Relationship of bone utilization and biomechanical competence in hominoid mandibles

archives of oral biology 52 (2007) 51–63

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Relationship of bone utilization and biomechanical competence in hominoid mandibles David J. Daegling * Department of Anthropology, University of Florida, Gainesville, FL 32611-7305, United States

article info

abstract

Article history:

This investigation explores regional variation in bone mass in the mandibles of large-bodied

Accepted 11 July 2006

hominoids with respect to the masticatory biomechanical environment. Cortical area, subperiosteal area, mandibular length, maximum and minimum area moments of inertia

Keywords:

are sampled at 7 sections along the mandibular corpus in 20 specimens each of Homo sapiens,

Stress

Pan troglodytes, Pongo pygmaeus and Gorilla gorilla. The null hypothesis is that bone is utilized

Strain

similarly among species, between sexes and among corpus locations in terms of economy of

Mastication

bone deployment (relative to subperiosteal area) and efficiency in producing structural

Allometry

stiffness (relative to cross-sectional moments of inertia). The alternative hypothesis is that

Primates

dietary toughness and the scaling of muscular force recruitment produces an unfavourable stress environment in the mandible such that larger species (Gorilla and Pongo) use relatively more cortical bone than Pan and Homo. Three-way factorial analysis of variance (with species, sex and location as main effects) indicates significant interaction of species and location for all indices of bone economy and efficiency. Sex is significant as a main effect or interacting with location in all indices of cortical area. While allometric effects are not readily discernible in these data, the null hypothesis of a common pattern of bone utilization is decisively rejected. Human mandibles use relatively more cortical bone than those of great apes, particularly in anterior regions of the corpus. Among the apes, orangutans use very little cortical bone to achieve mechanical stiffness. # 2006 Elsevier Ltd. All rights reserved.

1.

Introduction

Investigation of the relationship of primate mandibular form to diet, feeding behaviour and the masticatory stress environment motivates comparative studies of the biomechanics of corpus size and shape variation.1–15 These studies rely on the assumption that variation in external linear dimensions of the corpus is a reliable reflection of the underlying cortical bone mass and geometry.16 By estimating biomechanical variables of stiffness and strength in this manner, a question left unaddressed is whether different species or individuals utilize different strategies of cortical bone deployment to achieve the

same mechanical goals. In addition, by restricting analysis to consideration of external geometry, the important question of whether relatively more or less bone is utilized in regions subjected to relatively large loads is not considered. Mandibular functional morphology of great apes and humans is of particular interest to students of hominin evolution since they represent the closest living relatives of fossil forms and are therefore an appropriate comparative group for understanding the functional and ecological significance of mandibular form in the extinct taxa.17–21 Whether the dietary preferences of the three great ape genera can be functionally linked to mandibular morphology remains a topic

* Tel.: +1 352 392 2253x245; fax: +1 352 392 6929. E-mail address: [email protected]. 0003–9969/$ – see front matter # 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.archoralbio.2006.07.002

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archives of oral biology 52 (2007) 51–63

of ongoing investigation.12,13,15,16,19 The human mandible has undergone a dramatic morphological transformation since the advent of the genus Homo, and what remains unknown is whether the utilization of cortical bone in modern human jaws follows an ape-like pattern or is unique among primates. For the above reasons, and for addressing the general question of how cortical bone is utilized in meeting biomechanical requirements, a survey of cortical area and geometry in great ape and human mandibles provides insight into how well comparative surveys of linear mandibular dimensions reflect the underlying utilization and deployment of bone. It is reasonable to expect that given the metabolic costs of bone generation, maintenance and repair, natural selection would favour the most economical and efficient arrangements of bone to meet functional requirements in a given anatomical complex. The value of this insight depends on how these terms are defined. Bone economy here refers to the amount of bone present in a corpus section of given size, and can be summarized as an index of cortical bone area (CBA) over total subperiosteal area (TSA).19 Sections that use relatively less cortical bone are more economical (Fig. 1). Bone efficiency is intended to have a more precise biomechanical meaning. The amount of bone utilized to achieve a given level of structural stiffness under different sources of load is here defined as a measure of efficiency. It is conveniently quantified as an index

of cortical area relative to stiffness measures (e.g., area moments of inertia) or to a general size measure (mandibular length) that is thought to be proportional to bending moment arms.1,3–5 The null hypothesis is that bone use is consistent across all categories of comparison, i.e., among different species and at different locations in the mandibular corpus. This hypothesis is essentially the operative assumption in comparative work utilizing external mandibular dimensions for drawing functional inferences. A null hypothesis concerning the scaling of bone is that cortical area will scale isometrically with variables used in defining economy and efficiency; that is, bone mass and distribution is – proportionally speaking – uninfluenced by scale-effects related to body size or size-related changes in the masticatory apparatus. An alternative hypothesis follows from the observations of Ravosa and coworkers.3,6,7,9,10,22 This hypothesis hinges on two premises: (1) following the general trend in mammals,23–25 larger primates tend to have lower quality diets involving greater quantities of more fibrous foods,7,26 creating an unfavourable stress environment, and (2) muscle force scales with negative allometry such that larger species must recruit a greater amount of balancing-side muscle force, again resulting in a less desirable stress environment creating larger bending moments in both the working- and balancing-side corpus. The

