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Introduction

1.1 The nature of paleontological data

Paleontology is a diverse field, with many different types of data and a corresponding variety of analytical methods. For example, the types of data used in ecological, morphological, and phylogenetic analyses are often quite different in both form and quality. Data relevant to the investigation of morphological variation in Ordovician brachiopods are quite different from those gathered from Neogene mammal‐dominated assemblages for paleoecological analyses. Nevertheless, there is a surprising commonality of techniques that can be implemented in the investigation of such apparently contrasting data sets.

1.1.1 Univariate measurements

Perhaps the simplest type of data is straightforward, continuous measurements such as length or width. Such measurements are typically made on a number of specimens in one or more samples, commonly from collections from different localities or species. Typically, the investigator is interested in characterizing, and subsequently analyzing, the sets of measurements, and comparing two or more samples to see how they differ. Measurements in units of arbitrary origin (such as temperature on the Celsius or Fahrenheit scales) are known as interval data, while measurements in units of a fixed origin (such as distance and mass) are called ratio data. Methods for interval and ratio data are presented in chapter 4.

1.1.2 Bivariate measurements

Also relatively easy to handle are bivariate interval or ratio measurements on a number of specimens. Each specimen is then characterized by a pair of values, such as both length and width of a given fossil. In addition to comparing samples, we will then typically wish to know if and how the two variables are interrelated. Do they, for example, fit on a straight line, indicating a static (isometric) mode of growth or do they exhibit more complex (anisometric) growth patterns? Bivariate data are discussed in chapters 4 and 6.

1.1.3 Multivariate morphometric measurements

The next step in increasing complexity is multivariate morphometric data, involving multiple variables such as length, width, thickness, and, say, distance between ribs (Fig. 1.1). We may wish to investigate the structure of such data and whether two or more samples are different. Multivariate data sets can be difficult to visualize, and special methods have been devised to emphasize any inherent structure. Special types of multivariate morphometric data include digitized outlines and the coordinates of landmarks. Multivariate methods useful for morphometrics are discussed in chapters 5 and 6.

Figure 1.1 Typical set of measurements made on conjoined valves of the living brachiopod Terebratulina from the west coast of Scotland. A: Measurements of the length of ventral (LENPV) and dorsal (LENBV) valves, together with hinge (HINWI) and maximum (MAXWI) widths. B: Thickness (THICK). C: Position of maximum width (POSMW) and numbers of ribs per mm at, say, 2.5 mm (RAT25) and 5.0 mm (RAT50) from the posterior margin can form the basis for univariate, bivariate, and multivariate analysis of the morphological features of this brachiopod genus.

1.1.4 Character matrices for phylogenetic analysis

A special type of morphological (or molecular) data is the character matrix for phylogenetic analysis (cladistics). In such a matrix, taxa are conventionally entered in rows and characters in columns. The state of each character for each taxon is typically coded with an integer. Character matrices and their analyses are treated in chapter 14.

1.1.5 Paleoecology and paleobiogeography – taxa in samples

In paleoecology and paleobiogeography, the most common data type consists of taxonomic counts at different localities or stratigraphic levels. Such data are typically given in an abundance matrix, either with taxa in rows and samples in columns or vice versa. Each cell contains a specimen count (or abundance) for a particular taxon in a particular sample (Table 1.1).

In some cases, we do not have specimen counts available; instead, we only know whether a taxon is present or absent in the sample. Such information is specified in a presence‐absence table, where absences are typically coded with zeros and presences with ones. This type of binary data may be more relevant to biogeographic or stratigraphic analyses, where each taxon is weighted equally.

Typical questions include whether the samples are significantly different from each other, whether the biodiversity is different, whether there are well‐separated groups of localities, or any indication of an environmental gradient. Methods for analyzing taxa‐in‐samples data are discussed in chapters 5, 9, and 10 (Fig. 1.2).

1.1.6 Time series

A time series is a sequence of values through time. Paleontological time series include diversity curves, geochemical data from fossils through time, and thicknesses of bands from a series of growth increments. For such a time series, we may wish to investigate whether there is any trend or periodicity. Some appropriate methods are given in chapter 12.

1.1.7 Biostratigraphic data

Biostratigraphy is the correlation and zonation of sedimentary strata based on fossils. Biostratigraphic data are mainly of two different types. The first is a single table with localities in rows and events (such as the first or last appearance of a species) in columns. Each cell of the table contains the stratigraphic level, in meters, feet, or ranked order, of a particular event at a particular locality (Table 1.2).

Table 1.1 Example of an abundance matrix.

Figure 1.2 A muddy‐sand community from the Early Jurassic. Community reconstruction is based on the presence of and partly the relative abundance of taxa.

After Benton and Harper (2020), modified from McKerrow (1978).

Table 1.2 Example of an event table.

FAD, first appearance datum.

Such event tables form the input to biostratigraphic methods such as ranking‐scaling and constrained optimization.

The second main type of biostratigraphic data consists of a single presence‐absence matrix for each locality. Within each table, the samples are sorted according to stratigraphic level. Such data are used in the method of unitary associations.

Quantitative biostratigraphy is the subject of chapter 13 (Fig. 1.3).

Figure 1.3 Range chart of fossils, mainly graptolites, through Darriwilian and Sandbian (Middle and Upper Ordovician) strata in southern Sweden. The boundary between the two stages (green horizontal line) is fixed to coincide with the first appearance of the graptolite Nemagraptus gracilis.

Harper et al. (2022)/Geological Society of London.

1.2 Advantages and pitfalls of paleontological data analysis

During the last few decades, paleontology has comfortably joined the other sciences in its emphasis on quantitative methodologies. Statistical and explorative analytical methods, most of them depending on computers for their practical implementation, are now used in all branches of paleontology, from systematics and morphology to paleoecology and biostratigraphy. Over the last 100 years, techniques have evolved with available hardware, from the longhand calculations of the early twentieth century, through the time‐consuming mainframe implementation of algorithms in the mid‐twentieth century to the microcomputer revolution of the late twentieth century.

In general terms, there are three main components to any paleontological investigation. A detailed description of a taxon or community is followed by an analysis of the data (this may involve a look at ontogenetic or size‐independent shape variation in a taxon or the population dynamics and structure of a community) with finally a comparison with other relevant and usually similar paleontological units. Numerical techniques have greatly enhanced the description, analysis, and comparison of fossil taxa and assemblages. Scientific hypotheses can be more clearly framed and statistically tested with numerical data....