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P. David Polly
Department of Geological Sciences
Indiana University
1001 E. 10th Street
Bloomington, IN 47405 USA
http://www.indiana.edu/~geosci

Geometric Morphometrics is the analysis of shape using Cartesian geometric coordinates rather than linear, areal, or volumetric variables. Geometric morphometric methods (GMM) include 2D and 3D points representing landmarks, curves, outlines, or surfaces. This course is a practical, applied introduction to GMM. Students learn to collect, analyze, and interpret geometric morphometric data. Shape theory and methods are covered, including Procrustes superimposition and its statistical implications, analysis of curves and outlines, and Monte Carlo modeling of shape.

### Lecture 1 - Introduction to Geometric Morphometrics

Overview of principles of geometric morphometric methods (GMM), including definitions of landmarks, outlines and surfaces, differentiation between traditional morphometrics and GMM, short history of morphometrics, components of a morphometric study, and examples of equipment needed for GMM studies.

### Lecture 2 - Introduction to Mathematica

Learn basics of Mathematica, including basic operations, using cells and styles, writing short programs, defining functions, and making simple graphs.

### Lecture 3 - First GMM Analysis

Basics of Procrustes analysis, principal components analysis of shape, and morphospace. Introduction to the morphometrics functions tpsImport[], Procrustes[], PrincipalComponentsOfShape[]. Analysis of faces.

### Lecture 4 - Procrustes , PCA, and Morphospace

Details of Procrustes, Procrustes distances, Principal Components Analysis, Eigenvalues, Eigenvectors, Scores, and shape modelling.

### Lecture 5 - Statistical Analysis of Shape

Review of PCA, introduction to statistical tests, introduction to R-squared values, univariate regression, multivariate regression, ANOVA, MANOVA.

### Session 6 - Bootstrapping, Randomization, and Monte Carlo methods

This session is based on readings by Adams & Anthony (1996), Kowalewski & Novack-Gotshall (2010), and Efron & Tibshirani (1986). What are "statistics"? What is a statistical test? What is a statistical null hypothesis? How can resamppling and randomizations of real samples be used to construct customized statistical tests. Bootstrapping, jack-knifing, randomization, Monte Carlo.
[Assignment 5]

### Lecture 7- Bootstrapping, Randomization, and Monte Carlo methods

Continues previous topic.
[Assignment 5 with tips]

### Lecture 8 - Analysis of outlines and Euclidean DIstance Matrix Anlaysis (EDMA)

Intro to semilandmarks, Fourier analysis, semilandmark analysis, sliding semilandmarks, eigenshape, "Pinocchio effect", alternatives to Procrustes, EDMA.

### Lecture 9 - Phylogeny, trees, and morphospace

Phylogenetic signal in morphometric data, "factor thinking", tree building algorithms and terminology, building morphometric trees in Phylip, phylogenetic comparative statistics, trees in morphospace.

### Lecture 10 - Monte Carlo simulation of evolution of shape

Random walks, their properties and statistics, random walks in more than one dimension, random walks in morphospace, modeling random evolution.

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