Alamy

CITIES are often described as being alive. A nice metaphor, but does it mean anything? And, if it does, can town planners and biologists learn from one another? Steven Strogatz, a mathematician at Cornell University, wrote last year that Manhattan and a mouse might just be variations on a single structural theme. His point was that both are, in part, composed of networks for transporting stuff from one place to another. Roads, railways, water and gas mains, sewage pipes and electricity cables all move things around. So do the blood vessels of animals and the sap-carrying xylem and phloem of plants. How far can the analogy be pushed?

Peter Dodds of the University of Vermont draws a particular analogy between the blood system and a suburban railway network. The commuter-rail system of a city ramifies from the centre. The farther out you go, the sparser it is. By analogy, Dr Dodds predicted, the network of capillaries (the tiny blood vessels that permeate tissues) would not be as dense in large animals (where many of them are far from the centre) as it is in small ones. They, too, branch ultimately from a central source—the heart. Surprisingly, no one had looked for this before, but in a paper published recently in Physical Review Letters Dr Dodds shows that this does indeed turn out to be the case.

Dr Dodds's calculations overthrow a 70-year-old rule of thumb which is known as the ¾ law of metabolism. This suggests energy expenditure is proportional to body mass raised to the power of three-quarters. That a mouse expends more energy per gram than an elephant does is well known. But Dr Dodds's calculations show that metabolic rates must fall off faster than had previously been believed as animals get bigger because less glucose than thought is being transported by the smaller than predicted capillary network. The law needs to be adjusted to something more like two-thirds.

Two other studies published in the same volume similarly overthrow conventional wisdom about plants. Traditionally, biologists have celebrated the trunk, branch and twig system of a tree as no accident. Many mathematical formulas have suggested it is the best, least wasteful way to design a distribution network. But the very end of such a network, the leaf, has a different architecture. Unlike the xylem and phloem, the veins in a leaf cross-link and loop. Francis Corson of Rockefeller University in New York used computer models to examine why these loops exist.

From an evolutionary point of view, loops seem inefficient because of the redundancy inherent in a looped network. Dr Corson's models show, however, that this inefficiency is true only if demand for water and the nutrients it contains is constant. By studying fluctuations in demand he discovered one purpose of the loops: they allow for a more nuanced delivery system. Flows can be rerouted through the network in response to local pressures in the environment, such as different evaporation rates in different parts of a leaf.

Another group of researchers at Rockefeller, led by Marcelo Magnasco, also examined vein-loops in leaves. They found that as well as improving efficiency, they also help to ameliorate damage. They discovered this by injecting fluorescent dye into leaves to see if the vein network could distribute the dye to all parts of a leaf that had been damaged. They found the loops are structured in such a way that no matter which piece of a leaf's supply mechanism is disrupted, there is usually enough capacity in the rest to distribute water and nutrients. “It was very surprising,” Dr Magnasco observes. “The famous theorems that tell us that the optimal structure is a tree failed in a spectacular fashion.”

The leaf, then, is a resilient distribution network—one whose principles could be applied to, say, electricity grids. Next time your power is cut off because a tree has fallen on the cable, remember that.