Unexpectedly Intriguing!
12 August 2022

There's been a remarkable development in the field of ecology. An established belief that chaotic dynamics are a relatively rare factor in shaping ecosystems has turned out to not be true.

The story of how that discovery was made is just as interesting as the discovery itself. Here's how Quanta Magazine's Joanna Thompson tells it:

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.

The signs of chaos had been there all along, lurking within the reams of accumulated ecological data. But earlier researchers had missed it because their models were too simple. It wasn't until Rogers and her fellow researchers applied more complex models that the telltale signs of chaotic influences could be teased out.

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.

This is exactly the kind of study that spawns new research. The effort to find out what factors are at play and how they interact with each other will shape generations of work in the now understood to be underdeveloped field of ecological population growth dynamics.

We would expect the initial phase of that new work to resemble the equivalent of a design of experiments in statistics to verify which factors are most influential, followed by more detailed studies into the effects of their interactions over time. It's an exciting development for a field that's now coming out of a period of stagnation no one knew it was in as a result of the discovery.

More Information

For some basic information on how chaos can influence ecological population dynamics, we found Numberphile's 19-minute video on the Feigenbaum constant provides a nice introduction to the surprisingly simple population modeling math that produces chaotic outcomes:

For more background, we've also built a tool to model the chaotic growth of the population of a species over time. Our post also features Veratiseum's video exploring the logistic map and its role in the emergence of complexity.

We can also point you to HHMI Bioactive's Population Dynamics simulator, which features a good primer on the simpler logistic growth model math that wasn't capturing the extent of chaotic influences found by Rogers, Johnson and Munch.

References

Rogers, T.L., Johnson, B.J. & Munch, S.B. Chaos is not rare in natural ecosystems. Nature Ecology & Evolution. Volume 6, pp 1105–1111. (2022). DOI: 10.1038/s41559-022-01787-y.

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