Journal of Human Evolution 68 (2014) 36e46

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Geometric properties and comparative biomechanics of Homo floresiensis mandibles David J. Daegling a, *, Biren A. Patel b, William L. Jungers c a

Department of Anthropology, University of Florida, Gainesville, FL 32611-7305, USA Department of Cell and Neurobiology, Keck School of Medicine, University of Southern California, Los Angeles, CA, USA c Department of Anatomical Sciences, School of Medicine, Stony Brook University, Stony Brook, NY 11794, USA b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 24 December 2013 Accepted 10 January 2014 Available online 21 February 2014

The hypodigm of Homo floresiensis from the cave of Liang Bua on Flores Island in the archipelago of Indonesia includes two mandibles (LB1/2 and LB6/1). The morphology of their symphyses and corpora has been described as sharing similarities with both australopiths and early Homo despite their Late Pleistocene age. Although detailed morphological comparisons of these mandibles with those of modern and fossil hominin taxa have been made, a functional analysis in the context of masticatory biomechanics has yet to be performed. Utilizing data on cortical bone geometry from computed tomography scans, we compare the mechanical attributes of the LB1 and LB6 mandibles with samples of modern Homo, Pan, Pongo, and Gorilla, as well as fossil samples of Paranthropus robustus, Australopithecus africanus and South African early Homo. Structural stiffness measures were derived from the geometric data to provide relative measures of mandibular corpus strength under hypothesized masticatory loading regimes. These mechanical variables were evaluated relative to bone area, mandibular length and estimates of body size to assess their functional affinities and to test the hypothesis that the Liang Bua mandibles can be described as scaled-down variants of either early hominins or modern humans. Relative to modern hominoids, the H. floresiensis material appears to be relatively strong in terms of rigidity in torsion and transverse bending, but is relatively weak under parasagittal bending. Thus, they are ‘robust’ relative to modern humans (and comparable with australopiths) under some loads but not others. Neither LB1 nor LB6 can be described simply as ‘miniaturized’ versions of modern human jaws since mandible length is more or less equivalent in Homo sapiens and H. floresiensis. The mechanical attributes of the Liang Bua mandibles are consistent with previous inferences that masticatory loads were reduced relative to australopiths but remained elevated relative to modern Homo. Ó 2014 Elsevier Ltd. All rights reserved.

Keywords: Liang Bua Mastication Stress Strain Functional morphology

Introduction The hypodigm of the Late Pleistocene hominin species Homo floresiensis has been extensively scrutinized in order to establish its phylogenetic and taxonomic position in the broader context of human evolution (Brown et al., 2004; Morwood et al., 2005; Argue et al., 2006; Gordon et al., 2008; Brown and Maeda, 2009; Morwood and Jungers, 2009; Kaifu et al., 2011). Notwithstanding serial and mutually exclusive claims that the hypodigm represents an assemblage of tiny pathological humans (see Aiello (2010) and Brown (2012) for recent reviews), cladistic analysis supports hypotheses that the Liang Bua material has particular affinity to East

* Corresponding author. E-mail addresses: [email protected], daegling@ufl.edu (D.J. Daegling). 0047-2484/$ e see front matter Ó 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jhevol.2014.01.001

African and Georgian early Homo rather than with Asian H. erectus (Argue et al., 2009; but see Kaifu et al., 2011). Functional morphological investigations of the foot (Jungers et al., 2009), shoulder (Larson et al., 2007), and wrist (Tocheri et al., 2007; Orr et al., 2013) also indicate an anatomical mosaic that is relatively primitive. The mandible of H. floresiensis lacks the diagnostic modern human feature of a chin (Brown et al., 2004; Morwood et al., 2005) and symphyseal outlines of LB1 and LB6 are also most similar to those of australopiths and very different from modern humans (Brown and Maeda, 2009). External geometry elsewhere on the corpus resembles australopiths and early Homo rather than modern humans (Brown and Maeda, 2009). These observations on the mandibular morphology of the Liang Bua hominins suggest that masticatory biomechanics in this taxon may have been unlike modern humans and perhaps penecontemporary fossil Homo. Of particular interest is whether the

D.J. Daegling et al. / Journal of Human Evolution 68 (2014) 36e46

megadontia, thick enamel and heavy attrition that characterizes H. floresiensis (Brown et al., 2004; Brown and Maeda, 2009; Jungers and Kaifu, 2011) is associated with a craniofacial skeleton that is indicative of powerful or prolonged mastication. In the evolution of Homo, the advent of material culture and reduction of the dentition and facial skeleton are plausibly linked to reductions in masticatory stress due to behavioral adaptations for extraoral food processing. The tool-making Liang Bua hominins would thus appear to be anomalous among later Pleistocene Homo in their masticatory functional morphology. This conclusion is premature, however, since the most appropriate biomechanical and reference-scaling variables have not been calculated for H. floresiensis to date. Brown and Maeda (2009) extensively investigated corpus shape in LB1 and LB6 in comparative context. While this study primarily focused on identification of morphological patterns with reference to taxonomic variation, they did offer some speculation on the functional and mechanical significance of the H. floresiensis mandibles. Referencing a somewhat skeptical investigation of the relationship of diet to jaw morphology in colobine monkeys (Daegling and McGraw, 2001), Brown and Maeda suggested that “morphological differences between H. floresiensis and Homo sapiens mandibles greatly exceed those within the Colobinae, and surely highlight increased resistance to structural failure in the symphysis and corpus in H. floresiensis relative to H. sapiens.” (2009:590).1 This observation, however, must be reconciled with the conclusions of Kaifu et al. (2011), who argued that H. floresiensis exhibits the trend of facial reduction that is consistent with the hypothesis of reduced masticatory stresses in later human evolution. In this study, we examine the details of cortical bone distribution from computed tomography (CT) scans of the LB1 and LB6 mandibles for comparison with samples of modern humans and great apes, as well as samples of South African australopiths and specimens of early Homo. This investigation permits an assessment of whether or not the Liang Bua mandibles have equivalent relative strength and rigidity to other hominoids. The null hypothesis in this type of comparison is that, under the assumption that masticatory forces scale approximately isometrically with size, all taxa investigated will exhibit similar stress-resisting competence. It is already understood that this hypothesis is unlikely to be true given the overall geometry of australopith mandibles (Wood and Aiello, 1998; Daegling and Grine, 2007). In general, corpus dimensions and proportions in australopiths e when scaled to either body or mandible size e are exceptional in terms of strength and rigidity by hominoid standards. While the biomechanical consequence of this is uncertain, under an assumption of stress similarity, it is reasonable to infer that masticatory forces were elevated in these early hominins. By contrast, when evaluated relative to living great apes, modern humans also exhibit large corpus dimensions despite having corpus proportions similar to other living hominoids (Daegling, 2007a). Given reduced adductor mass in H. sapiens, this would indicate reduced stress in modern human mandibles relative to living apes; i.e., modern human jaws may in fact be ‘overdesigned.’ The functional or adaptive significance of this finding is unclear, but the CT data permit an evaluation of whether the architecture of the Liang Bua mandibles is patterned similarly to modern humans, early Homo, or australopiths. Understanding the potential uniqueness of the H. floresiensis mandibles in biomechanical attributes may shed light on the functional morphology of mastication in this recently extinct hominin.

