By the early 1990s, ecologists had accumulated enough time series data sets on species populations and enough computational power to test these ideas. There’s just one problem: The chaos doesn’t seem to be there. Only about 10 percent of the population examined seemed to change in a chaotic manner; the rest follows a stable cycle or random oscillation. Ecosystem chaos theories fell out of fashion in the mid-1990s.
New results from Rogers, Munch and their Santa Cruz mathematician colleagues Bethany Johnsonhowever, hinting that the old work missed out on where the chaos was hiding. To detect chaos, previous studies have used models that have one dimension – the population size of a species over time. They did not consider corresponding changes in real-world clutter factors such as temperature, sunlight, precipitation, and interactions with other species that might affect populations. Their one-way models capture how populations change, but not why they change.
But Rogers and Munch “searched for [chaos] in a more sensible way,” said Aaron King, a professor of ecology and evolutionary biology at the University of Michigan who was not involved in the study. Using three different complex algorithms, they analyzed 172 time series of different populations of organisms as models with at most six dimensions instead of just one, leaving room for the potential influence of unspecified environmental factors. In this way, they can test whether unnoticed chaotic patterns can be embedded in the one-way representation of population change. For example, more rainfall could be associated with a chaotic increase or decrease in population, but only after a few years of delay.
In population data for about 34% of species, Rogers, Johnson and Munch found, signs of nonlinear interactions were indeed present, significantly more chaotic than had previously been detected. In most of those datasets, the population change of species doesn’t seem chaotic at first, but the relationship of the numbers to the underlying factors is. They couldn’t say exactly what environmental factor was causing the chaos, but whatever it was, their fingerprints were on the data.
The researchers also discovered how an inverse relationship between an organism’s body size and its population dynamics tends to be chaotic. This may be due to differences in generation time, with smaller organisms that spawn more often also being influenced by exogenous variables more often. For example, diatom populations with generations lasting about 15 hours show much more chaos than wolf packs with generations lasting nearly 5 years.
However, that doesn’t necessarily mean that wolf populations are inherently stable. “One possibility is that we don’t see the chaos there because we don’t have enough data to go back for a long enough time to see it,” Munch said. In fact, he and Rogers suspect that due to their data constraints, their models may be underestimating the extent of potential chaos present in the ecosystem.
Sugihara thinks the new results could be important for conservation. For example, improved models with the right chaos factor could do a better job of predicting toxic algal blooms or monitoring fish populations to prevent overfishing. Looking at chaos can also help conservation researchers and managers understand how meaningfully predictable population size can be. “I think it’s very helpful to have this issue on people’s minds,” he said.
However, he and King both caution against placing too much faith in these conscious models of chaos. “The classical concept of chaos is essentially a fixed concept,” says King. It is built on the assumption that chaotic oscillations exhibit deviations from some stable, predictable norm. But as climate change plays out, most real-world ecosystems are becoming increasingly unstable even in the short term. Even taking into account many aspects, scientists will have to be aware of this ever-changing baseline.
However, considering the chaos is an important step towards creating a more accurate model. “I think this is really exciting,” Munch said. “It just runs counter to how we currently think about ecological dynamics.”
Original story Reprinted with permission of Quanta magazine, an editorially independent publication of The Simons Organization whose mission is to advance public understanding of science by including research developments and trends in mathematics as well as the physical and life sciences.