Fig. 1 – CT scans of the four species examined in this study at M2 (top) and midsagittal (bottom) sections. Pictured from left to right are (A) Gorilla gorilla, (B) Pongo pygmaeus, (C) Pan troglodytes and (D) Homo sapiens. Specimens are shown to the same scale. Cortical bone area as a fraction of total subperiosteal area is defined as bone economy, while cortical area relative to mandibular length is defined as a measure of bone efficiency. Alternative measures of bone efficiency with reference to parasagittal bending rigidity, transverse bending rigidity and torsional strength are defined as dimensionless indices of the maximum area moment of inertia, the minimum area moment of inertia, and Bredt’s formula over cortical area, respectively.

archives of oral biology 52 (2007) 51–63

net result is that larger animals will experience greater stress in their mandibles without some compensatory change in the structural rigidity of the mandible. In fact, available evidence suggests that these compensatory changes do occur,2,6,10–12 so that stress levels are probably comparable across a range of body sizes. Nevertheless, the veracity of this latter premise (i.e., negative allometry of muscle force as a rule in primates) is uncertain, given mixed conclusions from empirical studies.27,28 In the present context, the question is whether the added mechanical demands in larger animals are met with a more or less economical and efficient use of cortical bone. Informed speculation requires an understanding of what metabolic or competing functional constraints permit, and beyond recognition that these constraints are present, specific predictions are difficult to formulate. If we accept the premise that natural selection results in the optimal use of bone mass (i.e., bone is deployed to maintain physiological stress levels within a finite interval), one might reasonably infer that – within a given skeletal element – additional bone is deployed with increasing severity of the local loading environment. This assumption is undoubtedly context-specific and oversimplified,29 but if there are constraints on overall corpus dimensions (which there surely are), then it is reasonable to expect that in certain mechanical environments bone is utilized uneconomically and inefficiently relative to others. Thus, in the present study it is predicted that economy and efficiency of bone deployment varies as a function of the severity of the mechanical environment within the corpus, between individuals and among species. Specific outcomes are predicted if the alternative hypothesis is sound. First, modern humans should utilize bone economically and efficiently given reduction in masticatory muscle mass, cultural practices of food processing, and reduction of mandibular dimensions that predispose the jaw to large bending moments. The relative absence of dimorphism in Homo (and to a lesser extent Pan) suggests there should be no differences in cortical use between the sexes. Both Pongo and Gorilla process a more mechanically demanding diet than Pan and Homo (although there is substantial variation among subspecies,12,15) and thus, in conjunction with their larger body size, experience a more severe masticatory loading environment. To a lesser extent, males of these species may also face a more unfavourable stress environment due to scaling effects associated with dimorphism. The sources of stress and their relative impact at different locations in the primate mandible is well established.1,3,22 The most severe bending and twisting moments in the postcanine corpus occur at sections under the molars, and the most severe bending stresses in the anterior corpus occurs at and in the vicinity of the midsagittal plane. Theoretically, stresses associated with both bending and torsion are probably reduced at premolar sections. Thus, the alternative hypothesis predicts the most economical and efficient use of cortical bone at these locations.

2.

Materials and methods

The sample includes 10 adult male and female specimens each of Pan troglodytes, Gorilla Gorilla, Pongo pygmaeus, and

53

modern Homo sapiens. Adult status was determined dentally, by eruption of the M3s into occlusion. This criterion of dental maturity introduces some degree of bias because the relationship of dental to skeletal maturity may differ between the sexes, especially in more dimorphic taxa. Each specimen was CT scanned at seven locations along the mandibular corpus (denoted M3, M2, M1, P4, P3, C, S). All sections of the postcanine teeth were taken at the mesiodistal midpoint of the buccal tooth crown, the canine section was taken through the interstitial spece between the canine and I2, and the symphyseal section was taken in the midsagittal plane. Specimens were oriented to sample minimum sections at each location, with the CT beam passing perpendicular to the occlusal plane. The accuracy of depiction of cortical bone contours in CT scans was determined empirically through comparison of sectioned human mandibles with corresponding CT images. For eight specimens examined the average absolute error was 1.86%, with no error greater than 5%. Further details of image calibration are published elsewhere.16,19 The cortical bone area (CBA) of each section was determined as well as the corresponding total subperiosteal area (TSA). Maximum and minimum area moments of inertia (Imax, Imin) were calculated based on cortical bone contours. Area moments of inertia estimate stiffness in bending, and consider both the amount and distribution of cortical bone in their calculation. In the postcanine corpus, Imax represents resistance to parasagittal bending, a major source of stress in primate mandibles. Imin provides a measure of resistance to lateral transverse bending in the mandible, a load that is relatively unimportant in the postcanine corpus but is a major source of stress in the anterior corpus. Because the great ape mandibular symphysis is inclined relative to the occlusal plane, both Imax and Imin make significant contributions to lateral transverse bending resistance here. Total mandibular length (TML, from infradentale to the midpoint of the chord joining left and right gonion) was also measured on each specimen. Jaw length provides a general biomechanical reference variable that is assumed to be proportional to the moment arms in both parasagittal and lateral transverse bending. A measure of torsional strength known as Bredt’s formula (K) was also calculated for each section. This variable is calculated as the product of twice the area enclosed by the median axis of the cortical contour and the minimum cortical thickness. It was calculated assuming a closed section as experimental data indicate this is the appropriate modelling criterion.31 From the calculated variables several indices were derived to assess the nature of cortical bone utilization among the sample. As stated above, economy of bone use was quantified as an index of CBA over TSA. The efficiency of bone use was calculated in four ways: (1) relative to jaw length (CBA/TML), (2) relative to maximum bending resistance (Imax/CBA), (3) relative to minimum bending resistance (Imin/CBA), and (4) relative to torsional strength (K/CBA). Two indices of relative strength were also derived (Imax/TML, Imin/TML); they approximate the strength of a given section relative to moment arms in bending. No equivalent index can be calculated for K as the estimation of the twisting moment arm cannot be reliably

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Table 1 – Factorial analysis of variance d.f.