1 Brown and Maeda (2009) cite Daegling and McGraw (2007) in their discussion referencing colobine monkeys. This particular citation, however, was a comparative study of cercopithecine monkeys. It is very likely the paper to which they refer to was instead the contribution cited here.

37

Materials and methods Computed tomography (CT) scans of the LB1 and LB6 mandibles of H. floresiensis served as the source data for calculation of geometric biomechanical properties of the corpus based on cortical bone contours. Sections were defined to sample minimum crosssectional areas at M1, M2 and the symphysis (Fig. 1); orientation of sections was constrained to lie orthogonal to the occlusal plane. For the molar sections in both mandibles, and the symphysis section in LB6, a Siemens medical CT scanner was used to obtain DICOM images with the following parameters: 130 kV; 70 mA; 1.0 mm slice thickness; 0.1 mm slice interval, H50 reconstruction kernel. Slice resolutions for the LB1 and LB6 mandibles were 4.339 pixels/mm and 7.014 pixels/mm, respectively. For the symphysis section in the LB1 mandible, the same Siemens medical CT scanner was used to obtain DICOM images with the following parameters: 130 kV; 80 mA; 2.0 mm slice thickness; 0.1 mm slice interval, H70 reconstruction kernel, with a resolution of 2.783 pixels/mm. To obtain the desired sections through each molar and the symphyses (Fig. 1), the original CT data was digitally re-sliced in AMIRA 5.4 software using the ObliqueSlice (using three points) and ApplyTransform (with Lanczos interpolation) functions. Re-slicing resulted in the same image resolutions as the original scan data. The comparative sample consisted of 20 specimens each from modern samples of H. sapiens, Pan troglodytes, Pongo pygmaeus and Gorilla gorilla (Daegling, 2007a). Sexes were equally represented in these samples. Specimens representing Paranthropus robustus (N ¼ 8) and Australopithecus africanus (N ¼ 5) were also included for comparisons, as well as the type specimen of ‘Telanthropus capensis’ (SK15) and SK45, both representing early Homo. As preservation was incomplete among the fossil sample, not all sections and/or analyses could be completed; a listing of the sections analyzed is presented in Table 1. Calculated variables at each section included cortical bone area (CBA), total subperiosteal area (TSA), and maximum and minimum second moments of area (moments of inertia, Imax and Imin). Ideally, moments of inertia about anatomical axes would be used for comparisons because they provide better reflection of stiffness under parasagittal and transverse bending. Unfortunately, existing fractures (i.e., induced taphonomically) in LB1 and post-recovery damage to LB6 (Brown and Maeda, 2009) undermine confidence that these anatomical planes can be defined so as to be meaningfully compared with the remainder of the sample. Fortunately, calculation of Imax and Imin are unaffected by specimen orientation and specification of anatomical planes, and in postcanine sections differences in second moments of area about principal and anatomical axes by and large do not impact comparative inferences (Daegling and Grine, 1991). The sum of the principal moments of inertia yields a quantity known as the polar moment of inertia that is often used as an estimate of torsional rigidity in skeletal structures. The polar moment of inertia has been shown to be unreliable for estimating this mechanical property in mandibles (Daegling and Hylander, 1998), however, and we calculate a variable of torsional strength based on a variable thin tube model (Young and Budynas, 2002) that is appropriate for mandibular sections (Daegling and Hylander, 1998; Daegling, 2007b). This variable (K) was determined for molar sections only, as this region of the mandible is known to experience torsional shear stress (Hylander, 1979), whereas there is little evidence that the symphysis is twisted (Hylander, 1984). While the default method of size ‘correction’ e scaling of biomechanical variables to body size e is appropriate in many contexts, there are cogent arguments for utilizing size proxies that correspond to covariates within anatomical biomechanical systems

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D.J. Daegling et al. / Journal of Human Evolution 68 (2014) 36e46

Figure 1. Three-dimensional volume renderings derived from medical computed tomography scans of the LB1 (top row) and LB6 (bottom row) mandibles. Lateral views of the right side shown in a and d. Occlusal views of the right molars shown in b and e. Frontal view of the symphysis (Sym) shown in c and f. All views have the right first and second molars (M1 and M2, respectively) oriented with their occlusal plane (dotted lines in a and d). M1 and M2 sections (solid lines in a, b, d and e) are taken orthogonal to the occlusal plane of the right molars (dotted lines in a and d) and the right mandibular corpus (dashed lines in b and e). The symphysis section (solid lines in c and f) were taken at the level between the alveoli of the right and left first incisors for LB1, and to a point just right of this in LB6 (due to damage in this region of the mandible caused during preparation).

(Hylander, 1985; Smith, 1993). Mandibular length (ML) represents a reasonable independent variable in comparative mechanical analyses because it is proportional to various bending moment arms that are occurring during mastication and ingestion (Hylander, 1985). With respect to particular loading regimes, certain components of ML provide first-order approximations of moment arm lengths. Based on the static analysis of Hylander (1979), parasagittal bending rigidity is assessed relative to the parasagittal bending moment arm (PMA, the component of ML from infradentale to the section of interest). Additionally, lateral transverse bending rigidity is assessed relative to the ‘wishboning’ moment arm (WMA, the fraction of ML from the supra-angular incisures to the section of

