A DECONSTRUCTION OF SEPKOSKI'S PHANEROZOIC MARINE EVOLUTIONARY FAUNAS BASED ON NEW DIVERSITY ESTIMATES

Paleobiologists have long been faced with either using raw diversity counts biased by variation in sample size or flattening those counts by imposing uniform sample size quotas. Item quota methods such as rarefaction undersample when richness rises because they effectively draw only those taxa with a fixed minimum frequency, and adding more taxa lowers the relative frequency of the existing ones. We need to recast the problem in terms of frequency distribution coverage: if each taxon has a share of the underlying distribution, then the sum of the shares represented by the taxa in a subsample is the coverage. The new shareholder quorum subsampling method (SQ) involves drawing collections and crediting shares up to a fixed coverage level (quorum). Unlike rarefaction, SQ is perfectly accurate as long as additions and subtractions to the abundance distribution are random (as is easily shown by simulation). SQ produces a global Phanerozoic marine invertebrate diversity curve from the Paleobiology Database that is similar in many important ways to a recently published one, with no large difference between peak early Paleozoic and Cenozoic diversity. However, it does have a much higher amplitude. Analyzing all the major taxonomic groups separately and then summing their counts recovers the same high-amplitude global pattern (a result that could not have been obtained with rarefaction because its quotas are incommensurate across data sets). Multivariate analysis of the separate curves identifies some associations that resemble Sepkoski's three evolutionary faunas, but there are large differences between members of the same fauna. For example, the "Modern" groups Bryozoa and Gastropoda underwent large Cretaceous radiations but the associated class Bivalvia increased slowly throughout the entire post-Paleozoic. A semiparametric maximum likelihood method demonstrates that density dependent or otherwise complex dynamic models fit the curves for most major groups much better than either random walks or simple exponential growth coefficients. Coupling of curves does not improve the fits. Thus, it appears that overall tracking of a clearly visible but variable carrying capacity emerges from simpler but still strongly logistic dynamics that operate at lower taxonomic ranks.