J. H. Vandermeer and D. E. Goldberg, eds.
Princeton University Press, Princeton NJ, 2003
304 pp., $35.00
ISBN: 0-691-11441-2

In this latest addition to the growing number of texts aimed at life scientists interested in learning about population ecology, Vandermeer and Goldberg make a strong case for the necessity of mathematical literacy for practicing ecologists of any ilk. What is especially nice about their treatment of the material is that they include liberal doses of examples from up-to-date field experiments, with all of the appropriate caveats and emphasis on the difficulty of getting data that is "clean" enough for most worthwhile mathematical analyses. Students and professionals alike should come away from reading this book with a renewed or continued appreciation of the challenges and power of the application of mathematical models to ecological field data. Vandermeer and Goldberg write in an easy style, friendly but technically sound and precise. Apart from a few typographical errors early on, the equations and examples are clearly explained and easy to understand. More mathematically sophisticated readers will welcome new and updated examples of familiar concepts, whereas novices will appreciate the care the authors have taken to include thorough explanations of the concepts, including more detailed lessons in appendices where important.

After a brief introduction to simple models of dynamics, the authors move on to explain how life history data can be used in matrix model analyses, with a helpful extensive lesson on linear algebra. In the third chapter, the authors describe qualitative analyses of nonequilibrium systems. This section is well written and informs readers in a logical, clear fashion about techniques for analyzing dynamical systems while also explaining the historical context of these methods. In particular, the authors draw analogies between traditional equilibrium-based analyses of physical systems to older ecological perspectives, highlighting the more recent transition in the ecological sciences to a focus on nonequilibrium dynamics. In the next chapter, they continue with a discussion of more complex population dynamics, carefully dispelling popular misconceptions and explaining the nuances of chaos theory that are most relevant to ecological applications. In the final three chapters, Vandermeer and Goldberg move from single-species populations to multispecies interactions, first describing spatially explicit models through a primer on metapopulation theory (with some classic examples) and then moving on to predator-prey, host-parasite, competition/mutualism scenarios, and models.

The book in some ways is structured much like a typical textbook in ecology, with an emphasis on explanations of the quantitative aspects. The authors do, however, use several examples from the ecological literature to illustrate each of the basic quantitative principles covered. Despite the fact that both authors have backgrounds and extensive research experience in agricultural ecology, the examples provided are not particularly biased toward entomological or agroecological scenarios-a feature that renders this book as useful in teaching a basic ecology class as in teaching an applied entomological seminar.

While the book does a good job of covering most concepts important to basic population ecology, the level of detail given to different theoretical constructs is not entirely consistent. For instance, familiarity with basic ecological theory in some cases is assumed (e.g., the MacArthur-Wilson Equilibrium Theory of Biogeography as the inspiration for modern-day advances in spatially explicit modeling), but in other cases, the theory is derived from first principles (e.g., Lotka-Volterra predator-prey equations, the focus of chapter 6). This is not necessarily a liability but is worth keeping in mind if readers were planning to use the book to teach students with a background in either ecology/entomology or applied mathematics.

Finally, topics such as diffusion and other types of differential equation models, popular tools for a variety of applications in invasion ecology and predator-prey interactions, are not described or mentioned. Readers looking for more technical descriptions of these and other more complex models would be better off looking at recent texts by Kot (2001), Edelstein-Keshet (2005), or Turchin (2003). Population Ecology is really a primer rather than a comprehensive mathematical text; its purpose, as stated by the authors themselves, is to introduce readers to a range of basic quantitative principles that have proven to be essential for anyone aspiring to attain literacy in basic or applied population ecology. An elegant rationale for this need is given in the last chapter, which gives a thoughtful overview of how population ecology underlies many of today's global problems, from AIDS epidemics in Africa to economic development in Central America. The authors do a good job of providing a comprehensive overview of the tools essential for a basic understanding of these complex issues.

References
Edelstein-Keshet L. Mathematical models in biology. Philadelphia, PA, Society for Industrial and Applied Mathematics, 2005.

Kot M. Elements of mathematical ecology. Cambridge, UK, Cambridge University Press, 2001.

Turchin P. Complex population dynamics: a theoretical/empirical synthesis. Princeton, NJ, Princeton University Press, 2003.

John E. Banks
Environmental Science, Interdisciplinary Arts and Sciences
University of Washington
Tacoma, Washington

Environmental Entomology
Vol. 35, No. 3, June 2006, Page 811 - 811