《生态学》课程教学资源（书籍教材）Theoretical Ecology Principles and Applications，Third Edition

THEORETICAL ECOLOGY Third Edition PRINCIPLES AND APPLICATIONS ROBERT MAY & ANGELA MCLEAN OXFORD

OXFORDUNIVERSITYPRESSGreat Clarendon Street,Oxford OX2 6DPOxford UniversityPress is a department of the University of Oxford.It furthers the University's objective of excellence in research, scholarship,and education by publishing worldwide inOxford New YorkAuckland CapeTown Darees SalaamHongKongKarachiKuala Lumpur Madrid Melbourne Mexico City NairobiNew Delhi Shanghai Taipei TorontoWith offices inArgentina Austria Brazil Chile Czech Republic France GreeceGuatemala Hungary Italy Japan Poland Portugal SingaporeSouth Korea Switzerland Thailand Turkey Ukraine VietnamOxford is a registered trade mark of Oxford University Pressin the UK and in certain other countriesPublished in the United Statesby Oxford University Press Inc., New YorkC R. M. May and A. R. McLean 2007The moral rights of the authors have been assertedDatabaseright Oxford University Press (maker)First published 2007All rights reserved. No part of this publication may be reproduced,stored in a retrieval system, or transmitted, in any form or by any means,without the prior permission in writing of Oxford University Press,or as expressly permitted by law, or under terms agreed with the appropriatereprographics rights organization. Enquiries concerning reproductionoutside the scope of the above should be sent to the Rights Department,Oxford University Press, at the address aboveYou must not circulate this book in any other binding or coverand you must impose the same condition on any acquirerBritish Library Cataloguing in Publication DataData availableLibrary of Congress Cataloging in Publication DataData availableTypeset by Newgen Imaging Systems (P) Ltd, Chennai, IndiaPrinted in Great Britainon acid-free paper byAntony Rowe Ltd., Chippenham, WiltshireISBN978-0-19-920998-9 (Hbk)978-019-920999-6 (Pbk)10987654321

1 Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dare es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York # R. M. May and A. R. McLean 2007 The moral rights of the authors have been asserted Database right Oxford University Press (maker) First published 2007 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India Printed in Great Britain on acid-free paper by Antony Rowe Ltd., Chippenham, Wiltshire ISBN 978–0–19–920998–9 (Hbk) 978–0–19–920999–6 (Pbk) 10 9 8 7 6 5 4 3 2 1

ContentsviiAcknowledgementsixContributors11 IntroductionAngela R.McLean and Robert M.May72 How populations cohere: five rules for cooperationMartinA.NouwakandKarlSigmund173 Single-species dynamicsTim Coulson and H. Charles J. Godfray354 Metapopulations and their spatial dynamicsSean Nee465Predator-prey interactionsMichaelB.Bonsall andMichaelP.Hassell 62 6PlantpopulationdynamicsMichael J.Crazwley847Interspecificcompetitionandmultispecies coexistenceDavid Tilman988 Diversity and stability in ecological communitiesAnthony R. Ives1119Communities:patternsRobert M.May,Michael J.Crawley,and George Sugihara13210 Dynamics of infectious diseaseBryan Grenfell and Matthew Keeling14811 FisheriesJohn R.Beddington and Geoffrey P.Kirkzwood15812 A doubly Green Revolution:ecology and food productionGordon Conway17213Conservation biology: unsolved problems and their policy implicationsAndyDobson,Will R.Turner,and David S.Wilcove>

Contents Acknowledgements vii Contributors ix 1 Introduction 1 Angela R. McLean and Robert M. May 2 How populations cohere: five rules for cooperation 7 Martin A. Nowak and Karl Sigmund 3 Single-species dynamics 17 Tim Coulson and H. Charles J. Godfray 4 Metapopulations and their spatial dynamics 35 Sean Nee 5 Predator–prey interactions 46 Michael B. Bonsall and Michael P. Hassell 6 Plant population dynamics 62 Michael J. Crawley 7 Interspecific competition and multispecies coexistence 84 David Tilman 8 Diversity and stability in ecological communities 98 Anthony R. Ives 9 Communities: patterns 111 Robert M. May, Michael J. Crawley, and George Sugihara 10 Dynamics of infectious disease 132 Bryan Grenfell and Matthew Keeling 11 Fisheries 148 John R. Beddington and Geoffrey P. Kirkwood 12 A doubly Green Revolution: ecology and food production 158 Gordon Conway 13 Conservation biology: unsolved problems and their policy implications 172 Andy Dobson, Will R. Turner, and David S. Wilcove v

viCONTENTS19014 Climate change and conservation biologyJeremy T. Kerr and Heather M. Kharouba20515Unanswered questions and why they matterRobert M.May216References249Index

14 Climate change and conservation biology 190 Jeremy T. Kerr and Heather M. Kharouba 15 Unanswered questions and why they matter 205 Robert M. May References 216 Index 249 vi CONTENTS

