Ecological modelling is a discipline that has grown out of the early attempts to explain the dynamics of populations by scientists Lotka and Volterra in the 1920s, and Andrewartha and Birch in the 1950s. These earlier modelling activities were largely based on mean-field approaches with ordinary-differential equations (ODEs), which require mathematical skills that are beyond the experience of many biologists and ecologists. ODEs were needed to provide elegant summaries of system behaviour. Early ecological modelling was therefore somewhat esoteric. The appearance of the personal computer (PC) changed this, because high-level computer programming languages became available and discrete time models, which require fewer numerical skills, became within reach of any ecologist with simple computer skills. Modelling in discrete rather than continuous time effectively allowed ecologists to breakdown an ecological process into a series of events which could be modelled (albeit often crudely) as a series of sequential steps in a computer program. The PC effectively introduced the era of simulation, where the modeller can predict the trends in a system step-by-step repeatedly, thus allowing extensive opportunities for modelling the multiplicity of system responses to inputs. Whilst there has been increasing availability of modelling hardware resources, the development of an underlying theoretical basis for ecological modelling has been piecemeal. Indeed, it would be fair to say that in common with much molecular biology, where we can measure but often not explain, the technology for doing the discipline is ahead of the underlying theory. In effect, we have a discipline where many can participate, but there appears to be no unified way of doing it. This textbook is a valiant attempt to create this underpinning. It attempts to provide not only the scientific theory but also the practical means of carrying out modelling, but for one component of modelling only. The key question is does it succeed and how does it compare with other material? The bench mark book against which to compare this text is Jorgensen and Benderichio (Reference Jorgensen and Benderichio2001), which might be argued to be the best available text book.

This present book is divided into four parts. These are logically ordered from an introductory section (which could have been better named), through theory sections on the conceptual model, to formulating the mathematical form, to model evaluation and onto modelling practice. It has a final section linking theory and practice. A key feature of the book is the use of case studies which are based on straightforward ecological questions with a practical interest: Harvesting for winter, Population extinction and a Forage-grazing model. These models are of varying complexity and should give students some insights into modelling discrete-time dynamic processes. Given the broad spectrum of ecological modelling activities, other than this narrow field the title of the book is probably not a true representation of what ecological modelling is as a discipline. This notwithstanding, I found the underpinning modelling theory of interest, but not anywhere near as good as the material presented in Jorgensen and Bendericchio (Reference Jorgensen and Benderichio2001), which starts off at a lower level and is less complex. As an introductory text, the book clearly avoids any hard numerical representations in the examples used. Tables and figures are generated from the discrete time-step models, which should be easy for the reader to follow. The logic is usually clear. The authors avoid any mention of how the calculations are performed, although for some of the models simple spreadsheets are a clear way forward.

I have two major practical issues with the textbook that I think are likely to impact on its success in the field. Firstly, the authors have invented a coding system for the different stages in the modelling process (coding I to IV, with a series of subscripts) that they use throughout the book to define and then describe the modelling process. I found this short-hand extremely irritating: phrases like (Ii_b)(IDM₁) are not an effective shorthand, and I found the need to refer to a figure early in the book a major disincentive to reviewing the text, let alone using it. I would have much preferred the use of simple English. Second, the authors have used a conceptual diagram format that is very complicated and likely to turn off proto-ecological modellers. The format they have used is similar to that used in an ‘off the shelf’ software modelling package. As with the modelling notation, the curvy lines and multiple symbols use in this diagrammatic approach are not taken on board easily. I think students need to be led to complex pathway diagrams of this type by simpler model flowcharts, spider diagrams and circle models. These are more useful for forming concepts before dropping straight into a formalization of pathways.

So, does this book provide an easier route into ecological modelling than the currently available texts? I remain to be convinced. First, the title promises more than it actually delivers; discrete-time modelling is important, but it is not all there is to ecological modelling. Second, the text has not made the step from conceptualization to model formation as easy as it could have done. Third, the use of complex notation and a restricted form of model diagram presentation will almost certainly be a disincentive to read the text. In an age where there is an increasing need for ecological modelling and a comparatively low numerical skills base in biologists, I am afraid that I would still recommend Jorgensen and Bendericchio (Reference Jorgensen and Benderichio2001), even if it is a higher level text.