AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 128:623–629 (2005) Geometric Morphometric Analysis of Mandibular Ramus Flexure A.C. Oettlé, 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 skeleton can only be assessed morphologically, which may be problematic due to factors such as interobserver error and difﬁculties with standardization. Flexure of the mandibular 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 geometric 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 center 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 advantages 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 methods, and are thus usually assessed morphologically. Unfortunately 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 interpret the results. The relatively new method of geometric morphometrics provides a mechanism to quantify morphological characteristics. Moreover, it also allows for an assessment 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 Kendall (1981, 1984) forms the basis of geometric morphometrics, but this space is nonlinear and non-Euclidean, and therefore conventional linear multivariate statistical methods cannot be applied to it (Slice, 2001). Furthermore, 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 description 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 developed the tps series of programs, which performs the statistics and visualizations of geometric morphometrics. Other researchers like David H. Sheets further developed the statistics by adding the Integrated Morphometric Package (IMP) (Sheets, 2001). This package, among other things, allows one to calculate P-values, using the TwoGroup program, as well as do a discriminant 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- # 2005 WILEY-LISS, INC. 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: firstname.lastname@example.org 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). 624 A.C. OETTLÉ ET AL. gical structures and indicate relationships between taxa. The dynamic tps series of programs is continuously upgraded and improved by F. James Rohlf, and was used as a tool in the analysis of mandibular ramus ﬂexure in males and females in this study. The use of mandibular ramus ﬂexure as a method to distinguish between the sexes was introduced in Loth and Henneberg (1996), and was tested by others (e.g., Koski, 1996; Indryana et al., 1998; Donnely et al., 1998; Hill, 2000). Loth and Henneberg (1996) found a distinct angulation to be present at the posterior border of the mandibular ramus at the level of the occlussal plane in males. In most females, the ramus retained its straight juvenile shape. Initial results on South African skeletal remains yielded results of about 99% correct separation, which was slightly lower when other skeletal collections were added (Loth and Henneberg, 1996). Most other researchers, however, found signiﬁcantly lower accuracies, ranging from as low as 63% (Donelly et al., 1998) to 91.5% (Indryana et al., 1998). Hill (2000) and Kemkes-Grottenthaler et al. (2002) also claimed that the method was too inaccurate to be usable, and said it was unreliable as it was found to be much more accurate in males, and has a high inter- and intraobserver error. The aim of this study was to assess ramus ﬂexure by means of geometric morphometrics, in order to ascertain whether the said differences exist and are observable using a different method of assessment. Geometric morphometrics will also elucidate the exact nature and position of the morphological shape differences in the sexes, if present. MATERIALS AND METHODS Seventy-one mandibles (43 males and 28 females) were used in this study. These mandibles all belonged to known South African black individuals, and were randomly selected from the Pretoria Skeletal Collection at the Department of Anatomy, University of Pretoria. Their ages ranged between 20–87 years, and individuals with obvious bony pathologies and/or excessive tooth loss were excluded. The following landmarks were applied blindly (without knowing the sex of the specimens) on mandibular rami before they were photographed. Three homologous landmarks on each left ramus representing its shape were chosen and applied with pencil on each mandible. The lowest landmark, landmark 1, was positioned just above the gonion, i.e., where the ramus started to straighten from the gonial eversion. The upper landmark (landmark 2) was at the level of the mandibular notch, as measured by a spirit-leveling instrument, with the mandible on a level surface. A third landmark was chosen where the observed concavity (ﬂexure) was at its maximum. This concavity was at its maximum where the distance between the posterior border of the ramus of the mandible and a line connecting the two most posterior points (roughly corresponding to landmarks 1 and 2) of the mandibular ramus was at its maximum. Even though the concavity of some mandibles was less obvious, no ramus was completely straight. The position of each ramus, relative to the camera, was then standardized by rotating it through 458 on the horizontal plane, away from the vertical plane to which the digital camera was kept in a ﬁxed position. This provided an oblique view from the antero-lateral side that best elucidated the concavity. The focus point was oriented on the center Fig. 1. Lateral view of female mandibular ramus, indicating positions of 11 landmarks. of the mandibular ramus, as measured and calculated from its four borders. The captured electronic