Math discovery may aid resource management

With the aid of a chance discovery by a graduate student, scientists from Oregon State University have identified, dusted off and found a new use for an old math theory from the early 1800s that could revolutionize the management of lands, protection of species and study of ecology.

The discovery promises for the first time to address the enormous complexities of the natural world with the powerful tools of advanced mathematics – which, until now, have been of limited use in the study of many natural resource issues. Existing mathematical approaches have often been relegated to the sidelines, in favor of time-consuming and costly experiments or trial-and-error management.

The findings are being published in the journal American Naturalist and are co-authored by Jeffrey Dambacher, Hans Luh, Hiram Li and Philippe Rossignol.

“This research should have major implications for the management of natural resources around the world,” said Philippe Rossignol, a professor of fisheries and wildlife at OSU. “We’re going to be able to apply mathematics to predict what might happen with a great deal more certainty than ever before. It could significantly improve the ability of ecologists, land managers and other scientists to address many issues, anything from the clarity of Crater Lake to fisheries management or emerging diseases.”

OSU researchers are already using the new approaches and formulas described in this research to tackle problems from invasive species in Yaquina Bay to the ecological impact of bullfrogs and the stability of an Oregon sea urchin fishery. But the concepts are so useful and so broad, the scientists say, that these projects are barely scratching the surface of this technology’s potential.

This new insight in ecological science began when OSU researchers were struggling to resolve a mathematical paradox first suggested in 1973 by a famous ecologist named Robert May, who produced a mathematical theory that made perfect sense but seemed at odds with the way the world really worked.

“One of the basic concepts of ecology for generations had been that the complexity of the natural world is a big part of what makes it persistent, that the many interrelationships, interactions and food webs among different species evolved into stable systems that worked well together,” said Hiram Li, an OSU professor of fisheries and wildlife.

“But Robert May came along with a mathematical theory that suggested that increased complexity in a natural system should actually make it less stable,” Li said. “The math seemed to work perfectly, but our observations of the real world ran contrary to this.”

For 30 years researchers have debated this paradox between the way the world appeared to work – a “tangled web” of thriving organisms, as Charles Darwin described it – with May’s mathematical description of the way it should work. Since the mathematical theory had not been reconciled with real-world observations, many field ecologists dismissed its importance. Applied mathematics are being used to manage fishing, hunting and control of pests, Li said, in situations that only relate to one or two species – but they have not been applied to ecosystems or communities.

“What we came to realize, however, is that May’s mathematical analysis was not really wrong, it just didn’t go far enough, as even May conceded,” Rossignol said. “So what we’ve tried to do is shine some light into this black box, by identifying more degrees of stability and using more variables, allowing the math to consider complexity and eventually arrive at different conclusions.”

The researchers were struggling with their approach when Jeffrey Dambacher, then an OSU graduate student, had a chance conversation about what was needed with some faculty in OSU’s Department of Mathematics. They mentioned a largely forgotten theorem of matrix algebra developed in the early 1800s by the French mathematician Augustin Cauchy. The theory, so far as they knew, had never yet found any useful application. But it appeared to be ideal for the problem at hand.

“It became immediately clear that this mathematical approach would take us in the direction we needed,” Rossignol said. “It gives us a way to describe complex natural populations in more realistic terms, consider indirect interactions and really provide a much more accurate view of how natural systems will work. We’ll be far more accurate with our predictions and can use this approach in the new field of adaptive management, improving our natural resource management approaches as we go.”

The OSU scientists have fine-tuned this approach in continued research and outlined it in their new publication for other scientists to use in a comparatively simple, well-defined system.

“We’re now bridging the world of biology and mathematics in a way that will let people approach complex problems using descriptive, qualitative information,” Li said. “It complements data-hungry mathematical models by identifying key interactions to focus on when gathering quantitative data from a complex system. This reduces the need for complex, expensive and time-consuming experiments.

“With this approach, I can now do a computation in minutes that used to take forever. I’d literally write equations by hand on 20 feet of rolled-out butcher paper and hope I didn’t make a mistake along the way.” The technique is also reliable, Li said. Using only text descriptions, these qualitative models have duplicated the predictions of studies done with classical ecological experiments.

In one recent usage, an OSU graduate student used this system to study the stability of an Oregon sea urchin fishery and answer questions about the long-term value of reserves. This would have been almost impossible with real-world experiments, but after the computer ran through 12 million mathematical combinations of possible outcomes, the scientists had the answers they had sought.

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This research was supported by grants from the U.S. Geological Survey and the Oregon Department of Fisheries and Wildlife.

By David Stauth, 541-737-0787
SOURCES: Philippe Rossignol, 541-737-5509; Hiram Li, 541-737-4531