Table Of ContentLecture Notes in Biomathematics
Vol. 1: P. Waltman, Deterministic Threshold Models in the Theory Vol. 30: M. Eisen, Mathematical Models in Cell Biology and Cancer
of Epidemics. V, 101 pages. 1974. Chemotherapy. IX, 431 pages. 1979.
Vol. 2: Mathematical Problems in Biology, Victoria Conference 1973. 1101. 31: E. Akin, The Geometry of Population Genetics. IV, 205 pages.
Edited by P. van den Driessche. VI, 280 pages. 1974. 1979.
Vol. 3: D. Ludwig, Stochastic Population Theories. VI, 108 pages. Vol. 32: Systems Theory in Immunology. Proceedings, 1978. Edited
1974. by G. Bruni et al. XI, 273 pages. 1979.
Vol. 4: Physics and Mathematics of the Nervous System. Edited by VO'I. 33: Mathematical Modelling in Biology and Ecology. Proceed·
M. Conrad, W. Guttinger, and M. Dal Cin. XI, 584 pages. 1974. ings, 1979. Edited by W. M. Getz. VIII, 355 pages. 1980.
Vol. 5: Mathematical Analysis of Decision Problems in Ecology. Vol. 34: R. Collins, T. J. van der Werff, Mathematical Models of the
Proceedings 1973. Edited by A. Charnes and W. R. Lynn. VIII, 421 Dynamics of the Human Eye. VII, 99 pages. 1980.
pages. 1975.
Vol. 35: U. an der Heiden, Analysis of Neural Networks. X, 159 pages.
Vol. 6: H. T. Banks, Modeling and Control in the Biomedical Sciences. 1980.
V. 114 pages. 1975.
Vol. 36: A. Worz·Busekros, Algebras in Genetics. VI, 237 pages.
Vol. 7: M.C. Mackey, Ion Transport thro.ugh t;liological Membranes, 1980.
An Integrated Theoretical Approach. IX, 240 pages. 1975. Vol. 37: T. Ohta, Evolution and Variation of Multigene Families. VIII,
Vol. 8: C. Delisi, Antigen Antibody Interactions. IV, 142 pages. 1976. 131 pages. 1980.
Vol. 9: N. Dubin, A Stochastic Model for Immunological Feedback Vol. 38: Biological Growth and Spread: Mathematical Theories and
in Carcinogenesis: Analysis and Approximations. XIII, 163 pages. Applications. Proceedings, 1979. Edited by W. Jager, H. Rost and
1976. P. Tautu. XI, 511 pages. 1980.
Vol. 10: J.J. Tyson, The Belousov-Zhabotinskii Reaktion. IX, 128 Vol. 39: Vito Volterra Symposium on Mathematical Models in Biology.
pages. 1976. Proceedings, 1979. Edited by C. Barigozzi. VI, 417 pages. 1980.
Vol. 11: Mathematic~1 Models in Medicine. Workshop 1976. Edited Vol. 40: Renewable Resource Management. Proceedings, 1980.
by J. Berger, W. Buhler, R. Repges, and P. Tautu. XII, 281 pages. 1976. Edited by T. Vincent and J. Skowronski. XII, 236 pages. 1981.
Vol. 12: A. V. Holden, Models of the Stochastic Activity of Neurones. Vol. 41: Modeles Mathematiques en Biologie. Proceedings, 1978.
VII, 368 pages. 1976. Edited by C. Chevalet and A. Micali. XIV, 219 pages. 1981.
Vol. 13: Mathematical Models in Biological Discovery. Edited by Vol. 42: G. W. Swan, Optimization of Human Cancer Radiotherapy.
D. L. Solomon and C. Walter. VI, 240 pages. 1977. VIII, 282 pages. 1981.
Vol. 14: L.M. Ricciardi, Diffusion Processes and Related Topics in Vol. 43: Mathematical Modeling on the Hearing Process. Proceed·
Biology. VI, 200 pages. 1977. ings, 1980. Edited byM. H. Holmes and L.A. Rubenfeld. V, 104 pages.
Vol. 15: Th. Nagylaki, Selection in One-and Two-Locus Systems. 1981.
VIII, 208 pages. 1977. Vol. 44: Recognition of Pattern and Form. Proceedings, 1979. Edited
Vol. 16: G. Sampath, S. K. Srinivasan, Stochastic Models for Spike by D.G. Albrecht. III, 226 pages. 1982.
