 M2 M3 N Specimen sourcea

Cercocebus agilis 0 4 9 16 29 PCM, RMCACercocebus atys 1 5 4 19 29 BMNS, RMCACercocebus torquatus 1 3 3 20 27 AMNH, BMNS, PCM, TUMNHLophocebus aterrimus 4 5 7 16 32 RMCALophocebus albigena 4 3 6 28 41 BMNS, PCM, RMCAMacaca mulatta 4 4 5 8 21 AMNH, FMNHMandrillus sphinx 0 2 3 12 17 AMNH, PCMPapio kindae 1 6 12 6 25 BMNS, FMNHPapio anubis 5 9 5 29 48 FMNH, PCM, UMTC

Dental stage defined by eruption of the nominal tooth to full occlusion. Specimens are predominantly wild collected and ofknown provenience; Mandrillus sample includes one zoo-housed juvenile.aMuseum key: AMNH, American Museum of Natural History; BMNS, Royal Belgian Institute Museum of Natural Scien-ces; FMNH, Field Museum of Natural History; NMNH, National Museum of Natural History; PCM, Powell-CottonMuseum; RMCA, Royal Museum for Central Africa; TUMNH, Tulane University Museum of Natural History; UMTC, Uni-versity of Minnesota Tappen Collection.

Fig. 3. Three-dimensional osteometric landmarks used in this study. Landmark abbreviations followTable 2.

52 SINGLETON

2009). Generalized Procrustes analyses were performedin Morpheus (Slice, 1998); reflection and estimationwere executed using SAS IML 9.1 (SAS Institute, Cary,NC).

Geometric Morphometric Analysis

Form-space principal components analysis (FPCA)was used to explore ontogenetic and interspecific varia-tion in the masticatory system as a whole (Mitteroeckeret al., 2004). In FPCA, the matrix of Procrustes-alignedcoordinates is augmented by the natural logarithm ofcentroid size (lnCS). In theory, the first principal compo-nent (FPC1) should summarize a common ontogenetictrajectory, while higher-order FPCs summarize differen-ces within and between taxa (Mitteroecker et al., 2004).To prevent unequal sample sizes from biasing results,the FPCA was based on average values (lnCS and coor-dinates) for each dental stage–species group.

Generalized Procrustes analysis (GPA), which mini-mizes the summed squared Procrustes distances ofaligned configurations to the consensus configuration, isthe standard precursor to most geometric morphometricanalyses (Rohlf and Slice, 1990; Adams et al., 2004;

Mitteroecker and Gunz, 2009). However, the least-squares criterion employed in GPA has the result thatshape variation is distributed across all landmarks of thealigned configurations (Slice, 1996). To test hypothesesconcerning the position of newly erupted molars relativeto a fixed reference, the TMJ, an alternate superimposi-tion method was chosen. Using GRF-ND (Slice, 1999),specimens were aligned to the biglenoid line (RCGL toLCGL) and prosthion (PRO) and scaled to unit biglenoidlength, yielding 3D Bookstein shape coordinates for thealigned landmark configurations (Bookstein, 1984, 1991,1996). Use of PRO as a third point of alignment orientedspecimens to a common midsagittal plane and establishedthe anteroposterior dimension of the cranium as the y-axis of the 3D object space. Bookstein shape coordinates,which are based on registration of landmark configura-tions to a common baseline, represent a special case of aprojection from Kendall shape space to a tangent plane(Rohlf, 2000). They yield equivalent results to Procrustesresiduals provided that: (1) the magnitude of shape varia-tion is small; and (2) the chosen baseline is not short(Bookstein, 1996; Rohlf, 2000, 2003). Prior studies haveconfirmed the first condition for cranial shape variationin mammals generally and papionins in particular (Mar-cus et al., 2000; Singleton, 2002). The choice of baselinefor this study, the biglenoid line, is dictated by the ques-tion under study. While it is not a statistically optimalbaseline (Bookstein, 1996), it does encompass almost thefull breadth of the masticatory system and should furnishacceptable estimates of mean shape for the groups underconsideration (Rohlf, 2003).

Estimation of Resultant Coordinates

Trigonometric calculations and linear interpolationwere used to estimate 3D coordinates for the combinedmidline adductor resultant R for each species dental-stage mean (see Appendix). This estimate incorporatesseveral assumptions and/or approximations. First,Spencer’s (Spencer and Demes, 1993; Spencer, 1995b)calculation that R is located at 60% of the distancebetween the TMJ and the distalmost molar in the occlu-sal plane is accepted as a conservative estimate of R’slocation. Second, calculations of relative jaw length andperpendicular TMJ-DMX distance were made in themaxillary alveolar plane, defined by PRO and R/L DMX,rather than in the occlusal plane. This approximationallows inclusion of specimens with missing teeth. Third,the linear interpolation was made along the 3D vectorextending from the midpoint of the biglenoid line(mTMJ) to prosthion, which was found to incline anaverage of 11� relative to the maxillary alveolar plane(see Appendix, Table A1). These approximations havethe combined effect of shifting the coordinates of Rslightly anterior relative to its intersection with thealveolar and/or occlusal plane.