images (in jpg format) were then entered into the computer. At the time that they were analyzed digitally, their sex was not known. Four more landmarks were placed on the jpg image, between landmarks 1–3, and also between 3–2, at equal distances, using the computer program tpsdig (version 1.31, F. James Rohlf). These 11 landmarks represented points on the mandibular ramus that elucidated the presence or absence of ﬂexure in that area, as seen in Figures 1 and 2. These landmarks were then further analyzed by the tps series of programs. From this tps series of programs, the following analyses were performed: a relative warp analyses (RWA) and thin-plate spline analysis. Shape trends were further studied using the TwoGroup program and CoordGen-program from the Integrated Morphometric Package. The RWA analysis was only performed in order to determine general trends in shape between the two sexes; in other words, from this it can be seen whether a deﬁnite separation between the male and female data set exists, or whether there is no clear distinction between the shape of the two sexes. In full shape space (where ¼ 0), RWA is a principal components analysis (PCA) of the covariance matrix of the partial warp scores, and is performed by the program tpsRolw (Bookstein, 1991, 1993, 1996). An alternative is to perform a PCA of the aligned specimens; this will result in an identical ordination. Relative warps are computed, using tpsRelw (version 1.25, F. James Rohlf). This program allows for the analysis to be performed in full space, the uniform subspace, or the nonuniform subspace. The program allows choosing a value for (bending energy). Any value of other than zero converts the analysis to a relative principal component analysis of shape covariances with respect to bending energy instead of Procrustes distance (Bookstein, 1996). Furthermore, Bookstein (1996) suggested that all such computations apply only to the uniform subspace of shape space, because, according to GEOMETRIC MORPHOMETRICS OF RAMUS FLEXURE Fig. 2. Lateral view of male mandibular ramus, indicating positions of 11 landmarks. the author, the bending energy of every change of shape within the uniform subspace is uniformly zero. According to Bookstein (1996), for greater than zero, warps of larger scale (excluding the uniform component) are assigned more weight; with less than zero, they are more attenuated. Where ¼ 1 the researcher can, for example, search for growth gradients, while ¼ 1 could be used if the researcher is interested in shape phenomena at a small scale. Furthermore, when is greater than 0, geometrically small-scale variation is given less weight than large-scale variation; the result is that of reducing the weight given to regions having more landmarks relative to the weight given to regions having fewer and therefore more widely spaced landmarks (Rohlf et al., 1996). Each relative warp can be plotted as a deformation of the space of the reference conﬁguration of landmarks. The ﬁrst two relative warps are usually indicative of most of the variation between members of the data set, and therefore their scatterplot presents the most visual information about variation between the sexes. Shape changes implied by variation along the ﬁrst two relative warp axes can be shown as deformations using thinplate splines. The question that now arises is of which -value is most appropriate for the current analysis, and whether different -values will indeed make a difference in the RWA plot. To answer these questions, the analysis was performed using ¼ 0, ¼ 1, and ¼ 1, where both uniform and nonuniform components were included. Singular value decomposition was also determined for the ﬁrst time to relative warps. Thin-plate splines of the variation between specimens were also drawn, and shape variations were visualized. TpsSplin (version 1.17, F. James Rohlf) was used in the analyses of landmark positions of each specimen. This program allows visual determination of landmarks responsible for differences in shape. The computations involve calculations of a reference, using the generalized least-squares Procrustes superimposition method (also known as the GLS method) for the data set (including male and female specimens). The landmark distribution of the reference is represented by a perpendicular Carte- 625 sian grid. The shape differences of each specimen are represented by the deformation of the reference. Shape differences can therefore be visualized by studying each thin-plate spline, or the thin-plates splines of the means of males and females. In order to determine whether the shape distances were statistically signiﬁcant, a P-value was calculated using Hotelling’s t-test function of the TwoGroup program, after converting the tps data set into IMP data using the CoordGen program. A discriminant function analysis or canonical variates analysis (CVA) was then performed using the CVAGen6 program. A CVA assesses the ability to assign specimens in a data set to groups (e.g., male or female), rather than asking if the two groups have a different shape. To test for repeatability, all males in the male sample were reassigned the chosen landmarks. The ‘‘new’’ male landmark data were statistically compared to the ‘‘old’’ data set using Hotelling’s t-test function of the TwoGroup program. The ‘‘new’’ data set was also marked as ‘‘unknown’’ and compared to the full original data set using CVA analysis. Results of the ﬁrst analysis indicated a P-value of 1, while all ‘‘unknown’’ specimens