Geometric Morphometrics for Biologists

Geometric Morphometrics for Biologists

A Primer

2nd Edition - August 2, 2012

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  • Authors: Miriam Zelditch, Donald Swiderski, H. Sheets
  • eBook ISBN: 9780123869043
  • Hardcover ISBN: 9780123869036

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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.

Key Features

  • Contains updated coverage of methods, especially for sampling complex curves and 3D forms and a new chapter on applications of geometric morphometrics to forensics
  • Offers a reorganization of chapters to streamline learning basic concepts
  • Presents detailed instructions for conducting analyses with freely available, easy to use software
  • Provides numerous illustrations, including graphical presentations of important theoretical concepts and demonstrations of alternative approaches to presenting results


Advanced undergraduates, and graduates/research workers in taxonomy, ecology, evolution, comparative zoology and botany from the cellular to the whole organism levels. Any branch of biology where the analysis and comparison of shape and form is important

Table of Contents

  • Chapter 1. Introduction

    • A Critical Overview of Measurement Theory
    • Shape and Size
    • Methods of Data Analysis
    • Biological and Statistical Hypotheses
    • Organization of the Book
    • Software and Other Resources
    • References

    Part 1: Basics of Shape Data

    Chapter 2. Landmarks and Semilandmarks

    • Criteria for Choosing Landmarks
    • Bookstein’s Typology of Landmarks
    • Examples: Applying Ideals to Actual Cases
    • Designing Your Own Measurement Scheme
    • References

    Chapter 3. Simple Size and Shape Variables: Shape Coordinates

    • Shape Coordinates
    • Size
    • Statistics of Shape Coordinates
    • Procrustes Superimposition
    • Procrustes Superimposition in Three-Dimensions
    • Semilandmark Sliding
    • Resistant-Fit Superimposition
    • References

    Chapter 4. Theory of Shape

    • The Definition of Shape
    • Morphometric Spaces
    • Pre-Shape Space
    • Shape Spaces
    • The Spaces of Three-Dimensional Configurations
    • A Numerical Example for the Simplest Case
    • Tangent Spaces
    • Summary
    • References

    Chapter 5. The Thin-plate Spline: Visualizing Shape Change as a Deformation

    • Modeling Shape Change as a Deformation
    • The Physical Metaphor
    • An Intuitive Introduction to Partial Warps
    • An Algebraic Introduction to Partial Warps
    • Decomposing the Deformation of Three-Dimensional Data
    • Using the Thin-Plate Spline to Visualize Shape Change
    • Using Bending Energy to Superimpose Semilandmarks
    • Appendix
    • References

    Part 2: Analyzing Shape Variables

    Chapter 6. Ordination Methods

    • Principal Components Analysis
    • Canonical Variates Analysis
    • Between Groups Principal Components Analysis
    • References

    Chapter 7. Partial Least Squares Analysis

    • Analyzing Covariances Between Blocks and Significance Testing
    • Mathematical Details of Two Block PLS
    • Using PLS to Compare Patterns of Covariance Between Blocks Across Groups
    • Comparing PLS to Other Methods
    • Applications of PLS
    • References

    Chapter 8. Statistics

    • The Correlation Coefficient
    • Multivariate Regression
    • Distance-Based Methods of Hypothesis Testing
    • Comparing Two Means
    • One-Way ANOVA/MANOVA
    • Extension of the Univariate ANOVA to Multivariate Shape Data
    • Appendix: An Overview of Randomization and Monte Carlo Methods
    • References

    Chapter 9. General Linear Models

    • Factors and Experimental Design
    • Design Matrices
    • The Form of a General Linear Model
    • F-tests and Mean Squares
    • Generalizing and Extending the Simple Univariate ANOVA
    • Models
    • Unbalanced Designs and Sums of Squares
    • Working with Multivariate Sum of Squares
    • Permutation Approaches to General Linear Models
    • Models with Multiple Factors
    • Models with Covariates
    • Models with Multiple Factors and a Covariate
    • Analyzing Measurement Error
    • Implementing GLM
    • References

    Part 3: Applications

    Chapter 10. Ecological and Evolutionary Morphology

    • Incorporating Phylogeny in Comparative Studies
    • Evolutionary Allometry
    • Form and Function
    • Comparing Trajectories
    • Magnitude and Structure of Morphological Diversity
    • Analyzing the Structure of Disparity
    • References

    Chapter 11. Evolutionary Developmental Biology(1): The Evolution of Ontogeny

    • Why Allometry is Interesting in its Own Right
    • Formalisms for the Analysis of Ontogenetic Allometry: Traditional Morphometric Data
    • Hypotheses about the Evolution of Ontogenetic Trajectories
    • Testing Hypotheses about the Evolution of Ontogeny
    • Dissecting the Developmental Basis of Disparity
    • Age-Based Comparisons of Growth and Developmental Rates and Timings
    • Disparity of Ontogeny
    • References

    Chapter 12. Evolutionary Developmental Biology (2): Variational Properties

    • Phenotypic Plasticity: Quantifying Norms of Reaction
    • Canalization: Quantifying Variation
    • Developmental Stability: Quantifying Developmental Noise
    • Analyzing the Relationship Between Plasticity, Canalization and Developmental Stability
    • Predicting the Structure of Covariation: Morphological Integration and Modularity
    • References

    Chapter 13. Morphometrics and Systematics

    • Taxonomic Discrimination
    • Finding Characters
    • Coding
    • Summary
    • References

    Chapter 14. Forensic Applications of Geometric Morphometrics

    • Size and Shape
    • What Does it Mean for Shapes to “Match”?
    • Matching Shapes in the Human Dentition
    • Sex Estimation in a Forensic Context
    • Likelihood Ratios and Fetal Alcohol Syndrome
    • References

Product details

  • No. of pages: 488
  • Language: English
  • Copyright: © Academic Press 2012
  • Published: August 2, 2012
  • Imprint: Academic Press
  • eBook ISBN: 9780123869043
  • Hardcover ISBN: 9780123869036

About the Authors

Miriam Zelditch

Affiliations and Expertise

Museum of Paleontology, University of Michigan, Ann Arbor, MI, USA

Donald Swiderski

Affiliations and Expertise

University of Michigan Medical Center, Ann Arbor, MI, USA

H. Sheets

Affiliations and Expertise

Department of Physics, Canisius College, Buffalo, NY, USA

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