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biological and medical physics, biomedical engineering biological and medical physics, biomedical engineering Thefieldsofbiologicalandmedicalphysicsandbiomedicalengineering arebroad,multidisciplinaryand dynamic.Theylieatthecrossroadsoffrontierresearchinphysics,biology,chemistry,andmedicine.The BiologicalandMedicalPhysics,BiomedicalEngineeringSeriesisintendedtobecomprehensive,coveringa broadrangeoftopicsimportanttothestudyofthephysical,chemicalandbiologicalsciences.Itsgoalisto providescientistsandengineerswithtextbooks,monographs,andreferenceworkstoaddressthegrowing needforinformation. Booksintheseriesemphasizeestablishedandemergentareasofscienceincludingmolecular,membrane, andmathematicalbiophysics;photosyntheticenergy harvestingandconversion; informationprocessing; physicalprinciplesofgenetics;sensorycommunications;automatanetworks,neuralnetworks,andcellular automata.Equally important will be coverage ofapplied aspects of biologicaland medical physics and biomedicalengineeringsuchasmolecularelectroniccomponentsanddevices,biosensors,medicine,imaging, physicalprinciplesofrenewableenergyproduction,advancedprostheses,andenvironmentalcontroland engineering. Editor-in-Chief: SolM.Gruner,DepartmentofPhysics, PrincetonUniversity,Princeton,NewJersey,USA EliasGreenbaum,OakRidgeNationalLaboratory, OakRidge,Tennessee,USA JudithHerzfeld,DepartmentofChemistry, BrandeisUniversity,Waltham,Massachusetts,USA EditorialBoard: PierreJoliot,InstitutedeBiologie MasuoAizawa,DepartmentofBioengineering, Physico-Chimique,FondationEdmond TokyoInstituteofTechnology,Yokohama,Japan deRothschild,Paris,France OlafS.Andersen,DepartmentofPhysiology, LajosKeszthelyi,InstituteofBiophysics,Hungarian Biophysics&MolecularMedicine, AcademyofSciences,Szeged,Hungary CornellUniversity,NewYork,USA RobertS.Knox,DepartmentofPhysics RobertH.Austin,DepartmentofPhysics, andAstronomy,UniversityofRochester,Rochester, PrincetonUniversity,Princeton,NewJersey,USA NewYork,USA JamesBarber,DepartmentofBiochemistry, AaronLewis,DepartmentofAppliedPhysics, ImperialCollegeofScience,Technology HebrewUniversity,Jerusalem,Israel andMedicine,London,England StuartM.Lindsay,DepartmentofPhysics HowardC.Berg,DepartmentofMolecular andAstronomy,ArizonaStateUniversity, andCellularBiology,HarvardUniversity, Tempe,Arizona,USA Cambridge,Massachusetts,USA DavidMauzerall,RockefellerUniversity, VictorBloomfield,DepartmentofBiochemistry, NewYork,NewYork,USA UniversityofMinnesota,St.Paul,Minnesota,USA EugenieV.Mielczarek,DepartmentofPhysics RobertCallender,DepartmentofBiochemistry, andAstronomy,GeorgeMasonUniversity,Fairfax, AlbertEinsteinCollegeofMedicine, Virginia,USA Bronx,NewYork,USA MarkolfNiemz,KlinikumMannheim, BrittonChance,DepartmentofBiochemistry/ Mannheim,Germany Biophysics,UniversityofPennsylvania, Philadelphia,Pennsylvania,USA V.AdrianParsegian,PhysicalScienceLaboratory, NationalInstitutesofHealth,Bethesda, StevenChu,DepartmentofPhysics, Maryland,USA StanfordUniversity,Stanford,California,USA LindaS.Powers,NCDMF:ElectricalEngineering, LouisJ.DeFelice,DepartmentofPharmacology, UtahStateUniversity,Logan,Utah,USA VanderbiltUniversity,Nashville,Tennessee,USA EarlW.Prohofsky,DepartmentofPhysics, JohannDeisenhofer,HowardHughesMedical PurdueUniversity,WestLafayette,Indiana,USA Institute,TheUniversityofTexas,Dallas, Texas,USA AndrewRubin,DepartmentofBiophysics,Moscow StateUniversity,Moscow,Russia GeorgeFeher,DepartmentofPhysics, UniversityofCalifornia,SanDiego,LaJolla, MichaelSeibert,NationalRenewableEnergy California,USA Laboratory,Golden,Colorado,USA HansFrauenfelder,CNLS,MSB258, DavidThomas,DepartmentofBiochemistry, LosAlamosNationalLaboratory,LosAlamos, UniversityofMinnesotaMedicalSchool, NewMexico,USA Minneapolis,Minnesota,USA IvarGiaever,RensselaerPolytechnicInstitute, SamuelJ.Williamson,DepartmentofPhysics, Troy,NewYork,USA NewYorkUniversity,NewYork,NewYork,USA Y. Takeuchi Y. Iwasa K. Sato (Eds.) Mathematics for Ecology and Environmental Sciences With26Figures 123 Prof.YasuhiroTakeuchi ShizuokaUniversity FacultyofEngineering DepartmentofSystemsEngineering Hamamatsu3-5-1 432-8561Shizuoka Japan email:[email protected] Prof.YohIwasa KyushuUniversity DepartmentofBiology 812-8581Fukuoka Japan e-mail:[email protected] Dr.KazunoriSato ShizuokaUniversity FacultyofEngineering DepartmentofSystemsEngineering Hamamatsu3-5-1 432-8561Shizuoka Japan email:[email