Paleontological Data Analysis

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
	14.4 Algorithms for Parsimony Analysis
		14.4.1 Exhaustive search
		14.4.2 Branch and bound
		14.4.3 Heuristic algorithms
	14.5 Character state reconstruction
	14.6 Evaluation of characters and trees
		14.6.1 Consensus tree
		14.6.2 Consistency index
		14.6.3 Retention Index
		14.6.4 Bootstrapping
		14.6.5 Bremer support
		14.6.6 Stratigraphic congruency indices
	14.7 Case study: the systematics of heterosporous ferns
		14.7.1 Parsimony analysis
		14.7.2 Comparison with the fossil record
	14.8 Other methods for phylogenetic analysis
		14.8.1 Phylogenetic analysis with maximum likelihood
		14.8.2 Bayesian phylogenetic analysis
		14.8.3 Phylogenetic analysis with distance methods
	14.9 Phylogenetic Comparative Methods
		14.9.1 Phylogenetic independent contrasts
		14.9.2 Phylogenetic generalized least squares
		14.9.3 PGLS and phylogenetic signal
	References
Index
EULA