Morphometric Analysis:

Week

Topic

Material

Readings bold=mandatory

1

1: Introduction and History of Morphometrics

Zel: Ch 1

#5 , #26,  #8, OB: 2.1

1: Primary Data: Considerations

1

2: The Data of Morphometrics

Morphometric features, homology, linear distances, the truss, landmarks, outlines

Zel: Ch 2

2

3: Univariate Statistics and Matrix Algebra

Matrix algebra, bias, efficiency, consistency, correlation, ANOVA, regression, ANCOVA

4: The Basics of Multivariate Statistics

The jump to multivariate GLM, confirmatory methods (MANOVA, regression)

#15

3

5: Multivariate Statistics II

Exploratory multivariate methods (PCA, UPGMA), CVA, resampling methods

Zel: Ch 8

6: Data Acquisition

2-D systems (digitizing pads, digital cameras, scanners), 3-D systems (handheld digitizers, 3-D scanners, 3-D stereomicroscopes), data acquisition software

#11

2: Generate Shape Variables

4

7: Preliminary Concepts & Traditional Morphometrics

What is shape, shape variables, a general morphometric protocol, Dean’s principle of classification, Traditional Morphometrics, size standardization, Allometry and CPCA, the Truss

#14

OB: 4.2, 4.3, 4.4

8: Landmark Methods I:  Superimposition

Why bother with geometric methods, centroid size, differences between shapes, reflections,  Gaussian model of shape variation, Goodall’s F-test, Bookstein’s shape coordinates for triangles

Zel: Ch 3

OB: 93-95, 167-175

5

9: Landmark Methods II:  Superimposition cont.

Shape coordinates for objects other than triangles, 3-D shape coordinates, least-squares (Procrustes) superimposition (GPA)

Zel: Ch 5

#25

10: Landmark Methods III:  Superimposition cont. 2

Full vs. partial GPA fitting, affine parameters and GALS, resistant-fit methods

#25

Dryden and Mardia, 98

6

11: Landmark Methods IV: Visualization as Displacements

GPA displacements, GRF displacements, variation at each landmark (and PCA)

#25

12: Landmark Methods V:  Visualization as Deformations

D’Arcy Thompson and the history of deformations, computation of the thin-plate spline & U-function, principle and partial warps, uniform and non-uniform shape

Zel: Ch 6#27

7

13: Landmark Methods VI:  Visualization as Deformations cont.

Meaning of partial warps, relative warps, principle axes, strain and anisotropy, image unwarping

Midterm Exam

8

14: Shape Spaces for Landmark Data

Distances between objects, Procrustes Distance formulations,  figure space, perform space, form space, Kendall’s shape space, Procrustes-aligned space

Zel: Ch 4

#19, #21, #29

15: Shape Spaces for Landmark Data cont.

Kendall’s tangent space, Bookstein shape coordinate tangent space, relationship between shape spaces and tangent spaces, articulations in shape space,  Procrustes motion analysis

#21

9

16: Outline Methods: Open and Closed Contours

polynomials, cubic splines, Fourier of radii, tangent angles, and EFA, Eigenshape analysis

#12, #17

17: Semi-landmarks, combining Landmarks and Outlines

Procrustean relaxation methods for outlines

#7, #9

Zel: Ch 15

10

Spring Break

Spring Break

11

18: Other Approaches for Landmark Data

EDMA I, EDMA II, EDMA III, FESA, Distances (Rao and Suryawanshi), triangle interior angles (Rao and Suryawanshi)

#22

19: Statistical Comparison of Landmark Methods

Data spaces, Type I error rates, statistical power, bias, and MSE, why this is important

#16, #18,#21, #22, #23, #24

3: Biological Shape Variation: Analysis and Interpretation

12

20: Statistical Analysis of Shape I:  Exploratory Methods

Shape variables, Ordination: PCA, RWA (alpha parameter), Clustering: UPGMA

Zel: Ch 7#10

21: Statistical Analysis of Shape II:  Confirmatory Methods

MANOVA, regression, multi-factor MANOVA,  CVA, PLS

Zel: 9-11#4, #10, #28

13

22: Methodological Extensions

Applications to asymmetry, quantitative genetics, analysis of motion and shape of articulated structures

#2, #3

23: Shape Data and Phylogenies

Mapping shape onto a phylogeny, using shape to generate phylogenies, shape and the comparative method

Zel: Ch 14#1, #13, #20, #28

14

24: Variation and Disparity

Evolutionary shape variation, variation within and among taxa,

Zel: Ch 12

25: Applications and Examples

Taxonomy and group comparisons, ecomorphology (shape vs. other variables), accounting for phylogeny in data analysis, morphometrics and bioinrformatics

15

26: Other Morphological Data

Morphological color, fractals, morphological textures and patterns

27: The Future of Morphometrics

3-D data, surfaces, phylogeny, covariance structure, absent/missing data

16

Review and Conclusions

#5, #6

Student Projects

16

Final Exam