Table 1 Comparative sample. Taxon

Paranthropus robustus

Australopithecus africanus

Homo cf. erectus

Specimen

SK 6 SK 12 SK 23 SK 34 SKX 4446 SKX 5013 SKW 5 TM 1517 MLD 18 MLD 34 MLD 40 Sts 36 Sts 52 Stw 404 SK 15 SK 45

Mandibular length (ML)

x x x

x

x x x

CT sections analyzed M1

M2

x x x x x x x x x x x x

x x x x x x x x x x

x x

Symphyseal

x

x

x x x x

interest; Hylander, 1984). These analyses provide an estimate of relative stress in the mandible under an assumption of isometric scaling of adductor muscle force. Scaling of K versus mandibular length does not necessarily yield the same information, since the twisting moment arm is theoretically independent of jaw length. Thus, the discernment of relative stress under torsion is somewhat ambiguous. For this reason, we evaluated K relative to cortical and total subperiosteal area as well, which provides information on how efficiently a given amount of bone or section size achieves torsional strength. Measures of cortical bone and total crosssectional area scaled against ML provide an assessment of relative economy of bone utilization in different mandibles (Daegling, 2007a). To evaluate the biomechanical attributes of the Liang Bua mandibles, we utilized two basic approaches. First, for each bivariate comparison of interest we calculated a forced isometric line through the grand means of X and Y variables based on male and female means of modern taxa. We also calculated a forced isometric line through the individual specimens of fossil hominins for a given bivariate comparison. These procedures produced lines of mechanical or geometric equivalence in the modern and fossil samples. Since the H. floresiensis sample is insufficient (df ¼ 0) for an analysis of covariance or equivalent bivariate test, we evaluated the position of the Liang Bua mandibles relative to these two isometric lines through calculation of percentage prediction errors (Smith, 1980; Jungers, 1984). This procedure indicates whether the Liang Bua mandibles occupy positions in bivariate log space that are proximate to, above or below lines of geometric/mechanical equivalence in contemporary hominoids and fossil hominins, respectively. Our second approach involved calculation of a series of indices (e.g., CBA/TSA, K/ML) for modern and australopith taxa for comparison with the Liang Bua and Swartkrans Homo mandibles. With

D.J. Daegling et al. / Journal of Human Evolution 68 (2014) 36e46

N ¼ 2 for the focal taxon, employment of conventional statistics (e.g., ANOVA) is not ideal. For evaluation of the uniqueness of LB1 and LB6, we created 10,000 bootstrap estimates of species means for the modern taxa, yielding a resampling estimate for 95% confidence intervals (CI) for comparison to the fossil samples. In both bivariate regression and index calculations, variables were converted so as to ensure dimensional equivalence (e.g., Imax 0:25 /PMA yields a dimensionless index). Calculations, analyses and graphics were performed and created using the open-source platform R (R Core Team, 2013). Results The pattern of geometric property variation in LB1 and LB6 shares some attributes with modern Homo and South African australopiths. By contrast, the Liang Bua mandibles show no consistent affinity to Swartkrans Homo in biomechanical properties. The ways in which H. floresiensis mandibles differ from those of H. sapiens in mechanical competence is context-specific; i.e., interpretation depends on the mechanical variables under consideration. Cortical bone utilization Cortical area (CBA) in LB1 and LB6 occupies 41% and 34% of total subperiosteal area (TSA) in M1 sections (Table 2). The value for LB1 lies above the range for A. africanus and Pongo, and also above the CI of modern species with the exception of Gorilla. By contrast, the LB6 value falls below the CI for Homo, Pan and Gorilla but within their ranges. In SK15, CBA occupies 35% of TSA, a value between those observed for LB1 and LB6. At M2, CBA is 37% of TSA in LB1 and 33% of TSA in LB6. These values contrast with the index value in SK45 (42%) but lie within the range of both australopith taxa. The value in LB6 falls below the lower bound of the CI for the means of Homo and Gorilla, and both LB1 and LB6 are below the lower CI bound for the Pan mean. The values for LB1 and LB6 lie within the ranges observed for australopiths and modern hominoids. The symphyseal CBA/TSA index values for LB1 and LB6 are virtually identical (29.5 and 28.9%, respectively). These values lie below the CI for Pan, Pongo and below the range seen in modern Homo, and are lower than any values observed in A. africanus and P. robustus. Relative to ML, cortical area in H. floresiensis is intermediate between the averages in modern Homo and great apes at M1. The CBA0.5/ML index in both LB1 and LB6 is below the CI for Homo (albeit within the range) but above the CI for Pan, Pongo and Gorilla (Table 2). The value for LB1 lies beyond the ranges in the great apes, while LB6 only exceeds the range in Pongo. The Liang Bua values occupy the lower range of the Paranthropus sample, exceed the single A. africanus observation (Sts 36), and differ from SK15 from 2 to 6%. At M2 the same pattern prevails: LB1 and LB6 fall below the H. sapiens CI (with LB1 outside the range), lie beyond the CI but within the range for great apes, and are close to the lower values observed for P. robustus. In the symphyseal section, both H. floresiensis values fall below the CI for modern Homo (with LB1 beyond the range) and are similar to two of the four specimens of A. africanus and P. robustus (Sts 36 and SKW5). In terms of scaling of cortical to total area, relative to a forced isometric relationship based on modern hominoids, LB1 displays CBA values that are generally above expectation (i.e., more bone than predicted by hominoid or fossil standards) for its size, while LB6 has less bone than predicted by this relationship (Fig. 2, Table 3). Relative to ML in extant hominoids, LB1 and LB6 lie above the line of isometry at M1 (Fig. 3) and M2 sections, but below it at the symphysis (Table 3). Regression of CBA on ML is nonsignificant

39

Table 2 Cortical bone utilization. N CBA/TSA at M1 LB1 LB6 SK15 P. robustus 8 A. africanus 5 Homo 20 Pan 20 Pongo 20 Gorilla 20 CBA/TSA at M2 LB1 LB6 SK45 P. robustus 7 A. africanus 4 Homo 20 Pan 20 Pongo 20 Gorilla 20 CBA/TSA at symphysis LB1 LB6 P. robustus 2 A. africanus 2 Homo 20 Pan 20 Pongo 20 Gorilla 20 CBA/ML at M1 LB1 LB6 SK15 P. robustus 4 A. africanus 1 Homo 20 Pan 20 Pongo 20 Gorilla 20 CBA/ML at M2 LB1 LB6 P. robustus 4 Homo 20 Pan 20 Pongo 20 Gorilla 20 CBA/ML at symphysis LB1 LB6 P. robustus 2 A. africanus 2 Homo 20 Pan 20 Pongo 20 Gorilla 20

