Hidden Chaos Found to Lurk in Ecosystems

Physical scientists seem to find the phenomenon of chaos everywhere: in the orbits of planets, in weather systems, in a river’s swirling eddies. For nearly three decades, ecologists considered chaos in the living world to be surprisingly rare by comparison. A new analysis, however, reveals that chaos is far more prevalent in ecosystems than researchers thought.

Tanya Rogers was looking back through the scientific literature for recent studies on chaos in ecosystems when she discovered something unexpected: No one had published a quantitative analysis of it in over 25 years. “It was kind of surprising,” said Rogers, a research ecologist at the University of California, Santa Cruz and the new study’s first author. “Like, ‘I can’t believe no one’s done this.’”

So she decided to do it herself. Analyzing more than 170 sets of time-dependent ecosystem data, Rogers and her colleagues found that chaos was present in a third of them — nearly three times more than the estimates in previous studies. What’s more, they discovered that certain groups of organisms, like plankton, insects and algae, were far more prone to chaos than larger organisms like wolves and birds.

“That really wasn’t in the literature at all,” said Stephan Munch, an evolutionary ecologist at Santa Cruz and a co-author of the study. Their results suggest that to protect vulnerable species, it is both possible and necessary to build more complex population models as guides for conservation policies.

When ecology was first recognized as a formal science in the 19th century, the prevailing assumption was that nature follows simple, easily understood rules, like a mechanical clock driven by interlocking gears. If scientists could measure the right variables, they could predict the outcome: More rain, for example, would mean a better apple harvest.

In reality, because of chaos, “the world is a lot more whack-a-mole,” said George Sugihara, a quantitative ecologist at the Scripps Institution of Oceanography in San Diego who was not involved in the new research. Chaos reflects predictability over time. A system is said to be stable if it changes very little over a long timescale, and random if its fluctuations are unpredictable. But a chaotic system — one ruled by nonlinear responses to events — may be predictable over short periods but is subject to increasingly dramatic shifts the further out you go.

“We often give the weather as an example of a chaotic system,” said Rogers. A summer breeze over the open ocean probably won’t impact tomorrow’s forecast, but under just the right conditions, it could theoretically send a hurricane plowing into the Caribbean in a few weeks.

Ecologists began flirting with the concept of chaos in the 1970s, when the mathematical biologist Robert May developed a revolutionary tool called the logistic map. This branching diagram (sometimes known as a cobweb plot because of its appearance) shows how chaos creeps into simple models of population growth and other systems over time. Since the survival of organisms is affected so much by chaotic forces like the weather, ecologists assumed that species populations in nature would also often rise and fall chaotically. Logistic maps quickly became ubiquitous in the field as theoretical ecologists sought to explain population fluctuations in organisms like salmon and the algae that cause red tides.

By the early ’90s, 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% of the examined populations seemed to change chaotically; the rest either cycled stably or fluctuated randomly. Theories of ecosystem chaos fell out of scientific fashion by the mid-1990s.

The new results from Rogers, Munch and their Santa Cruz mathematician colleague Bethany Johnson, however, suggest that the older work missed where the chaos was hiding. To detect chaos, the earlier studies used models with a single dimension — the population size of one species over time. They didn’t consider corresponding changes in messy real-world factors like temperature, sunlight, rainfall 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 looking 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 organisms’ populations as models with as many as six dimensions rather than just one, leaving room for the potential influence of unspecified environmental factors. In this way, they could check whether unnoticed chaotic patterns might be embedded within the one-dimensional representation of the population shifts. For example, more rainfall might be chaotically linked to population increases or decreases, but only after a delay of several years.

In the population data for about 34% of the species, Rogers, Johnson and Munch discovered, the signatures of nonlinear interactions were indeed present, which was significantly more chaos than was previously detected. In most of those data sets, the population changes for the species did not appear chaotic at first, but the relationship of the numbers to underlying factors was. They could not say precisely which 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 how chaotic its population dynamics tend to be. This may be due to differences in generation time, with small organisms that breed more often also being more affected by outside variables more often. For example, populations of diatoms with generations of around 15 hours show much more chaos than packs of wolves with generations almost five years long.

However, that doesn’t necessarily mean that wolf populations are inherently stable. “One possibility is that we’re not seeing chaos there because we just don’t have enough data to go back over a long enough period of time to see it,” said Munch. In fact, he and Rogers suspect that because of the constraints of their data, their models might be underestimating how much underlying chaos is present in ecosystems.

Sugihara thinks that the new results might be important for conservation. Improved models with the right element of chaos could do a better job of forecasting toxic algal blooms, for example, or tracking fishery populations to prevent overfishing. Considering chaos could also help researchers and conservation managers to understand how far out it’s possible to meaningfully predict population size. “I do think that it’s useful for the issue to be in people’s minds,” he said.

However, he and King both caution against placing too much faith in these chaos-conscious models. “The classical concept of chaos is fundamentally a stationary concept,” King said: It is built on the assumption that chaotic fluctuations represent a departure from some predictable, stable norm. But as climate change progresses, most real-world ecosystems are becoming increasingly unstable even in the short term. Even taking many dimensions into account, scientists will have to be conscious of this ever-shifting baseline.

Still, taking chaos into consideration is an important step toward more accurate modeling. “I think this is really exciting,” said Munch. “It just runs counter to the way we currently think about ecological dynamics.”