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An introduction to mathematical models in ecology and evolution: time and space. 2nd edn.
M. Gillman 2009.
Oxford, UK: Wiley-Blackwell. £29.95 (paperback) 168 pp.
‘These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1. With these nine figures, and with this sign 0 which in Arabic is called zephirum, any number can be written, as will be demonstrated’. With this rather exciting beginning to a book, Fibonacci introduced the definition of algorithms to Western Europe in his Liber Abacci (1202). It is therefore no surprise that his rigorous problem description of the growth of rabbit populations, which would later lead to the discovery of exponential growth, is the unofficial precursor of ecological modelling.
It is this rigour, combined with an accessible reading, that characterizes the very approachable second edition of Gillman's book. In the challenging task of covering almost a century of work in the discipline in such a concise book, the author has succeeded in the delicate task of selecting which models are more relevant and self-explanatory, which have overarching consequences beyond the mere scope of their initial applications, and which transcend beyond the typical uncoupling between ecology and evolution. Had the reader already gone through the first edition, he or she will be especially delighted with those new subsections dedicated to evolutionary theory and stochastic processes.
The introduction highlights the definition of a model beyond the obscure mathematical techniques most ecologists attribute to theoretical ecologists, paying special attention to the basics of regression. Chapters 2–4 offer an incisive description of exponential growth from discrete and continuous, to stochastic and structured populations, emphasizing the link between all four approaches and the many commonalities of the exponential behaviour in ecological and evolutionary dynamics. Density dependence and the onset of chaos in simple populations is described in Chapter 5, leading to interacting populations and harvesting models in the next chapter, which also nicely introduces spatially implicit modelling with the Nicholson–Bailey model. Finally, Chapters 7–8 give rather short insights into multiple interacting populations and spatial models.
Nonetheless, the book presents some weaknesses. There is a slow progression from the exciting beginning towards more standard and superficial developments in the last two chapters which, interestingly, have not changed much from the first edition despite the enormous literature in recent years. The exclusion of the first edition's boxes explaining some key techniques relevant to students seems an unfortunate decision, since there are no appendices at all. Further, more highlighted keywords are needed to help the reader use the book also as a reference text. Other details, such as the sudden presentation of a model based on classical epidemiology without explanation of its basic assumptions point towards some lack of care in reviewing those last two chapters.
However, the book, especially suitable to undergraduates in their last year, graduates interested in an introduction to modelling, and lecturers alike, is an acknowledgeable reference. Unlike some other texts on ecological modelling, it deserves the merit of being one of the few books that have actual potential to attract readers that are often frightened by the mere vision of a Greek letter. This is not a trivial point. The ever-impending need for research into complex computational algorithms and mathematical modelling requires continuous recruitment of people attracted to interesting problems in mathematical biology. If your student comes to your office with a sudden interest in ecological models, chances are you can blame Michael Gillman for it.