at a bottle of aspirin. The dosage information will likely suggest giving
a fifty pound child about half as much aspirin as a hundred pound child,
who in turn is advised to take about half as much as an adult man. That’s
a linear dosage scale: twice the body size, twice the dose.
But that’s not the right
way to determine dosage, says UNM Professor of Biology James Brown. Metabolic
rate, not body mass, determines how much of a drug—or food, or any
substance—an organism needs or can handle.
Aspirin isn’t a particularly dangerous drug. But what about antibiotics?
Painkillers? Anesthetics? Over- or under-dosing can make a drug therapy
program useless at best—and possibly even fatal.
Brown is investigating
these and other implications of new research and theories. A recent discovery
of why every animal’s metabolic rate equals its mass raised to the
3/4 power (M3/4) is helping scientists
make new predictions about organisms’ behaviors, lifespans, and
In 1997, Brown and two colleagues published a short paper that all but
silenced critics of the 3/4 power law, which was first discovered in the
1930s. By finally showing why the 3/4 rule exists, the team was simultaneously
able to explain deviation from the rule and enable scientists to compare
varying forms of life.
Put simply, blood vessels have a finite amount of space to fill, so they
do so in the most efficient way possible: as a fractal network of vessels
branching out in diminishing size from the heart all the way to the capillaries.
(A fractal is a structure or pattern that is self-similar at different
resolutions; for example, a deciduous tree’s branches are the same
size and shape relative to the bigger limbs as the limbs are to the trunk.
Break off a small piece from the end of a branch, and you’ll see
the same structure.)
Complex math is involved, but the paper proposes that since heart rate,
aorta size, and time of blood circulation all follow quarter-scaling patterns,
metabolic rate must scale by 3/4.
The smallest level in a circulatory system, the capillary, is the same
size in all animals. “We don’t use giant doorknobs or electrical
outlets when we build skyscrapers,” Brown says. The ends of the
network are always the same size.
Organisms aren’t the only things whose scale can be amplified or
minimized in a predictable way. Professor of Biology Bruce Milne is examining
how streams branch within a watershed—like blood vessels, in a fractal
pattern. And like metabolic rate, the amount of runoff in a watershed
is scaled exponentially. Furthermore, the point at which the amount of
runoff shifts from a negative exponent to a positive one—also the
point at which an area’s designation shifts from arid to humid—is
believed to be where the most efficient plants grow: plants that maximize
their conversion of water and solar radiation to plant mass.
Brown points out that his team’s explanation of why the 3/4 law
exists also helps to show why not every animal displays a metabolic rate
that follows the law exactly. Think of gravity, he says: the theory of
gravity tells us that any two objects, regardless of size, will fall at
exactly the same rate. But go outside with a hammer and a feather, and
you’ll quickly see that they don’t hit the ground at the same
time. External factors—air pressure, wind resistance—must
be controlled or eliminated. For this experiment to uphold a law that
we all accept, it must take place in a vacuum.
But life doesn’t exist in a vacuum, and we don’t know what
external forces we must control in order to make the 3/4 law work, Brown
says. He believes that if we could control environments the way we can
control a vacuum, every single organism would display a metabolic rate
exactly equal to M3/4.
Brown explains metabolic rate is a “first-order predictor”
of a huge range of behaviors. Lifespan, rates of evolution, even mating
calls can all be determined once scientists know an animal’s size
and temperature. These and other behaviors “are direct expressions
of metabolic rate,” he says.
Since the 3/4 law appears to exist throughout biology, Brown says, it
should be considered one of a few known fundamental unifying theories
of life. He says the law is further evidence of a common ancestor, and
additional support for Darwin’s theory of evolution.