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to explain in a simple way why diversity appeared to increase exponentially in the Cretaceous and Cenozoic, toward the end of the Phanerozoic (Sepkoski, 1984). Instead, a model with multiple equilibria was invoked (Sepkoski, 1979, 1984).

More recently, evidence has accumulated that the late Phanerozoic radiation is actually a combined artifact of increased sampling intensity and a related effect called the Pull of the Recent (Foote, 2000a; Alroy et al., 2001, 2008; Peters and Foote, 2001). Thus, the question of diversity equilibrium has been reopened. The strong statistical patterns reported here show that diversity does not increase exponentially without constraints and therefore make it possible to predict the rebound from the current mass extinction in strict quantitative terms. First, however, a series of other major hypotheses concerning mass extinctions and diversity dynamics need to be addressed.

Pulsed Turnover Rates

Based on Sepkoski’s classic family- and genus-level data (Sepkoski, 1984, 1996), it has been suggested that turnover comes in large pulses that coincide with interval boundaries (Foote, 1994b, 2005). If true, this result has the profound implication that even background turnover is largely forced either by perturbations, such as eruptions, sea level and climate changes, and bolide impacts (Raup, 1992), or by episodic ecological interactions, such as cascading extinctions (Plotnick and McKinney, 1993). If turnover is not coupled with boundaries, an alternative hypothesis is that background extinction is effectively stochastic and results from the never-ending process of competition over a fixed or slowly changing resource base, i.e., the Red Queen hypothesis (Van Valen, 1973).

The pulsed turnover hypothesis implies that per-million year (Myr) rates will correlate inversely with interval lengths because the assumption that turnover is continuous is violated (Raup and Sepkoski, 1984). There is such a relationship for per-Myr extinction rates (Spearman rank-order correlation ρ = −0.409, P < 0.005). However, the same correlation does not exist in the unstandardized rates [ρ = −0.021, not significant (n.s.)] and is not significantly different from a distribution generated by bootstrapping (i.e., correlating raw rates with ratios of themselves to randomly drawn bin lengths). Thus, the relationship can be explained as resulting from random variation in the bin lengths because of random errors in the underlying timescale. The same pattern is seen with originations, i.e., first appearances of genera. Origination rates correlate negatively with bin length if they are standardized (ρ = −0.408, P = 0.005) but otherwise do not (ρ = 0.155, n.s.). These results, however, do not particularly endorse the Red Queen hypothesis because rates are still quite variable, as discussed below.

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