The hidden chaos that lurks in ecosystems

By the early 1990s, ecologists had amassed enough time-series data sets on species populations and enough computing power to test these ideas. There was just one problem: the chaos didn’t seem to be there. Only about 10 percent of the populations studied appeared to change chaotically; the rest either oscillated stably or fluctuated randomly. Ecosystem chaos theories fell out of scientific fad in the mid-1990s.

But the new findings by Rogers, Munch and their Santa Cruz mathematician colleague Bethany Johnson suggest the older work missed where the chaos was hiding. To detect chaos, the previous studies used models with a single dimension – the population size of a species over time. They did not account for corresponding changes in chaotic real-world factors such as temperature, sunlight, precipitation, and interactions with other species that might affect populations. Their one-dimensional models captured how the populations changed, but not why they changed.

But Rogers and Munch “went on the hunt [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 with the study. Using three different complex algorithms, they analyzed 172 time series of populations of different organisms as models with up to six dimensions instead of just one, leaving room for the potential influence of unspecified environmental factors. In this way, they could test whether unnoticed chaotic patterns could be embedded in the one-dimensional representation of population shifts. For example, more precipitation could be chaotically associated with population increases or decreases, but only with a lag of several years.

In the population data for about 34 percent of the species, Rogers, Johnson, and Munch discovered that the signatures of nonlinear interactions were actually present, which was far more chaotic than had previously been determined. In most of these datasets, the population changes for the species didn’t initially appear chaotic, but the relationship of the numbers to the underlying factors was. They couldn’t pinpoint exactly what environmental factors were responsible for the chaos, but whatever they were, their fingerprints were on the data.

The researchers also uncovered an inverse relationship between an organism’s body size and the chaotic tendency of its population dynamics. This may be due to differences in generation time, with small organisms that reproduce more frequently also being more likely to be affected by external variables. For example, populations of diatoms with generations of about 15 hours show much more chaos than wolf packs with generations of almost five years.

However, this does not necessarily mean that wolf populations are inherently stable. “One possibility is that we don’t see chaos there because we just don’t have enough data to look back long enough to see it,” Munch said. In fact, he and Rogers suspect their models may be underestimating how much underlying chaos exists in ecosystems due to the limitations of their data.

Sugihara believes the new findings could be important for conservation. For example, improved models with the right element of chaos could better predict toxic algal blooms or track fisheries populations to prevent overfishing. Accounting for the chaos could also help researchers and conservation managers understand how far away it is possible to meaningfully predict population size. “I think it’s useful when the issue is in people’s minds,” he said.

However, he and King caution against placing too much reliance on these chaos-aware models. “The classic concept of chaos is basically a stationary concept,” King said. It is based on the assumption that chaotic fluctuations represent a deviation from a predictable, stable norm. But as climate change progresses, most real ecosystems are becoming increasingly unstable, even in the short term. Even considering many dimensions, scientists need to be aware of this ever-changing baseline.

Still, considering the chaos is an important step towards more accurate modeling. “I find that really exciting,” Munch said. “It just goes against our current thinking about ecological dynamics.”

Original story Reprinted with permission from quanta magazine, an editorially independent publication Simons Foundation whose mission is to improve public understanding of science by covering research developments and trends in mathematics and the natural and life sciences.

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