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 ixAcknowledgements xi1 Introduction 11.1 The nature of paleontological data 11.2 Advantages and pitfalls of paleontological data analysis 51.3 Software 7References 82 Statistical concepts 92.1 The population and the sample 92.2 The frequency distribution of the population 92.3 The normal distribution 112.4 Cumulative probability 122.5 The statistical sample, estimation of distribution parameters 142.6 Null hypothesis significance testing 162.7 Bayesian inference 202.8 Exploratory data analysis 22References 223 Introduction to data visualization 243.1 Graphic design principles 243.2 Line charts 253.3 Scatter plots 263.4 Histograms 263.5 Bar chart, box, and violin plots 293.6 Normal probability plot 293.7 Pie charts 313.8 Ternary plots 323.9 Heat maps, 3D plots, and Geographic Information System 333.10 Plotting with R and Python 33References 374 Univariate and bivariate statistical methods 384.1 Parameter estimation and confidence intervals 384.2 Testing for distribution 404.3 Two-sample tests 434.4 Multiple-sample tests 524.5 Correlation 584.6 Bivariate linear regression 644.7 Generalized linear models 704.8 Polynomial and nonlinear regression 734.9 Mixture analysis 744.10 Counts and contingency tables 76References 785 Introduction to multivariate data analysis 815.1 Multivariate distributions 825.2 Parametric multivariate tests – Hotelling’s T 2 825.3 Nonparametric multivariate tests – permutation test 855.4 Hierarchical cluster analysis 865.5 K-means and k-medoids cluster analysis 92References 946 Morphometrics 966.1 The allometric equation 976.2 Principal components analysis 1016.3 Multivariate allometry 1086.4 Linear discriminant analysis 1126.5 Multivariate analysis of variance 1166.6 Fourier shape analysis in polar coordinates 1166.7 Elliptic Fourier analysis 1196.8 Hangle Fourier analysis 1226.9 Eigenshape analysis 1236.10 Landmarks and size measures 1256.11 Procrustes fitting 1276.12 PCA of landmark data 1306.13 Thin-plate spline deformations 1326.14 Principal and partial warps 1366.15 Relative warps 1396.16 Regression of warp scores 1416.17 Common allometric component analysis 1426.18 Landmarks in 3D 1436.19 Disparity measures 1446.20 Morphogroup identification with machine learning 1466.21 Case study: the ontogeny of a Silurian trilobite 153References 1577 Directional and spatial data analysis 1627.1 Analysis of directions and orientations in 2D 1627.2 Analysis of directions and orientations in 3D 1647.3 Spatial point pattern analysis 166References 1738 Analysis of tomographic and 3D-scan data 1748.1 The technology of x-ray tomography 1748.2 Processing of volume data 1758.3 Functional morphology with 3D data 180References 1829 Estimating paleobiodiversity 1849.1 Species richness estimation 1859.2 Rarefaction and related methods 1879.3 Diversity curves, origination, and extinction rates 1929.4 Abundance-based biodiversity indices 1969.5 Taxonomic distinctness 2029.6 Comparison of diversity indices 2079.7 Abundance models 208References 21210 Paleoecology and paleobiogeography 21610.1 Paleobiogeography 21610.2 Paleoecology 21710.3 Association similarity indices for presence-absence data 21910.4 Association similarity indices for abundance data 22310.5 ANOSIM and PerMANOVA 22810.6 Principal coordinates analysis 22910.7 Non-metric multidimensional scaling 23210.8 Correspondence analysis 23610.9 Detrended correspondence analysis 24010.10 Seriation 24210.11 Nonlinear dimensionality reduction 24510.12 Canonical correspondence analysis 24810.13 Indicator species 25110.14 Network analysis 25210.15 Size-frequency and survivorship curves 25410.16 Case study: Devonian paleobiogeography 256References 25911 Calibration – estimating paleoenvironments 26311.1 Modern analog technique 26311.2 Weighted averaging 26511.3 Weighted averaging partial least squares 26711.4 Which calibration method? 26911.5 Case study: Late Holocene temperature inferred from chironomids 271References 27112 Time series analysis 27312.1 Spectral analysis 27412.2 Wavelet analysis 28212.3 Autocorrelation 28412.4 Cross-correlation 28712.5 Runs test 29012.6 Time Series Trends and Regression 29112.7 Smoothing and filtering 293References 29713 Quantitative biostratigraphy 29913.1 Zonation of a single section 29913.2 Confidence intervals on stratigraphic ranges 30113.3 Regional and global biostratigraphic correlation 30413.4 Age models 330References 33514 Phylogenetic analysis 33814.1 A dictionary of cladistics 33814.2 Parsimony analysis 33914.3 Characters 34114.4 Algorithms for Parsimony Analysis 34214.5 Character state reconstruction 34714.6 Evaluation of characters and trees 34814.7 Case study: the systematics of heterosporous ferns 35514.8 Other methods for phylogenetic analysis 35914.9 Phylogenetic Comparative Methods 362References 368Index 371