Genetics and analysis of quantitative traits

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’

https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1991.tb01825.x

Procrustes methods in the statistical analysis of shape

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

https://www.onlinelibrary.wiley.com/doi/pdf/10.1111/cla.12160

TNT version 1.5, including a full implementation of phylogenetic morphometrics.

Superimposition methods for comparing configurations of landmarks in two or more specimens are reviewed. These methods show differences in shape among specimens as residuals after rotation, translation, and scaling them so that they align as well as possible. A new method is presented that generalizes Siegel and Benson's (1982) resistant-fit theta-rho analysis so that more than two objects can be compared at the same time. Both least-squares and resistant-fit approaches are generalized to allow for affine transformations (uniform shape change). The methods are compared, using artificial data and data on 18 landmarks on the wings of 127 species of North American mosquitoes. Graphical techniques .are also presented to help sum- marize the patterns of differences in shape among the objects being compared. (Morphometrics; resistant-fit; least-squares; theta-rho analysis; rotational fit; affine transformations.) An important problem in morphomet- is now easy to display a transformation grid rics is that of comparing configurations of that maps the configuration of landmarks landmarks in two or more specimens. of one organism exactly into those of Thompson (1917) suggested an elegant ap- another. proach, using "transformation grids," that An alternative approach to fitting a mod- depicts the overall form of one organism el that completely describes the differences as a distortion in the shape of a reference between two organisms is to fit a very sim- organism. The basic idea was to place a ple model that only takes into consider- Cartesian coordinate grid over the refer- ation global parameters such as differences ence organism and then distort the image in rotation, translation, and scale. Geo- of the organism (including the grid) in var- metrically, this corresponds to superim- ious ways until the form of the second or- posing one organism on top of another so ganism was achieved. The differences in that its landmarks align as well as possible shapes of the two organisms are shown by (in some sense) with the positions of the the deviations of the fitted grid (usually corresponding landmarks on the second. bent and stretched in various ways) from Differences in shape are then shown by the original simple square grid. Thompson differences in positions of corresponding (1917) sketched the grids subjectively landmarks. Shape differences between two without an explicit specification of which organisms are found by studying these re- landmarks were used. Not all landmarks siduals. These methods are the subject of shown in pairs of drawings are located ex- the present paper. actly where the superimposed grids would Sneath (1967) investigated the problem imply they should be. This means that the of finding the optimal translation, rota- grids should be more complex than those tion, and size change of one object in order shown in Thompson (1917) in order to ac- for it to be superimposed on another. The curately show the differences between two two objects were represented as sets of x,y- organisms. Bookstein (1978) developed the coordinates of landmarks. A least-squares method of biorthogonal grid analysis criterion was used to measure the goodness which quantifies Thompson's approach and of fit of one object to another. Gower (1971) makes it objective. But it is complex and further developed Sneath's (1967) method has not been applied very often. A recent and expressed the operations in terms of b~ak-through (Bookstein, 1989) is the use matrix algebra. Siegel and Benson (1982) of methods based on thin-plate splines. It made the important observation that a

https://www.jstor.org/stable/pdfplus/2992207.pdf

Extensions of the Procrustes Method for the Optimal Superimposition of Landmarks

Twenty years ago, Rohlf and Marcus proclaimed that a “revolution in morphometrics” was underway, where classic analyses based on sets of linear distances were being supplanted by geometric approaches making use of the coordinates of anatomical landmarks. Since that time the field of geometric morphometrics has matured into a rich and cohesive discipline for the study of shape variation and covariation. The development of the field is identified with the Procrustes paradigm, a methodological approach to shape analysis arising from the intersection of the statistical shape theory and analytical procedures for obtaining shape variables from landmark data. In this review we describe the Procrustes paradigm and the current methodological toolkit of geometric morphometrics. We highlight some of the theoretical advances that have occurred over the past ten years since our prior review (Adams et al., 2004), what types of anatomical structures are amenable to these approaches, and how they extend the reach of geometric morphometrics to more specialized applications for addressing particular biological hypotheses. We end with a discussion of some possible areas that are fertile ground for future development in the field.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1115&context=eeob_ag_pubs

A field comes of age: geometric morphometrics in the 21 st century

A glossary for morphometrics.- Modern Morphometrics.- Theory and Methods.- After Landmarks.- Semilandmarks in Three Dimensions.- An Alternative Approach to Space Curve Analysis Using the Example of the Neanderthal Occipital Bun.- Correcting for the Effect of Orientation in Geometric Morphometric Studies of Side-View Images of Human Heads.- Fourier Descriptors, Procrustes Superimposition, and Data Dimensionality: An Example of Cranial Shape Analysis in Modern Human Populations.- Problems with Landmark-Based Morphometrics for Fractal Outlines: The Case of Frontal Sinus Ontogeny.- An Invariant Approach to the Study of Fluctuating Asymmetry: Developmental Instability in a Mouse Model for Down Syndrome.- Applications.- Comparison of Coordinate and Craniometric Data for Biological Distance Studies.- Assessing Craniofacial Secular Change in American Blacks and Whites Using Geometric Morphometry.- Secular Trends in Craniofacial Asymmetry Studied by Geometric Morphometry and Generalized Procrustes Methods.- The Morphological Integration of the Hominoid Skull: A Partial Least Squares and PC Analysis with Implications for European Middle Pleistocene Mandibular Variation.- A Geometric Morphometric Analysis of Late Pleistocene Human Metacarpal 1 Base Shape.- A Geometric Morphometric Assessment of the Relationship between Scapular Variation and Locomotion in African Apes.- Functional Shape Variation in the Cercopithecine Masticatory Complex.- A Geometric Morphometric Assessment of the Hominoid Supraorbital Region: Affinities of the Eurasian Miocene Hominoids Dryopithecus, Graecopithecus, and Sivapithecus.

Modern Morphometrics In Physical Anthropology

Archaic and modern human frontal bones are known to be quite distinct externally, by both conventional visual and metric evaluation. Internally this area of the skull has been considerably less well-studied. Here we present results from a comparison of interior, as well as exterior, frontal bone profiles from CT scans of five mid-Pleistocene and Neanderthal crania and 16 modern humans. Analysis was by a new morphometric method, Procrustes analysis of semi-landmarks, that permits the statistical comparison of curves between landmarks. As expected, we found substantial external differences between archaic and modern samples, differences that are mainly confined to the region around the brow ridge. However, in the inner median-sagittal profile, the shape remained remarkably stable over all 21 specimens. This implies that no significant alteration in this region has taken place over a period of a half-million years or more of evolution, even as considerable external change occurred within the hominid clade spanning several species. This confirms that the forms of the inner and outer aspects of the human frontal bone are determined by entirely independent factors, and further indicates unexpected stability in anterior brain morphology over the period during which modern human cognitive capacities emerged. Anat Rec (New Anat): 257:217‐224, 1999. r 1999 Wiley-Liss, Inc.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/%28SICI%291097-0185%2819991215%29257%3A6%3C217%3A%3AAID-AR7%3E3.0.CO%3B2-W

Dennis E. Slice

Papers

Extensions of the Procrustes Method for the Optimal Superimposition of Landmarks

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

A field comes of age: geometric morphometrics in the 21 st century

Modern Morphometrics In Physical Anthropology

Comparing Frontal Cranial Profiles in Archaic and Modern Homo by Morphometric Analysis