AcknowledgementsThe aims and scope of this book are set out in thebring the authors and others together for a 2-daybeginning of the first chapter (unimaginativelyconference, in which the sweep of material in thislabelled Introduction). So these prefacing com-book was exposed to discussion and constructivecriticism. It helped shape the book.ments are confined to acknowledging some of thehelp we and the other authors have received inOur thanks are also owed to enthusiastic andhelpful people at Oxford University Press, parti-putting this book together.The two of us are deeply indebted to the other 21cularlythe commissioningeditor,lan Sherman,theauthors who have contributed to the book, bothproduction editor, Christine Rode, and the copy-for the work they did and for their exemplaryeditor, Nik Prowse.R.M.M's assistant, Chrisadherence to a rather fast production scheduleBond, was her usual invaluable self, helping inIndividual authors have wished to thank bothevery facet of the enterprise with unflappablefunding agencies and helpful colleagues who gavecompetence.assistance of various kinds.This would have beenSadly,one of the authorsGeoff Kirkwood-an impressively long list, but we unkindly decidedunexpectedly died the week after the gatheringagainst including it.in Oxford.Everyoneremembershim with affec-We must, however, recognize the generosity oftion, and his shadow lies on the book. He will beMerton Collegeand theZoologyDepartment atmissed.the University of Oxford, and particularly theirrespective heads,Dame Jessica Rawson andA.R. McLean and R.M. MayProfessor Paul Harvey.They made it possibleto22September2006vi

Acknowledgements The aims and scope of this book are set out in the beginning of the first chapter (unimaginatively labelled Introduction). So these prefacing com￾ments are confined to acknowledging some of the help we and the other authors have received in putting this book together. The two of us are deeply indebted to the other 21 authors who have contributed to the book, both for the work they did and for their exemplary adherence to a rather fast production schedule. Individual authors have wished to thank both funding agencies and helpful colleagues who gave assistance of various kinds. This would have been an impressively long list, but we unkindly decided against including it. We must, however, recognize the generosity of Merton College and the Zoology Department at the University of Oxford, and particularly their respective heads, Dame Jessica Rawson and Professor Paul Harvey. They made it possible to bring the authors and others together for a 2-day conference, in which the sweep of material in this book was exposed to discussion and constructive criticism. It helped shape the book. Our thanks are also owed to enthusiastic and helpful people at Oxford University Press, parti￾cularly the commissioning editor, Ian Sherman, the production editor, Christine Rode, and the copy￾editor, Nik Prowse. R.M.M.’s assistant, Chris Bond, was her usual invaluable self, helping in every facet of the enterprise with unflappable competence. Sadly, one of the authors—Geoff Kirkwood— unexpectedly died the week after the gathering in Oxford. Everyone remembers him with affec￾tion, and his shadow lies on the book. He will be missed. A.R. McLean and R.M. May 22 September 2006 vii

ContributorsJohn R.Beddington,Division of Biology,Faculty ofHeatherKharouba, Canadian Facility for EcoinformaticsNatural Sciences, RSM Building, Imperial CollegeResearch (CFER),Department of Biology,University ofLondon,SW72BP,UK.E-mail:j.beddington@Ottawa,Box450,StationA,Ottawa,ON,K1N6N5,imperial.ac.ukCanada.E-mail: hkar075@uottawa.caMichael B. Bonsall, Department of Zoology, TinbergenGeoffrey P. Kirkwood, Division of Biology, Faculty ofBuilding,University of Oxford,Oxford OX13PS,UKNatural Sciences, RSM Building, Imperial CollegeE-mail:michael.bonsall @zoo.ox.ac.ukLondon, SW72BP, UKGordon Conway,CentreforEnvironmental Policy,4thRobert M.May,Department of Zoology,TinbergenFloor, RSM Building, Imperial College, SouthBuilding, University of Oxford, Oxford Ox1 3PS, UKKensington, London SW7 2AZ, UK. E-mail:E-mail: robert.may@zoo.ox.ac.ukAngelaR.McLean,Department ofZoology,Tinbergeng.conway@imperial.ac.ukTim Coulson, NERC Centre for Population Biology andBuilding,University ofOxford,Oxford OX13PS,UKDivision of Biology, Imperial College London, SilwoodE-mail: angela.mclean@zoo.ox.ac.ukPark Campus, Ascot, Berkshire SL5 7PY, UK. E-mail:Sean Nee, Institute of Evolutionary Biology,School oft.coulson@imperial.ac.ukBiological Sciences, University of Edinburgh, WestMichael J. Crawley, Department of Biological Sciences,Mains Road, Edinburgh EH9 3JT, UK. E-mail:Imperial College London, Silwood Park, Ascot, Berk-sean.nee@ed.ac.ukshire SL5 7PY, UK.E-mail: m.crawley@imperial.ac.ukMartin A. Nowak, The Program for EvolutionaryAndy Dobson, Ecology and Evolutionary Biology,Dynamics,Faculty of Arts and Science,One BrattlePrinceton University,Princeton, NJ 08544, USASquare, Harvard University, Cambridge, MA 02138,USA. E-mail: nowak @fas.harvard.eduE-mail: dobber@princeton.eduH. Charles J. Godfray, Department of Zoology,Karl Sigmund,Faculty for Mathematics,University ofTinbergenBuilding,University of Oxford, OxfordVienna,Nordbergstrasse15,A-1090Vienna,Austria.OX1 3PS, UK.E-mail: charles.godfray@ zoo.ox.ac.ukE-mail:karl.sigmund @univie.ac.atBryanGrenfell,BiologyDepartment,208MuellerGeorge Sugihara, Scripps Institution of Oceanography,Laboratory, Pennsylvania State University, UniversityUniversity of California, San Diego,9500 GilmanPark,PA 16802,USA.E-mail:grenfell@psu.eduDrive,La Jolla,CA920930202,USAE-mail:Michael P.Hassell, Department of Biological Sciencesgsugihara @ucsd.eduImperial CollegeLondon, Silwood Park, Ascot, Berk-David Tilman, Department of Ecology,Evolution andshire SL5 7PY, UK.E-mail: m.hassell@ic.ac.ukBehavior, University of Minnesota, St. Paul, MN 55108,Anthony R. Ives, Department of Zoology, University ofUSA.E-mail:tilman@umn.eduWisconsin,Madison, WI 53706, USA.Will R. Turner, Center for Applied BiodiversityScience,Conservation International, 1919M St.NWE-mail: arives @wisc.eduMatthew Keeling, Department of Biological SciencesSuite 600, Washington, DC 20036, USA. E-mail:and Mathematics Institute, University of Warwickw.turner@conservation.orgGibbet Hill Road, Coventry CV4 7AL, UK. E-mail:David S. Wilcove, Ecology and Evolutionary Biology andm.j.keeling@warwick.ac.ukPrinceton Environmental Institute and WoodrowJeremy T.Kerr, Canadian Facilityfor EcoinformaticsWilson School of Public and International Affairs,Research (CFER),Department of Biology,University ofPrincetonUniversity,Princeton,NJ08544,USAOttawa,Box450,StationA,Ottawa,ON,K1N6N5E-mail:dwilcove@princeton.eduCanada. E-mail: jkerr@uottawa.caix

