The effects of sampling the fossil record are much greater then one would intuitively expect because most species are rare. That is, most species are represented by extremely few specimens and occur in extremely few collections. In many studies, species which occur only once are considered to be either endemic, stenotopic or of short species duration when in fact these species may not have any of these characteristics but, in fact, are very rare and thus occur in the fossil record very infrequently.

Many areas of paleontological enquiry, from questions of correlation to the characterization of macroevolutionary patterns, require estimates of taxonomic longevities. However, the fossil record is incomplete and biased and, as such, provides an incomplete sampling of true temporal ranges. “It is incomplete because many individuals, species, and higher taxa are not recorded as fossils. It is biased because the probability that a taxon is represented by a fossil is a function of the taxon's morphology, abundance, ecological habitat and spatial distribution, as well as the taxon's age.” (Pease, 1985, p. 272) To what extent do the inadequacies of the fossil record compromise our ability to estimate taxonomic longevities? What analytic methods exist for estimating true longevities from stratigraphic data, or for detecting situations where significant biases may be present? And perhaps most importantly, do analytic methods provide an effective way of dealing with the inadequacies of the fossil record?

I find myself in the position of discussing a rather unfortunate misnomer. In the first place, topics that traditionally have been called “quantitative biostratigraphy” seldom deal with quantities of anything. In the second place, much of “quantitative biostratigraphy” deals more with chronostratigraphy and geochronology than with biostratigraphy. The operational concept is time, not fossil content, although, of course, the fossil content is the starting point. Nonetheless, the phrase “quantitative biostratigraphy” is quite firmly entrenched in the working vocabulary and I will use it here. I will focus on three very different techniques that all involve stratigraphic correlation based on the ranges of fossils.

Taxonomic data analysis has benefited greatly from standardization of systematic and stratigraphic practices. In contrast, the unique features of each group of organisms and the specific nature of many workers' questions have helped make analysis of morphological data relatively less standardized and more idiosyncratic. In addition, paleobiological analysis of morphological data at larger (roughly, suprafamilial) scales seems to have lagged behind analysis, of taxonomic data because of the relative difficulty with which morphological data are collected (both from fossils themselves and from published sources). In this review, I will briefly touch upon some of the areas in which morphological analysis has contributed significantly to our understanding of life's history. Space limitations preclude a thorough treatment of all aspects of morphological analysis, and the decision to omit certain topics, such as functional morphology, is not a reflection of the importance of these fields.

Two quite different conceptual areas are understood today under the umbrella term of theoretical morphology: (1) the mathematical simulation of form, and (2) the analysis of the possible spectra of form via hypothetical morphospace construction. The second concept follows from the first, but has quite different goals.

Each of the perspectives on the fossil record represented by contributions to this short course (and many that are not) can claim a legitimate share of the mantle of “Analytical Paleontology,” earned by combining rigor and insight to provide some unique constraint on our understanding of the history of life. Dare I claim more for phylogeny? Certainly not, if “more” suggests that phylogeny is some final synthesis, complete unto itself, sought by all, and needing no further justification. Such a posture would make phylogenetic inference an end in itself, and, although it may sometimes appear that phylogeneticists have this in mind, I will argue here that it is the service role of phylogenetic analysis that makes it important in shaping our knowledge of evolution. Interpretation of the phylogenetic relationships of the organisms we study has profound implications for virtually all of our other ways of handling data from the fossil (or Recent) record.

The fossil record is replete with patterns. Nearly two centuries of intensive paleontological research has produced a vast number of apparent patterns: stratigraphic and temporal distributions of taxa, paleogeographic distributions, paleoecological relationships, patterns of co-occurrence, morphology and morphological variation, and so forth. Many of these patterns reflect the interplay of important intrinsic processes operating within the biosphere and extrinsic influences acting from without. Others, however, follow from the ordinary processes of everyday life and require no special explanation. How, then, are inquiring paleontologists to separate meaningful patterns from the meaningless? For the most part, the selection of patterns appropriate for further study and explication has remained a matter of subjective judgment.

Many aspects of a clade's history are reflected in its pattern of diversity through time. Evolutionary radiation is reflected in increasing diversity; cessation of radiation is reflected in stabilization of diversity; response to perturbation is reflected in rapid loss and then often recovery of diversity; and disappearance is sometimes reflected in attenuated decay of diversity. Often, it is of interest not only to describe the history of a clade's diversity, but also to investigate its dynamics: how various aspects of the history relate to its rates of origination and extinction and the response of these rates to evolutionary innovation, environmental fluctuation, and cladal interaction.

G. Udny Yule (1924) was perhaps the first to examine the subject of rates of taxonomic evolution mathematically, but George Gaylord Simpson was the first to examine the subject from within the confines of the so-called Modern Synthesis of Biology (Simpson, 1944). In that sense, therefore, Simpson's can be regarded as the first modern study of rates of taxonomic evolution. Although he is almost universally regarded as the catalyst behind the current interest in taxonomic evolutionary rates, it is a remarkable fact that Simpson's aims were almost entirely different from those of current workers. In a very important sense, Simpson's taxonomic rates of evolution were not taxonomic at all, but were morphological, or even more to the point, genetic.

Taxonomic survivorship curves were derived from ecological and biomedical techniques for examining population structure and demographic trends. In simplest form, survivorship curves are graphical representations of the numbers or proportions of taxa that survive specific lengths of time. These curves provide a basis for calculating longevity, extinction rates, and other “life history” attributes of higher taxa. Survivorship curves have also been fruitful for comparative studies of contemporaneous higher taxa (e.g., cohorts), or among higher taxa that existed at different periods of geologic time. Various modifications of the concepts, both theoretical and methodological, have changed the way these curves are used to analyze paleontologic data.

A new statistical term has been cropping up in the literature of paleobiological analysis: bootstrapping. This term, which refers to a relatively new general-purpose statistical method, has appeared in papers on subjects as diverse as rates of morphological change (Kitchell et al., 1987), patterns of morphological difference (between dextral and sinistral snail shells, for instance; Gould et al., 1985), survivorship analysis (Gilinsky, 1988), mass extinctions (Hubbard and Gilinsky, in press), the shapes of diversity paths (Gilinsky and Bambach, 1986), and periodicity of extinction (Connor, 1986). Some other papers do not explicitly mention the word bootstrapping, but nonetheless use methods that are quite similar (e.g., Raup and Sepkoski, 1984). Jennifer A. Kitchell convened an entire symposium on the subject at the Fourth North American Paleontological Convention in 1986. What is bootstrapping, and why is it being so widely applied in analytical paleobiology?

In the past few decades, we have come a long way in making paleobiology more rigorous. We have accumulated an impressive array of quantitative techniques – statistical and otherwise – and these are in use with the full range of paleobiological problems. Also striking is the way the added rigor of our science has spilled over into non-quantitative judgments and interpretations. No longer is the Just-So Story allowed to stand unchallenged. Rather, we respond to these bald assertions and ad hoc theories with: “Can you prove it?” or “Can this be tested?”