NEW STATISTICAL METHODS SUGGEST GREATER SEVERITY OF THE CRETACEOUS-PALEOGENE MASS EXTINCTION AND FASTER RECOVERIES FROM IT

All research on mass extinctions is premised on accurate estimates of extinction percentages and recovery rates. Standard methods greatly depress these estimates when applied to marine invertebrate data for the Phanerozoic in general and the Cretaceous-Paleogene boundary in particular. The simplest extinction metric, last appearances in an interval divided by all taxa ranging through it, suggests a 34% K-Pg mass extinction based on unstandardized Paleobiology Database ranges. The figure is somewhat higher for bivalves and lower for gastropods. About the same numbers are obtained with Foote's more sophisticated equation, which was designed to avoid sampling artifacts. However, a value of about 50% is produced by the three timer equation 1 - 2T/(3T Ps) regardless of standardization. This equation not only excludes the Signor-Lipps effect and the Pull of the Recent but builds in a correction term (Ps) for failure to resample survivors. Extinction intensities vary greatly by region: in the northeastern Atlantic they are 52 and 32% for bivalves and gastropods but in the northwestern Atlantic they are 63 and 73%. Recovery rates are also greatly compromised by sampling and edge effects. Range-based counts for the North Atlantic suggest a small net decrease in bivalve richness and small net increase in gastropod richness between the Maastrichtian and Danian. Rarefaction, the most common sampling standardization method, suggests a small net increase for bivalves and a doubling for gastropods. By contrast, shareholder quorum subsampling estimates that bivalve richness rose by about 35% and gastropod richness tripled. Simple theory and simulation analyses show that SQS accurately reflects changes in taxon pool sizes, and empirical data show that it yields the same result regardless of sampling levels. The reason is that SQS samples harder when richness is high. Rarefaction underestimates changes in pool size and is strongly dependent on quota levels because it always samples uniformly on the flawed theory that equal sampling is accurate sampling. 3T equations and SQS change our picture of diversification and extinction so greatly that paleobiologists must reconsider all previously published studies of diversity dynamics, regardless of whether they involved age ranges or nominally standardized counts.