Contributors John R. Beddington, Division of Biology, Faculty of Natural Sciences, RSM Building, Imperial College London, SW7 2BP, UK. E-mail: j.beddington @ imperial.ac.uk Michael B. Bonsall, Department of Zoology, Tinbergen Building, University of Oxford, Oxford OX1 3PS, UK. E-mail: michael.bonsall @ zoo.ox.ac.uk Gordon Conway, Centre for Environmental Policy, 4th Floor, RSM Building, Imperial College, South Kensington, London SW7 2AZ, UK. E-mail: g.conway @ imperial.ac.uk Tim Coulson, NERC Centre for Population Biology and Division of Biology, Imperial College London, Silwood Park Campus, Ascot, Berkshire SL5 7PY, UK. E-mail: t.coulson @ imperial.ac.uk Michael J. Crawley, Department of Biological Sciences, Imperial College London, Silwood Park, Ascot, Berk￾shire SL5 7PY, UK. E-mail: m.crawley @ imperial.ac.uk Andy Dobson, Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08544, USA. E-mail: dobber @ princeton.edu H. Charles J. Godfray, Department of Zoology, Tinbergen Building, University of Oxford, Oxford OX1 3PS, UK. E-mail: charles.godfray @ zoo.ox.ac.uk Bryan Grenfell, Biology Department, 208 Mueller Laboratory, Pennsylvania State University, University Park, PA 16802, USA. E-mail: grenfell @ psu.edu Michael P. Hassell, Department of Biological Sciences, Imperial College London, Silwood Park, Ascot, Berk￾shire SL5 7PY, UK. E-mail: m.hassell @ ic.ac.uk Anthony R. Ives, Department of Zoology, University of Wisconsin, Madison, WI 53706, USA. E-mail: arives @ wisc.edu Matthew Keeling, Department of Biological Sciences and Mathematics Institute, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK. E-mail: m.j.keeling @ warwick.ac.uk Jeremy T. Kerr, Canadian Facility for Ecoinformatics Research (CFER), Department of Biology, University of Ottawa, Box 450, Station A, Ottawa, ON, K1N 6N5, Canada. E-mail: jkerr @ uottawa.ca Heather Kharouba, Canadian Facility for Ecoinformatics Research (CFER), Department of Biology, University of Ottawa, Box 450, Station A, Ottawa, ON, K1N 6N5, Canada. E-mail: hkar075 @ uottawa.ca Geoffrey P. Kirkwood, Division of Biology, Faculty of Natural Sciences, RSM Building, Imperial College London, SW7 2BP, UK Robert M. May, Department of Zoology, Tinbergen Building, University of Oxford, Oxford OX1 3PS, UK. E-mail: robert.may @ zoo.ox.ac.uk Angela R. McLean, Department of Zoology, Tinbergen Building, University of Oxford, Oxford OX1 3PS, UK. E-mail: angela.mclean @ zoo.ox.ac.uk Sean Nee, Institute of Evolutionary Biology, School of Biological Sciences, University of Edinburgh, West Mains Road, Edinburgh EH9 3JT, UK. E-mail: sean.nee @ ed.ac.uk Martin A. Nowak, The Program for Evolutionary Dynamics, Faculty of Arts and Science, One Brattle Square, Harvard University, Cambridge, MA 02138, USA. E-mail: nowak @ fas.harvard.edu Karl Sigmund, Faculty for Mathematics, University of Vienna, Nordbergstrasse 15, A-1090 Vienna, Austria. E-mail: karl.sigmund @ univie. ac.at George Sugihara, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093 0202, USA. E-mail: gsugihara @ ucsd.edu David Tilman, Department of Ecology, Evolution and Behavior, University of Minnesota, St. Paul, MN 55108, USA. E-mail: tilman @ umn.edu Will R. Turner, Center for Applied Biodiversity Science, Conservation International, 1919 M St. NW Suite 600, Washington, DC 20036, USA. E-mail: w.turner @ conservation.org David S. Wilcove, Ecology and Evolutionary Biology and Princeton Environmental Institute and Woodrow Wilson School of Public and International Affairs, Princeton University, Princeton, NJ 08544, USA. E-mail: dwilcove @ princeton.edu ix

