Thursday, October 15, 2015

Chaos Theory and Ecology: "A Twisted Path to Equation-Free Prediction"

Complex-chaotic systems are the shoals upon which all the models run aground.
From Quanta:
A strange attractor helps researchers predict what will happen in a chaotic system.
Complex natural systems defy standard mathematical analysis, so one ecologist is throwing out the equations. 
Sometimes ecological data just don’t make sense. The sockeye salmon that spawn in British Columbia’s Fraser River offer a prime example. Scientists have tracked the fishery there since 1948, through numerous upswings and downswings. At first, population numbers seemed inversely correlated with ocean temperatures: The northern Pacific Ocean surface warms and then cools again every few decades, and in the early years of tracking, fish numbers seemed to rise when sea surface temperature fell. To biologists this seemed reasonable, since salmon thrive in cold waters. Represented as an equation, the population-temperature relationship also gave fishery managers a basis for setting catch limits so the salmon population did not crash.

But in the mid-1970s something strange happened: Ocean temperatures and fish numbers went out of sync. The tight correlation that scientists thought they had found between the two variables now seemed illusory, and the salmon population appeared to fluctuate randomly.

Trying to manage a major fishery with such a primitive understanding of its biology seems like folly to George Sugihara, an ecologist at the Scripps Institution of Oceanography in San Diego. But he and his colleagues now think they have solved the mystery of the Fraser River salmon. Their crucial insight? Throw out the equations.

Sugihara’s team has developed an approach based on chaos theory that they call “empirical dynamic modeling,” which makes no assumptions about salmon biology and uses only raw data as input. In designing it, the scientists found that sea surface temperature can in fact help predict population fluctuations, even though the two are not correlated in a simple way. Empirical dynamic modeling, Sugihara said, can reveal hidden causal relationships that lurk in the complex systems that abound in nature.

Sugihara and his colleagues are now putting their insight to use. Earlier this year they reported in the Proceedings of the National Academy of Sciences (PNAS) that their method predicted the 2014 Fraser River salmon run more precisely than any other method. Sugihara’s technique predicted a run of between 4.5 million and 9.1 million fish, while the Pacific Salmon Commission’s models predicted anywhere from 6.9 million to 20 million fish — a forecast so broad as to be of little benefit to, for instance, a fisher wanting to know how many boats to deploy in the coming season. The final count was around 8.8 million....MORE
We'll be back with more next month.