MS

Fs

P

Cortical bone fractional index (CBA/TSA) Taxon 737,293 Sex 21,215 Section 77,329 Taxon  sex 45,116 Taxon  section 570,504 Sex  section 2,152 Taxon  sex  section 42,211 Replications 1,898,275

3 1 6 3 18 6 18 504

245,764 21,215 12,888 15,038 31,694 358 2,345 3,766

65.26 5.63 3.42 3.99 8.42 0.09 0.62

<0.001 0.02 0.003 0.008 <0.001 0.997 0.88

Cortical bone area relative to size (CBA/TML) Taxon 135,659 Sex 109 Section 23,082 Taxon  sex 2,732 Taxon  section 6,343 Sex  section 975 Taxon  sex  section 506 Replications 78,816

3 1 6 3 18 6 18 504

45,219 109 3,847 910 352 163 28 156

289.9 0.70 24.7 5.84 2.26 1.04 0.18

<0.001 0.403 <0.001 <0.001 0.002 0.398 >0.999

Maximum bending rigidity relative to cortical bone area (Imax/CBA) Taxon 310,827 3 Sex 14 1 Section 95,737 6 Taxon  sex 37,454 3 Taxon  section 99,924 18 Sex  section 2,895 6 Taxon  sex  section 11,611 18 Replications 590,429 504

103,609 14 15,956 12,485 5,551 483 645 1,171

88.48 0.01 13.63 10.66 4.74 0.41 0.55

<0.001 0.920 <0.001 <0.001 <0.001 0.873 0.933

Maximum bending rigidity relative to total mandibular length (Imax/TML) Taxon 272,624 3 Sex 55 1 Section 109,588 6 Taxon  sex 1,736 3 Taxon  section 34,632 18 Sex  section 2,215 6 Taxon  sex  section 1,439 18 Replications 148,140 504

90,875 55 18,265 579 1,924 369 80 294

309.10 0.19 62.13 1.97 6.54 1.26 0.27

<0.001 0.663 <0.001 0.118 <0.001 0.274 0.999

Minimum bending rigidity relative to cortical bone area (Imin/CBA) Taxon 46,419 3 Sex 1,844 1 Section 6,310 6 Taxon  sex 344 3 Taxon  section 43,289 18 Sex  section 540 6 Taxon  sex  section 2,547 18 Replications 140,071 504

15,472 1,844 1,052 115 2,405 90 141 278

55.66 6.63 3.78 0.41 8.65 0.32 0.51

<0.001 0.010 0.001 0.746 <0.001 0.927 0.954

Minimum bending rigidity relative to total mandibular length (Imin/TML) Taxon 95,994 3 Sex 128 1 Section 23,293 6 Taxon  sex 3,166 3 Taxon  section 32,283 18 Sex  section 1,436 6 Taxon  sex  section 609 18 Replications 75,050 504

31,998 128 3,882 1,055 1,793 239 34 149

214.75 0.86 26.05 7.08 12.03 1.60 0.23

<0.001 0.354 <0.001 <0.001 <0.001 0.145 >0.999

524,881 301,218 186,096 5,753 136,128 6,032 11,002 13,404

39.16 22.47 13.88 0.43 10.16 0.45 0.82

<0.001 <0.001 <0.001 0.732 <0.001 0.845 0.677

Source

SS

Torsional strength relative to cortical bone area (K/CBA) Taxon 1,574,644 Sex 301,218 Section 1,116,574 Taxon  sex 17,260 Taxon  section 2,450,312 Sex  section 36,194 Taxon  sex  section 198,033 Replications 6,755,503

3 1 6 3 18 6 18 504

All analyses are treated as Model I (fixed effects); all interaction and factors are tested over the replication mean square. Ratios are rendered dimensionless prior to analysis by appropriate exponential transformations where required.

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made from mandibular material.6,24 All indices were rendered dimensionless by transformation of variables to the units of CBA (mm2). Each index was subjected to a factorial analysis of variance, with main effects of taxon (species, four levels), sex (two levels) and location (sections, seven levels). Assuming the main effects are best categorized as fixed, this is a Model I design. Accordingly, the ten replications per cell provided an error variance over which all main effects and interaction terms were tested. To assess allometric trends across species, each index was partitioned into its component variables and Model II regression was performed using the reduced major axis (RMA). Male and female means for each taxon defined the points for analysis. The dimensionally equivalent variables were log-transformed so that the slope defining isometric scaling was 1.0. Departures from isometry were tested by the criterion of Jolicoeur and Mosimann.32 Confidence intervals that did not include the slope value 1.0 provided the criterion for rejecting the null hypothesis of isometry. Because the human mandible clearly represents the derived condition among hominoids, all regressions were recalculated without the human sample (i.e., with N = 6) to assess potential influence of the human sample on scaling statistics.

3.

Results

The factorial ANOVAs for all indices are summarized in Table 1. In general, there are significant first-order interactions which preclude simple attribution of variation to the main effects of species, sex, or location. Second-order interaction is not significant for any index. When the indices are partitioned for determination of allometric scaling, the null hypothesis of isometry cannot be rejected for most bivariate comparisons (Tables 2 and 3), although scaling of bone area differs depending on the location under consideration. For each pair of variables considered below, ANOVA results are summarized followed by the RMA results.

