Life's Universal Scaling Law

It ain't easy being green. Biology has long suffered under the label "soft science," a term used (often disparagingly) to draw a contrast with the "hard sciences" of physics and chemistry, whose laws are guaranteed with the certainty of mathematics. But this picture is not altogether true. While biological processes are more complex than physical ones, making simple mathematical formulas harder to come by, there are yet some mathematical rules that hold with a remarkable degree of consistency.

One famous example is the relationship of a animal's mass to its metabolism (the rate at which it expends energy). This relationship is expressed in the simple formula

R = R₀M^3/4,

where R is the metabolic rate, R₀ is a constant, and M is the mass of the organism.

Separate laws exist for mammals, birds, unicellular organisms, and even living structures like mitochondria within cells. The values of R₀ are
different for each law, but the mysterious 3/4 exponent stays the same.

These laws have been observed since 1930, but the reason for the 3/4 exponent has been a mystery until recently. The discovery by Geoff West et al of a mechanism underlying this law was a major triumph for the complex systems movement: a universal law of life explained by complex systems principles.

Specifically, West showed that the 3/4 exponent comes from the way a living thing distributes its resources. If the cells in an animal acted like independent beings, each gathering and consuming its own food, the metabolic rate would be a simple multiple of the mass, that is

R = R₀M

with no exponent. But the cells of an animal aren't independent. They work together to collect, process, and consume energy. To do this they need networks (such as blood vessels) to move resources around. West and his collaborators showed that the 3/4 exponent is determined by the requirements that the network a) reach every part of the animal's body, and b) waste as little energy as possible.

Extending this approach, they were able to explain other scaling laws like the relationship between heart rate and mass. Currently, West is investigating scaling laws in large-scale living communities, such as forests and cities.

I haven't talked much about network theory (a topic for another time perhaps) but West's work suggests the great potential of this complex systems subfield to explain some of life's mysteries.