David M. Raup

Mass Extinctions in the Marine Fossil Record

A new compilation of fossil data on invertebrate and vertebrate families indicates that four mass extinctions in the marine realm are statistically distinct from background extinction levels. These four occurred late in the Ordovician, Permian, Triassic, and Cretaceous periods. A fifth extinction event in the Devonian stands out from the background but is not statistically significant in these data. Background extinction rates appear to have declined since Cambrian time, which is consistent with the prediction that optimization of fitness should increase through evolutionary time.

Stochastic Models of Phylogeny and the Evolution of Diversity

Equilibrium models in population biology have demonstrated that accurate predictions of species diversity can be made without reference to particular taxa. We have extended the use of equilibrium models to examine patterns of phyletic diversification in the fossil record. We assume that (1) regions become saturated with respect to the number of taxa that can coexist; and (2) after that limit is reached, rates of speciation and extinction are very similar. Using these minimal constraints, and the standard precepts of evolutionary taxonomy (monophyly), we have generated evolutionary trees by stochastic simulation and classified their lineages into clades. Random processes with minimal constraints yield phyletic trees similar to those based upon the fossil record. Of particular interest are the patterns of clade origination and extinction and of intraclade diversity. For comparison with computer simulations, we present actual clades for the Reptilia. The similarities are striking, but some patterns of the fossil record are not simulated by random processes. For example, the late Cretaceous extinction may represent a fundamentally different type of evolutionary event. The simulation program and its comparison with the real world permits a clearer separation of stochastic and deterministic elements in the evolutionary record.

Effects of sampling standardization on estimates of Phanerozoic marine diversification.

Global diversity curves reflect more than just the number of taxa that have existed through time: they also mirror variation in the nature of the fossil record and the way the record is reported. These sampling effects are best quantified by assembling and analyzing large numbers of locality-specific biotic inventories. Here, we introduce a new database of this kind for the Phanerozoic fossil record of marine invertebrates. We apply four substantially distinct analytical methods that estimate taxonomic diversity by quantifying and correcting for variation through time in the number and nature of inventories. Variation introduced by the use of two dramatically different counting protocols also is explored. We present sampling-standardized diversity estimates for two long intervals that sum to 300 Myr (Middle Ordovician-Carboniferous; Late Jurassic-Paleogene). Our new curves differ considerably from traditional, synoptic curves. For example, some of them imply unexpectedly low late Cretaceous and early Tertiary diversity levels. However, such factors as the current emphasis in the database on North America and Europe still obscure our view of the global history of marine biodiversity. These limitations will be addressed as the database and methods are refined.

Mammalian Evolution and the Great American Interchange

A reciprocal and apparently symmetrical interchange of land mammals between North and South America began about 3 million years ago, after the appearance of the Panamanian land bridge. The number of families of land mammals in South America rose from 32 before the interchange to 39 after it began, and then back to 35 at present. An equivalent number of families experienced a comparable rise and decline in North America during the same interval. These changes in diversity are predicted by the MacArthur-Wilson species equilibrium theory. The greater number of North American genera (24) initially entering South America than the reverse (12) is predicted by the proportions of reservoir genera on the two continents. However, a later imbalance caused by secondary immigrants (those which evolved from initial immigrants) is not expected from equilibrium theory.

Size of the Permo-Triassic Bottleneck and Its Evolutionary Implications

Rarefaction analysis of extinctions in the Late Permian indicates that as many as 96 percent of all marine species may have died out, thus forcing the marine biosphere to pass through a small bottleneck. With such severity of extinction, chance elimination of certain biologic groups would have been probable. Some of the changes in biologic composition observed at the Permo-Triassic boundary may be explained as an evolutionary founder effect that followed the bottleneck.