3.1.

CBA and TSA

The index describing economy of bone use (CBA/TSA) shows significant interaction of species and sex as well as species and location. The species–location interaction is due to humans tending to become less economical in their use of bone at anterior sections, with the opposite true of African apes (Fig. 2). Orangutans are consistently more economical in bone use, and their index values are less volatile from section to section. The species–sex interaction is more difficult to discern (Table 4). In only one case (Pan at M1) is there a significant difference between males and females of a given species at a given section. Nevertheless, mean index values for male Pan exceed the female mean at every section (a single classification ANOVA pooling sections is significant at P = 0.004). This is not true of Pongo or Gorilla, in which females have higher index values on average at 2 and 5 of the 7 sections, respectively (ANOVA for each taxon with sections pooled is nonsignificant). Human values for males and females are virtually identical at the three molar sections, while males have the higher average

Table 2 – Regression summaries: great apes and humans Section

Slope

95% CI

Intercept

r

CBA on TSA M3 M2 M1 P4 P3 C S

0.849 0.833 1.021 0.969 0.921 0.774 0.693

0.60–1.21 0.60–1.17 0.79–1.32 0.73–1.29 0.68–1.25 0.62–0.97 0.57–0.84

0.010 0.004 0.491 0.336 0.216 0.172 0.397

0.933 0.939 0.965 0.958 0.952 0.974 0.981

CBA on TML 2 M3 0.562 0.507 M2 M1 0.608 0.649 P4 0.771 P3 C 0.782 S 0.690

0.37–0.84 0.33–0.79 0.37–0.99 0.40–1.05 0.51–1.18 0.59–1.04 0.53–0.89

0.084 0.103 0.317 0.428 0.892 0.899 0.520

0.908 0.892 0.861 0.869 0.900 0.957 0.966

0:5 on CBA Imax M3 M2 M1 P4 P3 C S

1.142 1.200 1.076 1.008 0.977 1.086 1.396

0.83 1.57 0.90–1.60 0.84–1.39 0.71–1.43 0.75–1.28 0.87–1.35 1.16–1.63

0.038 0.077 0.210 0.355 0.439 0.207 0.493

0.946 0.956 0.967 0.934 0.963 0.975 0.986

0:5 Imax on TML 2 M3 M2 M1 P4 P3 C S

0.642 0.609 0.655 0.654 0.753 0.849 0.964

0.40–1.02 0.37–1.01 0.38–1.13 0.38–1.12 0.50–1.13 0.65–1.12 0.80–1.16

0.058 0.047 0.131 0.077 0.431 0.769 1.219

0.877 0.846 0.821 0.825 0.907 0.960 0.982

0:5 on CBA Imin M3 M2 M1 P4 P3 C S

1.090 1.045 0.973 1.124 1.200 1.247 1.187

0.88–1.36 0.87–1.25 0.84–1.12 0.85–1.48 0.89–1.61 1.00–1.55 1.00–1.41

0.055 0.049 0.189 0.160 0.333 0.441 0.306

0.975 0.984 0.989 0.959 0.954 0.975 0.985

0:5 on TML 2 Imin M3 M2 M1 P4 P3 C S

0.612 0.530 0.591 0.730 0.925 0.975 0.819

0.38–0.98 0.32–0.89 0.38–0.92 0.56–0.95 0.78–1.10 0.88–1.08 0.71–0.95

0.147 0.157 0.120 0.641 1.403 1.562 0.923

0.870 0.842 0.889 0.963 0.985 0.995 0.989

K0.67 on CBA M3 M2 M1 P4 P3 C S

1.088 1.247 0.974 1.001 0.980 1.361 1.318

0.82–1.44 0.94–1.65 0.69–1.37 0.59–1.69 0.65–1.47 0.96–1.93 0.96–1.81

0.460 0.764 0.162 0.272 0.219 1.020 0.934

0.958 0.959 0.938 0.836 0.908 0.934 0.947

Slopes are calculated using the reduced major axis in log–log space. The slope of isometry in each case is 1.0 as variables were rendered dimensionally equivalent prior to analysis. Confidence intervals were calculated by the method of Jolicoeur and Mosimann.32

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Table 3 – Regression summaries: great apes only Slope

