The presence of a prominent chin in modern humans has been viewed by some researchers as an architectural adaptation to buttress the anterior corpus from bending stresses during mastication. In contrast, ontogenetic studies of mandibular symphyseal form suggest that a prominent chin results from the complex spatial interaction between the symphysis and surrounding soft tissue and skeletal anatomy during development. While variation in chin prominence is clearly influenced by differential growth and spatial constraints, it is unclear to what degree these developmental dynamics influence the mechanical properties of the symphysis. That is, do ontogenetic changes in symphyseal shape result in increased symphyseal bending resistance? We examined ontogenetic changes in the mechanical properties and shape of the symphysis using subjects from a longitudinal cephalometric growth study with ages ranging from 3 to 20+ years. We first examined whether ontogenetic changes in symphyseal shape were correlated with symphyseal vertical bending and wishboning resistance using multivariate regression. Secondly, we examined ontogenetic scaling of bending resistance relative to bending moment arm lengths. An ontogenetic increase in chin prominence was associated with decreased vertical bending resistance, while wishboning resistance was uncorrelated with ontogenetic development of the chin. Relative to bending moment arm lengths, vertical bending resistance scaled with significant negative allometry whereas wishboning resistance scaled isometrically. These results suggest a complex interaction between symphyseal ontogeny and bending resistance, and indicate that ontogenetic increases in chin projection do not provide greater bending resistance to the mandibular symphysis.

Introduction During mastication, the anthropoid mandible is subjected to high repetitive loads, resulting in a predictable pattern of mechanical stresses and strains (e.g. Hylander, 1984, 1985). Variation in load magnitude and frequency associated with variability in dietary properties, as well as non‐dietary paramasticatory behaviors, has been used to explain variation in mandibular form across a wide range of extant and fossil primate taxa (Hylander, 1984, 1985; Ravosa, 1990, 1996a,b; Daegling & Grine, 1991; Ravosa & Simons, 1994; Vinyard & Ravosa, 1998; Daegling, 2001; Daegling et al. 2009, 2014). In particular, there has been considerable emphasis placed on the interaction between masticatory loads and mandibular symphyseal morphology. While the mandibular symphysis experiences a combination of mechanical stresses during mastication, the curvature of the symphyseal region contributes to particularly high lateral transverse bending stresses (i.e. wishboning), especially along the lingual aspect of the symphysis (Hylander, 1984). Resistance to lateral transverse bending across anthropoids is evident in architectural features of the mandibular symphysis such as thicker lingual cortical bone and the presence of superior and inferior transverse tori, which aid in resisting increased tensile stresses along the lingual symphysis (Hylander, 1984; Daegling & McGraw, 2009; Panagiotopoulou & Cobb, 2011). Moreover, allometric scaling of symphyseal dimensions during ontogeny and across static adult comparisons suggests that variation in symphyseal form maintains functional equivalency with regard to lateral transverse bending loads (e.g. Hylander, 1985; Vinyard & Ravosa, 1998; Daegling, 2001). In a similar fashion, the unique morphology of the modern human mandibular symphysis, i.e. the presence of a prominent chin, has also been viewed as an architectural adaptation to buttress the anterior corpus from bending stresses during mastication (DuBrul & Sicher, 1954; White, 1977; Daegling, 1993; Dobson & Trinkaus, 2002; Gröning et al. 2011). Although in vivo data for human mandibular strains do not exist, it is generally accepted that strain data from other anthropoids are applicable to humans as well, albeit with regard to a derived mandibular form. Following Daegling (1993), the combination of a reduction in mandibular length and a wide dental arch in modern humans would have lessened the relative severity of lateral transverse bending stresses at the mandibular symphysis. This would result in a relative increase in vertical bending in the coronal plane producing compressive forces along the alveolar region and tensile forces along the symphyseal base. Thus, if resistance to mechanical stress underlies the derived morphology of modern human symphyseal form, this would suggest that a prominent chin serves as a key functional adaptation to resisting vertical bending stresses during mastication. Recent biomechanical assessments of mandibular symphyseal form in archaic and recent Homo indicate that there is a general lack of consensus regarding the relationship between functional loading of the anterior corpus and the development of the chin. As such, whether a prominent chin in modern humans can be explained as a function of symphyseal loading remains