A way to make sense of ants' wanderings

Simulating spatial dynamics must rate as one of the sexiest things you can do with a computer. You can see fires spreading across a landscape, ants foraging for food, pattern emerging out of chaos, and plants growing in front of your eyes - then see it all again a few minutes later. Spatial simulations are also an important weapon in the armoury of the ecological scientist. They can be used to test hypotheses. They can also be used for prediction: a well-known example is the models used to explore the effect of increasing carbon dioxide on the earth's climate. Numerous studies have demonstrated that using spatially based models is crucial: the preceding generation of highly aggregated ("mean field") models, which ignore the spatial dimension, are incapable of capturing the dynamics of many ecological systems.

There are a couple of problems with spatial modelling. First, the simulations take a lot of computing time because the calculations have to be done repeatedly for each spatial unit. Moreover, many spatial models are stochastic (they include an element of randomness), and that means running a model repeatedly to distinguish the true response from random variation. Second, the only thing you can do with the model is to simulate its behaviour: you cannot inspect the equations and work out what sort of behaviour the model will show, as you could with some simple, first-generation models.

This book sets out to address these problems by showing that, for some classes of spatial model, you can extract equations for the behaviour of the whole system from the equations governing how the basic spatial units interact. You then do not need to simulate thousands of interactions each time step: you just solve the derived equations. For a dyed-in-the-wool simulationist like myself, this is revelatory.

The book is divided into four sections. The first section looks at the analysis of spatial patterns. The second gives a number of examples of reasonably conventional spatial-simulation models. The third introduces some of the techniques available for simplifying spatial complexity and shows how they give results that compare well with those obtained by conventional simulation. This section is the heart of the book, and its first three chapters should be the first part of the book you read. The fourth section provides more detail on methodology. This logical structure unfortunately does not extend to the contents of the individual chapters. One would expect the field data to provide the basis for the simulation models, and the models in turn to be simplified in the third section, but there is very little of this. This trait is particularly unfortunate in this case, since the editors clearly set out with a vision to produce a state-of-the-art handbook.

As a guide for practitioners, there are three significant weaknesses. First, it is hard to see how the techniques introduced can be applied to models other than those used to illustrate them. What happens if we wish to change a growth or competition equation? It is hard to find out how restrictive the techniques are, let alone how to apply them to even slightly different assumptions. The second weakness is the almost total absence of any structuring of information: classifications of different types of models, decision trees to help one choose an appropriate technique, or step-by-step instructions for applying a technique. Finally, there is no accompanying CD-Rom; one containing the various models presented in the book would make a huge difference to its impact and usefulness.

Robert Muetzelfeldt is senior lecturer in ecological modelling, University of Edinburgh.