**1. Introduction**

Comparison of anatomical characters between organisms has been a core element in comparative biology for centuries. Historically, taxonomic classification and understanding of biological diversity have been based mainly on morphological descriptions [1]. In the early twentieth century, comparative biology entered a transition from the description field and quantitative science, where morphological analysis had a similar revolution of quantification [2]. Based on this quantitative mathematical revolution, the study of morphology has had an important emphasis by developing statistical shape analysis. This made possible the combination of multivariate statistical methods and new ways to visualize a structure [3,4].

In geometric morphometrics (GM), the shape is defined as "any geometric information that remains when the effects of translation, scaling and rotation are removed from an object"[5]. According to [6,7] two techniques have been described: Landmark and Outline methods. Landmark geometric morphometrics is currently the most used tool in sexual dimorphism studies, where equivalent and homologous specific points are fixed in the biological structure being studied. Whereas outliner GM reduces contour shape in a structure by means of points built and located in its boundaries [8-10]. These tools allow studying organism shape and also size, providing sound graphic analyses to quantify and visualize morphometric variation within and between organism samples.

One of the most interesting sources of phenotypic variation in animals and plants has been sexual dimorphism, the study of which continues to be an important area of research in evolutionary biology. Sexual differences in morphological characters are a common phenomenon in many animal taxa, and their most conspicuous aspect is body size [11]. The direction of these differences, that is whether males or females are larger, varies from one group to another [12]. Most of the morphological variations of insects are due to effects

© 2013 Benítez, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

associated with the environment, either phenotypic responses (plasticity) or particularly those which act during ontogenetic development [13]. Females are generally larger than males, and this gives them adaptive advantages such as greater fecundity and better parental care [14,15]. However, in some species males are longer but have less relative mass e.g. [16], which implies that the determination of sexual dimorphism requires more complex measurement techniques related, for example, with geometric shape [17]. Sexual dimorphism is of interest in entomological studies since frequently the differences between sexes are not obvious or the individuals are very small; thus, finding discriminating characters allows easy determination of sexes.

Sexual Dimorphism Using Geometric Morphometric Approach 37

individual coordinate points are not biologically homologous to each other [29], but this issue is important only in cases where a one-to-one mapping between individual variables

The principal and most important analysis of geometric morphometrics is called Procrustes superimposition, where only the shape information is extracted and the other components of variation in size, position and orientation can be removed, while taking care not to alter shape in any step of the procedure [4,9,30]. The extra components of variation can be removed by rescaling the configurations to a standard size, shifting them to a standard position, and rotating them to a standard orientation (Figure 1). Moreover, since none of the steps has changed the shape of the configurations, the variation after the procedure is the

**Figure 1.** Summary of Procrustes superimposition. Components of variation other than shape are eliminated by scaling to the same size, translating to the same location of centroids, and rotating to an

Insects in many species vary greatly in the expression of sexual traits [14]. In some species variation in the expression of such traits is discontinuous, resulting in the co-occurrence of two or more discrete phenotypes within one sex. The discrete expression of sexual traits or secondary sexual traits has attracted particular attention, as it is thought to reflect alternative adaptations to heterogeneous social conditions [31]. Sexual size dimorphism

overall best fit of corresponding landmarks. (Figure Idea by C.P Klingenberg)

**3. Sexual shape dimorphism** 

and biological homology is required.

complete shape variation.

Studies of *Ceroglossus chilensis* shape have discussed that sexual dimorphism is usually concentrated in two sections of body shape: in the abdominal section, where this dimorphism variation is associated with an adaptative character due to the presence of female eggs; and changes in the pronotal section associated with male-male competition due to variation in sexual ratio in populations [17,18]. Other studies have used geometric variation of wing shape in insects as the dimorphism character, where the integrated geometric variation of veins is differentiated between male and female [19].

The following chapter is a brief description of sexual dimorphism of shape in insects and its evaluation by using new morphological tools that provide a visualization of the geometric shape, besides a description in 2 insect orders about the way in which sexual dimorphism variations that are not easily observed may be distinguished in different populations.

### **2. Geometric morphometrics methodology**

Morphometrics is the study of shape variation and its covariation with other variables. The development of its new properties, capable of capturing shape, renders this new morphology to be considered geometric, being its introduction received as a "revolution" for the morphological analysis realm [20]. Shape is mathematically defined as all the geometric features of an object except its size, position and orientation [4]. In other words, changes in size, position and orientation do not change the shape of an object. Most of the research efforts in geometric morphometrics have concentrated on landmark data. Morphological landmarks are points that can be located precisely on each specimen under study with a clear correspondence in a one-to-one manner from specimen to specimen [7,21]. There are several methods for the analysis of curves and outlines. Outlines can be analyzed using semi-landmarks, which are the points that fall at defined intervals along a curve between two landmarks [22]. Semilandmarks can be analyzed with Procrustes superimposition like ordinary landmarks. Another outline method is perhaps the oldest type of geometric morphometrics – Fourier analysis [23]. Fourier methods use sine and cosine harmonic functions to describe the positions of outline coordinates. Fourier analysis can be applied to 2D outlines [23,24] or 3D closed surfaces [25,26]. Eigenshape is a third method for the analysis of outlines or curves [27,28]. In eigenshape, the coordinate points of an outline or curve are converted to a phi function, which is a list of the angles from one point to the next one in the series. Outline methods have been criticized because their individual coordinate points are not biologically homologous to each other [29], but this issue is important only in cases where a one-to-one mapping between individual variables and biological homology is required.