unresolved. In their comparative functional analyses of the mechanical properties of the mandibular symphysis, both Dobson & Trinkaus (2002) and Gröning et al. (2011) found that resistance to vertical bending stress was maintained across the range of mandibular symphyseal form in later genus Homo, suggesting that a prominent chin in modern humans may act to resist altered patterns of mechanical strains associated with evolutionary changes in mandibular form. Consistent with Daegling's (1993) model, both Dobson & Trinkaus (2002) and Gröning et al. (2011) also found that there was a general trend for modern humans to be less resistant to wishboning stresses when compared with archaic Homo. Dobson and Trinkaus (2002) however, were unable to document a significant difference in lateral transverse bending resistance between Neandertals and modern humans. In addition to comparisons of function and mandibular symphyseal form across later genus Homo, both Gröning et al. (2011) and Ichim et al. (2006) examined whether the presence or absence of a chin in three‐dimensional models of modern human mandibles affected symphyseal strain distributions using finite element analysis. Gröning et al. (2011) concluded that a modern human mandible with a chin was better at resisting dorso‐ventral shear, lateral transverse bending and vertical bending when compared with a non‐chinned model. Ichim et al. (2006), on the other hand, found that there were no differences in symphyseal strains in their chinned and non‐chinned models leading them to conclude that the chin is likely unrelated to the functional demands of mastication. This latter result is consistent with a recent analysis by Daegling (2012), who was unable to document a meaningful correlation between chin prominence and symphyseal bending moment arm lengths in modern human samples. In contrast to the potential mechanical influences on the development of the modern human mandibular symphysis, others have suggested that a projecting chin may be the result of differential patterns of upper and lower facial prognathism during human evolution (Hrdlička, 1911; Waterman, 1916; Bolk, 1924; Weidenreich, 1936; Biggerstaff, 1977; Cartmill & Smith, 2009). As such, the degree to which a prominent chin may act to resist mechanical stresses during mastication may simply be a secondary consequence of differential jaw growth and associated changes in symphyseal form (e.g. Gröning et al. 2011; Daegling, 2012), rather than being a primary causal mechanism. Indeed, although a bony chin may act to increase resistance to bending, mandibular strains in humans are likely low to begin with as a result of an evolutionary reduction in the size of the masticatory apparatus and an increased reliance on technocultural adaptation and extraoral processing. Moreover, for a given size, the human mandible has significantly more cortical bone throughout its corpus (including the symphyseal region) when compared with mandibles of other apes, which do experience prolonged, forceful mastication (Daegling, 2007, 2012). As such, the human mandible has more cortical bone than is likely necessary to resist the relatively low stresses incurred during routine masticatory loading. With regard to non‐functional influences, it is well established that ontogenetic variation in chin prominence in modern humans is tied to larger craniofacial growth dynamics that affect the spatial relationship between the mandible and surrounding soft and hard tissue anatomy. During early postnatal development, for example, the position of the mental region is influenced by soft tissue (e.g. the tongue and suprahyoid muscles) and spatial constraints in the pharyngeal region, which, in turn, are affected by relative positions of the facial skeleton and cervical vertebral column (Coquerelle et al. 2013a,b). Chin prominence is further associated with variation in ontogenetic patterns of mandibular rotation during later postnatal development (Björk, 1969; Ödegaard, 1970a,b; Lavergne & Gasson, 1976; Björk & Skieller, 1983), where increased chin prominence is part of a larger suite of features associated with a pattern of forward mandibular rotation (Fig. 1). In contrast, reduced chin prominence is more closely associated with a pattern of backward mandibular rotation. Variation in mandibular rotation and associated correlated symphyseal form are tied to the complex interaction of mandibular posture, dentoalveolar development and the direction of growth of the condylar cartilage (Ödegaard, 1970a,b; Lavergne & Gasson, 1976; Buschang & Gandini, 2002; Araujo et al. 2004; Buschang et al. 2013). In addition, variation in chin prominence has also been tied to differential anterior‐posterior dimensions of the dentoalveolar complex and the lower border of the mandible both during ontogeny (Marshall et al. 2011) and across broader ranges of population variation (Scott et al. 2010; Scott, 2014). Figure 1 Open in figure viewer PowerPoint Examples of two 13‐year‐old male subjects who exhibit variation in mandibular growth resulting in