Trains of Single Neurons. VIII, 188 pages. 1977. Vol. 45: Competition and Cooperation in Neutral Nets. Proceedings,
Vol. 17: T. Maruyama, Stochastic Problems in Population Genetics. 1982. Edited by S. Amari and M.A. Arbib. XIV, 441 pages. 1982.
VIII, 245 pages. 1977. Vol. 46: E. Walter, Identifiability of State Space Models with applica·
Vol. 18: Mathematics and the Life Sciences. Proceedings 1975. tions to transformation systems. VIII, 202 pages. 1982.
Edited by D.E. Matthews. VII, 385 pages. 1977. Vol. 47: E. Frehland, Stochastic Transport Processes in Discrete
Vol. 19: Measuring Selection in Natural Populations. Edited by Biological Systems. VIII, 169 pages. 1982.
F.B. Christiansen and T.M. Fenchel. XXXI, 564 pages.lg77. Vol. 48: Tracer Kinetics and PhYSiologic Modeling. Proceedings,
Vol. 20: J. M. Cushing, Integrodifferential Equations and Delay 1983. Editecj by R. M. Lambrecht and A. Rescigno. VIII, 509 pages.
Models in Population Dynamics. VI, 196 pages. 1977. 1983.
Vol. 21: Theoretical Approaches to Complex Systems. Proceedings Vol. 49: Rhythms in Biology and Other Fields of Application. Pro·
1977. Edited by R. Heim and G. Palm. VI, 244 pages. 1978. ceedings, 1981. Edited by M. Cosnard, J. Demongeot and A. Le
Breton. VII, 400 pages. 1983.
Vol. 22: F. M. Scudo and J. R. Ziegler, The Golden Age of Theoretical
Ecology: 1923-1940. XII, 490 pages. 1978. Vol. 50: D. H. Anderson, Compartmental Modeling and Tracer
Kinetics. VII, 302 pages. 1983.
Vol. 23: Geometrical Probability and Biological Structures: Buffon's
200th Anniversary. Proceedings 1977. Edited by R. E. Miles and Vol. 51: Oscillations in Mathematical Biology. Proceedings, 1982.
J. Serra. XII, 338 pages. 1978. Edited by J.P.E. Hodgson. VI, 196 pages. 1983.
Vol. 24: F. L. Bookstein, The Measurement of Biological Shape and Vol. 52: Population Biology. Proceedings, 1982. Edited by
Shape Change. VIII, 191 pages. 1978. H. I. Freedman and C. Strobeck. XVII, 440 pages. 1983.
Vol. 25: P. Yodzis, Competition for Space and the Structure of Vol. 53: Evolutionary Dynamics of Genetic Diversity. Proceedings,
Ecological Communities. VI, 191 pages. 1978. 1983. Edited by G.S. Mani. VII, 312 pages. 1984.
Vol. 26: M. B Katz, Questions of Uniqueness and Resolution in Vol. 54: Mathematical Ecology. Proceedings, 1982. Edited by
Reconstruction from Projections. IX, 175 pages. 1978. S.A. Levin and T. G. Hallam. XII, 513 pages. 1984.
Vol. 27: N. MacDonald, Time Lags in Biological Models. VII, 112 Vol. 55: Modelling of Patterns in Space and Time. Proceedings,
pages. 197 B. 1983. Edited by W. Jager and J. D. Murray. VIII, 405 pages. 1984.
Vol. 28: P. C. Fife, Mathematical Aspects of Reacting and Diffusing Vol. 56: H. W. Het.hcote, J.A. Yorke, Gonorrhea Transmission Dynam
Systems. IV, 185 pages. 1979. ics and Control. IX, 105 pages. 1984.
Vol. 29: Kinetic Logic - A Boolean Approach to the Analysis of Vol. 57: Mathematics in Biology and Medicine. Proceedings, 1983.
