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

An up-to-date edition of the indispensable guide to analysing paleontological data Paleontology has developed in recent decades into an increasingly data-driven discipline, which brings to bear a huge variety of statistical tools. Applying statistical methods to paleontological data requires a discipline-specific understanding of which methods and parameters are the most appropriate ones, and how to account for statistical bias inherent in the fossil record. By guiding the reader to these and other fundamental questions in the statistical analysis of fossilized specimens, Paleontological Data Analysis has become the standard text for anyone with an interest in quantitative analysis of the fossil record. Now fully updated to reflect the latest statistical methods and disciplinary advances, it is an essential tool for practitioners and students alike. Readers of the second edition of Paleontological Data Analysis readers will also find: New sections on machine learning, Bayesian inference, phylogenetic comparative methods, analysis of CT data, and much more New use cases and examples using PAST, R, and Python software packages Full color illustrations throughout Paleontological Data Analysis is ideal for paleontologists, evolutionary biologists, taxonomists, and students in any of these fields.