morphological differences in mandibular symphyseal form. The individual in (A) is characterized by a pattern of forward mandibular rotation, while the individual in (B) exhibits backward mandibular rotation. Forward mandibular rotation is associated with greater vertical growth at the mandibular condyle and with a brachyfacial morphology (i.e. relatively shorter vertical facial dimensions, flat mandibular plane, reduced gonial angle, etc.). Backward mandibular rotation is associated with greater posteriorly oriented growth at the mandibular condyle. Individuals with greater posterior mandibular rotation exhibit a dolicofacial morphology (i.e. relatively longer anterior vertical facial dimensions, steep mandibular plane, larger gonial angle, etc.). While variation in the degree of chin prominence is clearly influenced by differential growth and spatial constraints in the facial skeleton, it is unclear to what degree these developmental dynamics influence the mechanical properties of the symphysis. That is, a spatial model of chin development does not rule out the possibility that an ontogenetic increase in chin prominence increases resistance to symphyseal bending stresses. Therefore, to further our understanding of the functional implications of chin prominence on the geometry of the mandibular symphysis, we examine whether ontogenetic changes in chin development in a longitudinal cephalometric sample result in a relative increase in symphyseal bending resistance. To accomplish this, we first assessed whether ontogenetic variation in measures of symphyseal bending resistance is correlated with mandibular symphyseal shape. If chin prominence is a response to symphyseal bending loads during development, then we would predict that increased bending resistance will be associated with ontogenetic increases in chin projection. Conversely, reduced chin projection early in development should correspond to a decrease in relative bending resistance. Secondly, we examined the allometric scaling of symphyseal bending resistance to determine whether there is an ontogenetic increase in resistance relative to bending moment arm proxies during development.

Materials and methods We collected 292 longitudinal cephalometric observations from a total of 37 individuals (19 male and 18 females) selected from the Iowa Facial Growth Study located at The University of Iowa Department of Orthodontics. This growth study, which began in 1946, consists of individuals predominantly of northwest European ancestry who resided in or around the Iowa City, IA area. Children were at least 3 years of age at enrollment with records taken quarterly until age 5 years, bi‐annually from 5 to 12 years, and annually from 12 to 18 years. Final records were taken once during early adulthood. The subjects included in our analysis were selected from the larger growth study sample based on the completeness of the individual radiographic sequences as well as the quality of the lateral cephalograms with respect to the variables of interest. Measurements were collected at nine different observations beginning at 3.0–4.0 years of age through 20+ years of age (Table 1). Table 1. Sample composition Age, years Female, n Male, n Total, n 3.0–4.9 14 17 31 5.0–6.9 19 17 36 7.0–8.9 17 19 36 9.0–10.9 18 18 36 11.0–12.9 18 18 36 13.0–14.9 18 17 35 15.0–16.9 17 16 33 17.0–18.9 11 8 19 20.0+ 15 15 30 Total n 147 145 292 We collected symphyseal cortical bone parameters from lateral cephalometric films by first tracing the external cortical symphyseal surface using dolphin imaging software. Because the developing permanent dentition obscured the endosteal surface of the posterior aspect of the mandibular symphysis in the younger age groups, we were unable to identify the border of the endocortical surface in this region. It was therefore necessary to model the symphysis as a cross‐section through a solid beam (Fig. 2) following the methods used by Dobson & Trinkaus (2002). All tracings were uploaded into imagej 1.45, scaled and rotated such that the mandibular plane (i.e. the lower border of the mandibular corpus from menton to gonion) was oriented horizontally. Figure 2 Open in figure viewer PowerPoint Lateral cephalograms of a subject at 6 years of age (A) and at 17 years of age (B). External symphyseal contours in the same subjects are outlined in (C) and (D). Next, using the shape of the external cortical surface, we measured symphyseal bending resistance using second moments of area (e.g. Daegling & McGraw, 2001; Organ et al. 2006; Fukase & Suwa, 2008; Antón et al. 2010). These values are a function of the amount and distribution of bone relative to specified axes about which bending is hypothesized to occur (Fig. 3). First, we calculated second moments relative to the X‐ and Y‐axes (i.e. parallel and perpendicular to the mandibular plane, respectively). I xx is a measure of resistance to vertical bending stresses relative to the horizontal axis (X in Fig. 3). We then calculated I yy as a measure of resistance to wishboning stresses relative to the