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The possibility of mathematical power laws governing the scaling of fundamental biological properties, such as metabolic rate, within a species group has been strongly suspected for almost a century. But since 1997, the laws have been confirmed by overwhelming experimental evidence and backed by convincing mathematical theory. Before, research biologists were puzzled by the fact that a wide range of ultimately related properties, such as aortal surface area in warm-blooded animals, and trunks or stems in plants, ranged in line with a fourth, rather than a third, power law. This latter law was established in 1932.
This long-awaited explanation of why biology scales in four rather than three dimensions emerged during the late 1990s, largely through the interdisciplinary work of' physicist Geoffrey West, and ecologists James Brown and Brian Enquist, with their 1997 publication. (1) Subsequent papers from this team showed that their theory is applicable to all life forms. (2-5)
The work has attracted attention--both positive and negative. "I think it's very important," says evolutionary biologist and popular science writer Richard Dawkins. "It's a powerful theory, explaining a wide range of biological scale rules with great economy." It tends, he says, "to be fully accepted by people who learn about it, and I would hope that it will become better known."
On the negative side, physicists such as Peter Dodds and others at the Massachusetts Institute of Technology claimed in 2001 that their analyses of data sets taken over a long period did not provide irrefutable evidence for 3/4 power scaling. (6) Other physicists argue that the West team's work is based on assumptions that need not be made. Jayanth Banavar, a theoretical physicist at Pennsylvania State University, believes that Brown's assumption that a resource network must have a fractal branching structure is unnecessary. "The question we asked is, `Which aspects of the problem are essential [for explaining the 3/4 power scaling] and which are really peripheral?'" says Banavar. "Fractality is not the underlying explanation."
Although the work is not yet well known among biologists, practical applications of these laws are emerging. Examples include determination of correct drug doses for humans based on trials on smaller animals, and acreage needs of animals of all sizes in the wild.
UNDERSTANDING POWER LAWS Here's a geometry refresher. A power law relates one variable to another raised to a constant power. The general form takes y = [x.sup.a], where y and x are variables, and a is a constant exponent (hence power) such as 2. By contrast, an exponential …