protected] LibraryofCongressCataloginginPublicationData:2006931399 ISSN1618-7210 ISBN-103-540-34427-6SpringerBerlinHeidelbergNewYork ISBN-13978-3-540-34427-8SpringerBerlinHeidelbergNewYork Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned, specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproduction onmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationorpartsthereofis permittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion, andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsareliabletoprosecutionunderthe GermanCopyrightLaw. SpringerisapartofSpringerScience+BusinessMedia springer.com ©Springer-VerlagBerlinHeidelberg2007 Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsand regulationsandthereforefreeforgeneraluse. CoverconceptbyeStudioCalamarSteinen Coverproduction:WMXDesignGmbH,Heidelberg Production:LE-TEXJelonek,Schmidt,VöcklerGbR,Leipzig Printedonacid-freepaper SPIN10995792 57/3141/NN-543210 Preface Dynamical systems theory in mathematical biology and environmental sci- encehasattractedmuchattentionfrommanyscientificfieldsaswellasmath- ematics.Forexample,“chaos” isoneofitstypicaltopics.Recentlythepreser- vation of endangered species has become one of the most important issues in biology and environmental science, because of the recent rapid loss of biodiversity in the world. In this respect, permanence or persistence, new concepts in dynamical systems theory, seem important. These concepts give anewaspectinmathematicsthatincludesvariousnonlinearphenomenasuch as chaos and phase transition, as well as the traditional concepts of stability and oscillation. Permanence and persistence analyses are expected not only to develop as new fields in mathematics but also to provide useful measures ofrobustsurvivalforbiologicalspeciesinconservationbiologyandecosystem management. Thus the study of dynamical systems will hopefully lead us to ausefulpolicyforbio-diversityproblemsandthe conservationofendangered species. The above fact brings us to recognize the importance of collabora- tions among mathematicians, biologists, environmental scientists and many related scientists as well. Mathematicians should establish a mathematical basis describing the various problems that appear in the dynamical systems of biology, and feed back their work to biology and environmental sciences. Biologists and environmental scientists should clarify/build the model systems that are important in their own global biological and environmental problems. In the end mathematics, biology and environmental sciences develop together. TheInternationalSymposium“DynamicalSystemsTheoryandItsAppli- cationsto BiologyandEnvironmentalSciences”,heldatHamamatsu,Japan, March14th–17th,2004,under the chairmanshipofone ofthe editors(Y.T.), gavethe editorsthe ideaforthe bookMathematics for Ecology and Environ- mental Sciences and the chapters include material presented at the sympo- sium as the invited lectures. VI Preface The editors asked authors of each chapter to follow some guidelines: 1. tokeepinmindthateachchapterwillbereadbymanynon-experts,who do not have backgroundknowledge of the field; 2. at the beginning of each chapter, to explain the biological background of the modeling and theoretical work. This need not include detailed information about the biology, but enough knowledge to understand the model in question; 3. to review and summarize the previous theoretical and mathematical works and explain the context in which their own work is placed; 4. to explain the meaning of each term in the mathematical models, and the reasonwhythe particularfunctionalformischosen,whatis different from other authors’ choices etc. What is obvious for the author may not be obvious for general readers; 5. thentopresentthemathematicalanalysis,whichcanbethemainpartof eachchapter.Ifitistootechnical,onlytheresultsandthemainpointsof the technique of the mathematical analysis should be presented, rather than of showing all the steps of mathematical proof; 6. in the end of each chapter, to have a section (“Discussion”) in which the authordiscussesbiologicalimplicationsoftheoutcomeofthemathemat- ical analysis (in addition to mathematical discussion). Mathematics for Ecology and Environmental Sciences includes a wide va- riety of stimulating topics in mathematical and theoretical modeling and techniquestoanalyzethemodels inecologyandenvironmentalsciences.Itis hoped that the book