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• W2034378031 abstract "In their response to our paper (Bookstein et al., 1999), Ravosa et al. (2000b) question our suggestion that “thinning minimizes bone mass without compromising necessary strength.” We respond to their questioning in various ways. First (and foremost) we point out that Ravosa et al. (2000b) do not question our data. We find this statement highly significant in light of the fact that our observation they object to is only one aspect of our findings. Nor do these authors question our methodology—Procrustes fit, interpolation by thin plate splines and statistics of relative warps. We agree with Ravosa et al. (2000b) that our data—as presented in Bookstein et al. (1999)—“can provide neither support for, nor a refutation of” the claim regarding masticatory stress determinants. We agree, however, because the same statement applies to these researchers themselves and other adherents of alternative views, such as the spatial model of supraorbital torus formation (Ravosa et al., 2000a). Ravosa et al. (2000a, b) seem to have either overlooked or disregarded the fact that there is indeed a thinning (from the Pliocene to the mid-Pleistocene) and we are entitled to a mechanical interpretation of this finding. Furthermore, we emphatically note that such an observation (the thinning) is not a support for the spatial model of supraorbital torus formation—nor is it at odds with such an interpretation. After all, it could be that the thinning may be advantageous to both mechanisms: masticatory stress issues and supraorbital torus formation. In our paper, we specifically (and cautiously) state “While the numerous small walls may help to absorb the masticatory stresses, there may be more to this variation of the external form of the frontal than simple structural resolution of chewing forces through mass minimization.” (Bookstein et al., 1999, p. 222) We do not, however, exclusively endorse the supraorbital torus formation, despite its possible consistency with our findings, for reasons listed below. One could argue that biomechanical, statistical and morphometric data—especially of the internal lamella structure and the thinness of the vault—supporting the spatial model of supraorbital torus formation is lacking. We think that Ravosa et al.'s (2000b) response can be summarized—and drawn into question—in the following way: by relying on in vivo measured strain gauge data (Hylander et al., 1991; Ross and Hylander, 1996), they assume that issues of masticatory stress do not relate to the morphology of the frontal sinuses, let alone the thinness of the vaults. We would like to point out that their presentation of the argument is incomplete. For instance, in our paper (Bookstein et al., 1999) we only present data of the mid-sagittal plane, and the spatial model of the supraorbital torus requires—at least—a morphometric analysis in a para-sagittal plane, one considerably lateral from the mid-sagittal one (for a suggested approach, see Schäfer et al., 1999). Second: in the analysis we have presented in the paper, we have re-orientated the cranial vault profiles so that the superposition is optimal (in a Procrustes sense) for the inner table curvature. One cannot infer the directions of stresses/strains directly from such an orientation, because in the Procrustes fit the palate and the dental occlusion plane are not coplanar in all the crania of our study. This aspect is crucial for the debate, as the directions of stresses and strains (in the masticatory stress views) and the geometric relations (in the spatial model of the supraorbital torus) can only be properly assessed in an orientation-independent manner with methods that do not rely on simple distance measurements. Third: we note that there are two bony shells (the outer browridge and the endocranial vault). The strength of such a complicated two-shelled vault is not straightforwardly assessable, which is why we question the strain gauge data (the gauges only register the strains on the outer surface of the outer shell) that adherents to the spatial model of supraorbital torus formation rely on so strongly. We ask how strain gauge data of the owl monkey (Ross and Hylander, 1996) and macaques (Hylander et al., 1991) can be directly applied to mid-Pleistocene human face morphology: the claimed allometry of the respective morphologies is inconclusive (Prossinger et al., 2000), and attempts at detecting isometric scaling are fraught with the difficulties of adequately representing skull size (Spoor and Zonneveld, 1999; Rae and Koppe, 2000). Because it has not been rigorously shown how stress and strain gauge data in monkeys can be applied to human mid-Pleistocene morphology, the graphs in Ravosa (1991) and in Hylander (1991) may be plausible, but to date they are only suggestive. The rhetoric question “why do orangutans … exhibit such diminutive browridges?” does clarify the issue: The average endocranial volume of orangutans is 413 cm3 (Aiello and Dean, 1996), that of the Petralona cranium is 1170 cm3 (Seidler et al., 1997). Although we cannot reliably model the endocranial vault with a sphere, we can infer that its radius R of curvature at the frontal vault is proportional to V1/3, while the meridional bending moment scales as R1 (Young, 1989). Thus, the ratio of curvatures would be 0.71:1; consequently the meridional bending moment