I must begin this review with a disclosure statement: I served as a beta-tester of pre-publication versions of this text. Thus, although my perspective is not that of a naïve subject, I also have the advantage of having taught from this book over several years. Ellner and Guckenheimer set out to introduce undergraduates to the art of applying dynamic models to a broad range of biological phenomena. They succeeded admirably well: students from both biology and mathematics can gain much from this book. Dynamic Models in Biology would be appropriate for use in a semester or two-quarter course; however, with judicious selection of topics, it can be used in a quarter. My students included undergraduates in biology with knowledge only of calculus, undergraduates in mathematics, and graduate students and academic staff in biology, all enrolled on a ten-week course.
The models discussed in the text include applications to population biology and conservation, animal locomotion, membrane channels, neurophysiology, gene regulation, epidemiology, pattern formation and several types of complex systems. Throughout, the authors skilfully weave together threads of mathematics and biology into a well-integrated fabric. For example, the authors use population dynamics to introduce matrix models and analysis, and then apply these techniques to study membrane channels. The subsequent chapter continues the study of membrane channels with an introduction to differential equations. The study of differential equations and dynamical systems continues with applications to gene regulation and epidemiology.
In selecting exemplar models, Ellner and Guckenheimer elected to include both classic and recently published mechanistic models that correspond directly to empirical results, and encourage students to read the primary literature. Their choices have several implications. First, some standard classic models (for example Lotka-Volterra competition models) may have been omitted. Second, because the authors include so much current work, in one sense the text already could be considered out of date. Third, some sections are heavy going for students who must keep track of nonlinear equations, mathematical analysis and biological details simultaneously. Fourth, and most importantly, students see the pertinence of modelling for biologists: compelling model results can clarify biological relationships that are difficult or impossible to understand by empirical means.
Throughout, the authors minimize technical details and present only the mathematics needed to understand biological phenomena, with the hope that students will be inspired to take additional mathematics courses. In addition, they promote the use of higher-level computer languages, such as R or Matlab, to do the work of modelling and provide downloadable exercises at a course web site. The text includes discussion of statistical considerations in modelling, dynamical systems and separation of timescales. These provide an accessible introduction to topics not generally available to undergraduates.
Further, the opening and closing chapters of the text are among the most important: they offer an entry into modelling philosophy and practice. In these chapters, students can gain considerable insight into precisely how biological observations can be translated into a model.
The exposition is clear, lucid, and generally makes mathematics very comprehensible for biologists. The authors use gentle humour to good effect. For example, students are apt to remember three principles of model development (a good model includes incorrect assumptions; it's acceptable to do things that would make a statistician nervous; if it worked for someone else, it might work for you too) because they are framed as ‘Three Commandments for Modellers’: lie, cheat and steal, respectively.
In a few places, mathematical language creeps into the prose (for example ‘the system. . .does not admit periodic solutions’, p. 121). The authors introduce differential equations via a model for a regulatory network (Elowitz & Leibler Reference Elowitz and Leibler2000), which is akin to introducing driving to a teenager via a turbocharged sports car rather than the stodgy family minivan. I wish that a more extensive discussion of change of variables had been included: this important and useful tool was introduced with an almost trivial example and then used frequently thereafter. But these rare departures from crystalline clarity give me, as a teacher, something to do that is not already well covered by the text.
The book is attractive, the figures are clear and well-labelled, and I found very few typographical errors. Even better, the purchase price is very reasonable.
Overall, Dynamic Models in Biology fills an important niche in the biological modelling canon. It occupies a place on my shelf next to Edelstein-Keshet (Reference Edelstein-Keshet1988) and Murray (Reference Murray1989), and like them, will become a well-thumbed reference.
