Pendulums, predators and prey: The ecology of coupled oscillations

ANN ARBOR, Mich.---Connect one pendulum to another with a spring, and in time the motions of the two swinging levers will become coordinated.

This behavior of coupled oscillators---long a fascination of physicists and mathematicians---also can help biologists seeking to understand such questions as why some locations overflow with plants and animals while others are bereft, University of Michigan theoretical ecologist John Vandermeer maintains.

In the cover article for the December issue of the journal BioScience, Vandermeer summarizes theoretical work he has done over the past decade, leading to his conclusion that ecologists seeking to understand complex interactions in nature should pay closer attention to coupled oscillations.

The basic idea of oscillating populations is not new to ecology.

"We know that any predator-prey system, say lions and zebras for example, shows oscillations," said Vandermeer, who is the Margaret Davis Collegiate Professor of Ecology and Evolutionary Biology. "If there are lots of lions preying on zebras, numbers of zebras decline; then because zebras are scarce, lions starve and their numbers dwindle, allowing the zebra population to build up again. You see this oscillation, changing on a regular basis from lots of predators with few prey to lots of prey with few predators. The pattern is like waves or pulsations."

What gets interesting is when two independently oscillating systems, such as lions preying on zebras and cheetahs preying on impalas, become connected through the invasion of a third predator---leopards, for instance.

"When they become connected, the situation is very much like connecting two springs together---the ups and downs get into regular patterns." In the case of lions, cheetahs and leopards, bringing leopards into the system causes lion and cheetah populations to oscillate in phase with each other----peaking and declining at the same time. That works to the le

Contact: Nancy Ross-Flanigan
University of Michigan

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