Camilo Lopez-Aguirre edited untitled.tex  almost 9 years ago

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After the Procrustes coordinates dataset was obtained for the original configurations, a second dataset for the reflected mirror images of all original configurations was obtained in order to perform the Generalized Procrustes Analysis (GPA). GPA is a statistical method to superimpose landmarks coordinates, while removing the influence non-morphological sources of variation as a result of scaling, rotation and translation. A consensus, tangent configuration is obtained from the average coordinates of the original-mirror dataset. To peform a GPA in configurations with object symmetry, each original configuration has to be combined with its mirror image, after relabeling landmarks of the mirror configuration, to ensure the correct pairing between original and mirror landmarks.   Further, a Procrustes ANOVA was performed in order to test statistical differences between species, as well as statistical presence of DA, and a MANOVA to check the presence of FA. DA.  Statistical significance on the "Side" component of the Procrustes ANOVA means that there is a consistent, asymmetrical distribution in the variation between both sides of the cranium, which indicates the presence of DA. Alternaly, Using the Procrustes ANOVA test makes the assumption that data points have a multivariate normal distribution in the tangent space, and that the variation is isotropic (equally distributed in all directions of the variation). This assumption has been considered to be inaccurate  when studying biological structures. Hence, using alternative analyses, like MANOVA is recommended. MANOVA was performed to check the presence of FA and DA without the assumption of isotropic variation. When  interpreting the MANOVA, statistical significance for the "Ind*Side" factor means that the morphological variation is due to the interaction between the within-group variation and the variation on each side of the cranium, reflecting presence of FA. Procrustes ANOVA and MANOVA were conducted using the MorphoJ software. A Canonical Variate Analysis (CVA) was used to assess the differences between the potential of the asymmetric and symmetric components to discriminate all three species. CVA is a multiple discriminant function that groups individuals within a sample into pre-established groups, based on multivariate data. CVA was performed for the symmetric and asymmetric component separately. All CVA analysis were  conducted using MorphoJ. Finally, using the Procrustes coordinates, thin-plate splines were obtained to illustrate more effectively the morphological differences in the asymmetric and symmetric variation between groups. This was repeated for each species, and each Canonical Component Variate  of the each  CVA. \section{Results}  Procrustes ANOVA provided statistical evidence of significant differences between species, and confirmed the presence of DA in the sample (Table 1). The "Sp*Side" factor was not significant, but since the mathematical interpretation of this factor does not reflect the presence of any kind of asymmetry or any other biologically relevant feature, this factor was excluded of further interpretations.   MANOVA showed statistical significance for the presence of both DA and FA, using a non-isotropic model of variation.