Geometric morphometric approach to sex estimation of human pelvis Paula N. Gonzalez *, Valeria Bernal, S. Ivan Perez Divisio��n Antropolog����a, Facultad de Ciencias Naturales y Museo, Universidad Nacional de La Plata, Paseo del Bosque s/n, La Plata 1900, Argentina 1. Introduction Accurate sex estimation is an important issue in both forensics and bioarchaeology. The skeletal components often investigated for this purpose are the pelvis and skull, although current opinion regards the hip bone as the most reliable sex indicator because it has long been recognized as the most dimorphic bone, particularly in adult individuals [1,2]. Numerous techniques of sex estimation have been proposed, based either on visual assessment or recording of lineal metric variables of the hip bone [3���12]. Visual or morphoscopic techniques are based on the scoring of diverse traits, such as subpubic angle, shape of the sciatic notch or the preauricular sulcus, and final sex assignment is made according to a rating which separates males from females [6,10,13]. Such an approach has been largely criticized because it is highly subjective, requires an experienced observer and is even more unreliable when the final score is close to the separating value [6,9,12,14,15]. Another problematic aspect of these techniques is the use of dichotomous or ordinal scoring that precludes an adequate description of continuous phenotypic traits, reducing the variation to a few discrete categories [16,17]. An alternative to sex estimation based on visual scoring is to quantify pelvis variation. Morphometric variables have some advantages over morphoscopic ones, such as higher levels of simplicity and consistency in their recording and the existence of powerful statistical methods for the analysis of continuous data [14]. These are frequently collected by using linear measurements (i.e., traditional morphometrics) however, quantification of size and shape of many pelvic traits, mostly curvilinear and with few conspicuous landmarks, is extremely difficult by means of these techniques. A reliable technique used to estimate the sex of individuals from morphology requires the selection of an adequate method for describing the differences between sexes, both in size and shape, and a suitable statistical approach for classifying the individuals. The application of semilandmark-based geometric morphometric techniques for detecting differences between the male and female pelvis was Forensic Science International 189 (2009) 68���74 A R T I C L E I N F O Article history: Received 13 August 2008 Received in revised form 30 March 2009 Accepted 14 April 2009 Available online 12 May 2009 Keywords: Sexual dimorphism Sciatic notch Ischiopubic complex Semilandmarks Discriminant analysis k-Means clustering A B S T R A C T Sex estimation of skeletal remains is an important issue in both forensics and bioarchaeology. The chance of attaining a high level of accuracy regarding sex allocations is related to the skeletal component analyzed and the ability of the techniques employed to describe shape and size differences among the sexes. Current opinion regards the hip bone as the most reliable sex indicator because it is the most dimorphic bone, particularly in adult individuals. The aim of this study was therefore to analyze the greater sciatic notch and the ischiopubic complex morphology by employing geometric morphometric techniques, based on semilandmark and multivariate statistical methods, in order to develop a reliable and accurate technique for adult sex estimation. The sample analyzed consisted of 121 adult left hip bones randomly selected from the collection of documented skeletons housed at the Museu Antropologico de Coimbra. Morphometric analysis was based on coordinates of landmarks and semilandmarks of the ilium and ischiopubic regions that were digitized on 2D photographic images. Discriminant analysis with leave-one-out cross-validation and k-means clustering of shape and shape- size variables were used in order to classify individuals by sex. For the greater sciatic notch, average accuracy of 90.9% was achieved with both multivariate analyses based on shape variables. For the ischiopubic complex, the values obtained with shape variables were 93.4% and 90.1% for discriminant and k-means, respectively. Females were misclassified more frequently than males, especially for the ischiopubic complex. When multivariate statistical analyses were performed using shape-size variables, the percentages of correct classifications were lower than those obtained with shape variables. We conclude that the use of geometric morphometrics and multivariate statistics is a reliable method to quantify pelvic shape differences between the sexes and could be applied to discriminate between females and males. �� 2009 Elsevier Ireland Ltd. All rights reserved. * Corresponding author at: Facultad de Ciencias Naturales y Museo, Museo de La Plata, Paseo del Bosque s/n, La Plata 1900, Argentina. Tel.: +54 0221 421 5184. E-mail address: pgonzalez@museo.fcnym.unlp.edu.ar (P.N. Gonzalez). Contents lists available at ScienceDirect Forensic Science International journal homepage: www.elsevier.com/locate/forsciint 0379-0738/$ ��� see front matter �� 2009 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.forsciint.2009.04.012