Hypothesis Testing

For each species, a 3D plot of superimposed species-stage mean shapes was inspected to assess ontogeneticvariation in the relative positions of: (1) successivelyerupting molars; (2) the estimated location of the result-ant vector R; and (3) landmarks representing cranialattachments of specific masticatory muscles. To compare

TABLE 2. Masticatory landmark definitions

Abbr. Description

Prosthion PRO Inferiormost point on alveolarseptum between centralincisors

Prosthion2 PRO2 Inferiormost point on I1-I2alveolar septum

Zygomaxillareinferiore

ZMI Inferiormost point on zygo-maxillary suture

Frontomalaretemporale

FMT Intersection of frontozygomaticsuture with anterior tempo-ral line

Articular tubercle ART Inferiormost point on tip ofarticular tubercle in lateralview

Central glenoid CGL Approximate geometric centerof glenoid articular surface

Zygotemporaleinferiore

ZTI Inferiormost point on zygoma-ticotemporal suture

Maxillarytuberosity

MXT Posteriormost point on alveo-lar process at articulationwith palatine

Distal molar DMX Buccal alveolar process atlevel of distal alveolar sep-tum of distalmost molari-form tooth

P4-M1 contact P4M1 Buccal alveolar process atlevel of P4-M1 contact or, indp4-stage juveniles, the dis-tal alveolar septum

P3-P4 contact P34 Buccal alveolar process atlevel of P3-P4 contact

Mesial P3 MP3 Buccal alveolar process atlevel of Canine-P3 contact

Premaxillareinferiore

PMI Inferiormost point onpremaxillary-maxillarysuture at alveolar margin

P4 Center P4C Approximate geometric centerof dp4/P4 occlusal surface

All landmarks except prosthion were collected bilaterallywhere preservation permitted.

FUNCTIONAL GEOMETRIC ANALYSIS OF PAPIONIN MASTICATORY ONTOGENY 53

the results of distance-based versus geometric methods,two variables were used to evaluate intraspecific differen-ces in distal–molar position. The first was the TMJ-DMXdistance d calculated from backscaled Bookstein shapecoordinates (see Appendix). The second was the Booksteiny-coordinate for right DMX relative to the unit biglenoidbaseline (DMXY). The first variable approximates thetrue perpendicular distance between the TMJ and DMX,while the second represents the position of DMX relativeto TMJ along the anteroposterior axis. This approach wasadopted to control for positional differences due to infe-rior growth of the alveolar process. Similarly, y-coordi-nates (FMTY, ZMIY, and ZTIY) were used to represent therelative anteroposterior positions of frontomalare tempo-rale, zygomaxillare inferiore, and zygotemporale inferiore,which register cranial attachments for the anterior tem-poralis, superficial masseter, and deep masseter muscles,respectively. For each variable, the Kruskal-Wallis testfor multiple samples was used to identify significant dif-ferences among dental stages within each species (Nar-ayanan and Watts, 1996; Schwartz, 2013). This rank-based test is preferable to parametric ANOVA when sam-ples are small and/or unbalanced. �Sid�ak’s correction wasused to adjust significance levels for multiple simultane-ous ANOVAs as well as for post hoc comparisons wheresignificant differences were found (�Sid�ak, 1967; SISA,1997). Although similar to the Bonferroni adjustment,�Sid�ak’s correction is less conservative, thus reducing therisk of Type II error (SISA, 1997).

RESULTS

Form-Space PCA

Results of the form-space PCA analysis are consistentwith well-established patterns of cercopithecine

ontogenetic and interspecific allometry (Ravosa, 1990;Profant and Shea, 1994; Ravosa and Shea, 1994; Ravosaand Profant, 2000; Collard and O’Higgins, 2001; O’Hig-gins and Collard, 2002; Singleton, 2002; Leigh et al.,2003; Singleton, 2004; Leigh, 2007). The first FPC(Fig. 4, x-axis; 96% form variance) ordinates species-stage means by centroid size (r2 5 0.9998; P< 0.0001)and summarizes variation in palate shape and relativejaw breadth. Larger phena are characterized by rela-tively longer and narrower palates; more medially posi-tioned TMJs and zygomatic arches; TMJs situatedrelatively higher above the alveolar plane; and greateranteroposterior separation between the anterior denti-tion and the TMJ and masticatory muscle attachments(FMT, ZMI, ZTI). These differences characterize earlierversus later dental stages within species as well as com-parable stages of larger versus smaller species. The sec-ond FPCA (Fig. 4, y-axis), accounting for only 2% ofform variance, summarizes shape differences independ-ent of size and ordinates species-stage means by dentalstage. Within each species, earlier stages have relativelypositive scores, while later stages have more negativescores. This axis also separates smaller-bodied species,which have relatively negative scores at any given den-tal stage, from Mandrillus and Papio. More negativescores are associated with a relatively longer posteriorpalate; a longer and more laterally flaring zygomaticarch; and a more anteriorly positioned molar row.

Variation in Distal–Molar Position

Ontogenetic variation patterns. Figure 5 showsplots of mean dental-stage masticatory configurations byspecies. These plots demonstrate a pronounced anteriormigration of the anterior dentition (i/I1–dp/P4) relative

Fig. 4. Form-space principal components analysis of Procrustes-aligned masticatory landmarks. The first principal component (FPC1,96% form variance) ordinates mean forms by centroid size and sum-marizes variation in palate shape and relative jaw position. The secondprincipal component (FPC2, 2% variance) ordinates mean forms bydental stage within species and summarizes variation in relative zygo-

matic breadth and distal palate length. Symbols represent mean mas-ticatory configurations calculated by species and dental stage (dp4–M3). Wireframes illustrate the extremes of shape variation summarizedby each axis (black) in comparison with the sample mean configura-tion (pink).