CHAPTER1IntroductionAngela R.McLean and Robert M.Maychurch, and the rest in some of the lowest and meanestIn this introductory chapter, we indicate the aimsthatched cottages. Now, as these eight pairs-allowanceand structureofthisbook.Wealsoindicate somebeing made for accidents-breed yearly eight pairs more,ofthewaysinwhichthebook is not synopticinitswhat becomes annually of this increase? and whatcoverage,butrather offers an interlinked accountdetermines every spring, which pairs shall visit us, andofsomemajordevelopments in our understand-re-occupy their ancient haunts?ing of the dynamics of ecological systems, frompopulationsto communities,along withpracticalThis passage is unusual in giving quantitativeapplicationstoimportantproblems.information about the population of swifts in Sel-Ecology is a young science.The word ecology itselfborne two centuries ago, a small exception to thewas coined not much more than 100 years ago, andalmost universal absence of population recordstheoldestprofessional society,the British Ecologicalgoing back more than a few decades. It is evenSociety,is less than a century old.Arguably the firstmore remarkablefor its clear articulation of thepublished work on ecology was Gilbert White's Thecentral question of population biology: what reg-Natural Historyof Selborne.Thisbook,published inulates populations? Interestingly,the swift popu-1789,was ahead of its time in seeingplants andlation of Selborne these days is steadily around 12animals not as individual objects of wonder-thingspairs, which in ecological terms is not much dif-to be assembled ina cabinet of curiosities-but asferent from eight, even though much of theirparts ofa communityofliving organisms,interactingenvironment has changedentries to the churchwiththeenvironment,otherorganisms,andtower all wired-off to keep out squirrels, and thehumans.Thebookhasnotmerelyremained inprint,gentrified cottages no longer low and mean withbut has run steadily through well over200 editionstheir thatch, when it remains, neatly wired downand translations,toattainthe status of thefourth(LawtonandMay,1983).Interpretedgenerously,most published book (in the sense of separate edi-these population data on Selborne's swifts couldtions) in the English language. Thefollowing excerptbe seen as one of ecology's longest time series, so itcaptures White's blend of detailed observation andis sobering to realize there is still no agreedconcernforbasicquestions.explanation of what actually regulates the swifts'numbers.Among the many singularities attending those amusingMoving on from Gilbert White, the first half ofbirds, the swifts, I am now confirmed in the opinion thatthe twentieth century saw some more explicitlywe have every year the same number of pairs invariably;mathematical models aimed at understanding theat least, the result of my inquiry has been exactly the samedynamical behaviour of populations.Notablefor a long timepast.The swallows and martins are soexamples include Ross' work on malaria, with itsnumerous, and so widely distributed over the village, thatfirstintroduction of thebasic reproductivenum-it is hardly possible to recount them; while the swifts,ber, Ro, discussed in later chapters of this book,though they do not all build in the church, yet so fre-and Lotka and Volterra's indication of the inher-quently haunt it, and play and rendezvous round it, thatthey are easily enumerated. The number that I constantlyently oscillatoryproperties ofprey-predator sys-find are eight pairs, about half of which reside in thetems.Despite this, ecology seems to us to have1

CHAPTER 1 Introduction Angela R. McLean and Robert M. May In this introductory chapter, we indicate the aims and structure of this book. We also indicate some of the ways in which the book is not synoptic in its coverage, but rather offers an interlinked account of some major developments in our understand￾ing of the dynamics of ecological systems, from populations to communities, along with practical applications to important problems. Ecology is a young science. The word ecology itself was coined not much more than 100 years ago, and the oldest professional society, the British Ecological Society, is less than a century old. Arguably the first published work on ecology was Gilbert White’s The Natural History of Selborne. This book, published in 1789, was ahead of its time in seeing plants and animals not as individual objects of wonder—things to be assembled in a cabinet of curiosities—but as parts of a community ofliving organisms, interacting with the environment, other organisms, and humans. The book has not merely remained in print, but has run steadily through well over 200 editions and translations, to attain the status of the fourth most published book (in the sense of separate edi￾tions) in the English language. The following excerpt captures White’s blend of detailed observation and concern for basic questions. Among the many singularities attending those amusing birds, the swifts, I am now confirmed in the opinion that we have every year the same number of pairs invariably; at least, the result of my inquiry has been exactly the same for a long time past. The swallows and martins are so numerous, and so widely distributed over the village, that it is hardly possible to recount them; while the swifts, though they do not all build in the church, yet so fre￾quently haunt it, and play and rendezvous round it, that they are easily enumerated. The number that I constantly find are eight pairs, about half of which reside in the church, and the rest in some of the lowest and meanest thatched cottages. Now, as these eight pairs—allowance being made for accidents—breed yearly eight pairs more, what becomes annually of this increase? and what determines every spring, which pairs shall visit us, and re-occupy their ancient haunts? This passage is unusual in giving quantitative information about the population of swifts in Sel￾borne two centuries ago, a small exception to the almost universal absence of population records going back more than a few decades. It is even more remarkable for its clear articulation of the central question of population biology: what reg￾ulates populations? Interestingly, the swift popu￾lation of Selborne these days is steadily around 12 pairs, which in ecological terms is not much dif￾ferent from eight, even though much of their environment has changed—entries to the church tower all wired-off to keep out squirrels, and the gentrified cottages no longer low and mean with their thatch, when it remains, neatly wired down (Lawton and May, 1983). Interpreted generously, these population data on Selborne’s swifts could be seen as one of ecology’s longest time series, so it is sobering to realize there is still no agreed explanation of what actually regulates the swifts’ numbers. Moving on from Gilbert White, the first half of the twentieth century saw some more explicitly mathematical models aimed at understanding the dynamical behaviour of populations. Notable examples include Ross’ work on malaria, with its first introduction of the basic reproductive num￾ber, R0, discussed in later chapters of this book, and Lotka and Volterra’s indication of the inher￾ently oscillatory properties of prey–predator sys￾tems. Despite this, ecology seems to us to have 1