Complex Regulatory Systems. Proceedings, 1977. Edited by R. Tho· Edited by V. Capasso, E Grosso and S. L. Paveri·Fontana. XVIII,
mas. XIII, 507 pages. 1979. 524 pages. 1985.
ctd. on inside back cover
Lectu re Notes in
Biomathematics
Managing Editor: S. Levin
72
Modeling and Management
of Resources under Uncertainty
Proceedings of the Second U.S.-Australia
Workshop on Renewable Resource Management
held at the East-West Center, Honolulu,
Hawaii, December 9-12, 1985
Edited byT. L. Vincent, Y. Cohen, w.J. Grantham,
G. P. Kirkwood, and J. M. Skowronski
Springer-Verlag
Berlin Heidelberg New York Tokyo
Editorial Board
M. Arbib H.J. Bremermann J. D. Cowan W. Hirsch S. Karlin
J. B. Keller M. Kimura S. Levin (Managing Editor) R. C. Lewontin R. May
J.D. Murray G.F. Oster A.S. Perelson T. Poggio L.A. Segel
Editors
Thomas L. Vincent
Aerospace and Mechanical Engineering
University of Arizona
Tucson, AZ. 85721, USA
Yosef Cohen
Department of Fisheries and Wildlife
University of Minnesota
St. Paul, MN 55108, USA
Walter J. Grantham
Department of Mechanical and Materials Engineering
Washington State University
Pullman, WA 99164-2920, USA
Geoffrey P. Kirkwood
Division of Fisheries Research
CSIRO Marine Laboratories
GPO Box 1538
Hobart, Tasmania, Australia
Jan M. Skowronski
Department of Mathematics
University of Queensland
St. Lucia Queensland 4067, Australia
Mathematics Subject Classification (1980): 34C 11, 34C35, 34020, 49A 10,
49E99, 60H99, 90099, 93005, 93C 15
ISBN-13: 978-3-540-17999-3 e-ISBN-13: 978-3-642-93365-3
DOl: 10.1007/978-3-642-93365-3
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, re·use 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 provisions 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·Veriag Berlin Heidelberg 1987
PREFACE
This vol ume contains the proceedings of the second U.S.-Austral ia workshop
on Renewable Resource Management held at the East-West Center, Honolulu, Hawaii,
December 9-12, 1985. The workshop was jointly sponsored by the National Science
Foundation (USA) and the Department of Science and Technology (Austral ia) under the
U.S.-Austral ia Cooperative Science Program.
The objective of the workshop was to focus on problems associated with the
management of renewable resource systems. A particular emphasis was given to
methods for handling uncertain elements whieh are present in any real system.
Toward this end, the partiei pants were chosen so that the collective expertise
included mathematical modeling, dynamical control/game theory, ecology, and
practical management of real systems.
Each participant was invited to give an informal presentation in his field of
expertise as related to the overall theme. The formal papers (contained in this
vo 1 ume) were written after the workshop so that the authors coul d util ize the
workshop experience in relating their own work to others. To further encourage this
exchange, each paper contained in this volume was reviewed by two other participants
who then wrote formal comments. These comments (with author's reply in some cases)
are attached to the end of each paper. feel that these comments (and repl ies)
form a very valuable part of this volume in that they provide to the reader a share
of the workshop experience. They al so provide a thread which hel ps tie many of the
papers together. Indeed the reader may wish to peruse the comments first.
For review purposes, the papers were originally grouped according to the
classifications Modelling/Biology, Controls/Techniques, and Management/Real Problems.
These headings give a flavor of the material presented here and the same headings
are used to group the papers in this volume. The fact that many of the papers cross
these boundaries reflects the focus and interdisciplinary nature of the workshop.
Since modelling is the key to analysis, the majority of papers in this volume
deal either directly or indirectly with system modelling. Papers dealing more
directly with the modelling question are contained in Part I. Topics include scale
and predictability, stochastic dynamic programming, stage structure, uncertain stock
sizes, random environmental variables, identification and verification, evolutionary
effects, and habitat selection.
A number of techniques particul arly appl icabl e to the determination of
management policy from models subject to uncertainty are contained in Part II. Both
discrete and continuous system model s are used. The first two papers use a
statistical approach to examine adaptive control and parameter estimation. The next
four papers use deterministic methods to deal with system uncertainty. The first
two of these use reachable set methods and the last two use Liapunov methods.
IV
The remaining two papers in this section use methods from optimal control and game
theory to arrive at management policy.
Part III is devoted to those papers dealing more directl y with the
management of real problems. These include the management of the Ogalalla Aquifer,
the Great Lakes, California sardines, Oregon groundfishery, tuna in the Western
Pacific, the California river system, and Western King prawns in Spencer Gulf.
