Huisman and Weissing made two graphs to illustrate the situation (see image). They enacted 160,000 matches among the same five competitors, each time altering only slightly 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 made the color of each point they graphed such that it showed the outcome of the contest¿yellow for a Trio 1 victory, blue for Trio 2. The graph appeared to be a fractal.
For reassurance, the duo staged another 160,000 bi-cycle races, in which they varied the same two species' abundances over a narrower range. This run produced a second graph that was, in effect, a 25-fold magnification of a tile from the first¿a zoom-in view. As was true of the first diagram, there were many places in the second where blue and yellow points stood side by side. There was no sign that detail was diminished with magnification and no way to guess what colors would reside in any one spot on closer inspection. This figure had "fractal" written all over it.
The fractal nature of this pattern means that anticipating winners is like forecasting the weather, Weissing remarks. "The most you can hope for is a kind of a probabilistic answer," he says. Near the fractal curve boundaries, the proportion of blue to yellow dots helps to set the two outcomes' odds, but certainty is not an option. Says plankton ecologist Dan Roelke of Texas A & M University, "The work is very cool."
Huisman says that his lab has jobs open for the work still left to do. Verification of even just the basic prediction of oscillations and chaos¿whether pursued in the field or in the lab¿demands daunting amounts of groundwork and ultimately lots of day-by-day measurements. The model too calls for further elaboration, he says. The unpredictable finales that he and Weissing showed in their report unfolded only after about 1,000 days, or about three years. But the precipitous toll that winters regularly take on plankton might perpetually "reset the clock" before such events occur, Huisman fears.
In fact, just the jiggling influences of the outside world might upset the dynamics that he and Weissing engineered with careful parameter choices¿although he suspects that adding such details can only make the model's behavior even more complicated. "These are long-term questions that are going to take decades to resolve," says ecologist Steve Hubbell of the University of Georgia. Meanwhile Huisman will recruit applicants. "A theoretical physicist would be really helpful," he says.