Increasingly, data on shape are analysed in combination with molecular genetic or ecological information, so that tools for geometric morphometric analysis are required. Morphometric studies most often use the arrangements of morphological landmarks as the data source and extract shape information from them by Procrustes superimposition. The MorphoJ software combines this approach with a wide range of methods for shape analysis in different biological contexts. The program offers an integrated and user-friendly environment for standard multivariate analyses such as principal components, discriminant analysis and multivariate regression as well as specialized applications including phylogenetics, quantitative genetics and analyses of modularity in shape data. MorphoJ is written in Java and versions for the Windows, Macintosh and Unix/Linux platforms are freely available from http://www.flywings.org.uk/MorphoJ_page.htm.

Morphoj: an integrated software package for geometric morphometrics

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’

We are now in the midst of a revolution in morphometric methodology. The new approaches are more effective in capturing information about the shape of an organism and result in more powerful statistical procedures for testing for differences in s shape. They are also more effective in enabling a researcher to visualize differences in shape and in suggesting simple traditional measurements that could be used in future studies. In this review we emphasize applications to exploratory studies in taxonomy and evolution.

A revolution morphometrics.

Summary 1. Many ecological and evolutionary studies seek to explain patterns of shape variation and its covariation with other variables. Geometric morphometrics is often used for this purpose, where a set of shape variables are obtained from landmark coordinates following a Procrustes superimposition. 2. We introduce geomorph: a software package for performing geometric morphometric shape analysis in the R statistical computing environment. 3. Geomorph provides routines for all stages of landmark-based geometric morphometric analyses in two and three-dimensions. It is an open source package to read, manipulate, and digitize landmark data, generate shape variables via Procrustes analysis for points, curves and surfaces, perform statistical analyses of shape variation and covariation, and to provide graphical depictions of shapes and patterns of shape variation. An important contribution of geomorph is the ability to perform Procrustes superimposition on landmark points, as well as semilandmarks from curves and surfaces. 4. A wide range of statistical methods germane to testing ecological and evolutionary hypotheses of shape variation are provided. These include standard multivariate methods such as principal components analysis, and approaches for multivariate regression and group comparison. Methods for more specialized analyses, such as for assessing shape allometry, comparing shape trajectories, examining morphological integration, and for assessing phylogenetic signal, are also included. 5. Several functions are provided to graphically visualize results, including routines for examining variation in shape space, visualizing allometric trajectories, comparing specific shapes to one another and for plotting phylogenetic changes in morphospace. 6. Finally, geomorph participates to make available advanced geometric morphometric analyses through the R statistical computing platform.

https://besjournals.onlinelibrary.wiley.com/doi/epdf/10.1111/2041-210X.12035

geomorph: an r package for the collection and analysis of geometric morphometric shape data

http://www.pdfsdocuments.com/geometric-morphometrics-for-biologists.pdf

Geometric Morphometrics for Biologists

SUMMARY Canalization may play a critical role in molding patterns of integration when variability is regulated by the balance between processes that generate and remove variation. Under these conditions, the interaction among those processes may produce a dynamic structure of integration even when the level of variability is constant. To determine whether the constancy of variance in skull shape throughout most of postnatal growth results from a balance between processes generating and removing variation, we compare covariance structures from age to age in two rodent species, cotton rats (Sigmodon fulviventer) and house mice (Mus musculus domesticus). We assess the overall similarity of covariance matrices by the matrix correlation, and compare the structures of covariance matrices using common subspace analysis, a method related to common principal components (PCs) analysis but suited to cases in which variation is so nearly spherical that PCs are ambiguous. We find significant differences from age to age in covariance structure and the more effectively canalized ones tend to be least stable in covariance structure. We find no evidence that canalization gradually and preferentially removes deviations arising early in development as we might expect if canalization results from compensatory differential growth. Our results suggest that (co)variation patterns are continually restructured by processes that equilibrate variance, and thus that canalization plays a critical role in molding patterns of integration.

/pdf/developmental-regulation-of-skull-morphology-i-ontogenetic-486wstgwo6.pdf

Developmental regulation of skull morphology. I. Ontogenetic dynamics of variance

Because development is epigenetic, diverse aspects of morphology are integrated during ontogeny. Using the method of thin-plate splines, and the decomposition of these splines by their principal warps, we examine the ontogeny of integrated features of skull growth of the cotton rat, Sigmodon fulviventer as observed in landmark locations in the ventral view. Postnatal growth of the skull in Sigmodon is not adequately described by the familiar contrast between relatively rapid facial elongation and slow, precocial growth of the cranial base. No developmental units corre- sponding to "facial skull" and "cranial base" emerge from analysis of geometric shape change. Rather, skull growth is both more integrated and more complex, exhibiting both skull-wide inte- gration and locally individualized regions. Like skull shape, integration has an ontogeny; different regions of the skull can be partitioned into developmentally individualized parts in different ways at different ages. The effective count of individualized parts decreases substantially before weaning occurs, suggesting that the integration required by the functionally demanding activity of chewing gradually develops before the functional transition occurs. Our description of skull growth and integration does not depend upon arbitrary a priori choices about what to measure; rather, we base our decomposition of the whole into parts upon results of the data analysis. Our approach com- plicates the study of heterochrony, but, because it expresses the spatiotemporal organization of ontogeny, it enables the study of heterotopy.

Ontogeny of integrated skull growth in the cotton rat sigmodon fulviventer.

Natural selection arising from resource competition and environmental heterogeneity can drive adaptive radiation. Ecological opportunity facilitates this process, resulting in rapid divergence of ecological traits in many celebrated radiations. In other cases, sexual selection is thought to fuel divergence in mating signals ahead of ecological divergence. Comparing divergence rates between naturally and sexually selected traits can offer insights into processes underlying species radiations, but to date such comparisons have been largely qualitative. Here, we quantitatively compare divergence rates for four traits in African mormyrid fishes, which use an electrical communication system with few extrinsic constraints on divergence. We demonstrate rapid signal evolution in the Paramormyrops species flock compared to divergence in morphology, size, and trophic ecology. This disparity in the tempo of trait evolution suggests that sexual selection is an important early driver of species radiation in ...

/pdf/sexual-signal-evolution-outpaces-ecological-divergence-e2yuto3704.pdf

Miriam Leah Zelditch

Papers

Geometric morphometrics for biologists: a primer

Geometric Morphometrics for Biologists

Developmental regulation of skull morphology. I. Ontogenetic dynamics of variance

Ontogeny of integrated skull growth in the cotton rat sigmodon fulviventer.

Sexual Signal Evolution Outpaces Ecological Divergence during Electric Fish Species Radiation