Elements of mathematical ecology. Reprint with corrections.

*(English)*Zbl 1060.92058
Cambridge: Cambridge University Press (ISBN 0-521-00150-1/pbk; 0-521-80213-X/hbk; 978-0-511-60852-0/ebook). ix, 453 p. (2003).

This textbook is suitable for a year’s course of study for upper level students and beginning researchers in ecology, mathematical biology and applied mathematics. The topics in the book, all of which concern the dynamics of biological populations, are divided into two types. The first part of the book deals with unstructured models (which ignore most of the variability found in natural populations). In this simplified context, the author covers a number of basic mathematical and biological topics, including stability, bifurcations, density dependence, basic multi-species interactions (predation, competition, and mutualism), demographic stochasticity, and some optimal control theory (in the context of the management of renewable resources).

The second part of the book is an introduction to structured population dynamics. The author considers modeling methodology and analysis of populations structured by physical space, chronological age, and gender. The reader is introduced to most of the classical modeling approaches in population and ecological dynamics, as well as to some current modeling methodology. Models of a wide variety of types make their appearance, including continuous and discrete time models, differential equations (ordinary, delay, and partial), integral equations, difference equations, and Markov chains and branching processes. The focus is on simpler mechanistic models concerned with interesting hypotheses or explanations as opposed to detailed models that provide detailed descriptions and predictions.

While mathematical concepts and methods are not slighted, no proofs are given. The author’s preference is “for solving problems over proving theorems” and he holds “to a middle course that should appear natural to applied mathematics and to theoretical biologists”. The book provides an excellent introduction to mathematical ecology for the reader with an appropriate mathematical background (calculus, differential equations and probability theory). Some exercises are provided (although no solutions are included).

The second part of the book is an introduction to structured population dynamics. The author considers modeling methodology and analysis of populations structured by physical space, chronological age, and gender. The reader is introduced to most of the classical modeling approaches in population and ecological dynamics, as well as to some current modeling methodology. Models of a wide variety of types make their appearance, including continuous and discrete time models, differential equations (ordinary, delay, and partial), integral equations, difference equations, and Markov chains and branching processes. The focus is on simpler mechanistic models concerned with interesting hypotheses or explanations as opposed to detailed models that provide detailed descriptions and predictions.

While mathematical concepts and methods are not slighted, no proofs are given. The author’s preference is “for solving problems over proving theorems” and he holds “to a middle course that should appear natural to applied mathematics and to theoretical biologists”. The book provides an excellent introduction to mathematical ecology for the reader with an appropriate mathematical background (calculus, differential equations and probability theory). Some exercises are provided (although no solutions are included).

Reviewer: Jim M. Cushing (Tucson)