A computer simulation at IBM suggests that ecosystems can evolve past
the verge of collapse toward long-term stability
In Brief:
Applying tools developed for the science of critical phenomena, a pair of IBM researchers have created a computer model that contradicts two widely accepted explanations of species extinctions. Ecosystems might be neither relatively stable nor chronically on the brink of collapse. Rather, the model says, a long period of susceptibility
to extinctions can give way to extraordinary stability.
After a summer of disaster films in which life as we know it is imperiled by asteroids, comets and other large falling objects, the question of extinction is in the air. Most scientists have come to accept that it was probably just such an impact that killed off the dinosaurs 65 million years ago. But catastrophic extinctions have been a fact of life as far back as the fossil record extends. Species come and species go, and scientists have been trying to understand the possible causes, including ones that entail no extraterrestrial agency.
Two IBM scientists have assembled a view of ecosystems that might shed new light on the extinction problem. In an article called "Critical Biodiversity," published in the Journal of the Society for Conservation Biology (June 1998), James Kaufman and Owen Melroy report on a computer model in which simulated species and their interactions evolve through natural selection. The resulting scenario for mass extinctions came as a big surprise to the researchers. They had begun their modeling with the intention of discriminating between two prevailing views of ecosystem dynamics, but instead found a third alternative that showed the incompleteness of both earlier models.
According to one such view, ecosystems evolve to a point of dynamic stability, after which most species can be driven to extinction only by a major external perturbation. That could mean a meteor impact or a drastic change in temperature, carbon dioxide levels or sea level. In any case, according to this view, aside from a major disruption of some kind, ecosystems do not undergo large-scale fluctuations.
The other view denies any long-term stability. It sees nature as inherently poised on the edge of disaster and able to topple over from time to time, even in the absence of external pushes. This notion has gained plausibility from the work of the biologist Stuart Kauffman of the Santa Fe Institute and the physicist Per Bak of the Bohr Institute in Copenhagen. In particular, the concept of self-organized criticality -- introduced by Bak and his collaborators in an attempt to explain the fractal, or self-similar, properties of nature, in which the same structures or events are found at all scales -- has been used to show how ecosystems are prone to extinctions.
Self-organized criticality is typically illustrated by the example of a sand pile. If grains of sand fall onto a tabletop, a conical pile forms until a critical slope is reached. At that point, any additional grains are likely to produce an avalanche, and the theory predicts that the probability of an avalanche of a given size is inversely proportional to the size of the avalanche: large avalanches are rare, small ones frequent. Many other natural phenomena, such as earthquakes, also appear to obey this so-called power-law behavior.
While a sand pile and an ecosystem may seem quite different, Bak and others suggest that they are analogous. Adding grains of sand can be compared to introducing new species or increasing the biodiversity, while the avalanches correspond to extinctions of varying numbers of species.
What Kaufman and Melroy found, however, was that self-organized criticality may provide an incomplete picture of patterns of extinction. Consonant with Bak, their model ecosystems would evolve to a point of critical biodiversity, at which they became highly susceptible to extinctions. "But what's unique about our theory," says Kaufman, "is that it would predict that this critical point is not an ecosystem's final state. Systems appear to be able to evolve through that point, after which they become remarkably stable."
SIMULATING EVOLUTION
Neither Kaufman nor Melroy is a biologist. Kaufman is a condensed matter physicist and Melroy is an electrochemist at IBM's Almaden Research Center. Both were intrigued by the new developments in the science of critical phenomena, which seeks to explain, for example, how discrete elements -- such as grains of sand, Wall Street stocks and biological species -- can self-organize into systems that display extraordinarily complex behavior.
As Melroy tells it, the work grew out of casual conversations between the two researchers and began in earnest after Melroy, on a flight from San Jose to New York, read The Diversity of Life, by the Harvard University biologist E. O. Wilson. "It really started me thinking about what happens to populations of animals over time," says Melroy. "People have performed studies of islands, looking at the amount of diversity as a function of the size of the island or its distance from the mainland. It occurred to me you could create a relatively simple model in which the interactions between 'species' could evolve through natural selection, and analyze the results using the mathematics of critical phenomena."
After Melroy returned to Almaden, he and Kaufman set about creating a simulation of an evolving ecosystem that made the minimum of assumptions about the interactions between species. Their model did not, for example, assume the existence of keystone species without which other species would be unable to survive. "We didn't set out to achieve self-organized criticality," says Kaufman. "We wanted to let species evolve through natural selection and watch what happened."
