But soon Huisman and Weissing had nine virtual species coexisting on three resources in the model that said it couldn't happen. Meanwhile they had also decided to pursue chaos¿the seemingly random vicissitudes that arise in physical and other rule-governed processes such as weather. Weissing, who had come to ecology from mathematics, says he knew that chaos had to emerge sooner or later. And they finally found it by combining certain species on five limiting resources.

In this arrangement, the numbers of the various competitors undulated erratically without pattern. A reenactment of any match always proceeded similarly at first, but following even a slight adjustment to the size of one subpopulation, it charted a rapidly diverging path. The researchers knew well that such sensitivity to initial conditions was the hallmark of chaos. Finally they showed that chaos too supported a diversity of species beyond resources.

Fleeting niches in time, Huisman says, create the increased opportunity for biodiversity. At equilibrium, the abundance of resources and the size of opponents' forces are constant. If you are alive, it's because your skills are suited to the prosperity you have obtained. Yet chaos and oscillations create changing conditions in which many species encounter circumstances that give them the edge only once in a while. Not every adversary will be thrown off its game. "If one species is the best in all resources, it just wins," Huisman says. "If all species are more or less equal competitors, then we see this chaotic phenomenon."

Does this unruly chaotic behavior undo the standard model? Huisman, Weissing and other ecologists don't think so. On publication of the Nature report, ecologist Mark Ritchie of Utah State University said that Huisman and Weissing had given ecologists a valuable tool: "They're identifying a new way in which multiple species can coexist that we've never thought of before."

One More Surprise

Huisman and Weissing's May report describes further encounters with chaos. In a turn of events that surprised no mathematician, the two turned up a fractal. Huisman thought up a strategy for producing chaos using not five, but three resources. He again used the rock-scissors-paper pattern but this time in the form of a "bi-cycle." He formed two trios from five species, making one a common member of both groups. While one trio cycles, the other two species vie aimlessly. Yet in doing so, they jostle the trio in play, sometimes ending up ideally positioned to engage their missing partner. In that case they jump in, and the other two "extras" vacillate. These exchanges occur chaotically, Huisman and Weissing found.

Image: Courtesy of JEF HUISMAN TRANSIENT CHAOS emerges when five species, grouped in two trios, compete for three resources. Depending on the initial conditions, the system winds up such that species 1, 2 and 3 (black, red and blue, respectively) are winners of the competition (top), or species 1, 4 and 5 (black, green and yellow, respectively) are winners (bottom). This kind of sensitivity to initial conditions is a hallmark of chaos.

All the previous species assemblages oscillated or chaotically wandered in seeming perpetuity¿even over simulations lasting 10,000 plankton generations. But when Huisman and Weissing tinkered with the bi-cycles, they saw chaos that would unexpectedly and permanently cease. The reason was simple: each dancing trio shaped the environment differently. When Huisman and Weissing linked very dissimilar trios and watched them alternate, one eventually pushed two members of the other to extinction. A single two thousandths of a percent change in one species' abundance could give the other trio the advantage.

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