Species diversity in the Phanerozoic: an interpretation

Species diversity among fossil invertebrates of the Phanerozoic is highly correlated with volume and area of sedimentary rocks. The correlations are statistically significant at the 1% level. The relationship holds even in regions (such as Canada) where the area and volume of rock do not increase through time. These results are interpreted as indicating that the apparent number of species is strongly dependent on sampling and that many of the changes in diversity seen in the Phanerozoic are artifactual. Consequently, there is no compelling evidence for a general increase in the number of invertebrate species from Paleozoic to Recent. This conclusion applies primarily to marine organisms. Diversity may have been in dynamic equilibrium throughout much of this time. A few intervals of the Phanerozoic have consistently fewer invertebrate species than would be predicted from the amount of sedimentary rock available for study. The Silurian, Permian, and Cretaceous stand out in this regard. This may result either from lower than normal diversity during these periods or from an unusual abundance of unfossiliferous rocks (evaporites, red beds, etc.).

Taxonomic diversity estimation using rarefaction

Benthic ecologists have successfully applied rarefaction techniques to the problem of compensating for the effect of sample size on apparent species diversity (= species richness). The same method can be used in studies of diversity at higher taxonomic levels (families and orders) in the fossil record where samples represent world-wide distributions of species or genera over long periods of geologic time. Application of rarefaction to several large samples of post-Paleozoic echinoids (totaling 7,911 species) confirms the utility of the method. Rarefaction shows that the observed increase in the number of echinoid families since the Paleozoic is real in the sense that it cannot be explained solely by the increase in numbers of preserved species. There has been no statistically significant increase in the number of families since mid-Cretaceous, however. At the order level, echinoid diversity may have been nearly constant since late Triassic or early Jurassic.

Theoretical Morphology of the Coiled Shell

In studying the functional significance of the coiled shell, it is important to be able to analyze the types that do not occur in nature as well as those represented by actual species. Both digital and analog computers are useful in constructing accurate pictures of the types that do not occur.

Fossil preservation and the stratigraphic ranges of taxa

The incompleteness of the fossil record hinders the inference of evolutionary rates and patterns. Here, we derive relationships among true taxonomic durations, preservation probability, and observed taxonomic ranges. We use these relationships to estimate original distributions of taxonomic durations, preservation probability, and completeness (proportion of taxa preserved), given only the observed ranges. No data on occurrences within the ranges of taxa are required. When preservation is random and the original distribution of durations is exponential, the inference of durations, preservability, and completeness is exact. However, reasonable approximations are possible given non-exponential duration distributions and temporal and taxonomic variation in preservability. Thus, the approaches we describe have great potential in studies of taphonomy, evolutionary rates and patterns, and genealogy. Analyses of Upper Cambrian-Lower Ordovician trilobite species, Paleozoic crinoid genera, Jurassic bivalve species, and Cenozoic mammal species yield the following results: (1) The preservation probability inferred from stratigraphic ranges alone agrees with that inferred from the analysis of stratigraphic gaps when data on the latter are available. (2) Whereas median durations based on simple tabulations of observed ranges are biased by stratigraphic resolution, our estimates of median duration, extinction rate, and completeness are not biased.(3) The shorter geologic ranges of mammalian species relative to those of bivalves cannot be attributed to a difference in preservation potential. However, we cannot rule out the contribution of taxonomic practice to this difference. (4) In the groups studied, completeness (proportion of species [trilobites, bivalves, mammals] or genera [crinoids] preserved) ranges from 60% to 90%. The higher estimates of completeness at smaller geographic scales support previous suggestions that the incompleteness of the fossil record reflects loss of fossiliferous rock more than failure of species to enter the fossil record in the first place.

Mathematical models of cladogenesis

The evolutionary pattern of speciation and extinction in any biologic group may be described by a variety of mathematical models. These models provide a framework for describing the history of taxonomic diversity (clade shape) and other aspects of larger evolutionary patterns. The simplest model assumes time homogeneity: that is, speciation and extinction probabilities are constant through time and within taxonomic groups. In some cases the homogeneous model provides a good fit to real world paleontological data, but in other cases the model serves only as a null hypothesis that must be rejected before more complex models can be applied. In cases where the homogeneous model does not fit the data, time-inhomogeneous models can be formulated that specify change, regular or episodic, in speciation and extinction probabilities. An appendix provides a list of the most useful equations based on the homogeneous model.