An Illustrated Guide to Theoretical Ecology

Abstract

AN ILLUSTRATED GUIDE TO THEORETICAL ECOLOGY by Ted J. case Oxford University Press, 2000, 449 pp. An Illustrated Guide to Theoretical Ecology may seem an unusual book review subject for this journal. After all, our readers are mathematics and computer science teachers, not ecologists or biologists. Nevertheless, I believe that this book warrants examination by mathematics teachers for several reasons. First, An Illustrated Guide to Theoretical Ecology is well written. The ecology is clear, even for a novice, and the mathematics is presented thoroughly and meticulously. Second, I am convinced that we best connect with our non-mathematics majors when we show some understanding of how the mathematics we are teaching plays a role in other disciplines. Ecology is a particularly well-suited field for showing mathematics at work. Finally, mathematical ideas often are best presented in context. It has been my experience that consumers of mathematics (scientists, economists, etc.) frequently have unique points of view on mathematical concepts that may help mathematics students learn their subject. An Illustrated Guide to Theoretical Ecology has two main foci: population ecology and community ecology. The author, Ted Case, a professor of biology at the University of California-San Diego, is a respected population and community ecologist. Case has used the mathematical methods he teaches in this book in his own work with lizards, desert ants, and habitat fragmentation. He has a wonderful grasp of mathematics and the ability to make the formalism come alive. Population ecology is concerned with the growth and decay of populations of species. Case takes the student from simple exponential growth through the whole panoply of ecological modeling techniques that address spatial, temporal, and individual variations in birth and death rates, age structures, density-dependent population growth, life history trade-offs, reproductive value, natural selection, and aging. The mathematics involved in studying these topics is equally broad. The student will learn about difference and differential equations, log scales, Gaussian distributions, geometric and arithmetic means, variance, central limit theorem, matrices and vectors, eigenvalues and eigenvectors, limits, Ricker diagrams, stability, combinatorics, and probability. Supporters of the reform movement in algebra and calculus will be pleased to see that An Illustrated Guide to Theoretical Ecology takes the Rule of Three quite seriously and uses symbolic, numeric, and graphic views of functions to describe and explain. …