vertical axis (Y in Fig. 3). Additionally, for a given symphyseal cross‐section there is an axis about which the second moment of area will be maximized (X′ in Fig. 3) and an orthogonal axis about which the second moment of area will be minimized (Y′ in Fig. 3). Thus, we calculated I max as a measure of maximum resistance relative to the X′ axis and I min as a measure of minimum bending resistance relative to the Y′ axis. Second moments of area were calculated using momentmacro for imagej (http://www.hopkinsmedicine.org/FAE/mmacro.htm). Figure 3 Open in figure viewer PowerPoint Axes used to calculate second moments of area. The X‐ and Y‐axes are oriented parallel and perpendicular to the mandibular plane, respectively. I xx is calculated relative to the X‐axis and I yy is calculated relative to the Y‐axis. X′ and Y′ are the axes for the major and minor principal axes, respectively. I max is calculated relative to X′ and I min relative to Y′. Although it is desirable to calculate biomechanical properties from actual cortical bone cross‐sections rather than external contours (i.e. a hollow beam model vs. a solid beam model), there is a very strong correlation between second moments of area calculated from both cortical bone and external bone contours. Stock and Shaw (2007), for example, found correlations in the range of 0.84–0.98 in various postcranial skeletal elements. Similarly, there is a high range of correlations (0.83–0.96) when using both methods to calculate second moments for the mandibular symphysis in CT scan images (N.E. Holton, unpublished data). The consistently high correlations between second moments of area calculated using both methods indicate that the results of our analysis are unlikely to be affected by the use of external contours vs. actual cortical bone cross‐sections. However, this precludes the examination of potentially meaningful developmental changes in symphyseal cortical cross‐sectional area and regional differences in cortical bone thickness. To assess the relationship between bending resistance and mandibular symphyseal shape, we collected a series of k = 8 mandibular landmarks (Fig. 4), which were superimposed using generalized Procrustes analysis. We then used multivariate regression analysis to examine the relationship between mandibular shape and our independent variables. First, we examined the relationship between mandibular shape and centroid size to illustrate ontogenetic variation in the mandibular symphysis. Next, we examined the relationship between mandibular shape and bending resistance values scaled to moment arm proxies to determine whether shape variation associated with an increase in relative bending resistance mirrored the ontogenetic increase in chin prominence. Figure 4 Open in figure viewer PowerPoint Landmarks used to quantify mandibular shape. 1 = infradentale; 2 = B point; 3 = pogonion; 4 = menton; 5 = genion; 6 = mandibular orale; 7 = gonion; 8 = articulare. Wishboning resistance was scaled to mandibular length (pogonion‐articulare) and vertical bending resistance was scaled to bigonial breadth (measured from posterior‐anterior cephalograms), which served as a proxy for the vertical bending moment arm. The magnitude of vertical bending stress is, in part, a function of width of the coronally oriented region of the anterior corpus. As such, other researchers have used measures such as bicanine or bimolar distances to scale estimates of vertical bending resistance (e.g. Daegling, 2001; Dobson & Trinkaus, 2002; Antón et al. 2010). Although dental casts are available for the subjects used in our analysis, we were unable to take transverse measures of the dentition during the mixed dentition phase. As such, we selected bigonial breadth (e.g. Holton et al. 2014) as a transverse measure, which was available for all subjects. All geometric morphometric analyses were conducted using morphoj (Klingenberg, 2008–2010). We examined the ontogenetic allometry of symphyseal second moments of area using reduced major axis regression. Second moments of area, which are measured in mm4, were converted to their fourth roots and log‐transformed. We then regressed log‐transformed second moments against log‐transformed symphyseal bending moment arm proxies for each individual ontogenetic trajectory. To assess the ontogentic scaling of measures of bending resistance, we calculated the mean of the individual regression slopes and the 95% confidence intervals (e.g. Lammers & German, 2002). Finally, because there is sexual dimorphism in masticatory function (Helkimo et al. 1977; Raadsheer et al. 1999; Kovero et al. 2002; Kiliardis et al. 2003) that manifests during adolescence (e.g. Ingervall & Minder, 1997), we examined growth allometries in the mixed‐sex sample and in the individual male and female samples. We tested for significant differences in male and female growth allometries using mixed model anova. Specifically, we compared least‐squares regression slopes by testing for the interactive effects of sex and moment arm length on second moments of area.

