Applied Mathematical Ecology PDF
Preview Applied Mathematical Ecology
Biom.athem.atics Volume 18 Managing Editor S. A. Levin Editorial Board M. Arbib 1. Cowan C. DeLisi M. Feldman 1. Keller K. Krickeberg" R. M. May 1. D. Murray A. Perelson T. Poggio L. A. Segel Simon A.Levin Thomas G.Hallam Louis J. Gross (Eds.) Applied Mathematical Ecology With 114 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Simon A. Levin Section of Ecology and Systematics and Environmental Research Center Cornell University Ithaca, NY 14853-0239 USA Thomas G. Hallam Louis 1. Gross Department of Mathematics and Graduate Program in Ecology University of Tennessee Knoxville, TN 37996-1300 USA Mathematics Subject Classification (1980): 92-01,92-02, 92AI5, 92A17 ISBN-13: 978-3-642-64789-5 e-ISBN-13: 978-3-642-61317-3 DOl: 10_1007/978-3-642-61317-3 Library of Congress Cataloging-in-Publication Data. Applied mathematical ecology / Simon A. Levin, Thomas G. Hallam, Louis J. Gross (eds.) p. cm. - (Biomathematics; v. 18) Proceedings of the Second Autumn Course on Mathematical Ecology, held Nov. - Dec. 1986 at the International Centre for Theoretical Physics in Trieste, Italy. Includes bibliographies and indexes. ISBN 0-387-19465-7 (aile paper) 1. Ecology - Mathematical Models - Congresses. 1. Levin, Simon A. II. Hallam, T. G. (Thomas G.) III. Gross, Louis J. IV. Autumn Course on Mathematical Ecology (2nd: International Centre for Theoretical Physics: 1986) V. Series. QH541.15.M3A66 1989 574.5'072'4-dc19 88-37326 CIP This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provi- sions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1989 Softcover reprint ofthe hardcover 1s t edition 1989 Typesetting: Thomson Press (India) Ltd., New Delhi 214113140-543210 Printed on acid-free paper Dedication This work is dedicated to the families of all the faculty and participants of the Second Autumn Course on Mathematical Ecology who tolerated extended absences. sacrificed companionship. or utilized finances so that we could gather in Trieste. The editors would particularly like to dedicate these efforts to their wives and children. Special recognition-to Marilyn Kallet and Heather Gross-to Rachel. Guy. and Bethany Hallam-to Carole. Jay. and Rachel Levin-for their love and understanding. Acknowledgments The Second Autumn Course on Mathematical Ecology was produced through the efforts of many. We appreciate the most gracious support of Professor Abdus Salam, Director of the International Centre for Theoretical Physics (ICTP) and Professor Luciano Bertocchi, Associate Director of ICTP, who provided financial, logistical and moral support for the Course. Professor Giovanni Vidossich, who suggested that we organize the First Autumn Course on Mathematical Ecology in 1982, again supported and coordinated the current efforts with his usual care and expertise. Gabriella DeMeo served as the Course Secretary and ably assisted with the organization and the many problems thrust in her direction by the directors, lecturers, and participants. The attitude and help of the ICTP staff was conducive to a most pleasant learning experience and working environment. The energetic group of scientists who came to Trieste eager to learn and the scientists who served as faculty found time to get acquainted, to discuss scientific problems of mutual interest, and to appreciate the academic needs and situations of their colleagues. We are grateful to all for their interest in the Course and their success in meeting its objectives. The efforts of the speakers and participants are greatly appreciated by the directors and by all who were able to survive the rigorous schedule. Many scientists provided thoughtful reviews of the manuscripts in this book. The drafts also were influenced by comments from the faculty, participants, and research scholars who were present in Trieste. To everyone involved with the Course, we acknowledge your contributions with pleasure. The Course was a delightful experience for each of us and we thank you for your efforts in making it so enjoyable. T.G. Hallam L.l. Gross S.A. Levin Preface The Second Autumn Course on Mathematical Ecology was held at the Intern- ational Centre for Theoretical Physics in Trieste, Italy in November and December of 1986. During the four year period that had elapsed since the First Autumn Course on Mathematical Ecology, sufficient progress had been made in applied mathemat- ical ecology to merit tilting the balance maintained between theoretical aspects and applications in the 1982 Course toward applications. The course format, while similar to that of the first Autumn Course on Mathematical Ecology, consequently focused upon applications of mathematical ecology. Current areas of application are almost as diverse as the spectrum covered by ecology. The topiys of this book reflect this diversity and were chosen because of perceived interest and utility to developing countries. Topical lectures began with foundational material mostly derived from Math- ematical Ecology: An Introduction (a compilation of the lectures of the 1982 course published by Springer-Verlag in this series, Volume 17) and, when possible, progressed to the frontiers of research. In addition to the course lectures, workshops were arranged for small groups to supplement and enhance the learning experience. Other perspectives were provided through presentations by course participants and speakers at the associated Research Conference. Many of the research papers are in a companion volume, Mathematical Ecology: Proceedings Trieste 1986, published by World Scientific Press in 1988. This book is structured primarily by application area. Part II provides an