Which Measures of Diaphyseal Robusticity Are Robust? A Comparison of External Methods of Quantifying the Strength of Long Bone Diaphyses to Cross-Sectional Geometric Properties Jay T. Stock* and Colin N. Shaw Leverhulme Centre for Human Evolutionary Studies, Department of Biological Anthropology, University of Cambridge, Cambridge CB2 1QH, UK KEY WORDS osteometrics; residual strength; long bones; biomechanics ABSTRACT Measures of diaphyseal robusticity have commonly been used to investigate differences in bone strength related to body size, behavior, climate, and other factors. The most common methods of quantifying robus- ticity involve external diameters, or cross-sectional geom- etry. The data derived from these different methods are often used to address similar research questions, yet the compatibility of the resulting data has not been thor- oughly tested. This study provides the first systematic comparison of externally derived measures of postcranial robusticity, with those based upon cross-sectional geome- try. It includes sections taken throughout the skeleton, comparisons of prediction errors associated with different measurements, and analysis of the implications of differ- ent methods of body size standardization on the prediction of relative bone strength. While the results show reasona- ble correlations between diaphyseal diameters and strengths derived from cross-sectional geometry, consider- able prediction errors are found in many cases. A new approach to externally based quantification of diaphyseal robusticity based upon moulding of sub-periosteal con- tours is proposed. This method maximizes correlation with cross-sectional geometry (r 2 5 .998) and minimizes prediction errors in all cases. The results underscore the importance of accurate periosteal measurement in the quantification of bone strength, and suggest that, regard- less of theoretical scaling predictions, external area based robusticity estimates involving the product of diaphyseal diameters are most directly comparable to cross-sectional geometric properties when they are standardized using the product of body mass and bone length. Am J Phys Anthropol 134:412–423, 2007. V V C 2007 Wiley-Liss, Inc. Skeletal robusticity, in the most general sense, refers to the strength of a bone as reflected by its size and shape. There is considerable evidence for a relationship between mechanical loading and functional adaptation in the human skeleton, resulting in differences in skeletal robus- ticity (see Ruff et al., 2006 for review). On this basis, stud- ies of skeletal robusticity have a long history of applica- tion in palaeontological and bioarchaeological research. In practice, the term robusticity has been used to refer to a variety of different methods of quantifying variation in skeletal size and shape. Initially the term was used to refer to diaphyseal thicknesses standardized to bone length (Martin and Saller, 1957; Bra ¨uer, 1988). This approach to the study of skeletal robusticity has been used in numerous studies (Collier, 1989; Pearson, 2000a; Stock et al., 2005; Wescott, 2006). Other studies have adopted more detailed means of quantifying diaphyseal robusticity, the most common of which involves the appli- cation of beam theory, in which the cross-sectional geome- try of long bone diaphyses is quantified in order to esti- mate the mechanical competence of a bone (Lovejoy et al., 1976; Lovejoy and Trinkaus, 1980; Ruff and Hayes, 1983; Ruff et al., 1984, 1993; Bridges, 1989, 1995; Trinkaus et al., 1994; Churchill, 1996; Larsen, 1997; Trinkaus, 1997; Trinkaus and Churchill, 1999; Ruff, 2000b; Stock and Pfeiffer 2001, 2004; Stock, 2006). Using this method, the calculation of biomechanical properties of cross-sec- tions of long bone diaphyses is dependent upon the accu- rate determination of periosteal and endosteal contours of the diaphysis. To avoid direct sectioning of diaphyses, non- invasive method of contour determination are commonly used, including computed tomography (Jungers and Minns, 1979; Ruff and Leo, 1986) and a method which uses a combination of silicone moulds and biplanar radio- graphs (e.g. Trinkaus and Ruff, 1989; Stock, 2002). The latter method has been shown to provide an accurate means of estimating cross-section contours without destruction of the sample (Stock, 2002; O’Neill and Ruff, 2004). Despite the accuracy of these methods, there are several drawbacks that restrict their widespread applica- tion: a) computed tomographic and radiographic imaging facilities are often unavailable in remote research loca- tions, or the transport of specimens to imaging facilities is impractical; b) the cost of these methods of imaging can be highly variable depending on research context, and is sometimes prohibitive, particularly in research involving Grant sponsor: Leverhulme Trust, Natural Environment Research Council, U.K. *Correspondence to: Jay T. Stock, Leverhulme Centre for Human Evolutionary Studies, Department of Biological Anthropology, University of Cambridge, Fitzwilliam St., Cambridge CB2 1QH, UK. E-mail: j.stock@human-evol.cam.ac.uk Received 20 March 2007; accepted 1 June 2007 DOI 10.1002/ajpa.20686 Published online 13 July 2007 in Wiley InterScience (www.interscience.wiley.com). V V C 2007 WILEY-LISS, INC. AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 134:412–423 (2007)