Results Correlated variation between mandibular shape and centroid size (P < 0.001) is illustrated in Fig. 5A. Smaller mandibular centroid sizes (left) are associated with a vertically oriented mandibular symphysis and a relatively flat labial symphyseal surface in the midsagittal plane. This is further associated with a more posteriorly oriented mandibular ramus and relatively wider gonial angle. As centroid size increases, the mental protuberance along the labial border becomes more prominent due to the relative posterior displacement of infradentale and B‐point along with a relative anterior displacement of pogonion, menton and genion. Additionally, the mandibular ramus becomes more vertically oriented and is associated with a relatively narrower gonial angle and flatter mandibular plane. Figure 5 Open in figure viewer PowerPoint Wireframe images illustrating mandibular shape variation (black wireframes) correlated with centroid size (A), scaled I xx (B) and scaled I yy (C). The gray wireframes represent the mean shape configuration. With regard to symphyseal bending resistance, scaled I xx , I yy , I max and I min were all significantly correlated with mandibular shape (P < 0.001). Since morphological variation in the mandibular shape associated with I xx and I max was virtually identical, only the results for I xx are illustrated in Fig. 5. Additionally, due to similarity in the results between I yy and I min , only the results for I yy are presented. Variation in resistance to vertical bending was correlated with mandibular symphyseal shape such that decreased resistance was associated with a relative decrease in symphyseal height and a relative increase in the prominence of the chin (Fig. 5B). In contrast, increased symphyseal resistance to vertical bending was correlated with an increase in symphyseal height and a flatter labial symphyseal border due to the anterior projection of B‐point relative to pogonion. The pattern reflected in the correlation between I xx and mandibular shape is in contradistinction to the pattern of ontogenetic development of the mandibular symphysis (Fig. 5A). Resistance to lateral transverse bending was correlated with the relative anterior‐posterior dimensions of the mandibular symphysis (Fig. 5C). Decreased lateral transverse bending resistance was associated with a reduction in symphyseal depth along both the labial and lingual borders of the symphysis (i.e. at pogonion and genion), whereas the more superior aspects of the symphysis (infradentale and B‐point) were relatively stable. As such, reduced lateral transverse bending resistance was associated with reduction in the prominence of the chin. Conversely, greater resistance to lateral transverse bending was associated with greater symphyseal depth resulting from an anterior displacement of pogonion and a posterior displacement of genion. Coupled with the relatively stable superior symphyseal region, increased lateral transverse bending resistance was associated with greater prominence of the chin. With regard to ontogenetic scaling of cortical bone parameters (Table 2, Fig. 6), the mean slopes for I xx and I max relative to bigonial breadth (slope = 0.71 and 0.75, respectively) scaled with negative allometry. In both cases, the upper limit of the 95% confidence intervals fell below isometry. In contrast, the mean slopes for I yy (slope = 0.96) and I min (slope = 0.98) approached an isometric relationship with mandibular length and the confidence intervals for both bivariate comparisons spanned isometry. It is of note that there was a considerable variation in regression slopes, with individual slopes spanning the range from negative to positive allometry for all measures of bending resistance (Table 2). Table 2. Mean RMA slopes, confidence intervals and ranges of variation in mean slopes n Slope 95%CI Slope range Combined I xx vs. bigonial breadth 37 0.71 0.53–0.90 0.42–1.12 I yy vs. mandibular length 37 0.96 0.72–1.19 0.49–1.52 I max vs. bigonial breadth 37 0.75 0.56–0.93 0.43–1.15 I min vs. mandibular length 37 0.98 0.72–1.16 0.49–1.52 Male I xx vs. bigonial breadth 19 0.73 0.55–0.90 0.49–1.12 I yy vs. mandibular length 19 1.01 0.77–1.23 0.55–1.28 I max vs. bigonial breadth 19 0.76 0.59–0.93 0.52–1.15 I min vs. mandibular length 19 1.01 0.77–1.18 0.56–1.28 Female I xx vs. bigonial breadth 18 0.72 0.50–0.90 0.42–1.02 I yy vs. mandibular length 18 0.91 0.50–1.14 0.49–1.52 I max vs. bigonial breadth 18 0.74 0.53–0.94 0.43–1.03 I min vs. mandibular length 18 0.91 0.67–1.14 0.49–1.51 Figure 6 Open in figure viewer PowerPoint Bivariate relationship between second moments of area and bending moment arm proxies. Males (gray circles) and females (open circles) exhibit the same scaling relationships for vertical bending resistance (A and B) and lateral transverse bending resistance (C and D). The individual male and female samples exhibited the same scaling patterns as the combined sample. I xx and I max scaled with negative allometry relative to bigonial breadth in both the males (slope = 0.73 and 0.76, respectively) and females (slope = 0.72 and 0.74, respectively). With regard to I yy and I min , both males (slope = 1.01 and 1.01, respectively) and females (slope = 0.91 and 0.91, respectively) tend to scale isometrically relative to mandibular length. With regard to patterns of sexual dimorphism in ontogenetic scaling, the results of our mixed‐model anova comparing least‐squares regression slopes indicated that there were no significant differences between males and females (Table 3). Table 3. Mixed model anova results Comparison F P I xx vs. bigonial breadth Sex 1.718 0.191 Bigonial breadth 22.471 < 0.001 Sex*bigonial breadth 1.842 0.179 I yy vs. mandibular length Sex 0.163 0.687 Mandibular length 48.456 < 0.001 Sex*mandibular length 0.154 0.695 I max vs. bigonial breadth Sex 1.157 0.283 Bigonial breadth 27.329 < 0.001 Sex*bigonial breadth 1.246 0.265 I min vs. mandibular length Sex 0.939 0.333 Mandibular length 19.110 < 0.001 Sex*mandibular length 0.986 0.322

Discussion If a prominent chin is a structural adaptation that increases resistance to symphyseal bending stresses, then correlated variation between bending resistance and symphyseal shape should mirror allometric changes in the symphysis during ontogeny. In the present study we examined ontogenetic changes in bending resistance of the mandibular symphysis, first to determine whether there is a correlation between increased bending resistance and ontogenetic changes in chin development, and secondly to examine ontogenetic scaling of bending resistance relative to bending moment arms. Collectively, the ontogenetic changes in symphyseal shape documented in our multivariate regression analysis generally reflect previously established symphyseal changes resulting from a typical pattern of anterior mandibular rotation during development (e.g. Björk, 1969; Ödegaard, 1970a,b; Lavergne & Gasson, 1976; Björk & Skieller, 1983). During ontogeny, there is a significant increase in chin projection resulting, in part, from an anterior displacement of the lower symphysis. Increased chin projection is further associated with a relative reduction in symphyseal height, a more vertically oriented ramus and a relatively flatter mandibular plane. An ontogenetic increase in chin prominence is also correlated with a relative posterior positioning of the superior alveolar region (e.g. Chen et al. 2000), which has been shown to result from differential anterior growth between the mandibular and maxillary region of the facial skeleton (You et al. 2001; Marshall et al. 2011). During ontogeny, the lower border of the mandible exhibits increased anterior growth relative to the maxilla as the result of a superior‐inferior gradient of growth cessation in which the lower regions of the facial skeleton cease growing later than the more superior regions (Buschang et al. 1983; Enlow & Hans, 1996; but see Bastir et al. 2006). However, although increased anterior mandibular growth is evident in the lower symphyseal region, developmental and functional integration between the maxillary and mandibular alveolar regions due to occlusal interlocking (You et al. 2001; Marshall et al. 2011) restricts the anterior growth of the mandibular alveolus, resulting in a relative posterior positioning of the superior symphysis during growth. Thus, increased chin projection results from a suite of morphological changes in the mandible associated with differential growth and complex spatial constraints that begins early in development (e.g. Coquerelle et al. 2013a,b) and continues through postnatal ontogeny and into adulthood (e.g. Björk, 1969; Ödegaard, 1970a,b; Lavergne & Gasson, 1976; Björk & Skieller, 1983; Scott et al. 2009; Marshall et al. 2011; Scott, 2014). With regard to the relationship between vertical bending resistance and symphyseal shape, our sample exhibited a pattern that largely contrasted with ontogenetic changes in chin projection. The results of our geometric morphometric analysis indicate that a relative increase in vertical bending resistance is associated with a morphological pattern seen during early ontogeny, i.e. a relatively taller symphysis along with a flatter labial surface. Reduced relative vertical bending resistance, on the other hand, was associated with a relatively shorter symphysis and a prominent chin, as seen in adults. This result is consistent with the ontogenetic scaling of I xx and I max relative to the vertical bending moment arm (i.e. bigonial breadth). In both cases, vertical bending resistance scaled with negative allometry, indicating that resistance to vertical bending stress relative to bigonial breadth decreases during development. Thus, in contrast to previous studies that have found that a prominent chin in modern humans may be important for resisting vertical bending stresses when compared with archaic Homo (e.g. Daegling, 1993; Dobson & Trinkaus, 2002; Gröning et al. 2011), our results suggest that increased chin prominence during modern human ontogeny is associated with reduced resistance to vertical bending stresses. As such, although the morphology of the mandibular symphysis affects the mechanical environment of the anterior corpus, our results suggest that the development of a projecting chin is likely independent of the need to resist