Monday, December 04, 2006


Theory of oscillations may explain biological mysteries

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 (website) 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.

Continued at "Theory of oscillations may explain biological mysteries"

Based on the Bioscience paper "Oscillating Populations and Biodiversity Maintenance"


Species persistence in the face of competitive or predatory pressure has long been assumed to be a consequence of either dynamic equilibrium or stochastic longevity. More recently, however, the complex intersection of nonlinear dynamics with elementary ecological interactions has provided a distinct platform for conceptualizing the problem of species coexistence. One well-known result from nonlinear dynamics is that oscillating systems will tend to coordinate with one another when coupled, even if the coupling is extremely weak. This elementary result yields remarkable insights in many fields of study. Here I summarize recent results showing that a particular structure emerging from a nonlinear analysis of the classic equations of ecology can be merged with more qualitative ideas to form a possible general framework for analyzing species diversity. As a specific example, I examine the case of two consumer-resource systems that, when coupled, inevitably produce some kind of phase coordination. Understanding the nature of that phase coordination provides a qualitative viewpoint for understanding exclusion and coexistence in this example. Finally, I discuss possible applications to other classical ecological questions.

Full text of the above paper is currently available via the American Institute of Biological Sciences (AIBS) press release

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