introduction to mathematical and statistical applications in resource management. Biological concepts are interwoven with economic constraints to attack problems of biological resource exploitation, conservation of our natural resources and agricultural ecology. Part III consists of articles on the fundamental aspects of epidemiology and case studies of the diseases rubella, influenza and AIDS. Part IV addresses some problems of ecotoxicology by modelling the fate and effects of chemicals in aquatic systems. Part V is directed to several topics in demography, population biology and plant ecology, with emphasis on structured popUlation models. The themes of the book-resource management, epidemiology, ecotoxicology, demography, and population ecology-are indicative of some of the Course developments. There were other areas of application presented in the course but not included here primarily because of other obligations of the speakers. Professor Peter Hammerstein addressed problems of behavioral ecology from an evolutionary game theoretic approach. Professor Mark Harwell directed a workshop on ecological x Preface consequences of nuclear war and gave several lectures on ecosystem processes. Professor J. Alberto Leon talked on aspects of population genetics. Professor G.P. Patil discussed topics of diversity and statistical ecology. Professor Luigi Ricciardi introduced stochastic population models and the associated analysis. We are pleased to acknowledge, with thanks, their efforts during the course. Knoxville, Tennessee, and T.G. Hallam, L.J. Gross and Ithaca, New York S.A. Levin Table of Contents Part I. Introduction Ecology in Theory and Application by Simon A. Levin 3 Part II. Resource Management Bioeconomic Modeling and Resource Management by Colin W. Clark . 11 Common Property and the Conservation of Natural Resources by Robert McKelvey. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Information and Area-Wide Control in Agricultural Ecology by Marc Mangel 81 Part III. Epidemiology Fundamental Aspects of Epidemiology Three Basic Epidemiological Models by Herbert W. Hethcote 119 The Population Biology of Parasitic Helminths in Animal Populations by Andrew P. Dobson . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Simple Versus Complex Epidemiological Models by Joan L. Aron . 176 Periodicity in Epidemiological Models by Herbert W. Hethcote and Simon A. Levin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Case Studies Rubella by Herbert W. Hethcote . 212 Influenza and Some Related Mathematical Models by Wei-min Liu and Simon A. Levin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Review of Recent Models of HIV/AIDS Transmission by Carlos Castillo-Chavez. . . . . . . . . . . . . . . . . . 253 The Transmission Dynamics of Human Immunodeficiency Virus (HIV) by Robert M. May and Roy M. Anderson . . . . . . . . . . . . . . . . . . 263 xii Table of Contents Part IV. Ecotoxicology Models in Ecotoxicology: Methodological Aspects by Simon A. Levin. 315 Deterministic and Statistical Models of Chemical Fate in Aquatic Systems by Robert V. Thomann ........................... 322 Effects of Toxicants on Aquatic Populations by Thomas G. Hallam. Ray R. Lassiter. and S.A.L.M. Kooijman . . . . . . . . . . . . . . . . . 352 Part V. Demography and Population Biology Mathematical Models in Plant Biology: An Overview by Louis J. Gross 385 Stable Population Theory and Applications by John Impagliazzo 408 Stage Structure Models Applied in Evolutionary Ecology by R.M. Nisbet. W.S.c. Gurney. and J.A.J. Metz . . . . . . . . . . 428 Some Applications of Structured Models in Population Dynamics by Carlos Castillo-Chavez. . . . . . . . . . . . . . . . . . . . . . . . . 450 Author Index 471 Subject Index . 483 List of Authors Roy M. Anderson, Department of Pure and Applied Biology, Imperial College, London University, London SW7 2BB, England Joan L. Aron, Department of Population Dynamics, Johns Hopkins School of Hygiene and Public Health, Baltimore, MD 21205, USA Carlos Castillo-Chavez, Center for Applied Mathematics, Section of Ecology and Systematics, and Biometrics Unit, Warren Hall, Cornell University, Ithaca, NY 14853, USA Colin W. Clark, Institute of Applied Mathematics, University of British Columbia, Vancouver B.c., Canada Andrew P. Dobson, Department of Biology, University of Rochester, Rochester, NY 14627, USA Louis J. Gross, Department of Mathematics and Graduate Programs in Ecology, and Plant Physiology and Genetics, the University of Tennessee, Knoxville, TN 37996-1300, USA William S.c. Gurney, Department of Physics and Applied Physics, University of Strathclyde, Glascow G4 ONG, Scotland, UK Thomas G. Hallam, Department of Mathematics and Graduate Program in Ecology, University of Tennessee, Knoxville, TN 37996-1300, USA Herbert W. Hethcote, Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA John Impagliazzo, Department of Computer Science, Hofstra University, Hempstead, NY 11550, USA S.A.L.M. Kooijman, Biologisch Laboratorium, Vrijie Universiteit, Amsterdam, The Netherlands Ray R. Lassiter, Environmental Research Laboratory, US Environmental Protection Agency, College Station Road, Athens, GA 30613, USA Simon A. Levin, Ecology and Systematics, E 347 Corson Hall, Cornell University, Ithaca, NY 14853-0239, USA Wei-min Liu, Ecology and Systematics, Corson Hall, and Center for Applied Mathematics, Cornell University, Ithaca NY 14853, USA (current address: Department of Mathematical Sciences, Indiana University Purdue, University at Indianapolis, Indianapolis, IN 46205, USA) Marc Mangel, Department of Zoology, University of California, Davis, CA 95616, USA
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