Certain animal populations that appear stable or predictable for decades or centuries suddenly may fluctuate wildly and irregularly, again for decades or centuries, even with no outside influences such as environmental changes or human interference, according to a new study by two University of California, Davis, researchers. The time it takes for these populations to finally settle into a pattern -- up to 10,000 years in this investigation -- indicates that these transient dynamics may hold the key to understanding and managing ecological resources, the researchers suggest in a report published in the Feb. 25 issue of the journal Science. The findings come from a simple computer model inspired by the biology of Dungeness crabs living along 1,000 miles of coastline. In the model, the crabs live most of their lives in one location except as juvenile larvae, when they are swept out to sea for several months before they settle down closer to shore. Most return to their birth habitats, some relocate nearby, and others settle farther away along the coast. No other factors, such as environmental changes, were included in the computer model. The researchers ran their model over a span of 10,000 years -- roughly the years since the last ice age and about 1,000 times longer than a typical ecological field study. The model crab population showed periods of steady patterns lasting a century or so interspersed with longer intervals of irregular fluctuations. Near the end of the simulation, the model settled down into slightly more predictable behavior described by the nonlinear mathematics popularly known as "chaos" or complexity. "Sudden changes in the ecological systems we're interested in, such as fisheries, may result from internal dynamics and not from externally imposed forces," said co-author Alan Hastings, UC Davis chair of the environmental studies division and member of the Center for Population Biology. Internal dynamics refer to the behavior of the population in the model under constant environmental conditions, with the only changes coming from competition within the population, presumably for food and space, and from redistribution of the population. This internal capacity of populations for sudden and unpredictable change suggests that certain animal species with similar characteristics may be in a more precarious situation than previously acknowledged, Hastings said. "Populations take so long to reach their final behavior that we're living in a world that we should be looking at as always transient," he said. "The level of unpredictability will increase when real-world phenomena are added to the model." The model builds on an approach used by Oxford ecologist Robert May, who is credited with introducing chaotic principles to ecological studies in the 1970s by demonstrating that the complex patterns of nature can arise from simple nonlinear descriptions. "We've taken the next step," said co-author Kevin Higgins, a UC Davis graduate student in ecology. "May showed that chaos can happen; we've shown that chaos can arrive or depart without warning." With the big picture being so big and still so blurry, ecologists have no way of knowing where their field observations of a species might fit into this chaotic continuum. The experience of gathering several years of data for the purpose of predicting the future of an animal population is akin to viewing a few frames of a film and trying to predict the plot and ending of the movie, Higgins said. The complex population behaviors generated by a relatively simple model are encouraging to Hastings. "This is possibly the beginning of an explanation for previously unexplained sudden changes in population levels," he said. Behaviors that might have been attributed to random external forces, such as weather, may be rooted instead in the deterministic forces underlying the chaotic behaviors inherent to the dynamics of a population. Funded by the U.S. Department of Energy and the U.S. Global Ocean Ecosystems Dynamic program, the study began as an attempt to understand the role of physical forces in ocean biology -- in this case, the dispersal by ocean currents of the Dungeness crab larvae. The model fits other animals whose life spans contain a dispersal phase and a stationary phase that is highly dependent upon local food sources. These animals include most insects and virtually all the shellfish that people eat, Hastings said. The computer model for this study was developed on Silicon Graphics workstations at the Computer Graphics Facility for Computational Biology, established one year ago on campus with financial support from the National Science Foundation at the UC Davis Institute of Theoretical Dynamics. -