The first edition of "Geometric Morphometrics for Biologists" has been the primary resource for teaching modern geometric methods of shape analysis to biologists who have a stronger background in biology than in multivariate statistics and matrix algebra. These geometric methods are appealing to biologists who approach the study of shape from a variety of perspectives, from clinical to evolutionary, because they incorporate the geometry of organisms throughout the data analysis. The second edition of this book retains the emphasis on accessible explanations, and the copious illustrations and examples of the first, updating the treatment of both theory and practice. The second edition represents the current state-of-the-art and adds new examples and summarizes recent literature, as well as provides an overview of new software and step-by-step guidance through details of carrying out the analyses. This title contains updated coverage of methods, especially for sampling complex curves and 3D forms and a new chapter on applications of geometric morphometrics to forensics. It offers a reorganization of chapters to streamline learning basic concepts. It presents detailed instructions for conducting analyses with freely available, easy to use software. It provides numerous illustrations, including graphical presentations of important theoretical concepts and demonstrations of alternative approaches to presenting results.

Geometric morphometrics for biologists: a primer

The analysis of shape is a fundamental part of much biological research. As the field of statistics developed, so have the sophistication of the analysis of these types of data. This lead to multivariate morphometrics in which suites of measurements were analyzed together using canonical variates analysis, principal components analysis, and related methods. In the 1980s, a fundamental change began in the nature of the data gathered and analyzed. This change focused on the coordinates of landmarks and the geometric information about their relative positions. As a by-product of such an approach, results of multivariate analyses could be visualized as configurations of landmarks back in the original space of the organism rather than only as statistical scatter plots. This new approach, called “geometric morphometrics”, had benefits that lead Rohlf and Marcus (1993) to proclaim a “revolution” in morphometrics. In this paper, we briefly update the discussion in that paper and summarize the advances in the ten years since the paper by Rohlf and Marcus. We also speculate on future directions in morphometric analysis.

Geometric morphometrics: Ten years of progress following the ‘revolution’

Geometric morphometrics is the statistical analysis of form based on Cartesian landmark coordinates. After separating shape from overall size, position, and orientation of the landmark configurations, the resulting Procrustes shape coordinates can be used for statistical analysis. Kendall shape space, the mathematical space induced by the shape coordinates, is a metric space that can be approximated locally by a Euclidean tangent space. Thus, notions of distance (similarity) between shapes or of the length and direction of developmental and evolutionary trajectories can be meaningfully assessed in this space. Results of statistical techniques that preserve these convenient properties—such as principal component analysis, multivariate regression, or partial least squares analysis—can be visualized as actual shapes or shape deformations. The Procrustes distance between a shape and its relabeled reflection is a measure of bilateral asymmetry. Shape space can be extended to form space by augmenting the shape coordinates with the natural logarithm of Centroid Size, a measure of size in geometric morphometrics that is uncorrelated with shape for small isotropic landmark variation. The thin-plate spline interpolation function is the standard tool to compute deformation grids and 3D visualizations. It is also central to the estimation of missing landmarks and to the semilandmark algorithm, which permits to include outlines and surfaces in geometric morphometric analysis. The powerful visualization tools of geometric morphometrics and the typically large amount of shape variables give rise to a specific exploratory style of analysis, allowing the identification and quantification of previously unknown shape features.

/pdf/advances-in-geometric-morphometrics-2qr05ayqqi.pdf

Advances in Geometric Morphometrics

The relatively new two-block partial least-squares method for analyzing the covariance between two sets of variables is described and contrasted with the well-known method of canonical correlation analysis. Their statistical properties, types of answers, and visualization techniques are discussed. Examples are given to show its usefulness in comparing two sets of variables—especially when one or both of the sets of variables are shape variables from a geometric morphometric study. (Canonical correlation; covariance; morphometrics; Mus musculus domesticus; partial least squares; Plethodon; visualization.)

https://www.jstor.org/stable/info/2585291

Use of two-block partial least-squares to study covariation in shape.

The development and the present state of the “tps” series of software for use in geometric morphometrics on Windows-based computers are described. These programs have been used in hundreds of studies in mammals and other organisms. Download the complete issue.

http://www.italian-journal-of-mammalogy.it/pdf-77186-13339?filename=The tps series of.pdf

The tps series of software

In press − − do not cite 2 The field of geometric morphometrics is relatively new (see Bookstein, 1991, Rohlf and Marcus, 1993) and has shown very rapid progress over the last few years. As might be expected during a period of rapid development, there can be technical problems in some of the pioneering studies as biologists attempt to apply the new tools. It is only now becoming clear how the new techniques should be combined in order to carry out comprehensive analyses of real datasets. Bookstein (1996b) gave a list of recommendations for such applications and Bookstein (1996a) gave several comprehensive examples of morphometric analyses. However, these accounts do not address some of the types of applications that are of particular interest in systematic biology. Bookstein (1994) pointed out problems with using geometric morphometric methods in the usual character-based cladistic studies. He emphasized that morphometrics cannot supply homologous shape characters. The purpose of this note is to comment some recent applications of morphometric methods in systematic biology. This note is particularly concerned with the morphometric methods used by Zelditch et al. These methods were also used by Burke et al. (1996). For convenience, these studies will be referred to using the acronym Z&F. In these studies the authors investigated the use of partial warps (Bookstein, 1991) as variables in ontogenetic and taxonomic studies. They were impressed by their observation that differences in partial warps scores (Rohlf, 1993b) corresponded to shape differences that could be localized on the bodies of the organisms. They also found differences in these variables between developmental stages and between species. They concluded that partial warps could be interpreted and used as traditional taxonomic characters and would be useful in evolutionary studies. Lynch et al. (1996) tried to interpret the partial warps they obtained in their study but they were cautious about using them in the ways advocated by Z&F. They suggested that extensive simulation studies needed to be done to validate the Z&F approach. Naylor (1996) investigated their approach using data based on a simulated phylogeny. Even though his simulated phylogeny was based on a sequence of simple morphological changes and had no homoplasy, the results showed high levels of homoplasy and did not recover the morphological changes used to create the phylogeny. The present paper is concerned with theoretical problems rather than empirical problems requiring validation through simulations. The fundamental problem is that Z&F …

http://www.filogenetica.org/cursos/deluna/morfometria/referencias%20en%20pdf/rohlf1998.pdf

Rohlf Fj

Papers

On applications of geometric morphometrics to studies of ontogeny and phylogeny.