Dynamic Models in Biology Stephen P. Ellner and John Guckenheimer Princeton University Press (2006), 352 pp., Price: US$99.50 (cloth) and US$45.00 (paperback) ISBN 0-691-11843-4 (cloth) and 0-691-12589-9 (paperback).
Reviewer: Glen Watson, Professor, Dept. of Mechanical Engineering, University of Saskatchewan, Saskatoon, Canada

Dynamic Models in Biology by Stephen P. Ellner and John Guckenheimer is the joint product of a biologist and a mathematician. Ellner is Professor of Ecology and Evolutionary Biology and John Guckenheimer is Professor of Mathematics; both are at Cornell University. The book was developed from a course taught by these noted scientists.

Dynamic Models in Biology will be very useful for helping biology students to gain a realistic view of what mathematics can do to help both students and practicing biologists predict the mixes of various species in the future. The level of this book is such that anyone with two or three calculus classes will not have too much trouble with the book. I do believe however that people who do not have a reasonable mathematical background will have some problems.

The discussion on spawning salmon was particularly useful and interesting. I very much liked the exercises on the killer whales and the “eigenvector discussion” was very informative. I feel that engineering students should be introduced to structured population dynamics. I also liked the portion on Elasticity Analysis and Reproductive success.

The book is excellently supplemented with Matlab and R exercises on the author’s website. Also included are computer labs in Matlab and R format.

Chapters in the book include the following:

1. What are dynamic models?
2. Matrix models and structured population dynamics
3. Membrane channels and action potentials
4. Cellular dynamics: pathways of gene expression
5. Dynamical systems
6. Differential equation models for infectious disease
7. Spatial patterns in biology
8. Agent-based and other computational models for complex systems
9. Building dynamic models