Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Acknowledgements -- Chapter 1 Introduction -- 1.1 The nature of paleontological data -- 1.1.1 Univariate measurements -- 1.1.2 Bivariate measurements -- 1.1.3 Multivariate morphometric measurements -- 1.1.4 Character matrices for phylogenetic analysis -- 1.1.5 Paleoecology and paleobiogeography - taxa in samples -- 1.1.6 Time series -- 1.1.7 Biostratigraphic data -- 1.2 Advantages and pitfalls of paleontological data analysis -- 1.2.1 Data analysis for the sake of it -- 1.2.2 The Texas sharpshooter -- 1.2.3 Explorative method or hypothesis testing? -- 1.2.4 Incomplete data -- 1.2.5 Statistical assumptions -- 1.2.6 Statistical and biological significance -- 1.2.7 Circularity -- 1.3 Software -- References -- Chapter 2 Statistical concepts -- 2.1 The population and the sample -- 2.2 The frequency distribution of the population -- 2.3 The normal distribution -- 2.4 Cumulative probability -- 2.5 The statistical sample, estimation of distribution parameters -- 2.6 Null hypothesis significance testing -- 2.6.1 Type I and type II errors -- 2.6.2 Power -- 2.6.3 Robustness -- 2.6.4 Effect size -- 2.6.5 NHST misunderstandings -- 2.7 Bayesian inference -- 2.7.1 Bayes' theorem -- 2.7.2 Markov Chain Monte Carlo -- 2.7.3 What is the point? -- 2.7.4 Bayes factors -- 2.8 Exploratory data analysis -- References -- Chapter 3 Introduction to data visualization -- 3.1 Graphic design principles -- 3.1.1 Vector graphics -- 3.1.2 Fonts -- 3.1.3 Colors -- 3.1.4 Fills -- 3.2 Line charts -- 3.3 Scatter plots -- 3.4 Histograms -- 3.5 Bar chart, box, and violin plots -- 3.6 Normal probability plot -- 3.7 Pie charts -- 3.8 Ternary plots -- 3.9 Heat maps, 3D plots, and Geographic Information System -- 3.10 Plotting with R and Python -- References -- Chapter 4 Univariate and bivariate statistical methods.

4.1 Parameter estimation and confidence intervals -- 4.1.1 Bootstrapping -- 4.1.2 Credible intervals -- 4.2 Testing for distribution -- 4.2.1 Shapiro-Wilk test for normal distribution -- 4.3 Two-sample tests -- 4.3.1 Student's t test for the equality of means -- 4.3.2 F test for the equality of variances -- 4.3.3 Mann-Whitney U test for equality of position -- 4.3.4 Kolmogorov-Smirnov test for equality of distribution -- 4.3.5 Permutation tests -- 4.4 Multiple-sample tests -- 4.4.1 One-way ANOVA -- 4.4.2 Kruskal-Wallis test -- 4.5 Correlation -- 4.5.1 Linear correlation -- 4.5.2 Non-parametric correlation -- 4.6 Bivariate linear regression -- 4.6.1 Ordinary least-squares linear regression -- 4.6.2 Reduced major axis regression -- 4.7 Generalized linear models -- 4.7.1 GLM regression of counts -- 4.7.2 GLM regression of percentages or proportions -- 4.7.3 GLM regression of binary data (logistic regression) -- 4.8 Polynomial and nonlinear regression -- 4.8.1 Akaike information criterion -- 4.9 Mixture analysis -- 4.10 Counts and contingency tables -- References -- Chapter 5 Introduction to multivariate data analysis -- 5.1 Multivariate distributions -- 5.2 Parametric multivariate tests - Hotelling's T2 -- 5.3 Nonparametric multivariate tests - permutation test -- 5.4 Hierarchical cluster analysis -- 5.5 K-means and k-medoids cluster analysis -- References -- Chapter 6 Morphometrics -- 6.1 The allometric equation -- 6.2 Principal components analysis -- 6.2.1 Transformation and normalization -- 6.2.2 Relative importance of principal components -- 6.2.3 Algorithms for PCA -- 6.2.4 PCA is not hypothesis testing -- 6.2.5 Factor analysis -- 6.3 Multivariate allometry -- 6.4 Linear discriminant analysis -- 6.4.1 Discriminant analysis for more than two groups -- 6.5 Multivariate analysis of variance -- 6.6 Fourier shape analysis in polar coordinates.