X

s

Min

Max

95% CI

414 337 349 373 345 367 382 327 398

32.9 42.1 46.7 60.8 46.5 55.1

319 300 257 211 208 281

421 410 480 515 383 513

346e386 355e408 307e345 374e422

367 328 424 353 332 379 425 316 385

63.7 47.9 47.7 68.5 67.2 51.6

269 288 270 269 180 259

467 400 462 538 449 449

359e400 395e454 288e346 362e406

295 289 450 337 486 359 319 306

96.1 0.4 98.7 57.0 50.4 44.7

382 336 321 233 230 216

518 337 723 474 426 387

444e529 334e383 298e341 286e324

14.8

102

138

6.2 8.4 7.5 6.7

104 76 70 83

127 105 99 105

113e119 87e94 86e92 91e97

101 106 116 118 95 89 92

10.6 7.2 8.8 9.1 7.9

105 103 77 70 79

131 130 107 107 107

115e121 90e98 86e93 89e95

105 108 121 110 124 112 109 107

24.5 9.6 10.5 12.3 10.4 9.2

104 104 107 90 89 88

139 117 138 132 127 127

119e128 106e117 105e114 103e111

108 104 102 120 88 116 91 89 94

Index values are expressed 103. Confidence intervals are calculated based on resampling (with replacement) at original sample sizes over 10,000 iterations. Cortical bone area (CBA) is raised to the 0.5 power for calculation of the CBA/ML index to yield a dimensionless ratio.

for the fossil hominins; thus, percentage prediction errors are not meaningful and were not computed (Table 3). The relationship of the Liang Bua mandibles to modern Homo as depicted in Fig. 3 holds for all sections with respect to regression of CBA on ML. That is, H. floresiensis utilizes less bone than modern humans. Corpus geometry (Imin/Imax) An index of minimum to maximum bending stiffness within sections is analogous to the commonly used ‘robusticity’ index of

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D.J. Daegling et al. / Journal of Human Evolution 68 (2014) 36e46

Figure 2. Cortical bone area (CBA) is evaluated relative to total enclosed subperiosteal area (TSA) in natural log-transformed space at M1. LB1 and LB6 can be seen to lie above and below (respectively) a forced isometric line through the male (closed symbols) and female (open symbols) means of modern hominoids. The empirical slope of this regression is 1.02 (reduced major axis).

Table 3 Mandibular scaling percentage prediction errors for Homo floresiensis. Model Extant hominoids Fossil hominins Extant hominoids Fossil hominins Extant hominoids Fossil hominins Extant hominoids Fossil hominins Extant hominoids Fossil hominins Extant hominoids Fossil hominins Extant hominoids Fossil hominins Extant hominoids Fossil hominins Extant hominoids Fossil hominins Extant hominoids Fossil hominins Extant hominoids Fossil hominins Extant hominoids Fossil hominins Extant hominoids Fossil hominins Extant hominoids Fossil hominins Extant hominoids Fossil hominins Extant hominoids Fossil hominins Extant hominoids Fossil hominins

Regression

Section

r

LB1

LB6

CBA on TSA CBA on TSA CBA on TSA CBA on TSA CBA on TSA CBA on TSA CBA on ML CBA on ML CBA on ML CBA on ML CBA on ML CBA on ML Imax on PMA Imax on PMA Imax on PMA Imax on PMA Imin on WMA Imin on WMA Imin on WMA Imin on WMA Imin on WMA Imin on WMA K on CBA K on CBA K on CBA K on CBA K on TSA K on TSA K on TSA K on TSA K on ML K on ML K on ML K on ML

M1 M1 M2 M2 Symphysis Symphysis M1 M1 M2 M2 Symphysis Symphysis M1 M1 M2 M2 M1 M1 M2 M2 Symphysis Symphysis M1 M1 M2 M2 M1 M1 M2 M2 M1 M1 M2 M2

0.96 0.92 0.94 0.77 0.98 ns 0.90 ns 0.90 ns 0.98 ns 0.73 0.78 0.83 ns 0.97 0.87 0.92 ns 0.99 0.59 0.94 0.83 0.96 0.60 0.86 0.87 0.87 0.78 0.79 ns 0.84 ns

þ13.4 þ15.3 1.3 þ5.6 þ10.4 e þ12.0 e þ3.8 e 6.5 e þ14.3 11.5 þ8.4 e þ22.5 þ2.9 þ9.3 e þ5.9 2.3 þ10.7 þ0.6 þ55.2 þ36.1 þ25.6 þ16.0 þ53.2 þ43.5 þ18.2 e þ29.5 e

7.7 6.2 11.8 5.7 19.4 e þ7.6 e þ8.5 e 3.8 e þ1.1 21.7 þ1.7 e þ22.3 þ2.8 þ21.1 e þ9.7 þ1.2 þ51.7 þ37.8 þ58.1 þ38.7 þ40.1 þ29.3 þ39.4 þ30.6 þ32.7 e þ36.5 e

Prediction errors are based on deviation from a forced isometric line through the bivariate mean, and are calculated from values transformed from log to linear scale as ([observed value  predicted value/predicted value]  100). Extant hominoid regressions are calculated from male and female means of Homo, Pan, Pongo and Gorilla. Fossil hominin regressions are calculated from individual specimens of Paranthropus, Australopithecus and early Homo (see Table 1 for specimens represented at different sections).

Figure 3. Cortical bone area (CBA) versus mandibular length (ML) in natural logtransformed space at M1. A forced isometric line through modern hominoid sample illustrates a general separation of hominins from great apes. Despite having jaws nearly as long as modern Homo, the Liang Bua mandibles have less bone in cross section. The empirical slope of the modern hominoid regression is 0.61 (reduced major axis). Male and female symbols as in Fig. 2.

corpus breadth over height (the ‘module’ ratio of Brown and Maeda, 2009), except that Imin/Imax gives a more mechanically informative assessment of shape independent of anatomical orientation. This ratio in Liang Bua mandibles at M1 and M2 is exceptional by modern standards, exceeding the ranges of modern hominoids examined with the exception of Homo at M2, although here both LB1 and LB6 lie beyond the modern human CI (Table 4). LB1 and LB6 have index values comparable with the higher values in the australopith samples at molar sections. The LB6 value is slightly larger than that of SK15 at M1 but LB1’s value is substantially larger (>30%); both LB1 and LB6 have much larger values than that of SK45 at M2. The same relationships are observed at symphyseal sections: LB1 and LB6 values lie beyond the CI for living apes and humans but lie within their ranges (with the exception of Gorilla versus LB1) and within the ranges of australopiths. Relative stiffness in parasagittal bending (Imax 0:25 /PMA) The Liang Bua mandibles are distinct from both modern Homo and living great apes, in that their index values fall below the CI for humans but near the upper bound or beyond the CI of other living hominoids at M1 and M2 (Table 5). The values for LB1 and LB6 are below the ranges of australopiths at both molar sections. The value for SK15 is marginally greater than that for LB1 at M1, and as such also falls below the range for P. robustus and below the CI for modern humans. At the symphysis, both H. floresiensis mandibles lie within the CI for Homo and Pan but below those for Gorilla and Pongo. LB1 and LB6 values fit well within modern hominoid ranges and are intermediate between the two values for P. robustus. With respect to A. africanus, H. floresiensis jaws have a larger index value than Sts36 but are virtually identical to Sts52. It should be noted that for symphyseal sections, PMA is essentially zero (such that parasagittal bending is absent here) and ML represents a general (rather than biomechanical) size proxy. The forced isometric relationship, or a line of ‘stress-equivalence,’ for hominoids nearly predicts the Imax value for LB6 but

