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Journal ArticleDOI

Advances in Geometric Morphometrics

TL;DR: 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.
Abstract: 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.

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Citations
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Journal ArticleDOI
TL;DR: The concept of sliding semilandmarks is introduced and the algorithm can be used to estimate missing data in incomplete specimens and applications and limitations of this method are discussed.
Abstract: Quantitative shape analysis using geometric morphometrics is based on the statistical analysis of landmark coordinates. Many structures, however, cannot be quantified using traditional landmarks. Semilandmarks make it possible to quantify two or three-dimensional homologous curves and sur- faces, and analyse them together with traditional landmarks. Here we first introduce the concept of sliding semilandmarks and discuss applications and limitations of this method. In a second part we show how the sliding semilandmark algorithm can be used to estimate missing data in incomplete specimens. Download the complete "Yellow Book" on "Virtual Morphology and Evolutionary Morphometrics in the new millenium".

646 citations


Cites background or methods from "Advances in Geometric Morphometrics..."

  • ...However, this redundant oversampling of morphology is critical for effective visualizations and exploratory studies, as well as for estimating missing data (Mitteroecker and Gunz, 2009; Gunz et al., 2009b)....

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  • ...of morphology is critical for effective visualizations and exploratory studies, as well as for estimating missing data (Mitteroecker and Gunz, 2009; Gunz et al., 2009b)....

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  • ...…as partial least squares analysis (Rohlf and Corti, 2000; Bookstein et al., 2003; Mitteroecker and Bookstein, 2007, 2008), between-group PCA (Mitteroecker and Bookstein, 2011), and permutation tests (Good, 2000); examples can be found in Mitteroecker et al. (2005) and Mitteroecker and Gunz (2009)....

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  • ...Shape analysis using geometric morphometrics (GM) is based on the statistical analysis of landmark coordinates (Bookstein, 1991; Dryden and Mardia, 1998; Adams et al., 2004; Slice, 2007; Mitteroecker and Gunz, 2009)....

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Journal ArticleDOI
TL;DR: This review is the first systematic comparison of allometric methods in the context of geometric morphometrics that considers the structure of morphological spaces and their implications for characterizing allometry and performing size correction.
Abstract: Allometry refers to the size-related changes of morphological traits and remains an essential concept for the study of evolution and development. This review is the first systematic comparison of allometric methods in the context of geometric morphometrics that considers the structure of morphological spaces and their implications for characterizing allometry and performing size correction. The distinction of two main schools of thought is useful for understanding the differences and relationships between alternative methods for studying allometry. The Gould–Mosimann school defines allometry as the covariation of shape with size. This concept of allometry is implemented in geometric morphometrics through the multivariate regression of shape variables on a measure of size. In the Huxley–Jolicoeur school, allometry is the covariation among morphological features that all contain size information. In this framework, allometric trajectories are characterized by the first principal component, which is a line of best fit to the data points. In geometric morphometrics, this concept is implemented in analyses using either Procrustes form space or conformation space (the latter also known as size-and-shape space). Whereas these spaces differ substantially in their global structure, there are also close connections in their localized geometry. For the model of small isotropic variation of landmark positions, they are equivalent up to scaling. The methods differ in their emphasis and thus provide investigators with flexible tools to address specific questions concerning evolution and development, but all frameworks are logically compatible with each other and therefore unlikely to yield contradictory results.

620 citations


Cites background from "Advances in Geometric Morphometrics..."

  • ...…natural log-transformed centroid size as an extra dimension to shape tangent space to produce a Bsize–shape space^ (Mitteroecker et al. 2004), also called Bform space^ or BProcrustes form space^ (Bastir et al. 2007; Mitteroecker and Gunz 2009; Weber and Bookstein 2011; Mitteroecker et al. 2013)....

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  • ...2004), also called Bform space^ or BProcrustes form space^ (Bastir et al. 2007; Mitteroecker and Gunz 2009; Weber and Bookstein 2011; Mitteroecker et al. 2013)....

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  • ...Space Shape space Form space (Mitteroecker and Gunz 2009; Weber and Bookstein 2011; Mitteroecker et al. 2013) Conformation space...

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Journal ArticleDOI
08 Jun 2017-Nature
TL;DR: A mosaic of features including facial, mandibular and dental morphology that aligns the Jebel Irhoud material with early or recent anatomically modern humans and more primitive neurocranial and endocranial morphology shows that the evolutionary processes behind the emergence of H. sapiens involved the whole African continent.
Abstract: Fossil evidence points to an African origin of Homo sapiens from a group called either H. heidelbergensis or H. rhodesiensis. However, the exact place and time of emergence of H. sapiens remain obscure because the fossil record is scarce and the chronological age of many key specimens remains uncertain. In particular, it is unclear whether the present day ‘modern’ morphology rapidly emerged approximately 200 thousand years ago (ka) among earlier representatives of H. sapiens1 or evolved gradually over the last 400 thousand years2. Here we report newly discovered human fossils from Jebel Irhoud, Morocco, and interpret the affinities of the hominins from this site with other archaic and recent human groups. We identified a mosaic of features including facial, mandibular and dental morphology that aligns the Jebel Irhoud material with early or recent anatomically modern humans and more primitive neurocranial and endocranial morphology. In combination with an age of 315 ± 34 thousand years (as determined by thermoluminescence dating)3, this evidence makes Jebel Irhoud the oldest and richest African Middle Stone Age hominin site that documents early stages of the H. sapiens clade in which key features of modern morphology were established. Furthermore, it shows that the evolutionary processes behind the emergence of H. sapiens involved the whole African continent.