54 SINGLETON

to the TMJ as ontogeny progresses. By contrast, DMXmaintains a relatively constant position anterior to theTMJ in most species. In only two species—C. torquatusand P. anubis—is there steady anterior migration of thedistal–molar position through ontogeny. Where anteriormigration occurs, it is of considerably smaller magnitudethan is observed for the anterior dentition. In only onecase, M1-stage of C. atys, is the average position of thedistal molar appreciably posterior to that observed inthe preceding dental stage.

Statistical tests of relative distal–molarposition. Table 3 summarizes the results of nonpara-metric ANOVA tests of distal–molar position variationwithin species. Results based on the two test variables,TMJ-DMX distance (d) and the DMX y-coordinate(DMXY), were largely concordant; however, tests basedon d were more likely to find significant differencesamong stages. The Kruskal-Wallis analysis of d was sig-nificant at �Sid�ak-adjusted P 5 0.0056 for two of the ninespecies examined: L. albigena and P. anubis. Post hocpairwise comparisons (Table 4) among dental stages forthese species found significant differences (�Sid�ak-adjusted P 5 0.0026) between distal–molar positions ofM3- versus dp4- and M2-stages in L. albigena as well asbetween M3- and dp4-stages in P. anubis. Kruskal-

Wallis analyses of DMXY yielded significant results forone species, C. torquatus; however, no post hoc compari-sons achieved significance at the adjusted P 5 0.0026.

Variation in Resultant and Masticatory–MusclePositions

Relative location of R. The average location ofthe adductor resultant vector R, based on Spencer’s 60%TMJ-DMX calculation, is �21% of jaw length for adultsand 23% of jaw length for the entire sample (see Appen-dix, Table A1). Variation in the location of R predictablymirrors that of DMX, whose coordinates were the basisof its calculation (Fig. 5). Given this relationship, statis-tical tests for intraspecific ontogenetic variation in R arenot informative and were not conducted.

Ontogenetic variation in relative masticatory–muscle position. Relative positions of two of thethree landmarks associated with masticatory muscleattachments, FMT (anterior temporalis) and ZTI (deepmasseter), also mirror the ontogenetic variation patternof DMX. In the majority of species, these landmarksmaintain a relatively constant position anterior to theTMJ through ontogeny (Fig. 5). In those species exhibit-ing anterior migration of the distalmost molar, the

Fig. 5. Ontogenetic shape variation in the masticatory system. Sym-bols represent mean Bookstein shape coordinates calculated by spe-cies and dental stage (dp4–M3). Mean configurations are aligned tothe biglenoid line and prosthion and are scaled to unit biglenoidlength. In most species, frontomalare temporale (FMT), zygotemporaleinferiore (ZTI), and the distalmost molar (DMX) maintain a consistentposition anterior to the temporomandibular joint (TMJ) throughout

ontogeny. By contrast, anterior dental landmarks and zygomaxillareinferiore (ZMI) show steady anterior displacement relative to the TMJduring ontogeny. Dental landmarks show minimal ontogenetic variationin mediolateral position relative to the TMJ, while landmarks associ-ated with masticatory muscles (FMT, ZMI, and ZTI) migrate laterallyrelative to the TMJ. Landmark abbreviations follow Table 2.

FUNCTIONAL GEOMETRIC ANALYSIS OF PAPIONIN MASTICATORY ONTOGENY 55

locations of FMT and ZTI also shift anteriorly by roughlythe same amount as DMX. By contrast, ZMI (superficialmasseter) shows a steady anterior shift during ontogenyin a pattern similar to that exhibited by the anteriordentition.

Statistical tests of relative masticatory–muscleposition. Table 3 summarizes the results of nonpara-metric ANOVA tests of ontogenetic variation in the rela-tive positions of FMT, ZTI, and ZMI. Results, shown forBookstein y-coordinates only, support the ontogenetic

variation patterns seen in Fig. 5. Kruskal-Wallisanalyses of FMTY yielded significant results (�Sid�ak-adjusted P 5 0.0056) for two species, L. albigena andP. anubis. Post hoc pairwise comparisons (see Table 4)among dental-stages within these species found signifi-cant differences in relative FMT position (�Sid�ak-adjustedP 5 0.0026) between the dp4- and M3-stages in L. albi-gena as well as between the M1- and M3-stages inP. anubis. Analyses of ZTIY were not significant for anysample species, while analyses of ZMIY found significantontogenetic variation (�Sid�ak-adjusted P 5 0.0056) for sixof the nine species examined. Given the preponderanceof significant results and correspondingly large numberof pairwise comparisons (with concomitant loss of statis-tical power), post hoc testing was not pursued for thislandmark.

