Paleontological Data Analysis

Paleontological Data Analysis......Page 5
Contents......Page 7
Preface......Page 11
Acknowledgments......Page 13
1.1 The nature of paleontological data......Page 15
1.2 Advantages and pitfalls of paleontological data analysis......Page 18
1.3 Software......Page 21
2.1 Introduction......Page 22
2.2 Statistical distributions......Page 26
2.3 Shapiro–Wilk test for normal distribution......Page 33
2.4 F test for equality of variances......Page 36
2.5 Student\'s t test and Welch test for the equality of means......Page 37
2.6 Mann–Whitney U test for equality of medians......Page 41
2.7 Kolmogorov–Smirnov test for equality of distribution......Page 44
2.8 Bootstrapping and permutation......Page 47
2.9 One-way ANOVA......Page 49
2.10 Kruskal–Wallis test......Page 53
2.11 Linear correlation......Page 56
2.12 Non-parametric tests for correlation......Page 60
2.13 Linear regression......Page 62
2.14 Reduced major axis regression......Page 67
2.15 Chi-square test......Page 71
3.1 Approaches to multivariate data analysis......Page 75
3.2 Multivariate distributions......Page 76
3.3 Parametric multivariate tests – Hotelling\'s T 2......Page 77
3.4 Non-parametric multivariate tests – permutation test......Page 80
3.5 Hierarchical cluster analysis......Page 81
3.6 K-means cluster analysis......Page 89
4.1 Introduction......Page 92
4.2 The allometric equation......Page 93
4.3 Principal components analysis (PCA)......Page 97
4.4 Multivariate allometry......Page 105
4.5 Discriminant analysis for two groups......Page 110
4.6 Canonical variate analysis (CVA)......Page 114
4.7 MANOVA......Page 117
4.8 Fourier shape analysis in polar coordinates......Page 119
4.9 Elliptic Fourier analysis......Page 122
4.10 Eigenshape analysis......Page 126
4.11 Landmarks and size measures......Page 129
4.12 Procrustes fitting......Page 131
4.13 PCA of landmark data......Page 135
4.14 Thin-plate spline deformations......Page 136
4.15 Principal and partial warps......Page 142
4.16 Relative warps......Page 146
4.17 Regression of warp scores......Page 148
4.18 Disparity measures and morphospaces......Page 150
4.19 Point distribution statistics......Page 155
4.20 Directional statistics......Page 159
Case study: the ontogeny of a Silurian trilobite......Page 162
5.1 Introduction......Page 171
5.2 Characters......Page 174
5.3 Parsimony analysis......Page 175
5.4 Character state reconstruction......Page 180
5.6 Consensus tree......Page 182
5.7 Consistency index......Page 184
5.8 Retention index......Page 185
5.9 Bootstrapping......Page 186
5.10 Bremer support......Page 188
5.11 Stratigraphic congruency indices......Page 189
5.12 Phylogenetic analysis with maximum likelihood......Page 192
Case study: the systematics of heterosporous ferns......Page 193
6.1 Introduction......Page 197
6.2 Biodiversity indices......Page 200
6.3 Taxonomic distinctness......Page 207
6.4 Comparison of diversity indices......Page 210
6.5 Abundance models......Page 212
6.6 Rarefaction......Page 216
6.7 Diversity curves......Page 220
6.8 Size–frequency and survivorship curves......Page 222
6.9 Association similarity indices for presence/absence data......Page 225
6.10 Association similarity indices for abundance data......Page 230
6.11 ANOSIM and NPMANOVA......Page 235
6.12 Correspondence analysis......Page 237
6.13 Principal coordinates analysis (PCO)......Page 247
6.14 Non-metric multidimensional scaling (NMDS)......Page 250
6.15 Seriation......Page 254
Case study: Ashgill brachiopod-dominated paleocommunities from East China......Page 258
7.1 Introduction......Page 268
7.2 Spectral analysis......Page 269
7.3 Autocorrelation......Page 274
7.4 Cross-correlation......Page 277
7.5 Wavelet analysis......Page 280
7.6 Smoothing and filtering......Page 283
7.7 Runs test......Page 285
Case study: Sepkoski\'s generic diversity curve for the Phanerozoic......Page 287
8.1 Introduction......Page 293
8.2 Parametric confidence intervals on stratigraphic ranges......Page 295
8.3 Non-parametric confidence intervals on stratigraphic ranges......Page 297
8.4 Graphic correlation......Page 300
8.5 Constrained optimization......Page 305
8.6 Ranking and scaling......Page 312
8.7 Unitary associations......Page 320
8.8 Biostratigraphy by ordination......Page 328
8.9 What is the best method for quantitative biostratigraphy?......Page 329
Appendix A: Plotting techniques......Page 331
Appendix B: Mathematical concepts and notation......Page 342
References......Page 347
Index......Page 359