D.J. Daegling et al. / Journal of Human Evolution 68 (2014) 36e46 Table 4 Cross-sectional geometry. N Imin/Imax at M1 LB1 LB6 SK15 P. robustus 8 A. africanus 5 Homo 20 Pan 20 Pongo 20 Gorilla 20 Imin/Imax at M2 LB1 LB6 SK45 P. robustus 7 A. africanus 4 Homo 20 Pan 20 Pongo 20 Gorilla 20 Imin/Imax at symphysis LB1 LB6 P. robustus 2 A. africanus 2 Homo 20 Pan 20 Pongo 20 Gorilla 20

X

s

Min

Max

95% CI

714 530 524 640 571 313 384 286 341

138.7 149.0 73.1 69.9 55.6 76.2

372 359 211 286 194 222

839 731 463 495 412 490

282e345 353e413 263e310 362e429

743 631 358 690 688 425 406 322 395

162.9 125.4 106.1 68.6 79.8 79.0

338 505 263 277 163 286

855 774 719 535 536 537

381e474 377e436 289e357 362e429

384 422 397 380 309 294 209 260

101.7 118.7 67.1 119.4 104.9 71.8

325 296 193 146 78 138

469 464 444 645 602 385

280e338 249e352 171e261 230e291

41

substantially underpredicts bending rigidity in LB1 (Fig. 4, Table 3). The bivariate relationship in fossil hominins, by contrast, indicates relatively low parasagittal bending stiffness of the Liang Bua mandibles at M1 (but at M2 the fossil regression is not significant, Table 3). Relative stiffness in lateral transverse bending (Imin 0:25 /WMA)

Index values are expressed 103. Confidence intervals are calculated based on resampling (with replacement) at original sample sizes over 10,000 iterations.

At M1 sections, the identical index values for LB1 and LB6 are larger than those for SK15 (H. erectus) and Sts 36 (A. africanus); H. floresiensis lies within the range for P. robustus and Homo but above the range for great apes (Table 6). The Liang Bua mandibles are situated above the CI for Homo. At M2, both LB1 and LB6 index values lie above the CI in great apes, but both fall within the ranges of Homo and Paranthropus (Table 6). LB1 lies below the human CI while LB6 resides within it. At symphyseal sections, the LB1 and LB6 index values are unusual by modern standards, lying above the CI for all modern species under comparison. Relative to fossil hominins, the LB1 and LB6 index values lie between the values for the two specimens sampled for both A. africanus and P. robustus. The LB1 and LB6 values are within the observed ranges of all taxa under comparison. The bivariate relationship of Imin to WMA places the Liang Bua sample in the vicinity of modern humans, above a forced isometric line defined by living hominoids at M1 and M2 but more coincident with it in midsagittal section (Fig. 5, Table 3). In the two cases where the Imin on WMA regression is significant (M1 and the symphysis), the fossil hominin regression predicts the location of H. floresiensis better than the hominoid lines. Relative torsional strength The magnitude of K in mandibular sections is evaluated relative to CBA, TSA and ML at molar sections (Table 7). The

Table 5 Parasagittal bending rigidity. N Imax/PMA at M1 LB1 LB6 SK15 P. robustus 4 A. africanus 1 Homo 20 Pan 20 Pongo 20 Gorilla 20 Imax/PMA at M2 LB1 LB6 P. robustus 4 Homo 20 Pan 20 Pongo 20 Gorilla 20 Imax/ML at symphysis LB1 LB6 P. robustus 2 A. africanus 2 Homo 20 Pan 20 Pongo 20 Gorilla 20

X

Min

Max

34.6

285

362

20.0 12.6 18.1 22.6

258 162 169 198

332 218 247 269

283e300 183e194 210e225 220e239

189 177 220 206 153 173 171

22.1 13.3 8.9 13.6 15.7

202 177 137 136 146

247 277 170 203 199

200e212 149e156 167e179 164e177

975 986 1051 961 997 997 1076 1021

212.8 24.7 65.1 85.4 80.3 55.3

901 944 894 822 869 946

1202 979 1148 1144 1208 1125

970e1026 961e1033 1040e1107 998e1045

261 231 263 311 271 291 188 218 229

s

95% CI

Index values are expressed 103 at M1 and M2 sections, 104 at the symphyseal sections. Confidence intervals are calculated based on resampling (with replacement) at original sample sizes over 10,000 iterations. In order to yield dimensionless ratios, the 4th root of Imax defines the numerator in index calculations. While Imax/ PMA provides a relative measure of bending strength at M1 and M2, at the symphysis there is not a comparable bending moment during mastication or incisal biting. Consequently, for the symphyseal index ML should be considered as a general size proxy, rather than a biomechanical moment arm proxy.

Figure 4. Regression of Imax on the length of the moment arm associated with parasagittal bending (PMA) provides an assessment of parasagittal bending strength. A forced isometric line through the modern hominoid grand mean at M1 is shown (reduced major axis slope is 0.66). Under this hypothesis of isometry, LB1 is stiffer than expected based on its size while LB6 is close to an expectation of equivalent stress. The position of the H. floresiensis jaws relative to modern Homo mandibles is indicative of diminished bending rigidity in the Liang Bua specimens. Male and female symbols as in Fig. 2.