LIFE ON AN ISLAND
The simulation begins with an unpopulated "island" covered with a grid comprising 10,000 squares, each randomly designated one of six environments, equivalent to, say, desert or forest. At the beginning of the simulation, the island has only one organism. Because it is adapted to a particular environment, it cannot spread very far. But by means of mutation, new species arise, with an increased level of fitness, and eventually there are many species, which can exist in other environments with varying degrees of fitness.
Multiple species can coexist at each site. Some live in the niche constituted by the environment itself, and others live on other species at the site, much as algae might thrive on rocks, leaves or animals. Fitness
is determined by a series of numbers -- randomly
assigned -- that identify the environments in which the species can survive and the other species on which they can live.
At each turn of the program's clock, species compete to occupy their present site as well as neighboring sites, according to their fitness. This process occurs in a probabilistic way, based on the relative fitness of the various species, and is somewhat like the game of musical chairs: those species without a niche at the end of the process perish from a site. Species go extinct, says Melroy, "when they can't compete for a niche, or their niche disappears, or a mutation leads to a more competitive species that replaces the parent species."
MEASURE FOR MEASURE
What makes the model truly distinctive, say the two IBM researchers, is the measures used to analyze the results, which come from the physics of critical phenomena. These measures can provide answers to such basic questions as whether extinction in an ecosystem is truly a critical phenomenon and how an ecosystem's susceptibility to extinctions depends on its biodiversity.
To apply these measures, the scientists had to find biological analogues to properties of other physical systems that exhibit critical behavior -- ferromagnetic materials, for example. Above a certain critical temperature, the atoms of such a material do not align with an imposed magnetic field. But as the material is cooled below the critical temperature, more and more atoms align, until at absolute zero they are all aligned.
In the case of a magnet, the degree to which atomic moments are aligned is what critical phenomena theorists call the order parameter. One choice for an order parameter in an ecosystem, says Kaufman, is the likelihood of a species surviving when any new species is created. The number, or diversity, of species is analogous to the magnet's temperature. Finally, another important measure, the susceptibility to extinction, is defined as the cumulative extinction events that occur as a function of the species diversity. This is analogous to the magnetic susceptibility, or probability, that flipping a single atomic moment in a ferromagnet will cause other moments (as far away as the size of the system) to flip.
When the order parameter and susceptibility are plotted against the diversity, they reveal a critical point of about 18 species. At that level, the model ecosystem is extraordinarily susceptible to mass extinctions. The slightest perturbation -- say, the loss of a single key species on which many others depend -- could lead to the demise of all but a few particularly lucky or hardy species.
THE END IS NOT NECESSARILY NEAR
Because of a phenomenon known as "critical slowing down," the model ecosystem spends a long time in the neighborhood of the critical point. But that doesn't mean the ecosystem has achieved self-organized criticality. Instead, as the researchers learned to their surprise, it can evolve past the critical point. "In this stage," says Kaufman, "the ecosystem diversified into many small local clusters of species that were relatively independent, and once the system passes the critical point, it would take something external to wipe out more than a few species at a time." In our world, that's when the only thing to fear would be an asteroid -- unless human intervention in the world's ecosystems goes unchecked.
The researchers, however, are under no illusions that they have simulated the way life has actually evolved. That is not what they set out to do, says Melroy. Nevertheless, the model did a remarkable job of mimicking the processes of natural systems. For example, it produced a complex web of food dependencies and resulted in many different, specialized organisms, just as in nature. And as in real island ecosystems, the number of species that were created scaled with the available area, in accordance with a law introduced by Robert MacArthur and E. O. Wilson.
EVOLVING MARKETS?
Kaufman and Melroy hope that, by publishing their model and findings, they will now spark other researchers to apply the new measures they have developed to real-world extinctions. "There are scientists out there with databases from the paleontological record," says Kaufman. "If you know both the diversity and the number of species that existed at different periods of time, and if that data is complete and accurate enough, you might be able to tell whether the earth is at a critical point, or if we have evolved through one." Such records might also help scientists to gauge the present status of the world's ecosystems in their evolution toward critical biodiversity and, beyond that, to a dynamically stable state.
In the meantime, Kaufman and Melroy are pondering other realms in which to apply their modeling approach. They believe, for example, that it should work just as well on corporate systems as on biological ones. "Corporations have a natural cycle," says Melroy. "They start, they grow, they compete, some of them don't make it, many of them change profoundly over time, they merge, and so on. We'd like to ask the same types of questions about the evolution of corporations that we do about ecologies."
The stock market may be another fertile area for study. "What if some type of critical diversity of portfolios turned out to be required for a mutual fund to perform well over extended periods of time?" Melroy asks. "We think it would be a fascinating area to investigate."
Gary Taubes is a freelance writer living in Santa Monica, California.