2THEORETICALECOLOGYremained a largely observational and descriptiveask whether particular factors may be moresubject up to the decade of the 1960s.Witnessimportant than others, and to see if such insight ortwo of the most influential texts of that time:guesswork does indeed provide testableexplana-Andrewartha and Birch (1954), an excellent booktions.Mathematical models can be precise tools forbut explicitly antithetic to theory in the form ofdoing this, helping us to make our assumptionsexplicit and unambiguous, and to explore “ima-anything resembling a mathematical model;Odum(1953),arguablyforeshadowingaspects ofginary worlds' as metaphors for such hypothetical'systems ecologywith its insightful focus onsimplicity underlying apparent complexity.Thepatterns of energy flow in ecosystems, but with1970s saw much activity of this kind in ecologicaltheemphasis descriptiveratherthan conceptual.research,helped inpartbybasicadvances in ourFor evolutionary studies as well as for ecologicalunderstanding of nonlinear dynamical systemsones, we think the 1960s saw a change in the zeit-and by the advent of increasingly powerful andgeist.For evolution, much of the stimulus deriveduser-friendly computers.from Bill Hamilton's conceptual advances.ForIn particular,the phenomenon of deterministicecology,itwas the reframingby EvelynHutchinsonchaos received wide recognition in the 1970s. The(1965)andhisstudentRobertMcArthur(1972;seefinding that very simple and purely deterministicalsoMacArthurandWilson,1967)ofold questionslaws or equations can give rise to dynamicalbehaviour that not merelylooks like random noise,inmoreexplicitlyanalyticways;onecouldperhapssay,rephrasing them in the idiom of theoreticalbut is so sensitive to initial conditions that long-term prediction is effectively impossible, has hugephysics. How similar can species be, yet persisttogether? What tends to govern the number ofimplications. It ends the Newtonian dream that ifspecies we see on an island, and how does thisthe system is simple (very few variables)andnumber depend on the size and isolation of theorderly (therules and parameters exactlyknown),then the future is predictable. The law' can beisland? Gilbert White's question of populationabundance was revisited-and expanded beyondas trivial as x(t+1)=2x(t) exp[-x(t)], with ^ athe sterile controversies of the 1950saboutwhetherknown and unvarying constant, but if is bigpopulations typicallyare governed by tight densityenough then an error of one part in one million inthe initial estimate of x(O) will end up producing adependence or fluctuate greatlyunder the influenceof environmental factors—toask the moreprecisecompletely wrong prediction within a dozen or sodynamical question of whydo somepopulationstime steps. Interestingly, it is often thought thatremain relatively steady,others show regularchaotic phenomena found applications in ecologycycles, and yet others fluctuate wildly? Given theafter others had developed the subject. In fact, oneobserved patterns of relative abundance of theof thetwo streams which brought chaos centredifferent species in particular communities, whatstage in the 1970s derived directly from ecologicalare the underlying causes? What is the relationresearch on models for a single populationbetween the complexity of a food web (variouslywith discrete, non-overlapping generations. Thesedefined) and its ability to withstand disturbance,models were first-order difference equations; thenatural or human created?other strand was Lorenz's metaphor for convect-These more deliberately conceptual or theoret-ive phenomena in meteorology,involving moreical approaches differed from early work, in ourcomplex-althoughstill relatively simplethree-view,in that they went beyond the codification ofdimensional differential equations.Advances in computing have also been of greatdescriptive material, and the search for patternswithin such codification,to ask questions abouthelp in all areas of ecology:statistical design ofunderlying mechanisms.To ask questions aboutexperiments;collectingand processingdata;and,why,rather than what.Mathematics enters intocomingtothepresentbook,developingandsuch studies, essentially as a tool for thinkingexploring mathematical models for both simpleclearly.In pursuing a‘whyorwhatifquestionand complicated ecological systems.There are,abouta complicated situation,it can be helpful tohowever, some associated dangers,which deserve

