Geometric Morphometric Analysis of Mandibular Ramus Flexure A.C. Oettle ´ , E. Pretorius,* and M. Steyn Department of Anatomy, University of Pretoria, Pretoria 0001, Republic of South Africa KEY WORDS sexual dimorphism; sex assessment; skeletal biology ABSTRACT Many characteristics of the human skele- ton can only be assessed morphologically, which may be problematic due to factors such as interobserver error and difficulties with standardization. Flexure of the mandibu- lar ramus is one of these traits, and various researchers found widely differing results using this morphological feature. The aim of this study was to determine whether differences between male and female mandibular rami could be observed using the computerized method of geo- metric morphometrics, a valuable tool that helps quantify shape differences. Twenty-eight mandibular rami of black females and 43 of black males were photographed in a standard plane and assessed. It was found that the females were more scattered on the graph (more variable in shape), while the males clustered more around the cen- ter point where the two axes met (shape more constant). There was, however, considerable overlap between the sexes. Although different tendencies exist between the rami of males (being more flexed) and females (tending to be straight), the extent of these differences is not adequate to predict the sex of a single individual. Am J Phys Anthropol 128:623–629, 2005. ' 2005 Wiley-Liss, Inc. Determination of sex from skeletal remains can be approached metrically or morphologically. The advan- tages of using measurements for this purpose are, among others, that the results are easy to assess and interpret. However, many characteristics in the human skeleton are not measurable through conventional meth- ods, and are thus usually assessed morphologically. Un- fortunately these types of analyses may sometimes be dependent on the experience of the observer, and may be difficult to standardize. It may also be difficult to inter- pret the results. The relatively new method of geometric morpho- metrics provides a mechanism to quantify morphological characteristics. Moreover, it also allows for an assess- ment of exactly where or in what aspect the morphology between various skeletons differs. Although it has been used to quantify morphology since the late 1980s, it is a method that just recently started to become popular in physical anthropology (e.g., Lynch et al., 1996; Wood and Lynch, 1996; Hennessy and Stringer, 2002; Rosas and Bastir, 2002), but its potential is enormous. Geometric morphometrics is a method dealing with the study of shape using either homologous landmarks (Rohlf and Marcus, 1993) or outlines of a morphological structure. Landmarks are the points at which biological structures are sampled, and these points capture shape changes between the same morphological structures in different species. The definition of shape space by Ken- dall (1981, 1984) forms the basis of geometric morpho- metrics, but this space is nonlinear and non-Euclidean, and therefore conventional linear multivariate statistical methods cannot be applied to it (Slice, 2001). Further- more, only via Procrustes superimposition does one enter into the shape space of Kendall (1981, 1984). Shape space can, however, be approximated by a linear space tangent to it. This approximated tangent space allows for the utilization of standard multivariate statistics on a data set of homologous landmarks (or x, y coordinates) of n number of specimens (Slice, 2001). The main purpose of the method is to permit analysis of the variability of a morphological structure using a powerful, comprehensive statistical analysis, and the use of thin-plate splines to describe the results in terms of deformations. This produces an exact geometric descrip- tion of the shape differences between the same structure in different specimens. Authors like Bookstein (1989, 1991), Rohlf and Slice (1990), Slice (1993), and Rohlf (1995) developed this method. F. James Rohlf also devel- oped the tps series of programs, which performs the sta- tistics and visualizations of geometric morphometrics. Other researchers like David H. Sheets further devel- oped the statistics by adding the Integrated Morpho- metric Package (IMP) (Sheets, 2001). This package, among other things, allows one to calculate P-values, using the TwoGroup program, as well as do a discrimi- nant function analysis (or canonical variates analysis; CVA) using the CVAGen6 program. Pretorius and Clarke (2000, 2001), Pretorius and Scholtz (2001), and Pretorius et al. (2001) used the tps programs to compare morpholo- Susan R. Loth passed away on 23 September 2002, and we are completing this paper in her memory. Grant sponsor: National Research Foundation; Grant number: 2054279. *Correspondence to: Prof. E. Pretorius, Department of Anatomy, University of Pretoria, PO Box 2034, Pretoria 0001, Republic of South Africa. E-mail: rpretori@medic.up.ac.za Received 6 March 2003; accepted 4 May 2004. DOI 10.1002/ajpa.20207 Published online 28 April 2005 in Wiley InterScience (www.interscience.wiley.com). # 2005 WILEY-LISS, INC. AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 128:623–629 (2005)