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SPOTLIGHT |
1 Department of Geological Sciences, California State University, Fullerton, California 92834-6850, USA nbonuso@fullerton.edu
| The first 20% of the full text of this article appears below. |
Zeno of Elea, the ancient Greek philosopher, proposed a paradox that captures one of the challenges facing evolutionary paleoecologists: that which is in motion must arrive at the halfway stage before it arrives at its goal (Aristotle, 1984). Zeno describes a footrace between Achilles and a tortoise and explains that if Achilles, a fast runner, gives the tortoise a head start, he will never overtake the tortoise. Achilles must traverse a finite series of distances before catching the tortoise, but in the time it takes Achilles to achieve this distance the tortoise crawls forward a tiny bit farther. As a result, Achilles is forever chasing a tortoise he can never actually catch.
This seeming paradox resembles one of the challenges facing evolutionary paleoecologists; that is, the ever-present challenge of keeping up with developments in modern community ecology—a swift opponent with a definite head start. Several major patterns of functional biology and life habits are well established for marine organisms throughout the Phanerozoic (Bambach, 1985, 1993; Sepkoski and Miller, 1985; Bottjer and Ausich, 1986). The lack of coherent theories to help understand these macroevolutionary trends, however, keeps evolutionary paleoecology a step behind (Jackson, 1988; Allmon, 1994; Allmon and Bottjer, 2001). The good news is that this paradox is not irresolvable. Perhaps evolutionary paleoecologists, like the mathematicians who used calculus to produce practical solutions to Zeno's paradox, can use math to gain headway; for example, the mathematical
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