A comprehensive, but simple-to-use software package for executing a range of standard numerical analysis and operations used in quantitative paleontology has been developed. The program, called PAST (PAleontological STatistics), runs on standard Windows computers and is available free of charge. PAST integrates spreadsheet-type data entry with univariate and multivariate statistics, curve fitting, timeseries analysis, data plotting, and simple phylogenetic analysis. Many of the functions are specific to paleontology and ecology, and these functions are not found in standard, more extensive, statistical packages. PAST also includes fourteen case studies (data files and exercises) illustrating use of the program for paleontological problems, making it a complete educational package for courses in quantitative methods.

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Past: paleontological statistical software package for education and data analysis

PAST: paleontological statistics software package for education and data analysis version 2.09

The International Commission on Stratigraphy (ICS) has a long tradition of producing international charts that communicate higher-order divisions of geological time and actual knowledge on the absolute numerical ages of their boundaries. The primary objective of ICS is to define precisely a global standard set of time-correlative units (Systems, Series, and Stages) for stratigraphic successions worldwide. These units are, in turn, the basis for the Periods, Epochs and Ages of the Geological Time Scale. Setting an international global standard is fundamental for expressing geological knowledge. It is also of considerable pragmatic importance as it provides the framework through which regional-scale higher-resolution divisions can be linked, equated and collated. This is a status update on the International Chronostratigraphic Chart and the ICS website www.stratigraphy.org.

The ICS International Chronostratigraphic Chart

Geological atlas of western and central Europe

Soils and other unconsolidated deposits in the northern circumpolar permafrost region store large amounts of soil organic carbon (SOC). This SOC is potentially vulnerable to remobilization following soil warming and permafrost thaw, but SOC stock estimates were poorly constrained and quantitative error estimates were lacking. This study presents revised estimates of permafrost SOC stocks, including quantitative uncertainty estimates, in the 0–3 m depth range in soils as well as for sediments deeper than 3 m in deltaic deposits of major rivers and in the Yedoma region of Siberia and Alaska. Revised estimates are based on significantly larger databases compared to previous studies. Despite this there is evidence of significant remaining regional data gaps. Estimates remain particularly poorly constrained for soils in the High Arctic region and physiographic regions with thin sedimentary overburden (mountains, highlands and plateaus) as well as for deposits below 3 m depth in deltas and the Yedoma region. While some components of the revised SOC stocks are similar in magnitude to those previously reported for this region, there are substantial differences in other components, including the fraction of perennially frozen SOC. Upscaled based on regional soil maps, estimated permafrost region SOC stocks are 217 ± 12 and 472 ± 27 Pg for the 0–0.3 and 0–1 m soil depths, respectively (±95% confidence intervals). Storage of SOC in 0–3 m of soils is estimated to 1035 ± 150 Pg. Of this, 34 ± 16 Pg C is stored in poorly developed soils of the High Arctic. Based on generalized calculations, storage of SOC below 3 m of surface soils in deltaic alluvium of major Arctic rivers is estimated as 91 ± 52 Pg. In the Yedoma region, estimated SOC stocks below 3 m depth are 181 ± 54 Pg, of which 74 ± 20 Pg is stored in intact Yedoma (late Pleistocene ice- and organic-rich silty sediments) with the remainder in refrozen thermokarst deposits. Total estimated SOC storage for the permafrost region is ∼1300 Pg with an uncertainty range of ∼1100 to 1500 Pg. Of this, ∼500 Pg is in non-permafrost soils, seasonally thawed in the active layer or in deeper taliks, while ∼800 Pg is perennially frozen. This represents a substantial ∼300 Pg lowering of the estimated perennially frozen SOC stock compared to previous estimates.

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Estimated stocks of circumpolar permafrost carbon with quantified uncertainty ranges and identified data gaps