DISCUSSION

In his 2008 review of size-adjustment techniques inclassical morphometrics, Chris Vinyard made a detailedand cogent argument for “a pluralistic approach, particu-larly for functional shape comparisons...emphasizingmultiple shape variables tailored to the biological ques-tions being considered” (Vinyard, 2008: 370). The logicalextension of this pluralism to encompass geometric mor-phometrics furnishes researchers with the broadestchoice of variables and analytical tools for studies ofcomparative functional morphology. This study usesstandard Procrustes-based GM analysis in tandem withalternate geometric approaches and traditional morpho-metric variables to investigate ontogenetic variation inthe papionin masticatory system and test a specific func-tional hypothesis: that biomechanical constraints on theontogeny of the masticatory system determine the loca-tion of molar eruption (Spencer and Schwartz, 2008;Schwartz, 2013). This hypothesis predicts that molari-form teeth will erupt at a consistent location anterior tothe temporomandibular joint. It further predicts thatjaw adductor muscles will maintain a consistent antero-posterior position relative to the TMJ and distal molar.

Relative Position of the Distal Molar

Traditional and geometrically derived variables—TMJ-DMX distance (d) and the DMX y-coordinate (DMXY),

TABLE 3. Kruskal-Wallis tests of distal–molar and masticatory–muscle position by dental stage

d DMXY FMTY ZTIY ZMIY

df. X2 P X2 P X2 P X2 P X2 P

C. agilis 2 2.49 0.2877 0.19 0.9109 5.02 0.0813 0.78 0.6769 7.61 0.0223C. atys 3 10.96 0.0119 2.59 0.4599 11.12 0.0111 3.10 0.3764 16.23 0.0010*C. torquatus 3 9.33 0.0252 14.05 0.0028* 9.69 0.0214 1.13 0.7701 14.68 0.0021*L. aterrimus 3 5.61 0.1320 5.27 0.1531 11.94 0.0076 0.45 0.9293 23.27 <0.0001*L. albigena 3 23.38 <0.0001* 9.94 0.0191 17.19 0.0006* 1.33 0.7209 24.58 <0.0001*M. mulatta 3 6.45 0.0915 6.07 0.1084 2.05 0.5614 4.36 0.2250 16.80 0.0008*M. sphinx 2 3.52 0.1724 3.29 0.1926 0.41 0.8139 1.12 0.5709 6.05 0.0487P. kindae 3 5.01 0.1713 2.68 0.4436 1.44 0.6958 2.97 0.3962 7.26 0.0642P. anubis 3 19.20 <0.0002* 1.76 0.6247 15.69 0.0013* 1.37 0.7117 19.41 0.0002*

d 5 unscaled distance from TMJ to distalmost molar DMX.DMXY, FMTY, ZTIY, ZMIY 5 scaled Bookstein y-coordinate for corresponding landmark (see Table 2).P 5 one-tailed probability.*Significant at �Sid�ak-adjusted P 5 0.0056.

TABLE 4. Selected post hoc comparisons of landmarkrelative positions

TMJ-DMX Distance (d)L. albigena dp4 M1 M2 M3

dp4 — NS NS **M1 0.7237 — NS NSM2 0.2008 0.4386 — **M3 0.0017 0.005 0.0008 —

P. anubis dp4 M1 M2 M3dp4 — NS NS **M1 0.0041 — NS NSM2 0.0283 0.7389 — NSM3 0.0004 0.0063 0.1658 —

DMX Y-Coordinate (DMXY)C. torquatus dp4 M1 M2 M3

dp4 — NS NS NSM1 0.1797 — NS NSM2 0.1797 0.2752 — NSM3 0.0986 0.0106 0.0081 —

FMT Y-Coordinate (FMTY)L. albigena dp4 M1 M2 M3

dp4 — NS NS **M1 1.0000 — NS NSM2 0.0105 0.0707 — NSM3 0.0014 0.0075 0.1902 —

P. anubis dp4 M1 M2 M3dp4 — NS NS NSM1 0.3173 — NS **M2 0.7540 0.6407 — NSM3 0.0028 0.0024 0.1033 —

P 5 one-tailed probability.**Significant at �Sid�ak-adjusted P 5 0.0026.NS 5 not significant.

56 SINGLETON

respectively—used to quantify variation in relative dis-tal–molar position yielded similar patterns of ontogeneticvariation; however, statistical tests using the distancevariable d were slightly more likely to be significant(Table 3). This accords with prior findings that geometri-cally derived shape variables yield equivalent results totraditional morphometric variables (Singleton, 2005).

In most species examined here, the relative positionsof the TMJ and the distalmost molar do not vary signifi-cantly among ontogenetic stages. Where significant dif-ferences are found, they involve anterior migration ofthe distal–molar position during post-dp4 ontogeny (Fig.5). In only one case, M1-stage C. atys, does average dis-tal–molar position fall appreciably posterior to that ofthe preceding dental stage. The rarity of this findingsuggests that it may be a sampling effect. There is noobvious commonality among species with significantresults (C. torquatus, L. albigena, and P. anubis), whichdiffer in size, ecology, and developmental patterns(O’Higgins and Collard, 2002; Leigh et al., 2003; Leigh,2007; Singleton et al., 2010; Swedell, 2011), making thisa question for further study. Because all significant posthoc contrasts involve the M3-stage (Table 4), it seemslikely that late adolescent facial growth contributes tosignificant positional differences between the M3-stageand earlier ontogenetic stages (see below). In those spe-cies exhibiting anterior migration of the distal–molarposition, between-stage differences (whether statisticallysignificant or not) are small in comparison with thosefor i/I1–dp/P4, which show pronounced anterior displace-ment between dental stages in all species (Fig. 5). Takentogether, these results are largely consistent with thoseof Spencer and Schwartz (2008; Schwartz, 2013) andsupport their hypothesis that molariform teeth erupt ata consistent minimum distance anterior to the TMJ.

