An introduction to mathematical models in ecology and evolution: time and space

AN INTRODUCTION TO

MATHEMATICAL MODELS IN

ECOLOGY AND EVOLUTION

ECOLOGICAL METHODS AND CONCEPTS SERIES

This series, successor to the Methods in Ecology series edited hy John Lavvion and Gene

Likens, presents the latest ideas and techniques across the whole Held oi ecology and

their application, írom genetic to the global, from pest management to policy

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Series Editor is Proíessor Roger Kitching oi Griítiih University, Brisbane, who vviil

vvelcome suggestions for vvorks vvithin the series. Email: [email protected]

Ecological Methods and Concepts Series

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Michael Gillman

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Brian A Maurer

A n Introductio n t o

Mathematical Models in

Ecology and Evolution

Time and Space

SECOND EDITION

MICHAEL GILLMAN

Department of Biological Sciences

The Open University

Walton Han

Milton Keynes

MK7 6AA

UK

ĐẠI HỌCTHẤINGUYỀN

•TRUNG TẮM Hục LIỆU

©WILEY-BLACKWELL

A lohn VViley & Sons, Ltd., Publication

This editionfirstpublished 2009, © 2009 by Michael Gillman

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Library of Congress Cataloguing-in-Publkation Data

Gillman, Michael.

An introduction to mathemaiical models in ecology and evolution : tiint' and space / Michael

Gillman. - 2nd ed.

p. em. - (Ecological mcthods and concepts series)

Rev. ed. oi: An introduction to ecological modelling / Mĩchael Gillman, Rosemary Hails. 1997.

[ncludes bibliographical reíerences and index.

ISBN 978-1-4051-7515-9 (pbk. : alk. paper) - ISBN 978-1-4051-9489-1 (hbk. : alk.

paper) 1. Ecology-Mathematical models. 2. Evolution (Biology)-Mathematical models.

[. Gillman, Michael. Introduction to ecological modelling. u. Title.

QH541.15.M3G5 2009

577.01'51I8-dc22

200804648]

A catalogue record for this book is available íroni the Britìsh Library.

Sét in 9.5 ôn 12 pt Meridien by SNP Best-set Typesetter Lui., Hông Rong

Printed and bound in Malaysia by Vivar Printing Sdn Bhd

I 200-5

Contents

Pretace, vi

Ì Introduction, Ì

2 Simple models oi temporal change, 21

3 Stochastic models, 44

4 Modelling structured populations, 60

5 Regulation in temporal models, 72

6 Modelling interactions, 96

7 Community models, 122

8 Spatial models, 135

Reterences, 149

Index, 157

Preíac e

This book is an introduction to the key methods and underlying concepts of

mathematical models in ecology and evolution. ít is intended to serve the

needs of a broad range of undergraduate and postgraduate ecology and evo￾lution students who need to access the mathematical and statistical modelling

literature essential to their subịects. ít assumes minimal mathematics and

statistics knovvledge (see belovv) vvhile covering a wide variety oi methods,

many oi vvhich are át the forefront ót ecological and evolutionary research.

The book will also highlight the applications of modelling to practical prob￾lcms such as sustainable harvesting and biological control.

There are many other ways in vvhich this book could have been vvritten

and you vvill find examplcs oi quite different treatments of modelling in the

literature. In particular the book could focus ôn (and be lead by) applications,

for example by asking vvhether models are helpful in understanding climate

change or saving cod populations or reducing the incidence of malaria. The

ansvver is yes to all of these bui Ít was íelt thát Ít is belter to try to understand

the general principles underlying the models and then examine the applica￾tions. Doubtless ray ideas of synthesis and generality are nót those oi others

bút Ít is an attempt to dctect and reveal order. ì also vvanted to vvrite a book

with a lighter touch and so have avoided vvriting lengthy dcscriptions of

method. Hopeíully this makes the book accessible to a wider readership.

Understanding of the text will be helped by a íamiliarity with the basics

oi tho following mathematical and statistical methods and concepts:

• manipulation oi algebraic equations,

• Iogarỉthms and povvers,

• differentiatỉon,

• variance and standard error,

• signiBcance and hypothesis testing.

Many thanks to Hils and Ed for encouragement and valuable comments. ì

have learnt much ươm interactions vvith colleagues át the Open University

and previouslỵ át Imperial College. My interest in mathemaiical models vvas

inspired by the lectures oi Brian Goodvvin and John Maynard Smith.

Michael Gillman

September 2008

vi