remained a largely observational and descriptive subject up to the decade of the 1960s. Witness two of the most influential texts of that time: Andrewartha and Birch (1954), an excellent book but explicitly antithetic to theory in the form of anything resembling a mathematical model; Odum (1953), arguably foreshadowing aspects of ‘systems ecology’ with its insightful focus on patterns of energy flow in ecosystems, but with the emphasis descriptive rather than conceptual. For evolutionary studies as well as for ecological ones, we think the 1960s saw a change in the zeit￾geist. For evolution, much of the stimulus derived from Bill Hamilton’s conceptual advances. For ecology, it was the reframing by Evelyn Hutchinson (1965) and his student Robert McArthur (1972; see also MacArthur and Wilson, 1967) of old questions in more explicitly analytic ways; one could perhaps say, rephrasing them in the idiom of theoretical physics. How similar can species be, yet persist together? What tends to govern the number of species we see on an island, and how does this number depend on the size and isolation of the island? Gilbert White’s question of population abundance was revisited—and expanded beyond the sterile controversies of the 1950s about whether populations typically are governed by tight density dependence or fluctuate greatly under the influence of environmental factors—to ask the more precise dynamical question of why do some populations remain relatively steady, others show regular cycles, and yet others fluctuate wildly? Given the observed patterns of relative abundance of the different species in particular communities, what are the underlying causes? What is the relation between the complexity of a food web (variously defined) and its ability to withstand disturbance, natural or human created? These more deliberately conceptual or theoret￾ical approaches differed from early work, in our view, in that they went beyond the codification of descriptive material, and the search for patterns within such codification, to ask questions about underlying mechanisms. To ask questions about why, rather than what. Mathematics enters into such studies, essentially as a tool for thinking clearly. In pursuing a ‘why’ or ‘what if’ question about a complicated situation, it can be helpful to ask whether particular factors may be more important than others, and to see if such insight or guesswork does indeed provide testable explana￾tions. Mathematical models can be precise tools for doing this, helping us to make our assumptions explicit and unambiguous, and to explore ‘ima￾ginary worlds’ as metaphors for such hypothetical simplicity underlying apparent complexity. The 1970s saw much activity of this kind in ecological research, helped in part by basic advances in our understanding of nonlinear dynamical systems and by the advent of increasingly powerful and user-friendly computers. In particular, the phenomenon of deterministic chaos received wide recognition in the 1970s. The finding that very simple and purely deterministic laws or equations can give rise to dynamical behaviour that not merely looks like random noise, but is so sensitive to initial conditions that long￾term prediction is effectively impossible, has huge implications. It ends the Newtonian dream that if the system is simple (very few variables) and orderly (the rules and parameters exactly known), then the future is predictable. The ‘law’ can be as trivial as x(t þ 1) ¼ lx(t) exp[
x(t)], with l a known and unvarying constant, but if l is big enough then an error of one part in one million in the initial estimate of x(0) will end up producing a completely wrong prediction within a dozen or so time steps. Interestingly, it is often thought that chaotic phenomena found applications in ecology after others had developed the subject. In fact, one of the two streams which brought chaos centre stage in the 1970s derived directly from ecological research on models for a single population with discrete, non-overlapping generations. These models were first-order difference equations; the other strand was Lorenz’s metaphor for convect￾ive phenomena in meteorology, involving more complex—although still relatively simple—three￾dimensional differential equations. Advances in computing have also been of great help in all areas of ecology: statistical design of experiments; collecting and processing data; and, coming to the present book, developing and exploring mathematical models for both simple and complicated ecological systems. There are, however, some associated dangers, which deserve 2 THEORETICAL ECOLOGY

INTRODUCTION3passing mention.The understanding derived fromexperiments,andtheoryexpressedin mathematicalcomputer studies of complicated models canterms. The comparison,for example, between thesometimes be substantially less complete than thatfirstedition of Begon,Townsend and Harper (1986)gained from the analytic methods of classicaland the earlierAndrewartha and Birch(1954)orapplied mathematics and theoretical physics.TheOdum (1953) ispronounced.Wethink thismarks aearly days of computers—mechanical calcula-maturation of the subject, although there undeni-tors-saw them used by theoretical physicistsably remain large and important areas where therein conjunction with analytic approximations, toare still more questions than answers.explorepreviously intractable problems.Theresult, however, wasthat at every step therewas1.1Thisbookand itspredecessorspreserved an intuitive understanding of the rela-tion between the underlying assumptions and theThis book (TEIIl) is essentially a greatly transmo-results.In contrast, many scientistswhotoday usegrified version of one first published in 1976 (TEI),computers to explore increasingly complex math-andfollowed with substantial changes in 1981(TEIl; this was not a perfunctory update, but hadematicalmodelshavelittleformalbackgroundinthree chapters completely re-written by differentmathematics,or haveforgotten what they wereonce taught. Most of this work is interesting andauthors, two new chapters added, and all othersrevised;TEI's 14 chapters involved 11 authors,excellent. But, absent any degree of intuitiveunderstanding of how the input assumptionsTEIl's16chaptershad13authors,ofwhomnineabout the system's biology relate to theconsequentwere fromTEI).This newversion,25yearson,hasoutput,we need tobe wary (May,2004).Toooften,15chaptersby23authors,onlythreeof whomarean'emergent phenomenon'means little more thanveterans of TEIL.Like the previous two, this book is not a basicT've no clue what is going on, but it looks kindaundergraduate ecology text, but equally it is not ainteresting.Happily,there are veryfew examplesof this in ecology.More particularly,throughouttechnical tome for the front-line specialist in one orthe present book we aim,wherever possible,tootheraspectoftheoreticalecology.Rather,thebookprovide intuitive understanding of the lessonsis aimed at upper-level undergraduate, post-learned frommathematical models.graduate,and postdoctoral students,andecologicalBe all this as it may, there has been a marked riseresearchers interested in broadening aspects of thein theoretical ecology as a distinct sub-disciplinecourses they teach, or indeed of their own work. Asoverthepastthreedecades or so.Manyof thesuch, we think it fairto claim that TEI and TEII inpractitioners are notto be found in the field ortheir own time played a part in the above-men-laboratory; a greater number, however, find theirtioned transition in the general subject of ecology,experimental contributions in field and/or lab-where earlier texts, in which mathematical contentoratory to be inextricably interwoven with theirwas essentially absent, contrast markedly withtheoretical and mathematical contributions.Ecol-today's,where theoreticalapproaches-sometimesogyhas come a long wayfrom the 1970s, when aexplicitlymathematical and sometimes not-playfew empirical ecologists resented outsiders, whoan important part, although nomore than a part, ofhad not paid their dues of years of toil in the field,the presentation of the subject. Some of ourpresuming to mathematize their problems (oftenacquaintances, indeed, still use the earlier volumesas supplements to their undergraduate courses.sweeping aside arguably irrelevant, but certainlyTEIl, although out of print, still trades actively onbeloved, details in the process).Others perhapstheonlinebooksellerAmazon.welcomed the intrusion too uncritically.The end result, however, is seen clearlyby com-This book, on the other hand, differs from theparing today's leading ecology texts with those ofprevioustwobyvirtueofthesechangesinhowthethe 1950s and 1960s. In the latter,you will find verysubject of ecology isdefined and taught.Muchoffew equations.Today,in contrast, you will find athematerial inTEIandTEII would now,25yearsbalanced blend of observation, field and laboratoryandmoreon,beseenasaroutinepartofanybasic