Relative Position of the Masticatory Muscles

Masticatory muscle attachments. In the major-ity of species examined, two of three muscle-associatedlandmarks, FMT and ZTI, maintain relatively constantpositions anterior to the TMJ throughout ontogeny.Where ontogenetic variation in DMX position is present,variation in the positions of FMT and ZTI tends to mir-ror the DMX pattern. This is seen both in plots of intra-specific shape variation (Fig. 5) and in the results ofsignificance tests for FMTY and ZTIY (Tables 3 and 4).Across all species, the position of ZTI, which correlatesto the location of the deep masseter, is somewhat morestable throughout ontogeny than that of FMT, whichmarks the anterior cranial attachment of the temporalismuscle. By contrast, the position of the inferior zygo-maxillary landmark (ZMI), which marks the maximumanterior extent of the superficial masseter, varies signifi-cantly across dental stages (Table 3). In the majority ofspecies sampled, the relative position of ZMI migratesanteriorly relative to the TMJ, following an ontogenetictrajectory more similar to that of the anterior dentition(Fig. 5). This effect is most pronounced in smaller spe-cies characterized by facial retraction (e.g., L. albigena).Thus, ontogenetic variation patterns for FMT and ZTI,but not ZMI, conform to the prediction that masticatory-muscle attachments should maintain consistent posi-tions anterior to the TMJ throughout ontogeny. Thesefindings give partial support to the hypothesis of

Spencer and Schwartz (2008; Schwartz, 2013); however,the discordance between the ontogenetic trajectories ofmuscle-associated landmarks (FMT/ZTI versus ZMI)merits further study.

Resultant location. Resultant vectors calculatedusing Spencer’s value of 60% of TMJ-DMX distancewere found to lie at 21% of jaw length for adults and23% of jaw length across all dental stages (see Appendix,Table A1). These values bracket Perry et al.’s (2011)adult anthropoid average of 22% of jaw length, suggest-ing that prior studies, despite differences in methodol-ogy, are deriving a common value for the resultantvector location. This finding also supports the adoptionof Spencer’s value as a reasonable approximation for thelocation of R, at least in adult papionins. Ontogeneticvariation in R, as calculated here, cannot be evaluateddirectly, owing to its dependence on the position of thedistal molar. However, it is instructive to compare varia-tion in estimated R position with ontogenetic variationpatterns for landmarks associated with the positions ofthe temporalis and masseter muscles. Across all species,ontogenetic variation in the calculated relative positionof R closely matches the variation patterns of landmarksFMT and ZTI, with R remaining stable where the latterare stable and shifting anteriorly where anterior migra-tion is observed. To the extent that these landmarks cor-relate to the location of the adductor resultant,Spencer’s formula for the location of R may provide areasonable estimate for juveniles as well as adults. But,all other factors being equal, anterior migration of thesuperficial masseter during ontogeny is expected tomove the combined midline adductor vector closer to theposterior molar. Unless age-related changes in the orien-tation of muscles not evaluated here (e.g., medial ptery-goid) offset this effect, the resultant would be expectedto lie relatively closer to the TMJ in juveniles, conferringa greater safety margin during posterior molar biting.This result is perhaps counterintuitive given that adultsexperience higher absolute bite forces and greater repeti-tive stress to the masticatory system (Ross et al., 2009a;Ross et al., 2009b). However, musculoskeletal immatur-ity and lack of experience with mechanically challengingfoods likely put juveniles at greater overall risk of seri-ous TMJ injury (Herring, 1985; Herring et al., 2005).Pending further investigation, Spencer’s R provides ananterior bound on juvenile adductor resultant location.But given that adult R, as calculated, also falls well pos-terior to the distalmost molar, it is likely that a substan-tial buffer against TMJ distraction during posteriormolar biting is maintained throughout ontogeny.

Developmental and Functional Implications

Adults and post-weaning juveniles face substantiallysimilar masticatory challenges yet differ markedly inbody size, facial shape, and tooth complement (Thomp-son et al., 2003; Leigh, 2007; McGraw et al., 2010).While numerous studies have examined the influence ofaltered masticatory function on craniofacial development(e.g., Avis, 1961; Moore, 1965; Hendrickson et al., 1982;Herring and Lakars, 1982; Kiliaridis et al., 1985; Kiliari-dis, 1986; Bouvier and Hylander, 1996; Ravosa et al.,2008), relatively few have considered the biomechanicaleffects of growth-related changes in craniofacial form

FUNCTIONAL GEOMETRIC ANALYSIS OF PAPIONIN MASTICATORY ONTOGENY 57

(Moss, 1973; Oyen et al., 1979; Weijs et al., 1987;Dechow and Carlson, 1990; Langenbach et al., 1991;Thompson et al., 2003; Schwartz, 2013). The results ofthis study uphold specific predictions concerning ontoge-netic variation in the primate masticatory system(Schwartz, 2013), but we must consider these findings ina broader context to understand how functional compe-tence is maintained throughout ontogeny.