95% CI

CBA on TSA M3 M2 M1 P4 P3 C S

0.798 0.791 1.019 1.094 1.110 0.940 0.821

0.46–1.39 0.47–1.33 0.68–1.54 0.74–1.62 0.73–1.69 0.70–1.26 0.68–0.99

0.133 0.122 0.488 0.685 0.753 0.310 0.025

0.907 0.920 0.952 0.957 0.950 0.976 0.991

CBA0.5 on TML 0.911 M3 0.850 M2 M1 1.062 1.115 P4 1.246 P3 C 1.107 S 0.925

0.68–1.21 0.67–1.08 0.84–1.34 0.83–1.49 0.87–1.79 0.88–1.40 0.74–1.15

1.572 1.356 2.253 2.413 2.912 2.281 1.516

0.978 0.985 0.986 0.977 0.964 0.985 0.987

0:5 on CBA Imax M3 M2 M1 P4 P3 C S

1.185 1.125 1.113 1.104 0.981 1.107 1.272

0.71–1.99 0.80–1.96 0.76–1.64 0.61–1.79 0.63–1.52 0.70–1.64 1.01–1.60

0.061 0.187 0.124 0.267 0.429 0.245 0.191

0.921 0.942 0.959 0.914 0.945 0.949 0.986

0:5 Imax on TML 2 M3 M2 M1 P4 P3 C S

1.080 1.061 1.183 1.165 1.223 1.185 1.176

0.73–1.59 0.71–1.59 0.84–1.67 0.76–1.78 0.91–1.64 0.87–1.61 0.78–1.57

1.924 1.879 2.384 2.254 2.429 2.198 2.120

0.958 0.954 0.968 0.949 0.976 0.975 0.970

0:5 on CBA Imin M3 M2 M1 P4 P3 C S

1.151 1.105 0.937 0.928 0.924 0.958 1.004

0.82–1.62 0.86–1.42 0.75–1.17 0.72–1.19 0.70–1.21 0.88–1.04 0.81–1.25

0.198 0.089 0.271 0.302 0.330 0.261 0.135

0.968 0.984 0.987 0.983 0.980 0.998 0.987

0:5 on TML 2 Imin M3 M2 M1 P4 P3 C S

K0.67 on CBA M3 M2 M1 P4 P3 C S

Intercept

Table 4 – CBA/TSA index species–sex interaction

Section

r

Section

Taxon

Sex

Mean

95% CI

M3

Pan

Female Male

432 487

381–403 444–529

M=F

M2

Pan

Female Male

404 447

347–460 411–484

M=F

M1

Pan

Female Male

356 409

312–400 373–445

M > Fa

Female Male

359 389

309–409 361–418

M=F

Female Male

328 379

285–372 341–416

M=F

P4 P3

0.75–1.46 0.70–1.27 0.79–1.26 0.85–1.26 0.93–1.43 0.84–1.34 0.71–1.21

2.007 1.587 1.840 1.938 2.359 1.925 1.387

0.970 0.976 0.985 0.989 0.987 0.985 0.981

Pan

Female Male

342 356

286–398 322–389

M=F

S

Pan

Female Male

358 359

308–408 328–390

M=F

Female Male

324 331

280–368 287–374

M=F

M3

0.76–1.67 0.88–1.99 0.64–1.69 0.46–2.25 0.43–1.63 0.64–1.07 0.58–1.36

0.563 0.940 0.310 0.315 0.122 0.279 0.103

0.957 0.953 0.931 0.776 0.859 0.982 0.948

Slopes are calculated using the reduced major axis in log–log space. The slope of isometry in each case is 1.0 as variables were rendered dimensionally equivalent prior to analysis. Confidence intervals were calculated by the method of Jolicoeur and Mosimann.32

Pongo

M2

Pongo

Female Male

321 312

267–375 267–356

M=F

M1

Pongo

Female Male

323 331

290–357 296–365

M=F

Female Male

332 337

283–382 300–375

M=F

Female Male

320 314

289–350 265–363

M=F

P3

Pongo

Pongo

C

Pongo

Female Male

299 299

264–333 238–360

M=F

S

Pongo

Female Male

315 324

283–346 282–366

M=F

Female Male

419 401

386–453 341–461

M=F

Female Male

382 389

360–404 340–437

M=F

M3 M2

Gorilla

Gorilla

M1

Gorilla

Female Male

385 411

361–409 361–461

M=F

P4

Gorilla

Female Male

421 414

382–461 356–471

M=F

Female Male

425 395

386–463 327–463

M=F

Female Male

360 328

316–403 275–381

M=F

Female Male

317 294

291–343 258–331

M=F

Female Male

398 400

354–442 367–434

M=F

Female Male

380 379

340–420 350–408

M=F

Female Male

368 365

331–404 333–397

M=F

M=F

P3 C

S 1.131 1.323 1.037 1.102 0.838 0.824 0.887

Pan

C

P4

1.049 0.939 0.995 1.035 1.151 1.061 0.928

Pan

Difference

M3 M2 M1

Gorilla

Gorilla

Gorilla

Homo

Homo

Homo

P4

Homo

Female Male

407 435

366–448 411–460

P3

Homo

Female

420

377–462

archives of oral biology 52 (2007) 51–63

Table 4 (Continued ) Section Taxon Sex

C

S

a

Homo

Homo

Mean

95% CI

Difference

Male

453

426–480

M=F

Female Male

432 485

379–485 443–527

M=F

Female Male

462 510

379–544 454–565

M=F

57

Significant by single-classification ANOVA at P < 0.05.

Fig. 4 – Interaction of species and section effects for the CBA/TML index. Lower values represent more efficient use of cortical bone given jaw size. Points represent mean values.

Fig. 2 – Interaction of species and section effects for the CBA/TSA index. Lower values represent more economical use of bone in a section. Points represent mean values.

index values at the remaining four sections (P = 0.06 by ANOVA with sections pooled). Statistically speaking, cortical area scales isometrically with subperiosteal area at five of the seven sections; in the anterior corpus the relationship is negatively allometric (Table 2). This indicates more economical use of cortical bone in the symphysis of larger hominoids. Excluding humans from the analysis has little influence on the strength of correlation (Fig. 3), although the human sample depresses sample slopes in the anterior corpus, augments slope values at the two posterior sections (M2 and M3), and has virtually no effect at the M1 section (Tables 2 and 3).

3.2.

Fig. 3 – Bivariate plot of male and female means for each species for cortical bone area (CBA) on total subperisoteal area (TSA) at M1. The RMA slope for the sample is essentially isometric (1.02). The correlation is 0.965.