is 1.4 times as high in Petralona when compared to orangutans. A smaller skull therefore is inherently more robust and may not need a supraorbital bar. In our paper (Bookstein et al., 1999), we point out that the curvature (as a shape variable) stayed invariant since before the mid-Pleistocene, but the Centroid Size (a good surrogate for radius in this context) changed considerably—by 11% (Bookstein et al., 1999, p. 220). Scaling arguments are subtle and perniciously difficult: we do not claim that a simple estimation justifies a frontal sinus (let alone its extent), because (ironically) chimpanzees do have a pronounced supraorbital bar, but it does show that caution is called for when making inferences. In Figure 1, we show how the lamellas inside the frontal sinus are easily interpreted as contributing to the increase in stiffening of the outer frontal vault, while at the same time reducing bone mass. When analyzing the CT scans of the mid-Pleistocene human crania (Seidler et al., 1997), we were surprised at how extremely thin the outer table is. The lamellas are perpendicular to the vault surface and most are vertical (roughly perpendicular to the dental occlusion surface), suggesting an ability to absorb vertically-directed forces associated with biting and chewing. The stiffness of the supraorbital bar, or beam, is achieved by horizontal lamellas (also perpendicular to the vault surfaces) interconnecting these vertical ones, producing a honeycomb structure. We seek a straightforward explanation for the presence of this rather complicated, intriguing and biomechanically intuitive lamella morphology and do not see how its presence is to be explained by detractors of the masticatory stress hypothesis. Suggestions such as “a structural adaptation to counter accidental loads” must be considered anecdotal: hypotheses of what these loads may be, how they are to be absorbed by the outer vault, their magnitude, and the mechanisms of evolutionary selection have neither been listed anywhere nor formally analyzed with respect to their viability under rigorous scrutiny. Our discussing biomechanical issues of the observed very large sinuses of the mid-Pleistocene hominids cannot be dismissed with musings that “it seems highly improbable that masticatory stresses in a hominid that cooked its food (if only occasionally) regularly exceeded …”. We are not aware of any publication documenting that cooking existed in the mid-Pleistocene. Left: A transvere cross section through the Petralona cranium. The inner table has been shaded in dark gray; it is quite thin (≈4 mm). The outer table is very thin (3–4 mm). Connected perpendicularly to the latter are thin lamellas (2–3 mm thick), which are sometimes also joined with other lamellas to form a type of honeycomb structure (as seen on the left). The frontal sinus is of enormous extent yet many of the lamellas interconnect the outer with the inner table (the disjointedness shown here is due to non-optimal preservation of parts of the fossil cranium as evidenced by parts of the ethmoid having been eroded away). Right: An “interior view” of the Petralona facial cranium. The inner table (visible in Left image) has been electronically removed in the interior view (Right) so as to reveal the geometry of the lamellas. Most lamellas are connected to the outer table, reminiscent of a buttress-type system. Not all the lamellas are from distal to proximal, however, some interconnect the ‘vertical’ ones in forming lateral arches. It is very reasonable to assume that such an interconnected system functions like internal honeycomb buttressing of a thin outer shell, using very little bone mass to achieve considerable rigidity. There are a few lamellas connected solely to the inner table (not shown), while many lamellas connect the inner with the outer table. Lastly, we would like to point out that the onus of refutation requested by Ravosa et al. (2000b) of us can just as easily be turned around: rather than asking “what kind of evidence would support a refutation of” the hypothesis that a “thin-walled supraorbital torus is especially designed for resisting masticatory stresses” (we did not use the word “especially” in our paper, please note), one could ask what kind of evidence would refute the spatial model of supraorbital torus formation. On the one hand, one can view this impasse of requiring refutation evidence by the adherents of a different view as a paradigm conflict. On the other, one could (and should) argue that biomechanical, statistical and morphometric data—especially of the internal lamella structure and the thinness of the vault—supporting the spatial model of supraorbital torus formation is lacking. We await such an analysis. Dr. Prossinger is a physicist, and Drs. Schäfer and Seidler are physical anthropologists, at the Institute for Anthropology, University of Vienna. There they, with other colleagues, develop applications of “virtual anthropology” techniques and morphometrics to paleoanthropological problems. Dr. Bookstein is a biometrician at the University of Michigan, Ann Arbor, USA. He has a particular interest in developing quantitative methods for comparative morphology." @default.
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• W2034378031 title "Reemerging stress: Supraorbital torus morphology in the mid-sagittal plane?" @default.
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