were correctly assigned as male in the CVA analysis, indicating that the placement of landmarks was repeatable. In Loth and Henneberg (1996, 1998), it was found that only the distinct ﬂexure at the level of the occlusal plane of the molars is a consistent indicator of sex. We therefore repeated our analysis, excluding those individuals (5 males and 6 females) in whom the maximum curvature was not exactly on the level of the occlusal plane. RESULTS The RWA analyses of the data set using ¼ 0, ¼ 1, and ¼ 1 were carried out including both uniform and nonuniform components. The six analyses all indicated the same broad result, i.e., that the males and females are scattered in such a way that no deﬁnite distinction between the sexes can be made. Only the two results where ¼ 0 were used will be discussed here. The ﬁrst two relative warps (using ¼ 0; excluding the uniform component) of the data set accounted for 88.18% of the variation among the specimens (computed by a singular-value decomposition of the weight matrix; Rohlf, 1993), while when the uniform component was included in the analysis, the ﬁrst two relative warps accounted for 95.14% of the variation. As an example of the extent of overlap in the scatter, Figure 3 indicates a two-dimensional ordination where ¼ 0, without the uniform component function activated in the tps analysis. Considerable overlap is found between the male and female distribution, as seen in Figure 3 (this was also the case in all other plots). Figure 4 represents the thin-plate splines of the males (arrow points) and females (black squares) in vector mode. Thin-plate spline analysis presents a visual aid to pinpoint the differences in shape. By studying the thinplate splines, the similarity between the averages of the two sexes is demonstrated. The posterior border of the mandibular ramus below the level of the occlusal plane of the molars in males (represented by the landmarks) shows a slightly more concave angulation backwards, as compared to the shape of the females. The mean shape for the total sample, represented by a perpendicular Cartesian grid as well as the mean male and female shapes, 626 A.C. OETTLÉ ET AL. Fig. 3. Two-dimensional relative warp ordination of overall male and female diversity in terms of nonafﬁne components of shape variation ( ¼ 0 and excluding uniform component). was calculated. The distortion of the mean male and female grids represents the amount of bending energy required to bend male and female shape to ﬁt mean shape. Figure 5 represents the thin-plate spline grids of the mean shape for the complete sample (Fig. 5a), males (Fig. 5b), and females (Fig. 5c). A statistically signiﬁcant P-value of 0.014 for malefemale shape difference was obtained using Hotelling’s ttest. Table 1 indicates the CVA analysis results obtained using the CVAGen6 program. Table 1 shows that only about 68–70% of individuals were correctly assigned. All analyses were repeated excluding those individuals (5 males and 6 females) whose maximum curvature did not correspond to the occlusal plane, and similar results were found. DISCUSSION Geometric morphometrics has proved to be a very valuable tool in elucidating morphological variation in human skeletal remains. It acts as a sort of independent observer, with less bias and observer error, as would be the case if the researcher scored the variations. According to Hennessy and Stringer (2002), geometric morphometrics is very useful in enhancing and understanding the results of more traditional morphometric studies. In this study, geometric morphometric analysis was used to assess the presence or absence of ramus ﬂexure as an indicator of sex. Few studies focusing on sexual dimorphism and using geometric morphometrics are available in literature. Rosas and Bastir (2002) concentrated on sexual dimorphism, but included the whole craniofacial complex, studied in lateral views of crania. Their results clearly indicated that differences between male and female mandibles exist. However, they used very few landmarks on the ramus: one landmark each at gonion, ramus, and condylion. They concentrated more on the basal border of the mandible, but did ﬁnd that in males, the gonion tends to be located more anteriorly, as was the condylion, which inﬂuenced the curvature of the posterior border of the ramus. Various studies investigating the sexual dimorphism of the mandibular ramus using direct visual assessment were published, e.g., Loth and Henneberg (1996), Don- Fig. 4. Vector analysis of average measurements. Females, solid squares; males, arrow points. nelly et al. (1998), Indrayana et al. (1998), Hill (2000), and Kemkes-Grottenthaler et al. (2002). The results of these studies were contradictory and did not always seem to be repeatable. Even if assessments on the mandibular ramus are done in a ‘‘blind’’ fashion, bias cannot be excluded, as the general appearance of the mandible cannot be hidden and can give some information regarding the gender of the mandible. Kemkes-Grottenthaler et al. (2002) commented on intra- as well as interobserver bias when using ramus ﬂexure as a means to determine sex. To study this para- GEOMETRIC MORPHOMETRICS OF RAMUS FLEXURE 627 Fig. 5. Thin-plate spline grids of mean male and female shape (A), mean male shape (B), and mean female shape (C). meter in a more objective manner, geometric morphometrics were used in this study. Using 11 landmarks, male-female differences relating to the shape of the posterior border of the ramus could not