Reemerging stress: Supraorbital torus morphology in the mid‐sagittal plane?

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. 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 orientationindependent 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 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. *Correspondence to: Prof. Horst Seidler, Institute for Anthropology, University of Vienna, Althanstrasse 14, 1090 Wien, Austria. Fax: 43-1-4277-5947; E-mail: horst.seidler@univie.ac. at THE ANATOMICAL RECORD (NEW ANAT.) 261:170–172, 2000