618 citations

Journal ArticleDOI
TL;DR: This review describes the Procrustes paradigm and the current methodological toolkit of geometric morphometrics, and highlights some of the theoretical advances that have occurred over the past ten years since the prior review (Adams et al., 2004).
Abstract: 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.

588 citations


Cites methods from "Advances in Geometric Morphometrics..."

  • ...Nearly a decade ago, we reviewed the field of geometric morphometrics and described the important advantages that these approaches have relative to alternative methods of shape analysis (Adams et al. 2004; for other reviews see: O’Higgins 2000; Slice 2005, 2007; Mitteroecker and Gunz 2009)....

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Book ChapterDOI
01 Jan 2017
TL;DR: This tutorial gives an introduction into landmark/surface-mesh based statistical shape analysis in R – specifically using the packages Morpho and Rvcg.
Abstract: The mathematical/statistical software platform R has seen an immense increase in popularity within the last decade. Its main advantages are its flexibility, a large repository of freely available extensions, its open-source nature and a thriving community. This tutorial gives an introduction into landmark/surface-mesh based statistical shape analysis in R – specifically using the packages Morpho and Rvcg. Beginning with examples based on sparse sets of anatomical landmarks, the tutorial will go on dealing with surface and curve landmarks and more challenging tasks such as mesh manipulations and surface registration. Apart from statistical analyses, emphasis will also be put on comprehensive visualization of the results. Extensive examples and code snippets are provided to allow the reader to easily replicate the analyses.

531 citations

References
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Journal ArticleDOI
TL;DR: 2 general approaches that come highly recommended: maximum likelihood (ML) and Bayesian multiple imputation (MI) are presented and may eventually extend the ML and MI methods that currently represent the state of the art.
Abstract: Statistical procedures for missing data have vastly improved, yet misconception and unsound practice still abound. The authors frame the missing-data problem, review methods, offer advice, and raise issues that remain unresolved. They clear up common misunderstandings regarding the missing at random (MAR) concept. They summarize the evidence against older procedures and, with few exceptions, discourage their use. They present, in both technical and practical language, 2 general approaches that come highly recommended: maximum likelihood (ML) and Bayesian multiple imputation (MI). Newer developments are discussed, including some for dealing with missing data that are not MAR. Although not yet in the mainstream, these procedures may eventually extend the ML and MI methods that currently represent the state of the art.

10,568 citations


"Advances in Geometric Morphometrics..." refers background in this paper

  • ...There exists a large body of literature on methods for estimating population parameters such as means or regressions in the presence of missing values (for reviews and examples see Schafer 1997; McLachlan and Krishnan 1997; Schafer and Graham 2002)....

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  • ...There exists a large body of literature on methods for estimating population parameters such as means or regressions in the presence of missing values (for reviews and examples see Schafer 1997; McLachlan and Krishnan 1997; Schafer and Graham 2002 )....

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Journal ArticleDOI
TL;DR: In this paper, the authors describe the steps involved in VBM, with particular emphasis on segmenting gray matter from MR images with non-uniformity artifact and provide evaluations of the assumptions that underpin the method, including the accuracy of the segmentation and the assumptions made about the statistical distribution of the data.

8,049 citations


"Advances in Geometric Morphometrics..." refers methods in this paper

  • ...Other frequently used morphometric methods are Euclidian distance matrix analysis (Lele and Richtsmeier 1991, 2001), elliptic Fourier analysis (Lestrel 1982), and non-label based approaches like voxel-based morphometry (e.g., Ashburner and Friston 2000), which is mainly applied in brain imaging....

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Book
01 Aug 1997
TL;DR: The Normal Model Methods for Categorical Data Loglinear Models Methods for Mixed Data and Inference by Data Augmentation Methods for Normal Data provide insights into the construction of categorical and mixed data models.
Abstract: Introduction Assumptions EM and Inference by Data Augmentation Methods for Normal Data More on the Normal Model Methods for Categorical Data Loglinear Models Methods for Mixed Data Further Topics Appendices References Index

6,704 citations

Book
15 Nov 1996
TL;DR: The EM Algorithm and Extensions describes the formulation of the EM algorithm, details its methodology, discusses its implementation, and illustrates applications in many statistical contexts, opening the door to the tremendous potential of this remarkably versatile statistical tool.
Abstract: The first unified account of the theory, methodology, and applications of the EM algorithm and its extensionsSince its inception in 1977, the Expectation-Maximization (EM) algorithm has been the subject of intense scrutiny, dozens of applications, numerous extensions, and thousands of publications. The algorithm and its extensions are now standard tools applied to incomplete data problems in virtually every field in which statistical methods are used. Until now, however, no single source offered a complete and unified treatment of the subject.The EM Algorithm and Extensions describes the formulation of the EM algorithm, details its methodology, discusses its implementation, and illustrates applications in many statistical contexts. Employing numerous examples, Geoffrey McLachlan and Thriyambakam Krishnan examine applications both in evidently incomplete data situations-where data are missing, distributions are truncated, or observations are censored or grouped-and in a broad variety of situations in which incompleteness is neither natural nor evident. They point out the algorithm's shortcomings and explain how these are addressed in the various extensions.Areas of application discussed include: Regression Medical imaging Categorical data analysis Finite mixture analysis Factor analysis Robust statistical modeling Variance-components estimation Survival analysis Repeated-measures designs For theoreticians, practitioners, and graduate students in statistics as well as researchers in the social and physical sciences, The EM Algorithm and Extensions opens the door to the tremendous potential of this remarkably versatile statistical tool.

5,998 citations


"Advances in Geometric Morphometrics..." refers background in this paper

  • ...There exists a large body of literature on methods for estimating population parameters such as means or regressions in the presence of missing values (for reviews and examples see Schafer 1997; McLachlan and Krishnan 1997; Schafer and Graham 2002)....

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