passing mention. The understanding derived from computer studies of complicated models can sometimes be substantially less complete than that gained from the analytic methods of classical applied mathematics and theoretical physics. The early days of computers—mechanical calcula￾tors—saw them used by theoretical physicists in conjunction with analytic approximations, to explore previously intractable problems. The result, however, was that at every step there was preserved an intuitive understanding of the rela￾tion between the underlying assumptions and the results. In contrast, many scientists who today use computers to explore increasingly complex math￾ematical models have little formal background in mathematics, or have forgotten what they were once taught. Most of this work is interesting and excellent. But, absent any degree of intuitive understanding of how the input assumptions about the system’s biology relate to the consequent output, we need to be wary (May, 2004). Too often, an ‘emergent phenomenon’ means little more than ‘I’ve no clue what is going on, but it looks kinda interesting’. Happily, there are very few examples of this in ecology. More particularly, throughout the present book we aim, wherever possible, to provide intuitive understanding of the lessons learned from mathematical models. Be all this as it may, there has been a marked rise in theoretical ecology as a distinct sub-discipline over the past three decades or so. Many of the practitioners are not to be found in the field or laboratory; a greater number, however, find their experimental contributions in field and/or lab￾oratory to be inextricably interwoven with their theoretical and mathematical contributions. Ecol￾ogy has come a long way from the 1970s, when a few empirical ecologists resented outsiders, who had not paid their dues of years of toil in the field, presuming to mathematize their problems (often sweeping aside arguably irrelevant, but certainly beloved, details in the process). Others perhaps welcomed the intrusion too uncritically. The end result, however, is seen clearly by com￾paring today’s leading ecology texts with those of the 1950s and 1960s. In the latter, you will find very few equations. Today, in contrast, you will find a balanced blend of observation, field and laboratory experiments, and theory expressed in mathematical terms. The comparison, for example, between the first edition of Begon, Townsend and Harper (1986) and the earlier Andrewartha and Birch (1954) or Odum (1953) is pronounced. We think this marks a maturation of the subject, although there undeni￾ably remain large and important areas where there are still more questions than answers. 1.1 This book and its predecessors This book (TEIII) is essentially a greatly transmo￾grified version of one first published in 1976 (TEI), and followed with substantial changes in 1981 (TEII; this was not a perfunctory update, but had three chapters completely re-written by different authors, two new chapters added, and all others revised; TEI’s 14 chapters involved 11 authors, TEII’s 16 chapters had 13 authors, of whom nine were from TEI). This new version, 25 years on, has 15 chapters by 23 authors, only three of whom are veterans of TEII. Like the previous two, this book is not a basic undergraduate ecology text, but equally it is not a technical tome for the front-line specialist in one or other aspect of theoretical ecology. Rather, the book is aimed at upper-level undergraduate, post￾graduate, and postdoctoral students, and ecological researchers interested in broadening aspects of the courses they teach, or indeed of their own work. As such, we think it fair to claim that TEI and TEII in their own time played a part in the above-men￾tioned transition in the general subject of ecology, where earlier texts, in which mathematical content was essentially absent, contrast markedly with today’s, where theoretical approaches—sometimes explicitly mathematical and sometimes not—play an important part, although no more than a part, of the presentation of the subject. Some of our acquaintances, indeed, still use the earlier volumes as supplements to their undergraduate courses. TEII, although out of print, still trades actively on the online bookseller Amazon. This book, on the other hand, differs from the previous two by virtue of these changes in how the subject of ecology is defined and taught. Much of the material in TEI and TEII would now, 25 years and more on, be seen as a routine part of any basic INTRODUCTION 3

