## Box The coupled logistic model for diversification in the sea

In a series of influential papers in the 1970s and 1980s, Jack Sepkoski of the University of Chicago presented a new model for the diversification of life in the sea (Sepkoski 1984). He had labored long and hard to compile the first comprehensive database on all the families of marine animals, and this database was the source of many of his macroevolutionary studies.

Sepkoski (1984) visualized the history of life in the sea as consisting of three great evolutionary "faunas": the Cambrian, Paleozoic and Modern (Fig. 20.4). Each "fauna" consists of a set of animal groups that possessed particular arrays of adaptations, and each of which had different competitive abilities. The large-scale replacements that happened during the Ordovician and Triassic, as the Cambrian fauna gave way to the Paleozoic, and the Paleozoic to the Modern, were the result of new forms entering adaptive zones that were already occupied, taking those over, and then expanding into new modes of life. The greater adaptability of the Paleozoic fauna allowed it to reach a higher global equilibrium level, of 400 families, than the Cambrian fauna, which could not exceed 100 families. The Modern fauna has yet to reach its global equilibrium diversity level of more than 600 families.

Sepkoski (1984) modeled each of the three "faunas" as following a logistic curve: expansion rates were low at first, then rose to a steep curve, before leveling off as the global carrying capacity was achieved. The mathematical formulation was based on establishing the net pattern of origination minus extinction through time. Just as in The Theory of Island Biogeography (MacArthur & Wilson 1967), Sepkoski argued that origination rates would be high and extinction rates low at first (Fig. 20.5). As more and more families originated, levels of competition between the families would increase, which would have the effect of restraining origination rates and sending extinction rates up. Eventually, as the oceans become full, extinction rates exactly balance origination rates and the equilibrium level is achieved. Note that the equilibrium is dynamic: families continue to originate, but new families drive out existing families.

The full title of Sepkoski's model is the three-phase coupled logistic model, where each of the faunas has its own characteristic logistic equation, and the three are coupled, or interact, as one fauna rises and another falls. But is this model just a mathematical abstraction or does it tell us something real about ecology and evolution? Note that the model is framed at the level of families, and not at species level. Further, this kind of model only seems to make sense of the marine fossil record - the model has not been applied to the diversification of land plants, insects or vertebrates (see Fig. 20.2). Alroy (2004) reanalyzed Sepkoski's data and found that the composition of the three faunas is debatable in part and that the rise of the Modern fauna has been slower than expected. Further, Stanley (2007) has argued that the constants used by Sepkoski in his models were unrealistic, and that the global marine diversification patterns more nearly approximate a complex exponential curve.

Read about Jack Sepkoski and models of Phanerozoic biodiversity through http://www. blackwellpublishing.com/paleobiology/.

1. Trilobita

2. Inarticulata 3. Hyolitha

4. Monoplacophora

1. Trilobita

5. Eocrinoidea

2. Inarticulata 3. Hyolitha

5. Eocrinoidea

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