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Figure 20.3 Theoretical models for the diversification of life plotted as if for the last 600 myr (a) in the absence of major perturbation and (b) with two mass extinctions superimposed.

The logistic model involves one or more classic S-shaped curves, each consisting of an initial period of slow diversity increase, a rapid rise, a slowing of the rate of increase as a result of diversity-dependent damping factors, and then a plateau corresponding to a limiting or equilibrium value. The logistic model has been used to explain patterns of diversification of marine organisms (Sepkoski 1984) and of plants (Niklas et al. 1983).

There is clearly no consensus on whether the exponential or logistic model best explains the diversification of major sectors of life through time, nor on whether all patterns of diversification adhere to the same model of increase. The choice of model is important because each makes profoundly different claims about evolution.

Equilibrium or expansion?

If the logistic model is correct, life has diversified in a controlled manner, reaching one or more equilibria, each of which is probably density limited. As the oceans or land filled with species, some limiting factor such as space or food came into play to stop diversification exceeding the global carrying capacity, the total number of species that can be accommodated. If the exponential model is correct, life has diversified in a less controlled manner, rising continually and never reaching an equilibrium level. This expansion model need not imply unfettered rates of diversification: food and space limitations can slow the rate of increase.

Equilibrium models for the diversification of life are based on an influential body of ecological theory, including classic experiments in competition where the increase of one population suppresses another that depends on the same limiting resource. In particular, Sepkoski (1984) based his logistic models (Box 20.2) on the theory of island biogeography (MacArthur & Wilson 1967), seeing the Earth's oceans as an island, arrival rates as evolutionary origination rates, and local extinction rates as global extinction rates. Like a Petri dish, or an island, the world's oceans are thereby assumed to have a fixed carrying capacity, a level that marks the limit of global species richness. Sepkoski (1984) argued for two, possibly three, equilibrium levels, each dominating the Earth's oceans for a time, and then being surpassed. In 2001, John Alroy of the National Center for Ecological Analysis and Synthesis in Santa Barbara and colleagues argued that in fact Raup (1972) had been right, and that there had really been just one equilibrium level (see Fig. 20.1a) that was achieved in the Ordovi-cian. The apparent step-like pattern identified by Sepkoski (Box 20.2) was an artifact of the poor quality of the Paleozoic and Mesozoic fossil records.

The alternative to equilibrium is expansion, where there is no carrying capacity for the Earth or that carrying capacity has not yet been reached. The overall pattern of diversification of life of course incorporates the

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