When an organism increases in size, two aspects of its geometry change, but at different rates. Surface area increases along two dimensions, or as a square of the increase, while volume changes along three dimensions, or a cube of the increase. Because organisms use their surface to dissipate the heat produced during metabolism, they would soon be in trouble if the rate of metabolism remained the same in large as in small species. For instance, a cat-size mouse would generate a hundred times as much heat as a regular mouse if its metabolic rate remained proportional to its mass, but its surface area for heat dissipation would increase only 22 times. That would be one hot cat-mouse.
Metabolic rate has to be lower in larger species if they are to avoid burning up.
That's the puzzle. Brown has been thinking about scaling and energy flows in nature for decades, but his recent work was initiated in the mid-1990s, when Enquist joined him as a graduate student. The answer was that as far as Kleiber's law was concerned, nothing much was known about plants. Within weeks of Enquist's simple question, he had assembled and analysed data for plants and come up with the equivalent of a relationship between metabolic rate and mass. The two ecologists began to analyse the structure and hydrodynamics of these networks, but pretty soon they realised they were out of their depth mathematically.