Slime mould turns heads

Imagine dropping grains of sand one by one on to the centre of a flat surface. As the pile builds up, there will be from time to time little avalanches of sand grains down its slope. The pile will get bigger, but one property - the slope of its sides - will remain pretty constant. In this state, the pile is at a point of criticality: each part is close to collapsing, and just one more grain may trigger a collapse.

Now let us assume that we plot the frequency distribution of avalanche sizes: how many small, medium and big ones. This distribution follows a power law: we get a large number of small ones and few big ones. There is evidence for the same type of pattern when we look at the extinction of biological species over geological time, suggesting that the two problems have something in common. As new species evolve and get added to the stock of current species, extinctions are triggered - some small, a few very large. Clear analogies exist between a physical and a biological system, and considerable insight can come from a very simple model.

In Signs of Life , Richard Sole and Brian Goodwin take us on a whirlwind tour of the new science of chaos, complexity and emergence, focusing on the insights it can give us into challenging problems in biology. The first two chapters lay the foundations. We are introduced to the notion of deterministic chaos, in which systems show extreme sensitivity to initial conditions and apparently random movement around "attractors". Emergence is illustrated with the formation of circulation cells in the atmosphere, which even leave a visible signal in the hexagonal arrangement of sand dunes in the Sahara, and the beautiful patterns formed by the amoeba stage of the slime mould as it aggregates under conditions of starvation. Complexity is introduced not as an attribute of system structure, but of the behaviour it shows: it is considered to be at a maximum when the system shows fractal behaviour, and this is frequently at a critical transition zone between chaos and order.

The remaining eight chapters take us through more than 40 examples, covering topics such as cell functioning, pattern formation in the growing embryo, brain behaviour, activity patterns and trail following in ant colonies, patterns of species abundance in tropical forests, the high mutation rates shown by some ribonucleic viruses, punctuated equilibrium in evolution, the growth of cities and stock-market behaviour.

A major theme is that biologically realistic patterns of behaviour can be generated from mathematically simple models consisting of idealised particles with simple behaviour. Complex behaviour comes from having large numbers of them, with interactions between them. Much of the book contains examples of such models, many defined with enough detail to enable them to be re-implemented, although it is a shame that the book is not accompanied by a CD containing a representative selection.

Sole and Goodwin deal admirably with the "what" of complex-systems behaviour and speculate on the "why" for biological systems subject to evolutionary pressure - why, for example, so many biological systems appear to be in the critical zone between chaos and order. There is, however, no concluding chapter: the book ends with its last example, the death of civilisations. It needs a final synthesis.

This challenging book is suitable for anyone interested in the nature of life. There is a considerable amount of mathematics, but most of it is presented in boxes, is not critical to understanding the story and is mostly within the grasp of a bright A-level student. My main problem is the book's reliance on prose. While the writing is clear and the figures well chosen and helpful, tables of properties, classification diagrams and rules giving the expected characteristics of different types of system would have helped to make it more accessible.

Robert Muetzelfeldt is senior lecturer, Institute of Ecology and Resource Management, University of Edinburgh.