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Table 6 Lateral transverse bending rigidity. N Imin/WMA at M1 LB1 LB6 SK15 P. robustus 4 A. africanus 1 Homo 20 Pan 20 Pongo 20 Gorilla 20 Imin/WMA at M2 LB1 LB6 P. robustus 4 Homo 20 Pan 20 Pongo 20 Gorilla 20 Imin/WMA at symphysis LB1 LB6 P. robustus 2 A. africanus 2 Homo 20 Pan 20 Pongo 20 Gorilla 20

X 122 122 107 125 108 114 98 96 92

Table 7 Relative torsional strength. s

Min

Max

17.4

101

143

8.0 9.7 7.8 7.5

95 79 82 76

127 114 110 106

135 150 154 153 121 116 111

24.0 13.5 13.4 12.4 12.9

119 122 95 94 88

173 178 143 143 132

768 795 826 752 740 725 714 723

114.6 79.2 57.9 81.7 70.9 52.7

745 696 621 572 590 608

907 808 843 913 916 831

95% CI

110e117 94e102 92e100 88e95

147e159 115e126 111e121 105e117

715e764 690e760 685e747 700e745

Index values are expressed 103 at M1 and M2 sections, 104 at the symphyseal sections. Confidence intervals are calculated based on resampling (with replacement) at original sample sizes over 10,000 iterations. In order to yield dimensionless ratios, the 4th root of Imin is divided by ML in index calculations. The Imin/WMA index provides a relative measure of lateral transverse bending strength at M1, M2, and the symphysis. The WMA at the symphysis is equivalent to ML.

Figure 5. Regression of Imin versus ML provides an assessment of relative strength under lateral transverse bending in midsagittal section. ML is equivalent to the wishboning moment arm proxy (WMA) for symphyseal sections. A forced isometric line based on the modern hominoid sample is shown (reduced major axis slope is 0.82). This isometric line cannot be considered a criterion of equivalent stress at the symphysis owing to curved beam effects (Hylander, 1985). The Liang Bua mandibles can be interpreted here as being prone to less stress relative to modern Homo, but for different reasons depending on whether males or females are under comparison. Relative to male modern humans, H. floresiensis are more ‘robust’ owing to shorter jaws, while relative to modern females this enhanced stiffness is due instead to corpus size. Male and female symbols as in Fig. 2.

K/CBA at M1 LB1 LB6 SK15 P. robustus A. africanus Homo Pan Pongo Gorilla K/CBA at M2 LB1 LB6 SK45 P. robustus A. africanus Homo Pan Pongo Gorilla K/TSA at M1 LB1 LB6 SK15 P. robustus A. africanus Homo Pan Pongo Gorilla K/TSA at M2 LB1 LB6 SK45 P. robustus A. africanus Homo Pan Pongo Gorilla K/ML at M1 LB1 LB6 SK15 P. robustus A. africanus Homo Pan Pongo Gorilla K/ML at M2 LB1 LB6 P. robustus Homo Pan Pongo Gorilla

N

X

s

Min

Max

95% CI

8 5 20 20 20 20

665 911 470 686 689 638 606 535 668

147.2 48.9 98.3 111.5 142.0 90.8

500 614 487 371 350 493

959 733 857 799 788 784

597e681 557e652 477e598 629e705

7 4 20 20 20 20

911 929 648 672 599 576 553 557 708

194.3 113.5 68.9 126.0 113.9 108.1

385 625 437 297 311 520

923 855 734 760 855 964

548e607 499e608 510e606 662e755

8 5 20 20 20 20

276 307 164 252 239 233 227 173 263

38.0 39.5 40.0 32.6 45.6 32.1

210 210 159 163 112 197

306 301 310 282 261 303

216e250 213e240 154e193 249e276

7 4 20 20 20 20

334 304 275 229 239 218 230 172 270

42.3 39.4 29.3 38.2 32.5 37.3

152 183 170 140 104 228

292 275 270 294 234 374

205e230 213e245 158e186 255e287

4 1 20 20 20 20

86 96 68 98 89 89 68 62 74

13.1

79

110

9.0 5.7 8.2 5.8

75 54 49 60

109 75 77 83

86e93 65e70 59e66 71e76

4 20 20 20 20

94 99 95 87 67 64 74

12.7 6.1 7.1 7.5 5.6

77 78 54 47 64

105 99 78 77 83

84e89 64e70 61e67 72e76

Index values are expressed 103. Confidence intervals are calculated based on resampling (with replacement) at original sample sizes over 10,000 iterations. In order to yield a dimensionless ratio, K is raised to the 0.67 power when calculating indices with CBA and TSA in the denominator and to the 0.33 power when ML is the denominator term. None of the reference variables (CBA, TSA, ML) represents a moment arm proxy, and instead should be viewed as alternative means of accounting for size differences in the evaluation of torsional strength.

K/CBA index reveals a large difference between LB1 and LB6 at M1. Despite this, these index values lie within the range in P. robustus. LB1 lies within the A. africanus range and within modern Homo’s CI. The SK15 mandible lies below the range of australopiths and below the lower bound of the CI of the modern comparative sample. Both Liang Bua M1 sections lie above the CI

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for both Pan and Pongo. LB6 lies above the range of A. africanus and modern hominoids. At M2 sections, the values for LB1 and LB6 are more similar to one another, exceeding the upper bound of the CI of the K/CBA index for all modern taxa (Homo, Pan, Pongo, Gorilla), and exceeding the range of these taxa with the exception of Gorilla. The H. floresiensis values are also above the range of A. africanus, and are larger than that of SK45 by 41% (LB1) and 43% (LB6). The Liang Bua index values are most similar to those at the upper end of the P. robustus sample range. While the K/CBA index essentially quantifies how efficiently cortical bone is deployed to achieve torsional strength, the K/TSA index does so with respect to overall cross-sectional size. At both molar sections, LB1 and LB6 display K/TSA values greater than the two early Homo specimens measured, most remarkably with respect to SK15 at M1 (Table 7). Both sections of LB6 are atypical, with index values beyond the upper range of both australopith taxa and beyond the upper bounds of the CIs for modern humans and great apes (although it does fit within the modern human range). The LB1 mandible lies within the range of australopiths, Homo and Pan, and within the Gorilla CI at M1; at M2 it exceeds the australopith range and the ranges of modern hominoids with the exception of Gorilla. LB1’s value does lie beyond the CI of Gorilla, however. The K/ML index provides a third dimensionless assessment of torsional strength. Here again, the Liang Bua sample displays relatively high values above SK15 and beyond the ranges of great apes. Both LB1 and LB6 lie within the range but above the CI of modern humans at M2; at M1 LB1 falls within the human CI (Table 7). Both LB1 and LB6 index values are comparable with australopiths at M1 and M2. In bivariate space, LB6 and, to a lesser extent, LB1 are elevated above the hominoid isometric line at M1 (Fig. 6). With the sole exception of LB1 lying nearly coincident to a hominoid line of isometry for K on CBA at M1, the Liang Bua mandibles are consistently underpredicted by modern hominoid and fossil lines of isometry irrespective of the reference variable (Table 3).

