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A MATHEMATICAL mystery that has dogged biology for decades may finally have
been solved. Researchers in New Mexico say that they have explained why there
are universal relationships between various properties of organisms—such
as blood volume or metabolic rate—and their body mass.

It has long been known, for instance, that the heavier an animal ,the more
slowly it breathes. Respiratory rate is inversely proportional to body mass
raised to the power 1/4. And in all organisms the metabolic rate—the
amount of energy used to sustain life—is roughly proportional to body mass
raised to the power 3/4. It is not obvious why this should be, notes team member
Geoffrey West of Los Alamos National Laboratory. At first glance it seems that
organisms’ energy use should grow in proportion to body mass itself, not some
power of it.

In last week’s issue of Science (vol 276, p 122) the team proposes a
model that explains several dozen such scaling laws. Noting that all organisms
need systems to distribute resources around the body—circulatory systems
in mammals, tracheal tubes in insects, vascular systems in plants, and so
on—the researchers made three assumptions.

First, in order to reach every part of an organism, a system must be a
branching, fractal-like network that fills the whole body. Second, the terminal
branches of a particular type of network—capillaries in a circulatory
system, for instance—are the same size in all organisms. And third,
evolution has tuned the networks to minimise the energy needed to deliver the
goods. So a circulatory system should make a heart work no harder than necessary
to send blood around the body.

When the researchers analysed the consequences of these rules mathematically,
they found exactly the same scaling laws as observed in the real world. “When we
put all this together,” says West, “to my utter amazement, out came these
quarter powers.” The researchers found that they could predict more than a dozen
scaling laws dealing with circulatory systems, such as heart rate and the size
of the aorta.

The results explained a similar number of scaling laws for respiratory
systems. And, since metabolic rate is closely related to factors like the amount
of oxygen transported by the circulatory system, the researchers were also able
to calculate that, as observed, metabolism should increase in proportion to body
mass raised to the 3/4 power.

William Calder, an ecologist at the University of Arizona, says that the
theory is the best explanation to date. “It’s beautiful,” he says. “This is the
most promising thing that has come along—it’s the only thing in town that
works.”

West’s colleagues, James Brown and Brian Enquist of the University of New
Mexico, hope to extend the model from individuals to ecological systems. “Many
ecological phenomena also scale with quarter powers,” Brown says, including life
span and duration of pregnancy in mammals.