CBA and TML

First-order interactions of species and sex as well as species and sections are significant. The latter interaction (Fig. 4) is presumably due to the Gorilla sample departing from the other taxa in deploying more bone at P3 and canine sections. The species–sex interaction is the expected outcome of large differences in mandibular dimorphism between Pongo and Gorilla on the one hand and Homo and Pan on the other. However, pooling sections to examine sex differences produces a more complicated picture: Gorilla and Homo show very little sex difference, while in Pan males tend toward higher index values and in Pongo females have the higher values. Best-fit slopes for scaling of cortical area on jaw length are best described as negatively allometric, but the large confidence intervals preclude rejection of the null hypothesis, except at M2 section (Table 2). There are two effects of excluding humans in this analysis: (1) correlation improves and (2) sample slopes are more nearly isometric (Table 3). This is attributable to the relatively short mandibles in Homo.

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Fig. 5 – Interaction of species and section effects for the Imax/CBA index. Higher values indicate a more efficient use of cortical bone in producing the maximum area moment of inertia. Points represent mean values.

3.3.

Imax and CBA

Two interaction terms are significant. The interaction of species and section is visualized in the distinct profiles of the mean species values at different locations (Fig. 5). Pongo is uniquely efficient in its use of cortical bone to achieve stiffness by this measure. The four species also show large disparities in efficiency at the symphysis, despite the near identity of values for the African apes and humans at the adjacent canine section. Isometric scaling is the rule between the two variables, with the notable exception of scaling at symphyseal sections (Table 2). Here the relationship is positively allometric with strong correlation. This indicates more efficient use of cortical bone in larger individuals. Exclusion of humans in the analysis does not alter this interpretation (Fig. 6).

3.4.

Fig. 6 – Bivariate plot of male and female means for each species for Imax on CBA at M1. The relative position of the sexes is similar among the taxa, but the levels of dimorphism are species-specific. This is presumably reflected by the significant taxon–sex interaction term for the factorial ANOVA of the Imax/CBA index. The RMA slope is 1.08 (r = 0.97); the confidence interval of the slope includes the isometric value of 1.0.

3.5.

Imin and CBA

There is significant taxon–section interaction, and the main effect of sex is also significant. Each taxon is characterized by a distinct profile across sections (Fig. 9). Humans are utilizing relatively more bone to achieve stiffness by this measure. The sex effect results from the female index values being generally

Imax and TML

Significant interaction is indicated between species and sections, and the main effect of sex is nonsignificant. This interaction is driven predominantly by the peculiar profile of humans in contrast to the congruence observed among the great apes (Fig. 7). Relative to jaw length, humans have mandibles that are very structurally stiff relative to apes. Best-fit slopes at each section are negatively allometric, but in each case there is no statistical justification for rejecting the null hypothesis of isometry (Table 2). This is due to the relatively poor correlations which result in large confidence intervals. Excluding the human sample from the analysis improves correlation markedly, and there is a dramatic change in the RMA slope (Table 3, Fig. 8). With humans left out of the regression, slopes are more suggestive of positive, rather than negative, allometry. Isometric scaling cannot be rejected, however.

Fig. 7 – Interaction of species and section effects for the Imax/TML index. Higher values indicate a stronger section relative to jaw size. Points represent mean values.

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Fig. 8 – Bivariate plot of male and female means for each species for Imax on TML at M1. The humans are outliers owing to their characteristically short mandibles. The effect on allometric interpretation is large. With humans included in an analysis, the slope is 0.66 (r = 0.82). When great apes are examined in isolation, the slope is 1.18 (r = 0.97). Statistically speaking, isometric scaling cannot be ruled out in either case.

larger than male values (P = 0.04 by a single-classification ANOVA pooling categories of species and sections). Since the main effect of sex is unaccompanied by any lower-level interaction, the attribution of sex differences to any particular taxon is inadvisable.

Fig. 10 – Interaction of species and section effects for the Imin/TML index. Higher values indicate a stronger section relative to jaw size. Points represent mean values.

The minimum area moment of inertia scales isometrically relative to cortical area (Table 2). The 95% confidence limits of the two most anterior sections barely include the isometric value, suggesting that Imin increases more rapidly relative to cortical area in these regions. Leaving humans out of the analysis, however, prompts a reinterpretation, because the great ape slopes at anterior sections become more nearly isometric (Table 3).

3.6.

Imin and TML

Species interaction with sex and location is significant. The interaction of species and sex is likely due to dimorphism differences alluded to above: mandibular length differences between males and females of Pan and Homo are slight, while in Gorilla and Pongo these differences are large and significant. The interaction of species and location (Fig. 10) is due to the human profile being distinct from what is essentially a shared pattern in the apes. As was the case for the Imax/TML index, humans have remarkably rigid mandibles relative to the apes. As is the case of scaling of the maximum area moment of inertia to jaw length, the minimum area moment of inertia is relatively poorly correlated with jaw length, particularly at posterior sections (Table 2). One cannot reject the null hypothesis of isometry as a result, despite the fact that the best-fit slope at each section is negatively allometric. Excluding the human sample improves correlation at all but the two most anterior sections (Table 3). This procedure also reveals that the suggestion of negative allometry is due to the human sample depressing slope values at the molar sections.

3.7. Fig. 9 – Interaction of species and section effects for the Imin/CBA index. Higher values indicate a more efficient use of cortical bone in producing the minimum area moment of inertia. Points represent mean values.