Figure 6. Torsional strength as a function of ML at M1. Mandibular length is not a moment arm approximation; consequently, the forced isometric line through the modern hominoid sample cannot be considered a line of equivalent strength or stress. For their size, LB1 and LB6 are relatively strong in torsion relative to early Homo (SK15) and Pan. They lie within the modern human range, but together span beyond the CI for Homo (see Table 7).

43

Discussion In their comparative survey, Brown and Maeda concluded that “[b]iomechanical adaptations in the Liang Bua mandibles, while not as extreme as in australopiths, suggest a similar adaptation to high masticatory loads.” (2009:592). The validity of this conclusion depends on what such adaptation entails with respect to measures of biomechanical performance. The assumption required for invoking ML or its components (PMA, WMA) as biomechanical size proxies is that this metric, in addition to providing information on moment arm scaling, also implicitly serves as an isometric surrogate for adductor force. Ultimately, force recruited by the jaw adductors is responsible for the production of high loads (realized as the combination of muscle, occlusal and joint reaction forces). In many contexts, this convenient assumption of isometric scaling of masticatory force is unlikely to be strictly true. The simplest approach to the question of mechanical adaptation is one in which stress levels are assumed to be constant across species. That is, the assumption is that robust australopiths did not experience more or less masticatory stress than chimpanzees today, rather they recruited more muscular force and their mandibles are of a size and proportion that permits an ideal range of stress or strain to be achieved (see Rubin, 1984; Hylander and Johnson, 1997). This could be confidently assessed if there were known skeletal markers that covaried strongly with muscular force; this is a promising avenue of current research (Perry et al., 2011; Eng et al., 2013), although application in the paleontological context still entails considerable uncertainty. An important consideration in comparative allometry is that scaling of anatomical features to body size on the one hand, and biomechanical variables on the other, can yield complementary information for adaptive inference (Smith, 1993). Examining mandibular mechanical competence relative to body size (Fig. 7) suggests that the Liang Bua hominins are very unlike australopiths (i.e., absolutely weak jaws) while comparison of K relative to jaw length (Fig. 6), for example, suggests a functional affinity to early hominins (relatively derived for torsional strength in the same manner as Paranthropus, Hylander, 1979, 1988). Homo floresiensis has weak jaws for its body size, and in this context the taxon departs substantially from the australopith morphotype. It would be incorrect to label the Liang Bua hominins as scaled-down australopiths with reference to body size, but it would be more appropriate to label them as such with respect to mandibular proportions (Fig. 8). The similarity of LB1 and LB6 to modern humans depends on the mechanical variable under consideration. With respect to K, the Flores material achieves equivalent or even superior strength with relatively less material. This means that per unit body mass, the Liang Bua hominins would have the luxury of recruiting more adductor force without compromising structural integrity. On the other hand, with respect to resisting parasagittal bending (Imax), the Liang Bua hominins would encumber substantially greater stress than modern humans if they recruited equivalent adductor force. The minimum second moment of area (Imin) is probably most critical in midsagittal section if lateral transverse bending is present (Hylander, 1985; Daegling, 2007a); both LB1 and LB6 appear to be well-disposed to accommodate this load relative to modern humans and manage to accomplish this with absolutely and relatively less cortical bone. The similarity of the Liang Bua mandibles to Swartkrans H. erectus is moot. Corpus proportions in SK15 and SK45 are very different from one another, with the former’s Imin/Imax value resembling LB6 and A. africanus, but with SK45 essentially falling within the midrange of living hominoids including H. sapiens. Relative torsional strength is greater in the Liang Bua sample

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Figure 7. Overall bending rigidity (Imin þ Imax, or the polar moment of inertia) versus body mass in the comparative sample. Two body mass estimates are provided for LB1 (Jungers and Baab, 2009). These utilize McHenry’s (1992) regressions based on femoral head diameter. The smaller estimate is based on prediction in raw space (see Auerbach and Ruff, 2004); the larger is predicted from equations in logelog space. LB1 has absolutely and relatively reduced stiffness by modern hominoid or fossil hominin standards. Assuming that mandibles are adapted to experience a relatively narrow range of peak stress, this finding suggests that available jaw-adductor muscle force (and resultant bite force) was considerably less in LB1 than in australopiths. Male and female symbols as in Fig. 2. Body size estimates for modern hominoids are based on Smith and Jungers (1997), and the australopith data points are averages for male and female estimates from McHenry (1992).

compared with the South African H. erectus, but relative bending stiffness is comparable among LB1, LB6 and SK15. The Liang Bua mandibles differ from those of apes in the same manner as modern Homo and the australopiths. This is presumably explicable on phylogenetic grounds, but the important question in terms of masticatory adaptations is whether H. floresiensis is ‘robust’ (¼ structurally strong) in the manner of modern Homo or

Figure 8. Cortical contours at M2 sections for H. floresiensis (LB1, LB6), representative modern hominoids, A. africanus (MLD18), and Paranthropus robustus (SKX5013), drawn to scale. Corpus shape in H. floresiensis contributes to relatively large values of Imin and K relative to ML. Despite smaller body size, corpus size in H. floresiensis falls within the lower range of modern humans. Lingual is to the left in each section.

