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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. Because this approach avoids the isotropic variation model, considers only the variation in the shape of the structure, making it statistically a more powerful tool.   By comparing the graphical output of the CVAs obtained for the symmetric and asymmetric component of the variation, it was clear that the asymmetric component is more accurate to discriminate the three species. The symmetric component was not useful to discriminate neither of the three species, overlapping almost completely the species all along the morphospace. Despite the presence of a certain degree of overlapping between species in the asymmetric component, most of the samples were accurately discriminated, suggesting that morphological differences between these species are better represented in their asymmetric variation.   The overlapping found on both components opens the question of what other mechanisms and patterns rely behind the morphological variation on \textit{Carollia} species.   Thin-plate splines for the canonical variates also showed differences on the distribution of both components of the variation along the cranium. While both canonical variates of the asymmetric component varied greatly in the Neurocranium, canonical variates of the symmetric component showed a slight variation in the Splachnocranium.   Species-specific patterns of asymmetric morphological variation were evident after comparing the thin-plate splines obtained for the species. Asymmetric variation on all three species was predominantly concentrated in the Neurocranium, specifically in the occipitomastoid suture region. Variation was greater at the anterior region of the occipitomastoid suture for \textit{C. castanea}, at the middle section for \textit{C. brevicauda}, and at the posterior region for \textit{C. perspicillata}.  \section{Discussion}  With this study, morphological variation in bilateral organisms was decomposed in its asymmetric and symmetric components for the first time, using principles of the methodology designed to study organisms with complex symmetries.   Our results support other recent studies that discuss the importance of shape variation for the discrimination of species and reject the assumption that size is the best way to distinguish \textit{Carollia} species. This also suggests that the complex morphological delimitation and boundaries of \textit{Carollia} species could be better understood by analyzing its asymmetric component, rather than focusing in the traditional approaches that are restricted to symmetric variation.