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K and CBA

The interaction of species and sections is significant, and the main effect of sex is significant as well. The interaction reflects the distinct species-specific pattern of index values from

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explain the patterning of variation in these data. While there are several contexts in which departures from isometry are suggested, there is no statistical basis for drawing such conclusions. These cases can arguably be viewed as a null hypothesis being ‘‘too null;’’33 that is, the degrees of freedom in the bivariate analyses are sufficiently small that large confidence intervals follow even in cases of strong correlation between variables. The remedy for this – using individuals as data points rather than male and female means – would achieve the desired effect of shrinking these confidence intervals but would necessarily entail a violation of the ideal of sampling independence. The remainder of the discussion focuses on the implications of these data to the alternative hypothesis—that differences in masticatory loading environments have predictable associations with patterns of cortical bone use.

4.1. Fig. 11 – Interaction of species and section effects for the K/ CBA index. Higher values indicate more efficient use of cortical bone in maintaining torsional strength. Points represent mean values.

section to section (Fig. 11). Similar to the case of the Imin/CBA index, the sex effect is due to larger average values for females (P = 0.0002 by a single classification ANOVA pooling categories of species and sections). Best-fit slopes differ from section to section in terms of whether isometry or negative or positive allometric scaling is suggested, but in no case does the confidence interval permit any interpretation other than isometric scaling. K appears to be as tightly correlated with cortical area as the maximum and minimum area moments of inertia. Excluding Homo from the analysis does little to alter interpretation, except at the canine and symphyseal sections, where their inclusion clearly increases slope values (Tables 2 and 3). Being at the smaller end of the size range of the hominoid sample, this result follows from the fact that the human anterior corpus is characterized by absolutely smaller dimensions.

4.

Discussion

The universal finding of significant interaction and main effects in the factorial analyses of variance provides a strong rejection of the null hypothesis that cortical bone area varies randomly with respect to species, sex, or location within the corpus. The presence of first-order interaction in every analysis indicates that main effects are not explicable in isolation, but are influenced by other main effects. This complicates interpretation but underscores the contextdependence of the use and deployment of bone in the mandibular corpus. Despite the significant results provided by analysis of variance, a complementary aspect of the null hypothesis is not rejected. That is, scaling of cortical area with respect to other variables is isometric in the vast majority of bivariate comparisons. Thus, allometry (in its strict sense) does not

Economy of bone tissue

Pongo is consistently more economical in its utilization of bone within sections (low CBA/TSA values) except in midsagittal section, where it is comparable to Gorilla. Gorillas are not particularly economical anywhere else. Pan is least economical at the most posterior sections, while humans pack unusually large amounts of bone in their anterior sections, despite the likelihood that they enjoy a relatively benign stress environment here in contrast to the apes.34 These findings run counter to expectations put forth in the alternative hypothesis: more bone is used in the smaller and less mechanically challenged Homo, while Pongo utilizes bone economically in spite of its obdurate diet. In Gorilla, the taxon in which lateral transverse bending has the most potentially severe effects in the anterior corpus,11,35 bone is utilized most economically at the symphyseal section. The expectation that premolar sections would show the most economical deployment of bone is not borne out by observation.

4.2.

Efficient use of bone tissue

Relative to jaw length, cortical area is least efficiently utilized (high CBA/TML ratio) in humans. Despite the reduction in bending moments experienced in human mandibles, a concomitant reduction in bone mass has not apparently evolved. Given the ubiquity of extraoral food processing in modern people, the human mandible probably experiences absolutely lower stresses in their jaws than apes during mastication. Why human jaws are overbuilt is an interesting question. If we assume that bone is metabolically expensive and that natural selection favours less mass rather than more for performing a given function, then the answer would seem to be that the bone in the human jaw is there for some function other than mastication. On the other hand, one could reject the selective premise articulated above and attribute the human pattern to phylogenetic inertia—we inherited this pattern from our ancestors and for some reason we cannot get rid of it. This is an unsatisfying explanation without specific evidence concerning what that reason might be. Without such evidence, the explanation is vacuous and immune to test. Among the great apes, the most bone is utilized in the anterior corpus, where large bending moments are acting. In

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contrast, bone is most efficiently utilized at M2 (Gorilla) and M1 (Pan and Pongo), locations subjected to the combined effects of parasagittal bending and axial torsion. The premolar sections have index values intermediate between those of the anterior corpus and molar sections. At the M2 sections the scaling of cortical area against jaw length is negatively allometric, indicating that in larger jaws relatively less bone is utilized to maintain biomechanical competence. Empirical slopes at other sections give similar indication, but confidence intervals include isometry. What these observations suggest is that, as dietary quality declines and the loading environment worsens at larger body sizes, bone is utilized relatively more efficiently. This explanation, however, works best when the outlier taxon (Homo) is included in the analysis; the efficiency of great apes – assessed allometrically – vanishes when only great apes are examined. Efficiency can also be quantified in terms of how well a given area of bone contributes to bending stiffness as measured by area moments of inertia. In terms of maximum bending rigidity, orangutans are exceptionally efficient, using very little bone to maintain structural stiffness. Modern humans are not at all exceptional in this regard, which suggests that they deploy bone in relatively similar fashion to the African apes in terms of bending rigidity. Generalizing as to what sections display the most efficient arrangement is impossible owing to the species-specific profiles of this index across sections (Fig. 5). Interestingly the Imin/CBA index does not mirror the findings for the Imax/CBA index, except that Pongo is most efficient among taxa in its deployment of bone to maintain rigidity. Humans’ inefficiency in the anterior corpus recalls the inefficiency indicated by the CBA/TML index as well as the uneconomical use of bone here (high CBA/TSA ratios). By several measures, humans seem to be using more bone than they need. Female specimens tend to have larger Imin/CBA values than males, and the absence of this main effect for the Imax/CBA index suggests dimorphism in corpus shape. That is, females deploy relatively more bone about the minor axis of a crosssection than do males. This difference does not appear to be consistently detectable from external measures of mandibular dimorphism.36 The absence of significant interaction of sex with sections or taxon suggests that this source of dimorphism is not attributable to particular regions of the corpus or – more surprisingly – particular species. The relative efficiency of Pongo for bending stiffness is not observed with respect to torsion (K/CBA). Orangutan economy and efficiency is accomplished by their relatively thin cortical shells,19 but this bending efficiency comes at a cost, since with cortical thinning comes higher shear stresses under torsion. Why females tend to be more efficient in torsion than males is not immediately clear, although very modest differences in minimum cortical thickness are sufficient to substantially raise index values. Sex differences in this and other indices may be a product of bimaturism, and although these data are not ontogenetic and cannot test this possibility directly, one would expect to see significant taxon-sex interaction given the speciesdependent nature of bimaturism. This is observed in some cases (CBA/TSA, CBA/TML, Imax/CBA, Imin/TML) but not others.

