What is the best way to measure extinction? A reflection from the palaeobotanical record

A three-phase kinetic model with time-specific perturbations is used to describe large-scale patterns in the diversification of Phanerozoic marine families. The basic model assumes that the Cambrian, Paleozoic, and Modern evolutionary faunas each diversified logistically as a consequence of early exponential growth and of later slowing of growth as the ecosystems became filled; it also assumes interaction among the evolutionary faunas such that expansion of the combined diversities of all three faunas above any single fauna's equilibrium caused that fauna's diversity to begin to decline. This basic model adequately describes the diversification of the evolutionary faunas through the Paleozoic Era as well as the asymmetrical rise and fall of background extinction rates through the entire Phanerozoic. Declines in diversity and changes in faunal dominance associated with mass extinctions can be accommodated in the model with short-term accelerations in extinction rates or declines in equilibria. Such accelerations, or perturbations, cause diversity to decline exponentially and then to rebound sigmoidally following release. The amount of decline is dependent on the magnitude and duration of the perturbation, the timing of the perturbation with respect to the diversification of the system, and the system's initial per-taxon rates of diversification and turnover. When applied to the three-phase model, such perturbations describe the changes in diversity and faunal dominance during and after major mass extinctions, the long-term rise in total diversity following the Late Permian and Norian mass extinctions, and the peculiar diversification and then decline of the remnants of the Paleozoic fauna during the Mesozoic and Cenozoic Eras. The good fit of this model to data on Phanerozoic familial diversity suggests that many of the large-scale patterns of diversification seen in the marine fossil record of animal families are simple consequences of nonlinear interrelationships among a small number of parameters that are intrinsic to the evolutionary faunas and are largely (but not completely) invariant through time.

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.