early hominins. The ‘robust’ australopith mandibles examined here are strong relative to living apes by virtue of large corpus dimensions and absolutely greater bone mass (Figs. 3, 4 and 6); A. africanus utilizes relatively less cortical bone but still maintains high structural stiffness, at least in the postcanine corpus. Australopith jaw lengths are comparable with male Pan and females of Gorilla and Pongo. Modern human jaws, by contrast, utilize relatively large amounts of bone (Daegling, 2007a) such that they essentially match the absolute structural stiffness of chimpanzees at molar sections, but in much shorter jaws (Figs. 3, 4 and 6). Interpreted simplistically, human jaws are strong because they are short while australopith jaws are strong owing to their large corpus dimensions. Cortical area relative to jaw size (ML) in LB1 and LB6 is reduced by modern human standards. This can be viewed as an economical use of bone for maintaining structural integrity, especially in the context of torsional loads (Table 3). In this respect, H. floresiensis recalls the condition in australopith molar sections, as it does with respect to strength in lateral bending (Imin/WMA). At the same time, parasagittal bending strength (Imax/PMA) in the Liang Bua jaws is reduced relative to modern Homo. Homo floresiensis jaws are thus mechanically ‘robust’ relative to modern Homo (and comparable with australopiths) under some loads but not others. It would be a mistake to argue from the above observations that H. floresiensis was ‘adapted’ to torsional and transverse bending loads but that parasagittal bending loads were unimportant in its masticatory regime. There are several reasons to eschew such an explanation. First, it is very difficult to conceive of a context in which parasagittal bending would be relatively reduced in light of the orientation of the jaw adductors and the necessity of a primarily vertical occlusal force for providing useful masticatory work. Second, this explanation presumes that load histories can be unambiguously read out of bone geometry, an assumption that is convenient but no longer sustainable (Daegling, 1993; Demes et al., 1998, 2001; Pearson and Lieberman, 2004). Finally, the presence of lateral transverse bending in hominin mastication is an open question. The observation that LB1 and LB6 show adequate resistance to this load at the symphysis may or may not be adaptively significant, but they are comparable with australopiths and unlike modern hominoids in this regard. The large transverse dimensions of the Liang Bua corpora are potentially explicable as a developmental correlate of postcanine megadontia. This explanation has been invoked to explain australopith corpus dimensions (Dart, 1948; Wolpoff, 1975; Wood, 1978), obviating structural biomechanical (i.e., stress-resistance) explanations for their exceptional corpus proportions (Smith, 1983). While intuitive, this explanation is not borne out by comparative or developmental data (Daegling and Grine, 1991; Boughner and Dean, 2004, 2008; Plavcan and Daegling, 2006; Cobb and Panagiotopoulou, 2011). The geometric property data inform the apparently discordant conclusions of Brown and Maeda (2009) and Kaifu et al. (2011). Brown and Maeda argue that the Liang Bua mandibles are “structurally robust” (2009:591), suggesting in light of other evidence that H. floresiensis had a tough, fibrous diet, which required powerful mastication. This conclusion is valid if qualified appropriately: depending on the nature of allometric scaling of adductor force with body size, H. floresiensis could conceivably afford to load its jaws for many more cycles daily than modern Homo or even australopiths. On the other hand, it is unlikely these hominins could produce masticatory forces of high magnitude that australopiths were capable of recruiting routinely. In contrast to Brown and Maeda’s (2009) characterization of masticatory functional morphology, Kaifu et al. (2011) described H. floresiensis as having “substantial facial gracilization associated with reduced

D.J. Daegling et al. / Journal of Human Evolution 68 (2014) 36e46

masticatory activities” (2011:679). This is a reasonable conclusion if the frame of reference for it is the australopith morphotype, but this is a harder case to make if a specimen of early Homo (SK15) is assumed to be a representative precursor. An important and deciding factor in reconciling these apparently disparate interpretations is discovering the phylogenetic origins of H. floresiensis (i.e., if H. floresiensis is a dwarfed hominin, how does insular dwarfism typically influence jaw adductor mass?). Without this knowledge, the inference of relative masticatory stress in H. floresiensis is necessarily speculative. Summary and conclusions The comparative data do not provide unambiguous insight into the nature of masticatory adaptation in the Liang Bua hominins. There are, however, a suite of observations that underscore the functional attributes of H. floresiensis mandibles: 1. Corpus proportions are unlike modern humans and modern great apes. This cannot reasonably be attributed to a scaling effect vis à vis modern humans since jaw size (ML) is essentially the same between H. floresiensis and H. sapiens. 2. Similarity in corpus proportions between Liang Bua and australopith mandibles does not also mean that H. floresiensis has biomechanically ‘robust’ jaws relative to humans and apes under all masticatory loads. H. floresiensis has enhanced structural stiffness with respect to transverse bending and perhaps torsion, but not with respect to parasagittal bending in comparison with modern Homo. 3. Relative to estimated body size, the mandibular corpus of H. floresiensis is relatively small by hominoid (including fossil hominin) standards. Consequently, the mandibles of this taxon were not hypertrophied in the manner as that observed in australopiths, despite shared traits of postcanine megadontia and corpus proportions. This suggests that available adductor force in the Liang Bua hominins was substantially reduced from that which characterized australopiths. The above observations suggest that the masticatory apparatus of H. floresiensis cannot be described simply as an allometric variant of australopiths, H. erectus, or modern humans. While aspects of their mandibular morphology indicate structural strength under specific loads, the Liang Bua specimens probably did not recruit masticatory forces on the order of what is utilized by modern chimpanzees or australopiths. Whether this reflects a lack of ability (small adductor mass) or an absence of need (extraoral food processing obviating heavy or prolonged mastication) is the critical question awaiting future investigation. Acknowledgments We dedicate this contribution to the memory of Mike Morwood, valued colleague and good friend, who encouraged this research project. Many thanks go to Thomas Sutikna and Wayhu Saptomo from ARKENAS for logistical support and to Matt Tocheri for assistance with CT-scanning in Jakarta. Luci Betti-Nash is thanked for her expert help with some of the artwork. We gratefully acknowledge support from the Wenner-Gren Foundation for Anthropological Research, the Leakey Foundation and the National Geographic Society. References Aiello, L.C., 2010. Five years of Homo floresiensis. Am. J. Phys. Anthropol. 142, 167e179.

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Argue, D., Donlon, D., Groves, C., Wright, R., 2006. Homo floresiensis: microcephalic, pygmoid, Australopithecus, or Homo? J. Hum. Evol. 51, 360e374. Argue, D., Morwood, M.J., Sutikna, T., Jatmiko, Saptomo, W.E., 2009. Homo floresiensis: a cladistic analysis. J. Hum. Evol. 57, 623e639. Auerbach, B.M., Ruff, C.B., 2004. Human body mass estimation: a comparison of “morphometric” and “mechanical” methods. Am. J. Phys. Anthropol.125, 331e342. Boughner, J.C., Dean, M.C., 2004. Does space in the jaw influence the timing of molar crown initiation? A model using baboons (Papio anubis) and great apes (Pan troglodytes, Pan paniscus). J. Hum. Evol. 46, 255e277. Boughner, J.C., Dean, M.C., 2008. Mandibular shape, ontogeny and dental development in bonobos (Pan paniscus) and chimpanzees (Pan troglodytes). Evol. Biol. 35, 296e308. Brown, P., 2012. LB1 and LB6 Homo floresiensis are not modern human (Homo sapiens) cretins. J. Hum. Evol. 62, 201e224. Brown, P., Maeda, T., 2009. 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