4.3.

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Relative strength

The discrimination of relative bending strength assumes that jaw length scales in rough proportion to bending moment magnitudes. Parasagittal bending is most important at molar sections. The index of interest in this case (Imax/TML) reveals humans to be relatively much stronger than the great apes. This, of course, is not due to robust corpora but rather short mandibles. Among the great apes, the high index values in Pongo establish that the economical and efficient use of bone translates to a relatively stronger jaw, at least in the case of this particular load. When oriented obliquely with respect to the plane of bending, both Imax and Imin contribute to lateral transverse bending rigidity, which is most critical in the anterior corpus. Humans are exceptionally strong in terms of the Imin/TML index, but only at sections where bending is probably a trivial source of masticatory stress. Among the apes, the generally congruent profiles for both Imax/TML and Imin/TML indices show dramatic increases in strength at progressively anterior sections. These increases support previous observations that minimizing stress at symphyseal sections due to lateral transverse bending is a mechanical imperative in several primate clades.3,9,10,22

4.4. Relationship of bone use to the mechanical environment The most important implication of these results is that there appears to be no general strategy of bone use and deployment that is common to the four taxa examined. Human mandibles appear to be needlessly massive, and even if humans are characterized by a masticatory loading environment distinct from apes, it is unlikely that humans can produce the forces necessary to produce stress levels comparable to what apes routinely experience. At the other end of the spectrum, gorillas and orangutans have fairly demanding diets, yet Pongo utilizes bone in a much more cost-effective matter. Among the apes, the anterior corpus of the mandible is prone to relatively high stresses and strains due to large bending moments and the pronounced curvature of the mandible in this region.11,35 While this local environment would seem to call for increases in bone mass, in fact the apes are more economical in their use of bone here than at other sections, including sections under the premolars, where the stress environment is probably relatively benign.30 In addition, the most efficient use of cortical bone for producing maximum bending rigidity is also realized at the symphyseal section.

4.5.

Implications for comparative biomechanics

There is no clear relationship between bone mass and the presumed severity of the masticatory loading environment, whether this is considered on the scale of individual mandibles or among different taxa. The hypothesis that relatively more bone is recruited in the context of more severe loading environments is not supported by these data. In fact, it would appear that larger cross-sectional dimensions (e.g., those found in the anterior corpus) can afford to deploy relatively less cortical bone to satisfy requirements of strength

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and rigidity. This follows from the fact that bending resistance is achieved by not only adding mass, but distributing it peripheral to the neutral axis (i.e., an element of area situated twice as far from the neutral axis contributes a four-fold increase in structural stiffness). This would explain why the finding of negative allometry of CBA on TSA at the symphysis is not necessarily surprising from a biomechanical perspective. In larger mandibles modest increases in bone area offer substantial improvements in bending rigidity, especially if this bone is deployed over an absolutely larger subperiosteal area. Humans offer an interesting counterpoint. The anterior corpus in Homo is much smaller in overall size than the corresponding region in apes, and humans depart from the ape pattern here by using relatively more bone. Static adult comparisons suggest that the relationship of CBA, Imax and Imin to TML is indicative of negative allometry at most sections. This is attributable in part to the human sample ‘‘pulling’’ the regression slope by virtue of the small TML dimension (recalculation of slopes excluding humans yields higher values that are more suggestive of isometry). Statistically speaking, cortical area and the area-based measures of bending stiffness and torsional strength scale isometrically to jaw size. External measures of corpus proportions scale with slight positive allometry to jaw length among more inclusive samples of apes (using RMA; a least squares criterion suggests isometric scaling).11 If the parameters of external corpus dimensions versus cortical area-derived measures of mechanical rigidity do in fact scale differently with respect to jaw length, then functional interpretations are potentially affected. For example, if an African ape pattern of bone use is assumed to apply to hominoids in general, the resultant interpretation would overestimate mechanical competence in Pongo and underestimate such measures in Homo. Functional comparisons derived from morphometric surveys (i.e., those based on external corpus dimensions) inherently assume a common pattern of underlying bone mass and geometry in the sampled taxa. The interpretive cost of this assumption is potentially large in narrow allometric contexts, although in broad allometric surveys the problem is likely trivial due to the overarching influence of size in conditioning absolute stiffness and strength.

Acknowledgments The curators and staff of the National Museum of Natural History and the American Museum of Natural History kindly permitted the CT scanning of material in their care. Supported by the NSF (BNS 8920592 and BCS 0096037).

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