The principal and most important analysis of geometric morphometrics is called Procrustes superimposition, where only the shape information is extracted and the other components of variation in size, position and orientation can be removed, while taking care not to alter shape in any step of the procedure [4,9,30]. The extra components of variation can be removed by rescaling the configurations to a standard size, shifting them to a standard position, and rotating them to a standard orientation (Figure 1). Moreover, since none of the steps has changed the shape of the configurations, the variation after the procedure is the complete shape variation.

**Figure 1.** Summary of Procrustes superimposition. Components of variation other than shape are eliminated by scaling to the same size, translating to the same location of centroids, and rotating to an overall best fit of corresponding landmarks. (Figure Idea by C.P Klingenberg)

#### **3. Sexual shape dimorphism**

36 Sexual Dimorphism

characters allows easy determination of sexes.

**2. Geometric morphometrics methodology** 

associated with the environment, either phenotypic responses (plasticity) or particularly those which act during ontogenetic development [13]. Females are generally larger than males, and this gives them adaptive advantages such as greater fecundity and better parental care [14,15]. However, in some species males are longer but have less relative mass e.g. [16], which implies that the determination of sexual dimorphism requires more complex measurement techniques related, for example, with geometric shape [17]. Sexual dimorphism is of interest in entomological studies since frequently the differences between sexes are not obvious or the individuals are very small; thus, finding discriminating

Studies of *Ceroglossus chilensis* shape have discussed that sexual dimorphism is usually concentrated in two sections of body shape: in the abdominal section, where this dimorphism variation is associated with an adaptative character due to the presence of female eggs; and changes in the pronotal section associated with male-male competition due to variation in sexual ratio in populations [17,18]. Other studies have used geometric variation of wing shape in insects as the dimorphism character, where the integrated

The following chapter is a brief description of sexual dimorphism of shape in insects and its evaluation by using new morphological tools that provide a visualization of the geometric shape, besides a description in 2 insect orders about the way in which sexual dimorphism

Morphometrics is the study of shape variation and its covariation with other variables. The development of its new properties, capable of capturing shape, renders this new morphology to be considered geometric, being its introduction received as a "revolution" for the morphological analysis realm [20]. Shape is mathematically defined as all the geometric features of an object except its size, position and orientation [4]. In other words, changes in size, position and orientation do not change the shape of an object. Most of the research efforts in geometric morphometrics have concentrated on landmark data. Morphological landmarks are points that can be located precisely on each specimen under study with a clear correspondence in a one-to-one manner from specimen to specimen [7,21]. There are several methods for the analysis of curves and outlines. Outlines can be analyzed using semi-landmarks, which are the points that fall at defined intervals along a curve between two landmarks [22]. Semilandmarks can be analyzed with Procrustes superimposition like ordinary landmarks. Another outline method is perhaps the oldest type of geometric morphometrics – Fourier analysis [23]. Fourier methods use sine and cosine harmonic functions to describe the positions of outline coordinates. Fourier analysis can be applied to 2D outlines [23,24] or 3D closed surfaces [25,26]. Eigenshape is a third method for the analysis of outlines or curves [27,28]. In eigenshape, the coordinate points of an outline or curve are converted to a phi function, which is a list of the angles from one point to the next one in the series. Outline methods have been criticized because their

variations that are not easily observed may be distinguished in different populations.

geometric variation of veins is differentiated between male and female [19].

Insects in many species vary greatly in the expression of sexual traits [14]. In some species variation in the expression of such traits is discontinuous, resulting in the co-occurrence of two or more discrete phenotypes within one sex. The discrete expression of sexual traits or secondary sexual traits has attracted particular attention, as it is thought to reflect alternative adaptations to heterogeneous social conditions [31]. Sexual size dimorphism (SSD) in body size is considered to be one of the major determinants of mating success in many species [32-35]. Because larger males are generally more aggressive and more competitive than smaller males, larger males often attain greater reproductive success through intrasexual selection [14]. In contrast, sexual shape dimorphism (SShD) has been much less investigated [17-19,36]. From those studies that considered SShD, most have discussed it as a diagnostic trait for diverse purposes, such as sex identification or the analysis of ontogeny [37-40]. Nevertheless, some other authors have considered sexual dimorphism evolution covering only some aspects of a limited number of taxa, such as: the evolution of cranium in primates [41-44]; the proportions and dimensions in lizard bodies [45,46]; newts [47]; or in flies [48]; and variation of shape in insect heads [49]; and variation of sexual dimorphism in *Drosophila* wings [36].

Sexual Dimorphism Using Geometric Morphometric Approach 39

**Figure 2.** Location of the 17 landmarks in ventral view of *Ceroglossus chilensis* 

**Figure 3.** Canonical Variate Analysis (CVA) for the sexual shape dimorphism population of *Ceroglossus chilensis* \*each point represents a shape variable for female and male individuals in ventral view. The figure shows the first two CV components' axes with shape deformation images associated, and their antennal structure that is differentiation characteristic based on optic microscopy (careens presence in

males).
