must fit itself inside a compact body existing in a three-dimensional world.
West, Brown, and Enquist do not have the field to themselves. While some biologists were accusing them of oversimplifying biology in trying to explain metabolic rate, some physicists thought their model wasn’t simple enough. “We read the paper, and it seemed somewhat complicated,” says Jayanth Banavar, a physicist at Pennsylvania State University. “We thought there must be some other explanation.”
Banavar teamed up with two other physicists, Amos Maritan and Andrea Rinaldo, and a biologist, John Damuth, to design a network using different criteria. Rather than looking for a network that maximized energy supply, they sought one that minimized the rate of flow in the system and so the volume of blood. They considered a body as a set of delivery stations, cells, serviced by a network of pipes stemming from a single source. Unlike the fractal model, the network can flow through its destination and go on to somewhere else. Cells in this model are not like twigs at the end of a branch. They are more like stations on a railway line, where some people (resources) get off. As the network expands, the amount of fluid in the system must rise. The team showed that, in the most efficient three-dimensional network, where the distance from source to destination is minimized, the amount of fluid must rise proportional to the volume of the network raised to the fourth power.
This model got the desired number 4—and, incidentally, also predicted the geometry and flow rates of river networks—but it created a problem. As a network, or an animal, grows, the amount of fluid that is in transit at any time, and so not available to be used, must increase. So for the rate of supply to keep pace with network size, more and more fluid is needed. If animals were like this, big ones would need a volume of blood larger than the volume of their body. So Banavar’s team thought again and forced their model network to stay contained inside the body. In this case, as the network grows, its capacity to supply resources declines, and so the cells receiving the resources must adjust