Â鶹ÒùÔº

Tipping points are the death of ecosystems. So scientists watch as warning signs gradually worsen until an ecosystem reaches the point of no return, when animal populations suddenly collapse. While tipping points can sometimes be predicted, what comes next is often shrouded in mystery, stymieing efforts to prevent the impending disaster or prepare for what's to come.

A new study by a team of researchers at the University of California, Santa Cruz, and the National Oceanic and Atmospheric Administration (NOAA) introduces a method for modeling the murky future beyond a tipping point.

The , published in PNAS, demonstrates how this model can act as a "crystal ball" into the future of ecosystems—providing enough lead time to intervene before there's nothing left to save.

"It gives us this fundamental insight into predicting what's going to happen in the future," said Eric Palkovacs, a senior author on the paper and professor of ecology and evolutionary biology at UC Santa Cruz. "That allows us to either do the things necessary to avoid that transition, or, if we're going to experience it, to plan for it and figure out the best ways to cope with it."

Seeing the future

In healthy ecosystems, species populations fluctuate in predictable ways: sea urchins feed on a kelp forest, otters then feed on the urchins, and the kelp regrows. But if the ecosystem loses equilibrium, disaster can suddenly strike.

If warming waters drive sea urchins to kill off a kelp forest, the ecosystem suddenly crosses a tipping point that can doom all the species it supports. The result is a new regime of population fluctuations that can be hard to correct.

"You have many of these cases where the system can live in different states. You have a state with lots of kelp, and a state without kelp," said Lucas Medeiros, the study's lead author and a former postdoctoral scholar at UC Santa Cruz.

Currently, researchers have some methods for predicting what lies beyond an ecosystem's tipping point, but each approach has its tradeoffs. Some existing methods make predictions using machine-learning algorithms. However, these approaches require large datasets, which often don't exist for research on ecosystems, where data might be collected yearly or even less frequently.

"That is particularly relevant in ecological applications, where a very long time series is 50 data points, which represents some person's entire career collecting data," said professor of applied mathematics Steve Munch, also a senior author on the paper.

Other methods can produce predictions based on small datasets, but require detailed information about the specific ecosystem, such as formulas describing the dynamics of each species. These bespoke approaches can't be readily applied to multiple, unrelated ecosystems.

In order to predict the future beyond tipping points, across a multitude of ecosystems and relying on limited data, the team developed a model that learns from historical trends in an ecosystem rather than detailed information about each species.

When presented with a hypothetical scenario, the model searches for a similar condition in the historical data to inform its prediction for what comes next.

By solely relying on trends in the data, rather than detailed understandings of individual species, this approach can be readily applied to a variety of ecosystems.

The model considers fluctuations in one species' population, such as the abundance of salmon, and one factor driving that fluctuation, such as the rate at which the salmon are being harvested through commercial fishing. By using a mathematical tool called "lagged coordinates embedding," the model can produce predictions about other species in the ecosystem as well.

"When you take lags of the prey, you incorporate information of how the predator affected the prey in the past," said Medeiros, now a postdoctoral investigator at the Woods Hole Oceanographic Institution.

Being able to predict the outcome for multiple species in an ecosystem is a mathematical "miracle" in their model, said Munch, a fisheries ecologist at NOAA. "You can take lags from a system that you have a small number of observations about and use those lags to reconstruct the dynamics of the entire system," he added.

From lakes to test tubes

To apply their model, the team examined data from two studies about very different ecosystems. One study looked at historical trends in Lake Zurich, where plankton populations fluctuate based on phosphorus levels driven by pollution.

In the past, as phosphorus levels increased, plankton populations reached a tipping point. The plankton consumed much of the lake's oxygen, suffocating other species, including those that feed on plankton.

Without predators, the plankton population surged unchecked, turning the lake's waters green and inhospitable. In the case of Lake Zurich, management strategies reversed this tipping point by restoring its ecosystem to a healthy equilibrium.

Using historical data on the lake's phosphorus levels and plankton population, the model was able to make predictions that matched when the ecosystem reversed back to a healthy equilibrium, as well as the resulting impact on the plankton. Palkovacs said that the team's model could help inform similar management efforts elsewhere.

"Our approach could be applied to other lakes currently experiencing algal blooms," said Palkovacs, citing the regular algal blooms at California's Clear Lake as an example.

"This would allow us to forecast how much reduction of phosphorus would be needed to restore the lake, how long restoration would take, and what the lake would look like following restoration."

The second study the team examined was a laboratory experiment in which scientists produced simple, three-species ecosystems by placing a protist and two types of bacteria in test tubes. The scientists controlled the population fluctuations of the various species by periodically diluting the tubes' solution.

The model was able to predict these fluctuations based on the experimental data. Importantly, this also means that the model can infer what the fluctuations would look like given conditions that were never explored in the original experiment. Simulating unexplored scenarios can allow scientists to uncover new research questions that could inspire future studies, said Medeiros, who led the data analysis along with Darian Sorenson, a researcher at UC Davis.

"When we first analyzed the experimental data, it occurred to us that the model was revealing things that had not yet occurred in the experiment,'" Medeiros said. "Then maybe researchers could go out and do other experiments to test what the model predicted."

Thriving research ecosystems

Interdisciplinary studies at UC Santa Cruz provide fertile ground for the type of collaboration that went into developing this model, Munch said. "We are sitting right at the intersection of applied math, machine learning, statistics, and really topical ecological problems," he added. "And I think that UC Santa Cruz is a terrific place to do that stuff."

This project is the outcome of the close collaboration between UC Santa Cruz and the NOAA Southwest Fisheries Science Center. "This close relationship is what allows us to do some of this fundamentally interesting work," said Palkovacs, who directs the UC Santa Cruz Fisheries Collaborative Program.

"It's a very close partnership, where the resources of both NOAA and UC Santa Cruz synergize in this really harmonious way."