masticatory stresses. The reduction in vertical bending resistance during development is likely due, in part, to ontogenetic changes in mandibular symphyseal orientation, which is thought to have a significant influence on the ability to resist bending stresses during mastication. For example, the oblique orientation of the symphysis in non‐human anthropoid primates is well suited to counter relatively greater wishboning stresses (e.g. Hylander, 1985; Vinyard & Ravosa, 1998; Daegling, 2001). Similarly, a more vertically oriented symphysis in modern humans relative to Neandertals (Daegling, 1993; Dobson & Trinkaus, 2002; Nicholson & Harvati, 2006; Gröning et al. 2011) has been argued to reflect changes in the biomechanical environment of the anterior corpus during mandibular loading. However, due to differential anterior growth of the alveolar region and lower symphysis during ontogeny (You et al. 2001; Marshall et al. 2011), the modern human mandibular symphysis, which is vertically oriented at younger ages, becomes more obliquely oriented during development (e.g. Coquerelle et al. 2013a,b; Fig. 5A). As a result, the distribution of symphyseal bone relative to the vertical bending axis may not be as well suited to resist vertical bending stresses during later development. Whereas our results suggest that a prominent chin does not increase resistance to bending stresses during development, Gröning et al. (2011) found that the absence of a chin in their model of an adult modern human mandible resulted in greater mechanical loads in the anterior corpus, including an increase in vertical bending stresses. It is important to consider, however, that the modeled mandibular symphyseal variation used by Gröning et al. (2011) may not realistically reflect the overall pattern of correlated morphology associated with variation in chin prominence in modern humans. For example, individuals with a less projecting chin, both during development and across static adult comparisons, are typically characterized by an increase in symphyseal height dimensions (Björk, 1969; Bastir & Rosas, 2004) that likely act to increase resistance to vertical bending stresses. Holton et al. (2014) recently documented that mandibles with increased vertical bending resistance were also characterized by increased symphyseal height dimensions and a pattern of increased posterior mandibular rotation. In spite of the increased resistance to vertical bending, this pattern of mandibular form is commonly associated with reduced chin prominence (e.g. Björk, 1969; Ödegaard, 1970a,b; Lavergne & Gasson, 1976; Björk & Skieller, 1983; Bastir & Rosas, 2004). As such, examining the functional consequences of altering chin prominence in a finite element model (e.g. Ichim et al. 2006; Gröning et al. 2011) while not accounting for correlated variation in symphyseal height (among other features), may not accurately represent the actual relationship between patterns of functional loading and mandibular form, at least with regard to within‐modern human comparisons. Whereas an increase in vertical bending resistance was associated with reduced chin prominence and thus contrasted with ontogenetic changes in symphyseal shape, an increase in the projection of the chin was associated with greater resistance to wishboning stresses. This pattern, however, did not track ontogenetic changes in chin prominence. Rather, relative wishboning resistance was associated with variation in symphyseal depth dimensions resulting from morphological changes along both the labial and lingual symphyseal borders. The lack of association between relative wishboning resistance and ontogenetic changes in the mandibular symphysis suggests that at least some of the variation in wishboning resistance is independent of ontogeny and that correlated morphological variation in aspects of symphyseal shape is established early in development and maintained through adulthood (e.g. Fukase & Suwa, 2008). Indeed, during ontogeny both I yy and I min scaled with isometry in the combined sample and in the individual male and female samples. This indicates that during development the mandibular symphysis does not exhibit an increase in wishboning resistance, at least relative to mandibular length. In spite of the average isometric relationship between wishboning resistance and mandibular length there was, nevertheless, a considerable range of variation in individual regression slopes with both I yy and I min . An examination of the range of slope values shows that there were individuals who scaled with negative allometry, whereas others scaled with positive allometry (a wide, albeit narrower, range was also documented for I xx and I max ). The variability in individual ontogenetic allometries may suggest that the distribution of symphyseal cortical bone may be less constrained by functional loading and therefore influenced to a greater degree by variables unrelated to symphyseal stresses. This result may be due, in part, to the use of a 20th century sample that subsisted on relatively processed diets. If increased masticatory function (e.g. tougher diets that require greater intraoral processing) has