According to the model, a species secures its existence through a few key skills that keep it a step ahead of its competitors. It's hard to imagine Darwin calling such a scheme newfangled: species exist through specialization. Yet ecologists have had to bend or circumvent the model more often than they have been able to apply it. The diversity of phytoplankton in the field typically exceeds the number of limiting nutrients around them. In an average tablespoonful of lake or ocean, for example, there are about 50 times more species than the model would predict.

In doctoral research at Amsterdam, Huisman studied how algae compete for sunlight. In addition to experimental observations, he described the competition theoretically under Weissing's supervision at Groningen. He used the standard model for competition, obtained more or less standard results and had already filed his dissertation when something very nonstandard occurred.

Huisman had accepted a postdoctoral fellowship at Stanford University, but with a few weeks left in Amsterdam, he sat down again to play with the model. He and Weissing had once mused about abstract parallels between Huisman's model and models of natural selection that Weissing used. Weissing knew that in his models some trios of species coexisted perpetually in a rock-scissors-paper cycle of ascendancy: the first drove down the second, which held back the third, which on resurgence suppressed the first, so that the second recovered and so on.

The arrangement was immune to equilibrium. On a whim, Huisman tried assembling a trio of complementary species with the competition model and three limiting resources. He succeeded easily. Observing cycles with one set of parameters after another, it occurred to Huisman that he had tried something no one had thought to try before (or that if they had, they couldn't have tried very hard). The secret was three resources. "In a sense, it was really surprising that nobody had discovered it before, about say 10 or 20 years ago," Huisman says.

Another Personality Emerges

Image: Courtesy of JEF HUISMAN BI-CYCLE RACES among five competing species grouped in two overlapping trios yielded fractal patterns when graphed. For each of the first 160,000 races, the researchers varied the abundances of the same one or two species. They made one species' starting population the x-axis and the other the y-axis, and they colored each point either yellow for a Trio 1 victory or blue for a Trio 2 victory (top). When they varied the same species' abundances over a narrower range in another 160,000 races (bottom), they got the same pattern magnified.

At Stanford, Huisman continued collaborating via e-mail with Weissing on this non-equilibrium angle. Based on several influential theories and experiments, they knew that a buffeting by external factors¿predators, parasites or spurts of nutrients¿kept competitors from equilibrating and enabled more species than resources to coexist. Yet in their rock-scissors-paper oscillations, the competitors buffeted themselves.

At their respective keyboards, across 10 time zones, Huisman and Weissing cracked their knuckles and started tossing more species into the standard model with three resources to see what would happen. One worked while the other slept. Using various combinations of parameters, they defined different species, assembled them into groups and watched the results on their PCs. Plenty went extinct, Huisman says. "Most parameter sets lead to a worthless species that is unable to survive at all," he notes. "Some parameter combinations may lead to a superspecies that wipes out all resident species."

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