Background and Aims:

Quantitative methods have accumulated for the use of linear measurements and Cartesian coordinates of landmark points in analyses of morphometric variation. Unlike previous reviews, here I emphasize the theoretical bases of mathematical spaces and morphospace of a taxonomic character. The goal of this contribution is to provide conceptual elements for a basic understanding of morphometric and statistical methods useful in systematics under a phylogenetic approach.

Methods:

Morphometric data are being applied in comparative biology research, using a phylogeny as a reference. In contrast, applications of morphometrics in systematics have been with the aim of phenetic grouping and distinguishing taxonomic groups with overall similarity. Under a phylogenetic approach, morphometric data can also be used for the study of taxonomic character variation, character state identity and phylogenetic inference. Taxonomic groups should be proposed from monophyletic groups discovered with phylogenetic methods.

Key results:

I review the basic morphometric theory, vector geometry, Kendall shape space, Procrustes distance, projection of tangential spaces, and construction of morphospace hypercubes. Remainders of statistical concepts useful for the application of Principal Component Analysis and Canonical Variate Analysis in systematics are presented. Particularly, I give examples and recommendations on the use of linear measurements and landmark coordinates in morphometric analyses for the identification of species, the variation of taxonomic characters and in the inference of phylogeny and classification.

Conclusions:

The current broad collection of methods provides an opportunity to integrate morphometric data to discover taxic and transformational homology. This implies an epistemological change necessary to move from applications in systematics under a phenetic approach to the integration of morphometric analyses as part of phylogenetic research.

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