They call it "biology's theory of everything".

A single formula that could explain everything from the growth of a single cell to the lifespan of an elephant to the spread of species across the world.

The theory of "metabolic ecology" was devised 10 years ago by a maverick US physicist. Some think his theory might be as important to biology as Newton's work was to physics. Others feel it is simply a magic bullet.

"Metabolic ecology is a bit like biology's version of string theory," says John Whitfield, author of a new book on the subject, which he will discuss on Monday at the Edinburgh International Science Festival. "If it's correct, it explains an awful lot. But many biologists reject such grand notions, preferring to deal only with what can be seen and sniffed."

Whitfield's book tells the story of the search for the fundamental laws of living organisms, in particular the link between an animal's body size, its heart rate and its lifespan.

Big animals have relatively slower metabolic rates - this is why a shrew must eat more than its body weight each day to survive, but an elephant eats only one-50th of its bulk per day. The net result is that both species share the same number of heartbeats in a lifetime.

This remarkable phenomenon can be expressed mathematically as a scaling law, which states that the metabolic rate of a species is proportional to its mass raised to the power of three-quarters.

This formula holds true for almost every living organism. From whales to trees, the relationship is the same - but no-one understood why.

Then, in 1997, Geoffrey West, a physicist at the Santa Fe Institute in New Mexico, working with ecologists Jim Brown and Brian Enquist, published a theory. They argued that the scaling is the result of the fractal-like structure of the network of blood vessels that supply nutrients to the cells in an animal's body. A similar fractal geometry can be seen in plant veins.

West, Brown and Enquist believe that metabolic rate is the conductor of life's orchestra, setting the tempo for a host of other processes. Understand it, and we can predict many other things about a creature - how quickly it will grow and how many offspring it will have. They argue that their theory can predict the properties of large-scale ecological networks, such as forests.

Their work has drawn praise from many biologists, including the popular science writer and Oxford professor Richard Dawkins, who describes it as "a theory of enormous power, explaining a huge range of facts with great economy". But it has also drawn criticism, due to some notable exceptions. Crayfish stubbornly refuse to comply with the scaling law.

Despite the cynicism, a growing band of scientists are making bolder claims about metabolic ecology. For instance, the amount of energy needed to create a new species of microscopic sea creature is around the same as the energy that the sun shines on the earth in a day. "This story is not finished," says Whitfield. "Metabolic ecology is sure to be hot for years to come."

  • John Whitfield is at the Edinburgh International Science Festival on Monday.