Extinction rate

FIGURE 11.3 Key relationships between variables that govern marine invertebrate diversity dynamics on the Phanerozoic scale. Paleozoic points (black diamonds) and Meso-Cenozoic points (gray circles) show the same patterns in each case, and the values including the Permo-Triassic mass extinction (triangle) are consistent with the trends. (A) Correlation between diversity in one interval and extinction rates in the next interval. (B) Correlation between extinction rates in one interval and origination rates in the next.

Causal Model

Obviously, origination rates cannot respond directly to a memory of extinction rates in the far past. Ghosts do not speak, so their empty niches must somehow beckon. The problem is how to reproduce such a process without making origination density-dependent, which cannot be accomplished in any way with conventional logistic models (Sepkoski, 1978), simple lattice-based niche incumbency models (Walker and Valentine,

218 / John Alroy

1984), or percolation models in which all empty cells are filled immediately by origination (Plotnick and McKinney, 1993).

The only way I have been able to predict all of the key relationships is with a cell model in which the number of cells is effectively infinite, underlying origination rates follow a random walk, new species can only fall in unoccupied neighboring cells, and underlying extinction rates are some joint function of white noise and the overall current number of species. Any other combination of factors seems to either create density dependence of origination rates or remove one or both of the two key correlations.

In plain English, this model depends on direct competition to regulate both speciation and extinction. The former process is basically niche incumbency (Walker and Valentine, 1984) with limited rates of adaptation, local interactions, and no fixed number of niches, and the latter process is a routine logistic function (Sepkoski, 1978). Competition is the opposite of the interdependency built into percolation and self-organization critical-ity models (Plotnick and McKinney, 1993; Sneppen et al., 1995; Solé and Bascompte, 1996; Solé et al., 1996). Meanwhile, the assumption of slowly changing origination rates is consistent with slow sorting of large clades that have distinctive turnover rates (Gilinsky, 1994), whereas adding a high-frequency random component to extinction rates is consistent with evidence that the Permo-Triassic and Cretaceous-Tertiary mass extinctions involved unpredictable physical forcing mechanisms (Erwin, 2001). The overall scenario may seem restrictively complex, but at least complexity maximizes testability. Perhaps a simpler theory can be found that predicts the correlations, but even this moderately rich one fails to cleanly predict the apparent nonlinearity of the origination rate response to mass extinction (Fig. 11.3B).

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