a greater influence on symphyseal cortical bone, then it is possible that other samples (e.g. hunter‐gatherer populations) may exhibit relatively lower ranges of within‐sample morphological variability. In contrast to our results, other studies indicate that wishboning may have a significant influence on symphyseal cortical bone. We recently documented, for example, that wishboning resistance was correlated with in vivo bite force magnitude and estimated wishboning forces modeled from data‐derived computed tomography scans of living human subjects (Holton et al., 2014). Furthermore, additional studies have documented that cortical bone along the lingual symphysis is characterized by greater thickness (Fukase, 2007; Fukase & Suwa, 2008) and density (Schwartz‐Dabney & Dechow, 2003) relative to the labial aspect of the symphysis. Given that tensile strains along the lingual symphysis are predicted to be greater than compressive labial strains during wishboning (Hylander, 1984), the pattern of symphyseal cortical bone thickness and density is consistent with the predicted osseous response to wishboning stresses. Despite the results of these studies, there are reasons to think that wishboning of the mandibular symphysis is an unimportant loading regime during mastication in modern humans. First, the modern human mandible is reduced in length relative to archaic Homo. This has the effect of reducing the length of the wishboning moment arm and, therefore, theoretically should reduce wishboning stresses in the symphyseal region (Daegling, 1993). Moreover, the human mandible does not exhibit the same degree of curvature as other anthropoid mandibles and therefore estimated lingual stresses in the human symphysis are only around 1.5 times greater than labial stresses (Hylander and Johnson, 1994). This is in contrast to anthropoids such as baboons, in which lingual stresses are estimated to be as high as 5.0 times greater than labial stresses (Hylander, 1984, 1985; Hylander & Johnson, 1994). In addition to mandibular geometry, humans do not exhibit the same masticatory muscle recruitment patterns that are associated with wishboning in other anthropoids. Wishboning stresses in anthropoid primates are associated with the recruitment of the balancing‐side deep masseter muscle late during the power stroke (Hylander & Johnson, 1994; Hylander et al. 1998; Vinyard et al. 1998). In humans, however, the balancing‐side deep masseter reaches peak activity earlier in the chew cycle (e.g. van Eijden et al. 1993). Ultimately, a more thorough assessment of symphyseal cortical bone geometry and in vivo functional data in humans (e.g. masticatory force production, muscle activity patterns) will be necessary to resolve potential incongruities between different datasets (e.g. ontogenetic allometries, population variation in cortical bone properties, modeled mandibular stresses, etc.).

Conclusions Our results indicate that the ontogenetic development of the chin does not result in an increase in resistance to symphyseal bending stresses relative to moment arm proxies. In the case of vertical bending, an ontogenetic increase in chin prominence was associated with decreased bending resistance. Moreover, although relative symphyseal depth was correlated with wishboning resistance, this was independent of ontogeny. We note that while we have examined symphyseal form relative to bending moment arm lengths, a better understanding of the effects of masticatory function on mandibular symphyseal form would benefit from a thorough examination of ontogenetic scaling of masticatory force production and modeled symphyseal stresses in humans. In the present study, we only considered bending resistance relative to bending moment arm lengths (e.g. Daegling, 2012). Although symphyseal bending is, in part, a function of bending moment arm length, there are of course other variables such as masticatory adductor force that are needed to estimate bending forces during mastication (e.g. Vinyard & Ravosa, 1998; Holton et al. 2014). In the present cephalometric study, we were unable to assess how bending resistance scales with regard to masticatory force production and symphyseal bending forces during human ontogeny. Indeed, the ontogenetic scaling of these variables is currently unknown. It is possible, for example, that vertical bending resistance scales isometrically with vertical bending force to maintain functional equivalency during ontogeny as documented in papionin primates (Vinyard & Ravosa, 1998). If symphyseal bending resistance in humans scales isometrically with estimated symphyseal bending forces, then our conclusions would need to be reconsidered. Ontogenetic analyses of masticatory loads and symphyseal bending forces in human samples are needed to fully resolve this issue. Nevertheless, our analysis provides important data that furthers our understanding of the complex interaction between symphyseal form and jaw function during development.

Acknowledgements The authors thank the Editor, Associate Editor and reviewers for their valuable comments and suggestions. We also thank Terris Williams for assistance with data collection.