Ontogenetic shape variation in the papionin mastica-tory system as a whole (Fig. 4) reflects well-documentedpatterns of positive facial allometry (Freedman, 1962;Cochard, 1985; Bouvier, 1986a; Ravosa, 1990; Richtsme-ier et al., 1993; Profant and Shea, 1994; Ravosa andShea, 1994; Profant, 1995; Ravosa and Profant, 2000;Collard and O’Higgins, 2001; O’Higgins and Collard,2002; Singleton, 2002; Leigh et al., 2003). The data pre-sented here indicate that stability in the relative antero-posterior positions of the TMJ, distalmost molar, andmasticatory muscle attachments (Fig. 5) is maintainedin the midst of significant ontogenetic changes in overallfacial size and shape. The pattern of ontogenetic shapevariation documented in Fig. 5 suggests the papioninmasticatory system, sensu Spencer (1999), comprises twodevelopmental modules: an anterior dentognathic mod-ule characterized by anterior displacement relative tothe TMJ and a posterior masticatory module character-ized by stability of its absolute and relative AP dimen-sions. This pattern resembles previous divisions of thecranium into anterior and posterior compartments sepa-rated by the posterior maxillary (PM) plane, which isdefined by the anterior border of the middle cranialfossa and the maxillary tuberosity. (Enlow and Azuma,1975; Enlow, 1990; McCarthy, 2001, 2004; Lieberman,2011). A crucial difference is that the distal molar, partof the posterior masticatory module, lies anterior to themaxillary tuberosity. This discrepancy may be explainedby Oyen’s (1984) observation that the mesial border ofthe distal molar is consistently aligned with the trans-verse palatine suture (see Fig. 3), the principal center ofpalatal growth during the juvenile (dp4–M2) period(Oyen, 1984). Thus, successive molars erupt into a posi-tion of equilibrium between opposing maxillary growthfields. The late, rapid growth of the palatine associatedwith maxillary M3 eruption likely contributes to signifi-cant differences in relative M3 position (Table 4) in somepapionin species (Oyen, 1984).

Of the landmarks associated with masticatory muscleattachments, FMT (anterior temporalis) and ZTI (deepmasseter) maintain a constant anteroposterior (AP) posi-tion while ZMI (superficial masseter) migrates anteriorlyrelative to the TMJ. These results match those ofDechow and Carlson (Dechow and Carlson, 1990), whofound that the moment arm of the anterior masseter issignificantly greater in adult macaques than in juvenileswhile that of the temporalis muscle increases onlyslightly through ontogeny. In the past, they and othersinterpreted the anterior shift of the masseter attachmentas increasing mechanical advantage during molar biting(Oyen et al., 1979; Dechow and Carlson, 1990). Underthe constrained lever model, this shift is insteadexpected to offset reduced anterior bite forces as faciallength increases (Oyen et al., 1979; Spencer, 1999;Greaves, 2012). So it is probably not coincidental thatontogenetic variation in ZMI position tracks that of theanterior dentition or that its anterior migration is most

pronounced in species (e.g., L. albigena and C. atys)known to engage in anterior dental loading behaviors(Chalmers, 1968; Happel, 1988; Daegling and McGraw,2007; McGraw et al., 2010; Daegling et al., 2011).

Whereas anteroposterior relationships within the pos-terior masticatory system are stable throughout ontogeny,landmarks associated with muscle attachments showvarying degrees of lateral displacement relative to theTMJ (Fig. 5). This trend is strongest for ZTI, indicatingan increase in relative bizygomatic and temporal fossabreadths. At the same time, the anterior shift in ZMIposition results in an increase in relative temporal fossalength. These findings are consistent with results of theform-space analysis (Fig. 4), which also indicates an onto-genetic increase in relative temporal fossa length andbreadth, as well as numerous prior studies that havedemonstrated positive allometry for zygomatic breadths(e.g., Cochard, 1985; Ravosa, 1991; Singleton, 2002).Increases in the relative size of the temporal fossa arenot unexpected because physiological cross-sectional area(PCSA) of the masticatory muscles, a proxy for maximumbite force, scales with positive allometry relative to cra-nial and facial size (Weijs and Hillen, 1985; Dechow andCarlson, 1990; Ant�on, 1999, 2000; Anapol et al., 2008;Perry and Wall, 2008). Relative bite force should be fur-ther enhanced during ontogeny by an increase inmechanical advantage of the adductor muscles as theircranial attachments shift laterally relative to the TMJ.