clearly be distinguished by studying the thin-plate splines of each specimen in this study. The RWA analysis using the ﬁrst two relative warps also indicated an overlap in clustering of males and females (Fig. 3). It seems as if male mandibular ramus morphology is less variable than female morphology, as indicated in the wider distri- bution of the female specimens on the relative warp analysis plot. This ﬁnding ﬁts with the results of Hill (2000), who found that males could be more accurately sexed. Hill (2000) suggested that the pattern of ﬂexion was more consistent in males, while the female shape was more variable. In the vector analysis, comparing mean male and female shape, the slightly more concave angulation backwards in males, as compared to the shape in females, can be seen (Fig. 4); this is also seen in thin-plate spline grids of the mean male and female shape (Fig. 5b,c). 628 A.C. OETTLÉ ET AL. TABLE 1. Percentage males and females correctly and wrongly assigned using canonical variates analysis1 CVA assignment based on shape data Sex as assigned in data set Female (28) Male (43) 1 Correctly assigned Wrongly assigned Percentage males and females correctly assigned by CVA 19 correctly assigned as female 30 correctly assigned as male 9 wrongly assigned as male 13 wrongly assigned as female 67.8% 69.6% CVAGen6 program of IMP series of programs. This could represent the more prominent ramus ﬂexure that was noted in males previously (Loth and Henneberg, 1996). A statistical comparison of the male and female data sets produced a P-value of 0.014, which indicates that the two data sets are statistically signiﬁcantly different. However, the CVA analysis indicated that 9 of 28 females have a male shape, while 13 of 43 males have a female shape. Therefore, only 67.8% of the females and 69.9% of the males are correctly assigned. We therefore believe that, although the P-value suggests a signiﬁcant difference between the male and female data sets, this difference is not of such magnitude and clarity that ramus ﬂexure can be used as a good indicator of sex. Loth and Henneberg (1996, 1998) found the ramus ﬂexure a good indicator of sex, if the ramus ﬂexure was at the level of the occlusion plane. In our study, even when we excluded those individuals whose ramus ﬂexure was not at the level of the occlusal plane, we could not achieve results which clearly discriminated between males and females. Also, we are not convinced that it is a good idea to exclude certain individuals on the ground of the position of the ramus ﬂexure, as this is variable and difﬁcult to assess. Conclusions made on a sample which has certain exclusions will be more difﬁcult to apply on an unknown specimen with conﬁdence. Koski (1996) gave a short overview of the factors inﬂuencing the growth and thus shape of the mandible. This author concluded that the whole soft-tissue environment and the occluding dentition, together with the bony jaw, form a functioning entity whose parts are capable of inﬂuencing each other. The relationship between the ramus and the condylar process appears to depend on the functional environment of the lower jaw. The direction of the condyle is approximately perpendicular to the lateral skull base. In varying functional instances, the ramus must be the adapting part between the articulating condyle and the tooth-bearing body of the jaw. This leads to ﬂexures of different degrees, having different relative positions between the lower ramus and the condylar process that are thus created. In the experience of Koski (1996), the ﬂexures occur in most individuals, be they male or female, young or adult. Loth and Henneberg (1996), in their review of the biological reasons for sexual diversity in mandibles, concluded that the mandible is shaped in response to hormonal inﬂuences and both directly and indirectly by the muscle development thus stimulated. The possible dimorphism seen may arise in response to sex-speciﬁc hormones. Walker and Kowalski (1972) also linked this sexual dimorphism to continuing postpubertal mandibular bone growth in males in response to hormonal inﬂuences. The results from the current study are more in agreement with the statements by Koski (1996), indicating that the observed variations in mandibular ramus morphology have a biomechanical rather than hormonal origin. Our ﬁnal conclusion is that ramus ﬂexure does not provide a deﬁnite means of sex determination that can be used as an isolated sex marker on unknown skeletal remains. Although the ramus ﬂexure seems to be greater and more constant in males, the overlap between the shapes of male and female rami is too great to make it usable. These results should be followed up on a larger data set. ACKNOWLEDGMENTS We sincerely thank David Sheets for his valuable comments and continued help on the use of the IMP programs, and also F.J. Rohlf for his suggestions. The comments of the anonymous reviewers also helped improve the paper. We also thank the Department of Anatomy, University of Pretoria, for allowing us access to skeletons from the Pretoria Collection, and A. da Silva, who helped with testing the repeatability of allocation of landmarks. The research of M.S. is funded by National Research Foundation grant 2054279. LITERATURE CITED Bookstein FL. 1989. Principal warps: thin-plate splines and the decomposition of deformations. Trans Pattern Anal Mach Intell 11:567–585. Bookstein FL. 1991. Morphometric tools for landmark data. 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