In the July 2004 issue of Ecology, Enquist, Brown and West go further and suggest that their quarter power formula (with some refinements involving not only mass but also temperature) describes the metabolic rates of all living organisms, plant as well as animal. As an associate, biologist James Gillooly has observed, "When you correct for size and temperature, the metabolic rates of a shark, a tomato plant and a tree are remarkably similar."
The authors even claim these metabolic considerations apply generally to biological phenomena on all scales ranging from the mutation rate for DNA to the speed with which ecosystems change. Again very simplistically put: small, hot phenomena proceed at a faster pace than do large, cold ones.
At the risk of losing readers who refuse to attend Imax theaters showing evolution-themed work, I note that it is this line of thought that also leads to a nice resolution of a problem in evolution. Why do various methods of calculating when two species branched apart often lead to quite different answers?
For example, by examining the DNA of rats and mice, seeing how many dissimilarities there are, and calculating how long it would take for this many mutations to come about, geneticists have placed the branching around 40 million years ago. But archaeologists looking at the fossils say that the divergence between rats and mice occurred much more recently, about 12 million years ago.
How can we reconcile these numbers? One answer suggested by Gillooly is based on the work above on metabolic rates. In the January issue of the Proceedings of the National Academy of Sciences, he and his colleagues stress that although small animals don't live as long as larger ones, their metabolic rates are such that their life spans, when measured by these rates rather than by physical times, are comparable to those of bigger animals.
In other words rats and mice, being small, live at a faster metabolic pace than do larger animals. Because of this and an associated quicker accumulation of mutation-inducing free radicals, their DNA mutates faster than that of larger animals, and hence they require less physical time to diverge as much as they have, not 40 million or so years but approximately 12 million years as the fossil record indicates. Similar reconciliations using animal-specific "metabolic clocks" rather than physical ones exist for other pairs of small animals.
Of course, these scaling laws are crude measuring instruments and admit of many exceptions, and not every biologist is convinced of their utility. Nevertheless, scaling laws do give us a rough handle on metabolic rates that is, on the whole, very suggestive. They also explain why there are no 30-foot-tall people walking around, except possibly in the imagination of those who believe that humans and dinosaurs co-existed.
-- Professor of mathematics at Temple University, John Allen Paulos is the author of best-selling books, including "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on ABCNEWS.com appears the first weekend of every month.