Wide, short jaws are often listed among the“handicaps” that juvenile mammals face when transi-tioning to an adult diet (Biknevicius, 1996; Binder andVan Valkenburgh, 2000; Thompson et al., 2003). Thedirect relationship between jaw length and gapepresents an obstacle to juveniles’ consumption of largefood items (Lucas, 1981, 1982; Ravosa, 1990), but widejaws per se are not inherently disadvantageous. Underthe constrained lever model, increasing palate breadthrelative to biarticular breadth reduces Region II biteforces (Spencer, 1999). Like prior analyses (Ravosa,1990; Profant and Shea, 1994; Ravosa and Shea, 1994;Ravosa and Profant, 2000; Collard and O’Higgins, 2001;O’Higgins and Collard, 2002; Singleton, 2002; Leighet al., 2003; Singleton, 2004; Leigh, 2007), this studyfound a pattern of negative ontogenetic scaling for bothpalate breadth and jaw breadth (Fig. 4); however, maxi-mum palate breadth appears to be isometric relative tobiglenoid breadth in all papionin species examined(Fig. 5). Thus juveniles may be disadvantaged byrestricted gape, smaller absolute muscle size, and incom-plete dentitions, but relative jaw width does not appearto be a significant limiting factor. Taken together, isome-try of relative jaw and palate breadths, increasingmechanical advantage of adductor muscles, and positivescaling of masticatory PCSA help explain the fact thatmaximum bite force scales isometrically during ontogenyand across primate species despite increases in relativefacial length (Anapol et al., 2008; Perry et al., 2011).

CONCLUSIONS

In this study, standard Procrustes analysis, Booksteinshape coordinates, and traditional morphometric varia-bles were used to investigate ontogenetic variation inthe papionin masticatory system and test the hypothesisthat biomechanical constraints on the configuration of

58 SINGLETON

the masticatory system determine the timing and loca-tion of molar eruption (Schwartz, 2013). This hypothesispredicts that molariform teeth will erupt at a consistentlocation anterior to the temporomandibular joint andthat jaw adductor muscles should maintain a consistentposition relative to the TMJ and distal molar. In themajority of taxa studied, the distal molar does maintaina consistent position relative to the TMJ. The relativestability of the distal–molar position contrasts with asteady anterior migration of the anterior dentition. Thisstability appears to be achieved by erupting the distalmolar into a developmentally “neutral” location betweenopposing maxillary growth fronts. Where significant dif-ferences among ontogenetic stages occur, they involveanterior (rather than posterior) migration of the distal–molar position in later dental stages and are likely dueto late, rapid growth of the posterior palate in coordina-tion with M3 eruption (Oyen, 1984).

Like the distal molar, landmarks associated withattachments of the anterior temporalis and deep mass-eter muscles maintain a consistent position relative tothe TMJ; however, the superficial masseter attachmentmigrates anteriorly throughout ontogeny, following atrajectory more similar to that of the anterior dentition.This migration partially offsets loss of mechanicaladvantage at anterior bite points due to positive facialallometry. All muscle attachments migrate laterally rela-tive to the TMJ, reflecting known patterns of mastica-tory muscle scaling. Consistent with independentestimates (Perry et al., 2011), Spencer’s estimate of mid-line adductor resultant position places the resultant at22% of jaw length in adults. The calculated resultanttracks the ontogenetic patterns of the anterior tempora-lis and deep masseter attachments. Pending future stud-ies incorporating additional masticatory muscleattachments, Spencer’s R may be considered an anteriorbound on the resultant location in juveniles. Even allow-ing for variation in AP position of the adductor result-ant, the masticatory system appears well bufferedagainst distraction of the TMJ throughout ontogeny, asevidenced by the fact that juvenile papionins are capableof consuming even obdurate food items (McGraw et al.,2010). Taken in total, the results of this study supportthe predictions of the constrained eruption hypothesisand point to mechanisms by which relative functionalcapacity is maintained throughout ontogeny.

APPENDIX

Calculation of TMJ-DMX Distance d

The midline perpendicular distance d between theTMJ and the distalmost molar DMX was calculatedusing: (1) Bookstein shape coordinates aligned to thebiglenoid line and prosthion and scaled to unit biglenoidlength; and (2) backscaled (i.e., size-restored) Booksteinshape coordinates. The first value was used to derivescaled shape coordinates for the midline resultant vectorR. The second value, which approximates the actualobject space distance, was used in statistical tests ofTMJ-DMX distance.

In the following equations, 3D coordinate vectors forosteometric landmarks are represented by their corre-sponding landmark abbreviations (see Table 2). The mid-line distance d was derived as follows (see Fig. A1):

1. Coordinates for midpoint of biglenoid line:

mTMJ5RTMJ1LTMJ

2

2. Coordinates for midpoint of distal bimolar line:

mDMX5RDMX1LDMX

2

3. Euclidean distance between mDMX and prosthion:

b5

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX3

1

mDMX i½ �2PRO i½ �ð Þ2vuut

4. Euclidean distance between mTMJ and prosthion:

c5

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX3

1

ðmTMJ i½ �2PRO i½ �Þ2vuut

5. Coordinates of Euclidean vector between mTMJ andprosthion (c):

BA�!

5mTMJ2PRO

6. Coordinates of Euclidean vector between mDMX andprosthion (b):

CA��!