will be useful as a source of future researchprojects on aspects of mathematical or theoreticalmodeling in ecology and environmen- talsciences.Itisalsohopedthatthebookwillbeusefultograduatestudents in the mathematical and biologicalsciences as well as to those in some areas of engineering and medicine. Readers should have had a course in calculus, and a knowledge of basic differential equations would be helpful. We are especially pleased to acknowledge with gratitude the sponsorship and cooperation of Ministry of Education, Sports, Science and Technology, The Japanese Society for Mathematical Biology, The Society of Population Ecology, Mathematical Society of Japan, Japan Society for Industrial and Applied Mathematics, The Society for the Study of Species Biology, The Ecological Society of Japan, Society of Evolutionary Studies, Japan, Hama- matsu City and Shizuoka University, jointly with its Faculty of Engineering; Department of Systems Engineering. SpecialthanksshouldalsogotoKeitaAshizawaforexpertassistancewith TEX. Drs. Claus Ascheron and Angela Lahee, the editorial staff of Springer- Verlag in Heidelberg, are warmly thanked. Shizouka, Yasuhiro Takeuchi Fukuoka, Yoh Iwasa June 2006 Kazunori Sato Contents 1 Ecology as a Modern Science Kazunori Sato, Yoh Iwasa, Yasuhiro Takeuchi ...................... 1 2 Physiologically Structured Population Models: Towards a General Mathematical Theory Odo Diekmann, Mats Gyllenberg, Johan Metz ...................... 5 3 A Survey of Indirect Reciprocity Hannelore Brandt, Hisashi Ohtsuki, Yoh Iwasa, Karl Sigmund ........ 21 4 The Effects of Migration on Persistence and Extinction Jingan Cui, Yasuhiro Takeuchi ................................... 51 5 Sexual Reproduction Process on One-Dimensional Stochastic Lattice Model Kazunori Sato .................................................. 81 6 A Mathematical Model of Gene Transfer in a Biofilm Mudassar Imran, Hal L. Smith ................................... 93 7 Nonlinearity and Stochasticity in Population Dynamics J. M. Cushing .................................................. 125 8 The Adaptive Dynamics of Community Structure Ulf Dieckmann, Åke Brännström, Reinier HilleRisLambers, Hiroshi C. Ito............................ 145 Index......................................................... 179 List of Contributors Hannelore Brandt Ulf Diekmann Fakultät für Mathematik, Evolution and Ecology Program, Nordbergstrasse 15, 1090 Wien, International Institute for Applied Austria Systems Analysis, [email protected] Schlossplatz 1,2361 Laxenburg, Austria Åke Brännström [email protected] Evolution and Ecology Program, International Institute for Applied Mats Gyllenberg Systems Analysis, Rolf Nevanlinna Institute De- Schlossplatz 1, 2361 Laxenburg, partment of Mathematics and Austria Statistics, Jingan Cui FIN-00014 University of Helsinki, Department of Mathematics, Finland Nanjing Normal UniversityNanjing [email protected] 210097,China Reinier HilleRisLambers [email protected] CSIRO Entomology, 120 Meiers J. M. Cushing Road, Indooroopilly, QLD 4068, Department of Mathematics, Australia InterdisciplinaryPrograminApplied Mathematics, Mudassar Imran University of Arizona, Arizona State University, Tempe, Tucson, Arizona 85721 USA Arizona, 85287 USA [email protected] [email protected] Odo Diekmann Hiroshi C. Ito Department of Mathematics, Graduate School of Arts and University of Utrecht, P.O. Box Sciences, 80010, 3580 TA Utrecht, University of Tokyo, The Netherlands 3-8-1 Komaba, Meguro-ku, [email protected] Tokyo 153-8902,Japan X List of Contributors Yoh Iwasa Kazunori Sato Department of Biology, Department of Systems Engineering, Faculty of Sciences, Faculty of Engineering, Kyushu University, Japan Shizuoka University, Japan [email protected] [email protected] Karl Sigmund J.A.J. Metz Fakultät für Mathematik, Evolutionary and Ecological Nordbergstrasse 15, 1090 Wien, Sciences, Leiden University, Austria Kaiserstraat63,NL-2311GPLeiden, [email protected] The Netherlands and Adaptive Dynamics Network, IIASA, Hal L. Smith A-2361 Laxenburg, Austria Arizona State University, Tempe, [email protected] Arizona, 85287 USA [email protected] Hisashi Ohtsuki Department of Biology, Yasuhiro Takeuchi Faculty of Sciences, Department of Systems Engineering, Kyushu University, Japan Faculty of Engineering, [email protected]. Shizuoka University, Japan kyushu-u.ac.jp [email protected]