Mathematical models underpin much ecological theory, and are widely used in many areas of applied ecology and environmental management. Yet most students of ecology and environmental science receive much less formal training in mathematics than their counterparts in other scientific disciplines. Motivating both graduate and undergraduate students to study ecological dynamics thus requires an introduction which is initially accessible with limited mathematical and computational skill, and yet offers glimpses of the state of the art in at least some areas. This volume represents our attempt to reconcile these conflicting demands, using material drawn from recent courses in a variety of universities, at both undergraduate and graduate level. The minimum prerequisite is `to have mastered, but forgotten, introductory calculus'. However there is no miracle recipe for acquiring mathematical skills which normally require years of experience, and the serious student with a weak mathematical background will need to supplement our material with sustained study of basic calculus.
The book is in three parts. Part I, Methodologies and Techniques, defines our modelling philosophy and introduces essential concepts for describing and analysing dynamical systems. Part II, Individuals to Ecosystems, is the heart of the book and introduces the issues that arise in formulating models at different levels of ecological organization. Here, the flow of argument is dictated by ecological reasoning, not by the mathematics. Part III, Focus on Structure, which is targeted at the more advanced reader, introduces models of `structured' and spatially extended populations.
Approximately 25% of the book is devoted to case studies, drawn from our own research, where models are used to address ecological questions. When introducing experimental or observational data, we emphasize the broad ecological or environmental context, together with any specialized concerns that motivated the original study. We also detail the questions to be answered and guide the reader through the many judgement calls involved in model formulation. Finally, we outline the key steps in the analysis and offer our interpretation of the results. All the case studies are open-ended; we encourage readers to explore them further and to challenge our approaches wherever possible.
All chapters (other than Chapter 1) end with exercises and projects. Exercises have the narrow, but important, aim of enhancing the reader's technical proficiency, through execution of tightly defined tasks. Projects are longer and/or more flexible in scope, and provide a context for thinking more broadly about some of the technical and modeling issues raised in the chapter.
Almost all work on ecological dynamics requires numerical solutions of dynamic equations. While enthusiasts may wish to write their own programs in a high-level language such as c,pascal, or fortran, most readers will prefer to use purpose-built software. Although there is no optimal choice for this purpose, it is often sensible for the beginners to use the same set-up as friends or colleagues! We have therefore designed this book to be as near as possible independent of the reader's choice of computing environment.
Solutions to many of our simpler equations can be generated on any reputable spreadsheet (e.g. Microsoft excel), but such implementations are distressingly slow for more elaborate models. An alternative approach for the committed theorist is to use `computer algebra' programs such as mathematica or maple; but this involves a too steep a learning process to be universally attractive.
Our preferred solution for most models is to use a purpose-built suite of program templates (SOLVER), in which a given model is specified by a short segment of pascal code. Most problems can be tackled by minor editing of existing (supplied) definitions, so no pascal programming expertise is required. You can download the manual set and source code for both the PC-Windows and the UNIX versions of SOLVER elsewhere on this site.
A PowerPoint slide show, including all figures in the book is available elsewhere on this site.
We have tried to design the combination of text, exercises, projects, and software as a flexible system within which individual instructors can devise a wide variety of customized courses. To illustrate the possibilities, we describe some of the courses we have given at the University of Strathclyde (US), the University of Calgary(UC) and the University of California at Santa Barbara (UCSB). All laid strong emphasis on the laboratory component of the work.