A kinetic model of Phanerozoic taxonomic diversity. III. Post-Paleozoic families and mass extinctions

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.