Scientists have devised a computer model that may help solve a long-standing mystery: how physiological factors such as metabolic rate and life-span are related to body size. The model, described in today's issue of Science,* suggests that the circulatory system's branching pattern may be a major factor in the evolution of the vast array of shapes and sizes in the living world.
From microbes to whales, organisms span at least 21 powers of 10 in size. But the relationship between heft and physiology has left biologists perplexed. Metabolic rate, for example, varies in proportion to the 3/4 power of an organism's mass--the bigger the creature, the slower its metabolism--and similar relationships have been found for variables such as life-span, age at sexual maturation, and length of pregnancy (1/4, 3/4, and -1/4 powers of mass). The common factor of a 1/4 power would seem odd: 1/3 powers would be much more logical if metabolic rate reflected only the three-dimensional constraints of body size.
Determined to solve this puzzle, ecologists James Brown and Brian Enquist of the University of New Mexico, Albuquerque, and physicist Geoffrey West of Los Alamos National Laboratory analyzed organisms in terms of the geometry and physics of a network of linear tubes that transport nutrients and wastes through the body. A key insight came when the team realized that such a network could best be described as a space-filling, fractallike branching system. Fractal geometry, pioneered by physicist Benoit Mandelbrot, has been used to model many seemingly complex natural structures, from snowflakes to the branching patterns of streams, by repeatedly applying a simple mathematical formula. "Researchers previously have tended to focus on individual parts of transport systems, such as major vessels or capillary beds, and have not focused on the whole network," says Brown.
Using this approach, the team developed a general model for the design of distribution networks that incorporates both fractal geometry and hydrodynamics. The researchers believe that their model incorporates the most fundamental features of a real network. One thing it predicts is the degree of branching in a circulatory system: A whale is 107 heavier than a mouse, but the model suggests that a whale needs only 70% more branches in its circulatory system to supply its body. And, to the team's delight, the model predicts the enigmatic 1/4-power scaling. "They have really come up with something quite unexpected," says ecologist William Calder of the University of Arizona. "It's stronger than any model that has come along before."