Edition: U.S. / Global

Of Mice and Elephants: a Matter of Scale

Published: January 12, 1999
(Page 2 of 3)

Long before meeting Dr. Brown and Dr. Enquist, Dr. West was interested in how scaling manifests itself in the world of subatomic particles. The strong nuclear force, which binds quarks into neutrons, protons and other particles, is weaker, paradoxically, when the quarks are closer together, but stronger as they are pulled farther apart -- the opposite of what happens with gravity or electromagnetism. Scaling also shows up in Heisenberg's uncertainty principle: the more finely you measure the position of a particle, viewing it on a smaller and smaller scale, the more uncertain its momentum becomes.

''Everything around us is scale dependent,'' Dr. West said. ''It's woven into the fabric of the universe.''

The lesson he took away from this was that you cannot just naively scale things up. He liked to illustrate the idea with Superman. In two panels labeled ''A Scientific Explanation of Clark Kent's Amazing Strength,'' from Superman's first comic book adventure in 1938, the artists invoked a scaling law: ''The lowly ant can support weights hundreds of times its own. The grasshopper leaps what to man would be the space of several city blocks.'' The implication was that on the planet Krypton, Superman's home, strength scaled to body mass in a simple linear manner: If an ant could carry a twig, a Superman or Superwoman could carry a giant ponderosa pine.

But in the rest of the universe, the scaling is actually much slower. Body mass increases along three dimensions, but the strength of legs and arms, which is proportional to their cross-sectional area, increases along just two dimensions. If a man is a million times more massive than an ant, he will be only 1,000,000 to the two-thirds power stronger: about 10,000 times, allowing him to lift objects weighing up to a hundred pounds, not thousands.

Things behave differently at different scales, but there are orderly ways -- scaling laws -- that connect one realm to another. ''I found this enormously exciting,'' Dr. West said. ''That's what got me thinking about scaling in biology.''

At some point he ran across Kleiber's law. ''It is truly amazing because life is easily the most complex of complex systems,'' Dr. West said. ''But in spite of this, it has this absurdly simple scaling law. Something universal is going on.''

Brian Enquist became hooked on scaling as a student at Colorado College in Colorado Springs in 1988. When he was looking for a graduate school to study ecology, he chose the University of New Mexico in Albuquerque partly because a professor there, Dr. Jim Brown, specialized in how scaling occurred in ecosystems.

There are obviously very few large species, like elephants and whales, and a countless number of small species. But who would have expected, as Dr. Enquist learned in one of Dr. Brown's classes, that if one drew a graph with the size of animals on one axis and the number of species on the other axis, the slope of the resulting line would reveal another quarter-power scaling law? Population density, the average number of offspring, the time until reproduction -- all are dependent on body size scaled to quarter-powers.

''As an ecologist you are used to dealing with complexity -- you're essentially embedded in it,'' Dr. Enquist said. ''But all these quarter-power scaling laws hinted that something very general and simple was going on.''

The examples Dr. Brown had given all involved mammals. ''Has anyone found similar laws with plants?'' Dr. Enquist asked. Dr. Brown said: ''I have no idea. Why don't you find out?''

After sifting through piles of data compiled over the years in agricultural and forestry reports, Dr. Enquist found that the same kinds of quarter-power scaling happened in the plant world. He even uncovered an equivalent to Kleiber's law.

It was surprising enough that these laws held among all kinds of animals. That they seemed to apply to plants as well was astonishing. What was the common mechanism involved? ''I asked Jim whether or not we could figure it out,'' Dr. Enquist recalled. ''He kind of rubbed his head and said, 'Do you know how long this is going to take?' ''

They assumed that Kleiber's law, and maybe the other scaling relationships, arose because of the mathematical nature of the networks both animals and trees used to transport nutrients to all their cells and carry away the wastes. A silhouette of the human circulatory system and of the roots and branches of a tree look remarkably similar. But they knew that precisely modeling the systems would require some very difficult mathematics and physics. And they wanted to talk to someone who was used to trafficking in the idea of general laws.

''Physicists tend to look for universals and invariants whereas biologists often get preoccupied with all the variations in nature,'' Dr. Brown said. He knew that the Santa Fe Institute had been established to encourage broad-ranging collaborations. He asked Mike Simmons, then an institute administrator, whether he knew of a physicist interested in tackling biological scaling laws.

The Collaboration

Learning to Speak New Languages