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Figure 20.5 Sepkoski's three-phase coupled logistic model for diversification of animal life in the sea. (a) The family-level diversification curve for marine animals, showing the three evolutionary "faunas" from Fig. 20.4, each shaded differently. Numbers I to V are the five big mass extinctions, in sequence from left to right, Late Ordovician, Late Devonian, end-Permian, Late Triassic and Quaternary-Cretaceous. (b) The handover from the Cambrian to the Paleozoic "fauna" involved a shift in equilibrium diversity (D); equilibrium diversity is achieved when origination (ks) and extinction (ke) rates match. (c, d) The coupled logistic model gives a simple representation of the broad outlines of the progress of the three evolutionary "faunas" 1, 2 and 3 (c), and perturbations, shown by vertical arrows, may be added to correspond to the mass extinctions (d). (Based on information in Sepkoski 1979, 1984.)

Figure 20.5 Sepkoski's three-phase coupled logistic model for diversification of animal life in the sea. (a) The family-level diversification curve for marine animals, showing the three evolutionary "faunas" from Fig. 20.4, each shaded differently. Numbers I to V are the five big mass extinctions, in sequence from left to right, Late Ordovician, Late Devonian, end-Permian, Late Triassic and Quaternary-Cretaceous. (b) The handover from the Cambrian to the Paleozoic "fauna" involved a shift in equilibrium diversity (D); equilibrium diversity is achieved when origination (ks) and extinction (ke) rates match. (c, d) The coupled logistic model gives a simple representation of the broad outlines of the progress of the three evolutionary "faunas" 1, 2 and 3 (c), and perturbations, shown by vertical arrows, may be added to correspond to the mass extinctions (d). (Based on information in Sepkoski 1979, 1984.)

models of the diversification of life. The first four speak in favor of equilibrium, the last four more in favor of expansion.

1 There was an evolutionary explosion of marine animals during the Early Cambrian, and diversification rates slowed after this initial exponential rise. This strongly suggests a logistic/equilibrium explanation.

2 There were rapid rebounds after mass extinctions, in which local and global diversity recovered to pre-extinction levels during relatively short spans of time (see Fig. 20.5). This suggests that ecospace that had been vacated as a result of an extinction event could refill at a higher rate than entry into new ecospace. Such rapid rebounds suggest a logistic/equilibrium model of diversification.

3 Late phases of diversification cycles are associated with declining rates of origination and increasing rates of extinction, as the logistic curve approaches the equilibrium level. The marine record generally confirms such expectations - evidence for the logistic model.

4 The Paleozoic plateau in marine animal diversity is strong evidence for equilibrium. But note that the plateau appears clearly only in the family-level data compilation. At generic level, the plateau is lower and appears less regular; perhaps it disappears entirely at species level. Could the Paleozoic plateau be an artifact of the level of analysis (Benton 1997)?

5 There is debate among the supporters of equilibrium models about how many equilibria there have been. Sepkoski favored three (see Box 20.2), but Raup (1972) and Alroy et al. (2001) suggest just one. A single equilibrium level is easier to understand in terms of a global equilibrium model; otherwise each equilibrium level has to be justified as representing a complete overhaul of the evolutionary and ecological world. How many such equilibrium levels can be allowed before we accept that the pattern is really one of continual expansion (Benton 1997)?

6 There is no evidence for a global carrying capacity for species, and so a fundamental assumption behind the equilibrium model has yet to be demonstrated independently.

7 The radiation of life on land, and of certain major marine and continental clades, appears to have followed an exponential pattern, and there is no sign of slowing down in the rate of increase, nor of the occurrence of any equilibrium levels. These radiations strongly suggest patterns of expansion.

8 The Modern "fauna" radiated dramatically over the last 100 myr and shows no sign of reaching an equilibrium level; this is a weakness of any equilibrium model since the last 100 myr represent the best-sampled part of the fossil record and might be expected to show something closer to the biological pattern than earlier records.

Perhaps the best conclusion is that there is no point in seeking an overarching mathematical model to explain the diversification of life. After all, evolution happens at the level of species, and species react and interact in ever-changing ways. As environments change, families and larger groups come and go. With all the vicissitudes of history - moving continents, changing sea levels, changing atmospheres and temperatures - it could be argued that the global sum of diversification is bound to be a highly irregular pattern with no fundamental meaning or driver.

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