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MATERIALS AND METHODS

The data consist of genus counts for 48 intervals, averaging 11.0 Myr and ranging from the traditional Early Cambrian through the Neogene. These temporal bins sometimes correspond to marine stages, but often comprise sets of neighboring stages lumped to minimize variance in duration. The counts are derived from 281,491 occurrences of 18,541 genera within 42,627 fossil collections that have been sampling standardized by randomly drawing entire collections up to a quota of 15,800 specimens per bin. When the specimen count for an individual collection is not directly available, it is estimated from the occurrence count by examining rarefaction patterns for other collections in the same bin. Each collection’s sampling probability is inversely weighted by its specimen count to avoid having a few large collections from a narrow range of environments and geographic areas dominate the analysis. Collections from entirely unlithified sediments are excluded. Details concerning the data and methods are reported in Alroy et al. (2008).

A large number of equations have been proposed to quantify origination and extinction, using paleontological data (Foote, 1994b, 2005). Traditional measures consisted of simple first and last appearance counts that sometimes were divided by some form of a diversity count to create a proportion. Proportions are biologically meaningful if they describe a sudden turnover event, but a more realistic general approach is to view turnover as an exponential decay process (Raup, 1985) and, therefore, compute instantaneous rates that are equivalent to decay constants (Alroy, 2000, in press; Foote, 2000a,b).

The problem with all existing equations is that they were developed to handle traditional compilations that only record first and last appearances. Simple range data are subject to edge effects, such as the Signor–Lipps effect and Pull of the Recent, that create systematic smearing of rates backward before a large extinction begins, smearing of rates forward after a burst of origination, and drops in extinction rates before a large sampling spike such as the Recent (Foote, 2000a). For example, backward smearing is clearly visible in family-level data on both marine and continental organisms (Benton, 1995), and the Pull of the Recent seems to amplify the downward trend in Sepkoski’s genus-level extinction rates (Foote, 2000a; Peters, 2006).

Two new continuous rate equations (Alroy, in press) remove the edge effects by ignoring ranges and focusing instead on occurrence data that show which fossil taxa are actually sampled in which time intervals. These methods are only made possible by the existence of occurrence-based relational databases, and could not have been applied to the Phanerozoic marine record before the development of the Paleobiology Database (Alroy et al., 2001). The new rates depend on five fundamental counts: taxa



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