6.7 Elliptic Fourier analysis -- 6.8 Hangle Fourier analysis -- 6.9 Eigenshape analysis -- 6.10 Landmarks and size measures -- 6.10.1 Sliding landmarks -- 6.10.2 Size from landmarks -- 6.10.3 Landmark registration and shape coordinates -- 6.11 Procrustes fitting -- 6.12 PCA of landmark data -- 6.13 Thin-plate spline deformations -- 6.14 Principal and partial warps -- 6.14.1 The affine (uniform) component -- 6.14.2 Partial warp scores as shape coordinates -- 6.15 Relative warps -- 6.16 Regression of warp scores -- 6.17 Common allometric component analysis -- 6.18 Landmarks in 3D -- 6.19 Disparity measures -- 6.19.1 Morphometric disparity measures -- 6.19.2 Disparity measures from discrete characters -- 6.19.3 Sampling effects and rarefaction -- 6.19.4 Morphospaces -- 6.20 Morphogroup identification with machine learning -- 6.20.1 K-nearest-neighbor classification -- 6.20.2 Naïve Bayes -- 6.20.3 Decision trees and random forests -- 6.20.4 Neural networks -- 6.20.5 Image classification and convolutional neural networks -- 6.21 Case study: the ontogeny of a Silurian trilobite -- 6.21.1 Size -- 6.21.2 Distance measurements and allometry -- 6.21.3 Procrustes fitting of landmarks -- 6.21.4 Common allometric component analysis -- References -- Chapter 7 Directional and spatial data analysis -- 7.1 Analysis of directions and orientations in 2D -- 7.1.1 Plotting circular data -- 7.1.2 Testing for preferred direction -- 7.2 Analysis of directions and orientations in 3D -- 7.3 Spatial point pattern analysis -- 7.3.1 Nearest-neighbor analysis -- 7.3.2 Ripley's K analysis -- 7.3.3 Correlation length analysis -- References -- Chapter 8 Analysis of tomographic and 3D-scan data -- 8.1 The technology of x-ray tomography -- 8.2 Processing of volume data -- 8.2.1 Volumes and surface meshes -- 8.2.2 Segmentation -- 8.2.3 Landmarks from CT data.

8.2.4 Analysis of volume data -- 8.3 Functional morphology with 3D data -- 8.3.1 Structural analysis - stresses and strains -- 8.3.2 Computational fluid dynamics -- References -- Chapter 9 Estimating paleobiodiversity -- 9.1 Species richness estimation -- 9.1.1 Species richness estimation from single-sample abundance data -- 9.1.2 Species richness estimation from multiple-sample presence-absence data -- 9.2 Rarefaction and related methods -- 9.2.1 Classical rarefaction -- 9.2.2 Unconditional variance rarefaction -- 9.2.3 Shareholder quorum subsampling -- 9.2.4 Sample rarefaction -- 9.3 Diversity curves, origination, and extinction rates -- 9.4 Abundance-based biodiversity indices -- 9.4.1 Confidence intervals for abundance-based diversity indices -- 9.4.2 Rarefaction of abundance-based diversity indices -- 9.5 Taxonomic distinctness -- 9.6 Comparison of diversity indices -- 9.7 Abundance models -- References -- Chapter 10 Paleoecology and paleobiogeography -- 10.1 Paleobiogeography -- 10.2 Paleoecology -- 10.3 Association similarity indices for presence-absence data -- 10.4 Association similarity indices for abundance data -- 10.5 ANOSIM and PerMANOVA -- 10.6 Principal coordinates analysis -- 10.6.1 Metric distance measures and the triangle inequality -- 10.7 Non-metric multidimensional scaling -- 10.8 Correspondence analysis -- 10.9 Detrended correspondence analysis -- 10.10 Seriation -- 10.11 Nonlinear dimensionality reduction -- 10.11.1 ISOMAP -- 10.11.2 Spectral embedding -- 10.11.3 UMAP -- 10.12 Canonical correspondence analysis -- 10.13 Indicator species -- 10.14 Network analysis -- 10.15 Size-frequency and survivorship curves -- 10.16 Case study: Devonian paleobiogeography -- References -- Chapter 11 Calibration - estimating paleoenvironments -- 11.1 Modern analog technique -- 11.2 Weighted averaging.

11.3 Weighted averaging partial least squares -- 11.4 Which calibration method? -- 11.5 Case study: Late Holocene temperature inferred from chironomids -- References -- Chapter 12 Time series analysis -- 12.1 Spectral analysis -- 12.1.1 Discrete Fourier transform -- 12.1.2 Spectral analysis with the REDFIT procedure -- 12.1.3 Spectral analysis with the multitaper method -- 12.1.4 Evolutive spectral analysis -- 12.2 Wavelet analysis -- 12.3 Autocorrelation -- 12.4 Cross-correlation -- 12.5 Runs test -- 12.6 Time Series Trends and Regression -- 12.6.1 Mann-Kendall trend test -- 12.6.2 Regression in the presence of autocorrelation -- 12.7 Smoothing and filtering -- 12.7.1 Moving average -- 12.7.2 Exponential moving average -- 12.7.3 Moving median -- 12.7.4 Non-local means -- 12.7.5 FIR filtering -- 12.7.6 Fitting to models -- References -- Chapter 13 Quantitative biostratigraphy -- 13.1 Zonation of a single section -- 13.1.1 Stratigraphically constrained clustering -- 13.2 Confidence intervals on stratigraphic ranges -- 13.2.1 Parametric confidence intervals on stratigraphic ranges -- 13.2.2 Non-parametric confidence intervals on stratigraphic ranges -- 13.3 Regional and global biostratigraphic correlation -- 13.3.1 Graphic correlation -- 13.3.2 Constrained optimization -- 13.3.3 Ranking and scaling -- 13.3.4 Normality testing and variance analysis -- 13.3.5 Correlation (CASC) -- 13.3.6 Unitary Associations -- 13.3.7 Biostratigraphy by ordination -- 13.3.8 What is the best method for biostratigraphic correlation? -- 13.4 Age models -- 13.4.1 Simple interpolation -- 13.4.2 Simple regression and smoothing -- 13.4.3 Classical age models with Monte Carlo simulation -- 13.4.4 Bayesian age modeling -- References -- Chapter 14 Phylogenetic analysis -- 14.1 A dictionary of cladistics -- 14.2 Parsimony analysis -- 14.3 Characters.