4THEORETICALECOLOGYecology text. Other bits, of course, are just out ofThe past three decades have seen extraordinarydate, overtaken by later advances.advances in our understanding of the behaviouralOne essential similaritywith itspredecessors isecology and life-history strategies of individualsthat the present book does not aim at synoptic(e.g.Krebs and Davies,1993).On the one hand,coverage. Instead, it attempts first (in Chaptersthis is a formidable field to cover concisely, but onthe other hand, only in a relativelyfew corners does2-9)togiveanaccountofsomeof thebasicprin-ciples that govern the structure, function, andthis work deal directly with deducing the overalltemporal and spatial dynamics of populations anddynamics of a population from the behaviouralcommunities.These chapters are not tidilykept toecology of its constituent individuals.There areuniform length; we think thedynamics of plantsomeinterestingexamplesofphenomena whosepopulationshaveprobablyreceivedlessattentionunderstanding unavoidably requires bringing thethanthose of animal populations, and so havetwo together-for instance,odd aspects of broodencouraged the authors in this area to go intoparasitism where you cannot understand thesomewhat greater detail.Conversely,we recognisepopulation dynamics without understanding thethat there are important and interesting areas ofevolution of individual'sbehaviour,and converselytheoretical ecology—aspects of macroecology,or(NeeandMay,1993)buttheyarefew,andseemtoenergyflowsinecosystems,forexample-whichhave evoked little interest so far. A good review ofare not covered here.By thesame token,thesome other open questions at the interface between‘applied'chapters are a selection from the largernatural selection and population dynamics is byuniverse of interesting and illuminating possibi-Saccheri and Hanski (2006).Resource managers getlities.In short, advances over the past quarterby,and seem to be content, with treating the para-century have seen significant growth in field andmeters in population models as phenomenologicallaboratory studies, along with major theoreticalconstants, fitted to data.One really big problem, however, which is inadvances andpractical applications.Anybookon"theoretical ecologysimply has much moremany ways as puzzling today as it was to Darwin,ground to cover-many more subdisciplines andis how large aggregations of cooperating indivi-specialized areas—than was the caseforTEIl.Theduals (where group benefits are attained for aresultis inevitablythatthepresentbookhasmorerelativelysmall cost toparticipating individuals,gaps and omissions than its predecessors; inclu-but where the whole thing is vulnerable to cheatssions and exclusions are bound to be more quirky.who take the benefits without paying the cost) canA charitable interpretation would bethat, just asevolve and maintain themselves.Relatively earlythe gates to Japanesetemples,tori,havedeliberatework by Hamilton and Trivers pointed the way toa solutionofthisproblemforsmallgroupsofimperfections to avoid angering thegods,so toowe have avoided the sublime. The real reason is aclosely related individuals.But much of this workmixture of our own interests, and a feeling thatis so restricted as to defy application to largeenough is enough.aggregations of human or other animals.Thepastfew years have, however, seen a diverse array ofsignificant advances in this area, and we thought it1.2 What is inthe bookwould be better to begin with a definitive reviewPrevious editions of this text began with a chapterof this underpinning topic, which is still wide openontheevolutionaryforceswhichshapethebehav-to further advances.Hence Chapter 2, Hozo popu-iour of individuals on a stage set by specificlations cohere:fiverules for cooperation.environmental and ecological factors,and thenshow how such individual behaviour ultimately1.2.1 Basic ecological principlesdeterminesthedemographicparameters-densityThe next two chapters deal with singlepopuladependentbirthand death rates,movementpatterns, and so on-governing the population'stions.InChapter3CoulsonandGodfraydistilthebehaviour in space and over time.essence of several recent monographic treatments

ecology text. Other bits, of course, are just out of date, overtaken by later advances. One essential similarity with its predecessors is that the present book does not aim at synoptic coverage. Instead, it attempts first (in Chapters 2–9) to give an account of some of the basic prin￾ciples that govern the structure, function, and temporal and spatial dynamics of populations and communities. These chapters are not tidily kept to uniform length; we think the dynamics of plant populations have probably received less attention than those of animal populations, and so have encouraged the authors in this area to go into somewhat greater detail. Conversely, we recognise that there are important and interesting areas of theoretical ecology—aspects of macroecology, or energy flows in ecosystems, for example—which are not covered here. By the same token, the ‘applied’ chapters are a selection from the larger universe of interesting and illuminating possibi￾lities. In short, advances over the past quarter century have seen significant growth in field and laboratory studies, along with major theoretical advances and practical applications. Any book on ‘theoretical ecology’ simply has much more ground to cover—many more subdisciplines and specialized areas—than was the case for TEII. The result is inevitably that the present book has more gaps and omissions than its predecessors; inclu￾sions and exclusions are bound to be more quirky. A charitable interpretation would be that, just as the gates to Japanese temples, tori, have deliberate imperfections to avoid angering the gods, so too we have avoided the sublime. The real reason is a mixture of our own interests, and a feeling that enough is enough. 1.2 What is in the book Previous editions of this text began with a chapter on the evolutionary forces which shape the behav￾iour of individuals on a stage set by specific environmental and ecological factors, and then show how such individual behaviour ultimately determines the demographic parameters—density￾dependent birth and death rates, movement patterns, and so on—governing the population’s behaviour in space and over time. The past three decades have seen extraordinary advances in our understanding of the behavioural ecology and life-history strategies of individuals (e.g. Krebs and Davies, 1993). On the one hand, this is a formidable field to cover concisely, but on the other hand, only in a relatively few corners does this work deal directly with deducing the overall dynamics of a population from the behavioural ecology of its constituent individuals. There are some interesting examples of phenomena whose understanding unavoidably requires bringing the two together—for instance, odd aspects of brood parasitism where you cannot understand the population dynamics without understanding the evolution of individual’s behaviour, and conversely (Nee and May, 1993)—but they are few, and seem to have evoked little interest so far. A good review of some other open questions at the interface between natural selection and population dynamics is by Saccheri and Hanski (2006). Resource managers get by, and seem to be content, with treating the para￾meters in population models as phenomenological constants, fitted to data. One really big problem, however, which is in many ways as puzzling today as it was to Darwin, is how large aggregations of cooperating indivi￾duals (where group benefits are attained for a relatively small cost to participating individuals, but where the whole thing is vulnerable to cheats who take the benefits without paying the cost) can evolve and maintain themselves. Relatively early work by Hamilton and Trivers pointed the way to a solution of this problem for small groups of closely related individuals. But much of this work is so restricted as to defy application to large aggregations of human or other animals. The past few years have, however, seen a diverse array of significant advances in this area, and we thought it would be better to begin with a definitive review of this underpinning topic, which is still wide open to further advances. Hence Chapter 2, How popu￾lations cohere: five rules for cooperation. 1.2.1 Basic ecological principles The next two chapters deal with single popula￾tions. In Chapter 3 Coulson and Godfray distil the essence of several recent monographic treatments 4 THEORETICAL ECOLOGY