recently proposed [16,18]. Geometric morphometric methods quantify the shape of an object, employing 2D and 3D coordinates of anatomical landmarks and semilandmarks. These methods are preferable to linear distances because they retain the geometry of the objects throughout the analysis and allow for the description of subtle differences among structures [19��� 22]. Although this approach is a useful tool for the description of sexually dimorphic structures with few landmarks, it has not yet been extensively applied to the development of techniques for sex estimation. The aim of this work is therefore to analyze the greater sciatic notch and the ischiopubic complex morphology by employing geometric morphometric techniques based on semilandmarks and multivariate statistical methods. This will develop a reliable and accurate procedure for adult sex estimation. 2. Materials and methods The sample consisted of 121 adult left hip bones randomly selected from the collection of documented skeletons housed at the Museu Antropologico de Coimbra (University of Coimbra, Coimbra, Portugal). The individuals used in this study (Table 1) are of European ancestry and were buried during the 19th and 20th centuries [23]. For the morphometric analysis we took 2D photographic images of the greater sciatic notch and ischiopubic region of each left hip bone with a digital camera (Olympus Camedia C-3030). In this study we chose to utilize the description of these two structures based on configurations of landmarks and semilandmarks obtained from photographs because they principally vary in two dimensions. The right hip bone was used when the left one was not present or damaged. Each bone was placed with the auricular surface facing upwards. Sciatic notch photographs were taken with the camera lens 250 mm from the bone and parallel to the ilium surface. The ischiopubic region was placed 250 mm from the camera and parallel to the camera lens. All the hip bones were placed in exactly the same position for photography. Two landmarks, i.e., points placed on homologous morphological features [20], and 14 semilandmarks were digitized on the greater sciatic notch (Fig. 1a). Landmark 1 was placed at the base of the ischial spine, and landmark 2 at the tip of the piriform tubercle. When the tubercle was absent, the landmark was placed at the end of the sciatic notch just before the bone curves backward toward the auricular surface [24]. Two landmarks and 25 semilandmarks were digitized on the ischiopubic region (Fig. 1b). Landmark 3 was placed at the intersection of the upper edge of the pubis with the perpendicular line that reaches the uppermost point of the obturator groove, and landmark 4 on the intersection between the external margin of the ischium and the inferior border of the acetabulum. To digitize evenly distributed points along the contour line of the two analyzed structures guidelines named ������fans������ were placed onto the images using MakeFan6 software [25]. In both structures the lines were positioned in a semi-circular pattern, between the landmarks previously defined. Next, both landmarks and semilandmarks were digitized using software tpsDIG 1.40 [26]. Intra- and inter-observer errors associated with the placement of point coordinates in geometric morphometric analysis were evaluated previously [18]. The analysis showed that the use of geometric morphometrics results in high intra- and inter-observer agreement. Within geometric morphometrics the shape is defined as the information remaining after the effects of position, orientation and scale have been held constant [27]. In this study, the Generalized Procrustes analysis [27,28] was used to remove these effects in landmark and semilandmark configurations, and centroid size was employed as the size measurement [21]. To convert the evenly distributed points along contours into semilandmarks, they were aligned by means of the perpendicular projection or minimum Procrustes distance criteria [29,30]. This operation extends the Generalized Procrustes analysis [27,28] by sliding the semilandmarks until they match the positions of corresponding points along an outline in a reference specimen as closely as possible, thereby minimizing the Procrustes distance [30]. This results in an alignment of the semilandmarks along the curve so that the semilandmarks on the target form lie along the lines perpendicularly to a curve passing through the corresponding semilandmarks on the reference form [30,31]. To describe major trends in shape variation within the sample, we performed a principal component analysis of the uniform components plus partial warps variables, which were obtained from thin plate spline analysis [32]. Within geometric morphometrics this analysis is known as Relative Warps [RW 20, 33]. The alpha parameter, which determines the relative weight of the principal warps on different scales, was fixed at 0 (zero) value, as suggested by Rohlf [33]. In order to visualize sexual dimorphism, graphical representations of shape differences were generated as deformation grids of female and male individuals relative to the reference configuration (i.e., consensus configuration). Likewise, a principal component analysis based on a matrix that includes shape coordinates and an additional column with log centroid size was performed in order to describe the differences in the shape-size space [34]. The value of centroid size represents a measurement of overall bone size and was obtained as the sum of the values corresponding to the ischiopubic complex and ilium [18]. We analyzed the size because sexual dimorphism in this variable is reported by previous studies [35]. To estimate the sex of individuals, we used two statistical methods, discriminate analysis with leave-one-out cross-validation and k-means clustering. Their performance was examined by comparing the percentage of cases in which the estimated sex of individuals correctly matched their true sex (i.e., the percent of correct classification). These methods were applied to the greater sciatic notch, the ischiopubic complex and both structures simultaneously. Discriminant analysis is a method used to find a set of axes that possesses the greatest possible ability to discriminate between two or more groups [36]. A major purpose of discriminant analysis is to achieve a predictive classification of individuals. The first step is to estimate the discriminant functions that best differentiate between groups, computing the classification scores for the individuals. The next step is to classify the individuals according to the group Table 1 Composition by age and sex of the sample used to analyze ischiopubic complex (IPC) and greater sciatic notch (SN). Age (years) Female Male 15���19.9 4 7 20���24.9 6 4 25���29.9 12 13 30���34.9 7 11 35���39.9 10 11 40���44.9 3 12 45���49.9 4 6 50 6 5 Total 52 69 Fig. 1. (a) Allocated landmarks (1 and 2) and semilandmarks (circles) on sciatic notch (b) allocated landmarks (3 and 4) and semilandmarks (circles) on ischiopubic complex. P.N. Gonzalez et al. / Forensic Science International 189 (2009) 68���74 69