Øyvind Hammer, PhD, is Professor of Paleontology at the University of Oslo, Norway. He has published very widely on paleontological subjects, and is co-author of the paleontological data analysis software PAST.

David A.T. Harper, DSc, is Emeritus Professor of Paleontology at Durham University, UK. He has published extensively, including numerous monographs and textbooks, and developed the software PAST along with Øyvind Hammer.

Preface ix

Acknowledgements xi

1 Introduction 1

1.1 The nature of paleontological data 1

1.2 Advantages and pitfalls of paleontological data analysis 5

1.3 Software 7

References 8

2 Statistical concepts 9

2.1 The population and the sample 9

2.2 The frequency distribution of the population 9

2.3 The normal distribution 11

2.4 Cumulative probability 12

2.5 The statistical sample, estimation of distribution parameters 14

2.6 Null hypothesis significance testing 16

2.7 Bayesian inference 20

2.8 Exploratory data analysis 22

References 22

3 Introduction to data visualization 24

3.1 Graphic design principles 24

3.2 Line charts 25

3.3 Scatter plots 26

3.4 Histograms 26

3.5 Bar chart, box, and violin plots 29

3.6 Normal probability plot 29

3.7 Pie charts 31

3.8 Ternary plots 32

3.9 Heat maps, 3D plots, and Geographic Information System 33

3.10 Plotting with R and Python 33

References 37

4 Univariate and bivariate statistical methods 38

4.1 Parameter estimation and confidence intervals 38

4.2 Testing for distribution 40

4.3 Two-sample tests 43

4.4 Multiple-sample tests 52

4.5 Correlation 58

4.6 Bivariate linear regression 64

4.7 Generalized linear models 70

4.8 Polynomial and nonlinear regression 73

4.9 Mixture analysis 74

4.10 Counts and contingency tables 76

References 78

5 Introduction to multivariate data analysis 81

5.1 Multivariate distributions 82

5.2 Parametric multivariate tests - Hotelling's T 2 82

5.3 Nonparametric multivariate tests - permutation test 85

5.4 Hierarchical cluster analysis 86

5.5 K-means and k-medoids cluster analysis 92

References 94

6 Morphometrics 96

6.1 The allometric equation 97

6.2 Principal components analysis 101

6.3 Multivariate allometry 108

6.4 Linear discriminant analysis 112

6.5 Multivariate analysis of variance 116

6.6 Fourier shape analysis in polar coordinates 116

6.7 Elliptic Fourier analysis 119

6.8 Hangle Fourier analysis 122

6.9 Eigenshape analysis 123

6.10 Landmarks and size measures 125

6.11 Procrustes fitting 127

6.12 PCA of landmark data 130

6.13 Thin-plate spline deformations 132

6.14 Principal and partial warps 136

6.15 Relative warps 139

6.16 Regression of warp scores 141

6.17 Common allometric component analysis 142

6.18 Landmarks in 3D 143

6.19 Disparity measures 144

6.20 Morphogroup identification with machine learning 146

6.21 Case study: the ontogeny of a Silurian trilobite 153

References 157

7 Directional and spatial data analysis 162

7.1 Analysis of directions and orientations in 2D 162

7.2 Analysis of directions and orientations in 3D 164

7.3 Spatial point pattern analysis 166

References 173

8 Analysis of tomographic and 3D-scan data 174

8.1 The technology of x-ray tomography 174

8.2 Processing of volume data 175

8.3 Functional morphology with 3D data 180

References 182

9 Estimating paleobiodiversity 184

9.1 Species richness estimation 185

9.2 Rarefaction and related methods 187

9.3 Diversity curves, origination, and extinction rates 192

9.4 Abundance-based biodiversity indices 196

9.5 Taxonomic distinctness 202

9.6 Comparison of diversity indices 207

9.7 Abundance models 208

References 212

10 Paleoecology and paleobiogeography 216

10.1 Paleobiogeography 216

10.2 Paleoecology 217

10.3 Association similarity indices for presence-absence data 219

10.4 Association similarity indices for abundance data 223

10.5 ANOSIM and PerMANOVA 228

10.6 Principal coordinates analysis 229

10.7 Non-metric multidimensional scaling 232

10.8 Correspondence analysis 236

10.9 Detrended correspondence analysis 240

10.10 Seriation 242

10.11 Nonlinear dimensionality reduction 245

10.12 Canonical correspondence analysis 248

10.13 Indicator species 251

10.14 Network analysis 252

10.15 Size-frequency and survivorship curves 254

10.16 Case study: Devonian paleobiogeography 256

References 259

11 Calibration - estimating paleoenvironments 263

11.1 Modern analog technique 263

11.2 Weighted averaging 265

11.3 Weighted averaging partial least squares 267

11.4 Which calibration method? 269

11.5 Case study: Late Holocene temperature inferred from chironomids 271

References 271

12 Time series analysis 273

12.1 Spectral analysis 274

12.2 Wavelet analysis 282

12.3 Autocorrelation 284

12.4 Cross-correlation 287

12.5 Runs test 290

12.6 Time Series Trends and Regression 291

12.7 Smoothing and filtering 293

References 297

13 Quantitative biostratigraphy 299

13.1 Zonation of a single section 299

13.2 Confidence intervals on stratigraphic ranges 301

13.3 Regional and global biostratigraphic correlation 304

13.4 Age models 330

References 335

14 Phylogenetic analysis 338

14.1 A dictionary of cladistics 338

14.2 Parsimony analysis 339

14.3 Characters 341

14.4 Algorithms for Parsimony Analysis 342

14.5 Character state reconstruction 347

14.6 Evaluation of characters and trees 348

14.7 Case study: the systematics of heterosporous ferns 355

14.8 Other methods for phylogenetic analysis 359

14.9 Phylogenetic Comparative Methods 362

References 368

Index 371