5mDMX2PRO

TABLE A1. Mean relative R position and TMJ elevation by species and dental stage

tx h

dp4 M1 M2 M3 dp4 M1 M2 M3

C. agilis — 0.25 0.22 0.20 — 11.07 10.61 11.18C. atys 0.27 0.22 0.23 0.20 9.60 10.73 10.52 8.64C. torquatus 0.25 0.23 0.22 0.21 10.86 12.67 8.96 9.67L. aterrimus 0.26 0.23 0.21 0.20 12.94 15.15 12.61 12.20L. albigena 0.27 0.23 0.20 0.21 10.61 11.05 11.25 12.09M. mulatta 0.28 0.24 0.22 0.22 14.09 13.99 11.97 10.74M. sphinx — 0.24 0.25 0.23 — 10.57 7.11 8.70P. kindae 0.25 0.26 0.24 0.21 13.10 10.47 8.94 8.85P. anubis 0.27 0.26 0.24 0.23 10.42 9.92 7.25 8.47X 0.26 0.24 0.23 0.21 11.66 11.74 9.91 10.06

tx 5 perpendicular distance between mTMJ and R expressed as a proportion of mTMJ-PROh 5 angular elevation of the TMJ relative to the occlusal plane

FUNCTIONAL GEOMETRIC ANALYSIS OF PAPIONIN MASTICATORY ONTOGENY 59

7. Calculate angle h between b and c using vector corre-lation (dot product):

u5cos 21ðBA�! � CA

��!Þ3 180

3:14159

8. Apply law of sines and Pythagorean theorem to solvefor d:

d5

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffic22 csin uð Þ2

q2b

Calculation of 3D Coordinates for R

After calculating the midline perpendicular distance dbetween TMJ and DMX, linear interpolation was usedto derive 3D Bookstein shape coordinates for the midlineadductor resultant R. Calculations were based onSpencer’s conservative estimate that R is located at 60%of the midline perpendicular distance between the tem-poromandibular joint and the most distal molar (Spencerand Demes, 1993; Spencer, 1995). This calculation incor-porates several additional approximations. Jaw lengthand perpendicular TMJ-DMX distance were calculatedin the maxillary alveolar plane rather than in the maxil-lary occlusal plane. Additionally, the linear interpolationwas executed using the 3D vector extending from themidpoint of the biglenoid line (mTMJ) to prosthion. Let-ting tx represent the distance between mTMJ and Rexpressed as a proportion of the distance c betweenmTMJ and prosthion (see Fig. A2):

tx50:60d=cand

R5 12txð ÞmDMX1txPRO

RESULTSTable A1 summarizes selected results of the preceding

calculations by species and dental stage. Spencer’s 60%criterion places the resultant between 21% and 26% ofjaw length for adults and dp4-stage juveniles, respec-tively. The adult papionin average corresponds closely tothe 22% value obtained for adult anthropoids by Perryet al. (2011), suggesting that prior studies, despite differ-ences in methodology, are deriving a common value forthe location of the resultant vector. This finding alsosupports the adoption of Spencer’s value as a reasonableapproximation for the location of R, at least in adultpapionins (see Discussion).

The angle of elevation h between the alveolar planeand the vector joining mTMJ and prosthion varies

inversely with relative jaw length and ranges from anaverage of 10� in adults to 12� in dp4-stage juveniles(Table A1). Because the location of R was interpolatedalong the mTMJ-PRO vector, it is expected that the cal-culated coordinates will lie slightly anterior to the resul-tant’s actual intersection with the alveolar and occlusalplanes and that this anterior shift will be more pro-nounced in juveniles.

Given that the calculated location of R is directlydependent on the coordinates of the distalmost molar,juvenile variation in R position cannot be meaningfullyassessed on the basis of these estimates. However, theyprovide a useful benchmark for comparison with ontoge-netic variation in the relative positions of landmarksassociated with jaw adductor muscle attachments.

ACKNOWLEDGMENTS

I wish to thank Claire Terhune and Siobh�an Cooke fortheir invitation to contribute to this special issue as wellas for organizing the symposium on which it is based.My thanks also go to the following institutions and indi-viduals for access to specimens, curatorial assistance,and extraordinary hospitality: L. Heaney, W. Stanley,and R. Banasiak (Field Museum of Natural History); E.Gilissen and W. Wendelen (Royal Museum for CentralAfrica); Georges Lenglet (Royal Belgian Institute of Nat-ural Sciences); Darren Lunde and Eileen Westwig(American Museum of Natural History); Craig Hood andNelson Rios (Tulane University Museum of Natural His-tory); and John Soderberg, Kieran McNulty, and Martha

Fig. A1. Calculation of TMJ-DMX distance d. Lateral view of themasticatory configuration showing landmarks and variables used tocalculate the perpendicular midline distance between the TMJ anddistal molar.

Fig. A2. Calculation of 3D coordinates for R. Dorsal view of themasticatory configuration showing landmarks and variables used tocalculate 3D coordinates of the midline adductor resultant R.

60 SINGLETON

Tappen (Tappen Primate Collection, Department ofAnthropology, University of Minnesota). For data collec-tion and other research and technical assistance, I amgrateful to Brielle Seitelman, Laura Pionek, Amy Mar-tiny, Leila Wagner, and Richard Galbraith. I also thankSiobh�an Cooke, Brielle Seitelman, and two anonymousreviewers for their helpful comments on early versionsof this article. For ongoing contributions to thisresearch, I thank E. Delson and members of the NYCEPMorphometrics Group. This research was supported byMidwestern University, NYCEP, the Field Museum ofNatural History, the University of Illinois–Urbana-Champaign, and NSF (IIS-0513660). This paper isNYCEP Morphometrics Contribution #85.

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