Preface. Acknowledgments. 1 Introduction. 1.1 The nature of paleontological data. 1.2 Advantages and pitfalls of paleontological data analysis. 1.3 Software. 2 Basic statistical methods. 2.1 Introduction. 2.2 Statistical distributions. 2.3 Shapiro-Wilk test for normal distribution. 2.4 F test for equality of variances. 2.5 Student's t test and Welch test for equality of means. 2.6 Mann-Whitney U test for equality of medians. 2.7 Kolmogorov-Smirnov test for equality of distributions. 2.8 Permutation and resampling. 2.9 One-way ANOVA. 2.10 Kruskal-Wallis test. 2.11 Linear correlation. 2.12 Non-parametric tests for correlation. 2.13 Linear regression. 2.14 Reduced major axis regression. 2.15 Nonlinear curve fitting. 2.16 Chi-square test. 3 Introduction to multivariate data analysis. 3.1 Approaches to multivariate data analysis. 3.2 Multivariate distributions. 3.3 Parametric multivariate tests. 3.4 Non-parametric multivariate tests. 3.5 Hierarchical cluster analysis. 3.5 K-means cluster analysis. 4 Morphometrics. 4.1 Introduction. 4.2 The allometric equation. 4.3 Principal components analysis (PCA). 4.4 Multivariate allometry. 4.5 Discriminant analysis for two groups. 4.6 Canonical variate analysis (CVA). 4.7 MANOVA. 4.8 Fourier shape analysis. 4.9 Elliptic Fourier analysis. 4.10 Eigenshape analysis. 4.11 Landmarks and size measures. 4.12 Procrustean fitting. 4.13 PCA of landmark data. 4.14 Thin-plate spline deformations. 4.15 Principal and partial warps. 4.16 Relative warps. 4.17 Regression of partial warp scores. 4.18 Disparity measures. 4.19 Point distribution statistics. 4.20 Directional statistics. Case study: The ontogeny of a Silurian trilobite. 5 Phylogenetic analysis. 5.1 Introduction. 5.2 Characters. 5.3 Parsimony analysis. 5.4 Character state reconstruction. 5.5 Evaluation of characters and tree topologies. 5.6 Consensus trees. 5.7 Consistency index. 5.8 Retention index. 5.9 Bootstrapping. 5.10 Bremer support. 5.11 Stratigraphical congruency indices. 5.12 Phylogenetic analysis with Maximum Likelihood. Case study: The systematics of heterosporous ferns. 6 Paleobiogeography and paleoecology. 6.1 Introduction. 6.2 Diversity indices. 6.3 Taxonomic distinctness. 6.4 Comparison of diversity indices. 6.5 Abundance models. 6.6 Rarefaction. 6.7 Diversity curves. 6.8 Size-frequency and survivorship curves. 6.9 Association similarity indices for presence/absence data. 6.10 Association similarity indices for abundance data. 6.11 ANOSIM and NPMANOVA. 6.12 Correspondence analysis. 6.13 Principal Coordinates analysis (PCO). 6.14 Non-metric Multidimensional Scaling (NMDS). 6.15 Seriation. Case study: Ashgill brachiopod paleocommunities from East China. 7 Time series analysis. 7.1 Introduction. 7.2 Spectral analysis. 7.3 Autocorrelation. 7.4 Cross-correlation. 7.5 Wavelet analysis. 7.6 Smoothing and filtering. 7.7 Runs test. Case study: Sepkoski's generic diversity curve for the Phanerozoic. 8 Quantitative biostratigraphy. 8.1 Introduction. 8.2 Parametric confidence intervals on stratigraphic ranges. 8.3 Non-parametric confidence intervals on stratigraphic ranges. 8.4 Graphic correlation. 8.5 Constrained optimisation. 8.6 Ranking and scaling. 8.7 Unitary Associations. 8.8 Biostratigraphy by ordination. 8.9 What is the best method for quantitative biostratigraphy?. Appendix A: Plotting techniques. Appendix B: Mathematical concepts and notation. References. Index

Paleontological Data Analysis

Rapid magma emplacement in the Karoo Large Igneous Province

Only the GSSPs for the Bashkirian (base of the Pennsylvanian), Visean and Tournaisian (base of the Mississippian) have been formalized, although the latter now has complications.

The Carboniferous Period

The supercontinent Pangea completes its assembly and moves north during the Permian. The 47-million-year-long period begins with a great ice age and ends with the Earth’s greatest extinction. The interval is characterized by icehouse to greenhouse climate transition, major evaporites, changes in internal and external carbonate invertebrate skeletons, major diversification of fusulinacean foraminifers, ammonoids, bryozoans, and brachiopods. It concludes with the major end-Permian extinction of fusulinacean foraminifers, trilobites, rugose and tabulate corals, blastoids, acanthodians, placoderms, and pelycosaurs and dramatic reduction of bryozoans, brachiopods, ammonoids, sharks, bony fish, crinoids, and land vertebrates.

Øyvind Hammer

Papers

Past: paleontological statistical software package for education and data analysis

Paleontological Data Analysis

Rapid magma emplacement in the Karoo Large Igneous Province

The Carboniferous Period

The Permian Period