I would like to acknowledge the service that coeditor Jan Skowronski
provided in helping to organize the workshop. I am also indebted to coeditors Yosef
Cohen, Walt Grantham, and Geoff Kirkwood who did most of the work in organizing the
reviews and comments.
T. L. Vincent
Tucson, Arizona
March 2, 1987
PARTICIPANTS
Dr. Ann Lowes Blackwell. Mechanical Engineering, University of Texas, Arlington,
Texas 76019 USA.
Dr. Louis W. Botsford. Department of Wildlife and Fisheries Biology, University of
California, Davis, California 95616 USA.
Dr. Colin W. Clark. Institute of Applied Mathematics, University of British Columbia,
Vancouver, B.C., Canada V6T lW5.
Dr. Yosef Cohen. Department of Fisheries and Wildlife, University of Minnesota, St.
Paul, Minnesota 55108 USA.
Dr. Michael E. Fisher. Department of Mathematics, University of Western Australia,
Nedlands, Western Aust~alia 6009.
Dr. Wayne M. Getz. Division of Biological Control, University of California,
Berkeley, California 94720 USA.
Dr. Walter J. Grantham. Department of Mechanical Engineering, Washington State
University, Pullman, Washington 99164-2920 USA.
Dr. Susan Hanna. Department of Agricultural and Resource Economics, Oregon State
University, Corvallis, Oregon 97331-3601 USA.
Dr. Ray Hilborn. Tuna and Billfish Assessment Programme, South Pacific Commission,
Post Box 0-5, Noumea Cedex, New Caledonia.
Dr. Geoff P. Kirkwood. Division of Fisheries Research, CSIRO Marine Laboratories, GPO
Box 1538, Hobart, Tasmania, Australia.
Dr. Cho Seng Lee. Department of Mathematics, University of Malaya, Kuala Lumpur
22-11, Malaysia.
Dr. George Leitmann. Departme.nt of Mechanical Engineering, University of California,
Berkeley, California 94720 USA.
Dr. Paul F. Lesse. CSIRO, Building Research Division, Graham Road, Highett, Victoria
3190, Aust ra 1 i a.
Dr. Simon A. Levin. Ecology and Systematics and Ecosystems Research Center, Cornell
University, Ithaca, New York 14853 USA.
Dr. Donald Ludwig. Institute of Animal Resource Ecology, The University of British
Columbia, 2204 Main Mall, Vancouver, British Columbia, Canada V6T 1W5.
Dr. Marc Mangel. Department of Mathematics, University of California, Davis,
California 95616 USA.
Dr. Robert McKel vey. Department of Mathematical Sciences, University of Montana,
Missoula, Montana 59812 USA.
Mr. Brodie Nicol. Department of Mathematics, University of Queensl and, St. Lucia,
Brisbane, Queensland 4067 Australia.
Dr. Michael L. Rosenzweig. Department of Ecology and Evolutionary Biology, The
University of Arizona, Tucson, Arizona 85721 USA.
Dr. Jan M. Skowronski. Department of Mathematics, Uni versity of Queensl and, St.
Lucia, Brisbane, Queensland 4067, Australia.
VI
Dr. Philip R. Sluczanowski. Department of Fisheries, Box 1625, G.P.O., Adelaide,
South Australia, 5001.
Dr. George R. Spangler. Department of Fisheries and Wildlife, 200 Hodson Hall,
University of Minnesota, St. Paul, Minnesota 55455 USA.
Dr. Russel J. Stonier. Department of Mathematics and Computing, Capricornia
Institute of Advanced Education, Rockhampton, Queensland, Australia.
Dr. Thomas l. Vincent, Department of Aerospace and Mechanical Engineering, The
University of Arizona, Tucson, Arizona 85721 USA.
Dr. Carl J. Walters. Institute of Animal Resource Ecology, The University of British
Columbia, Vancouver, B.C., Canada V6T lW5.
CONTENTS
PREFACE •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• I I I
PARTICIPANTS v
PART I MODELLING/BIOLOGY
SCALE AND PREDICTABILITY IN ECOLOGICAL MODELING ••••••••••••••••••••••••••• 2
Simon A. Levin
BEHAVIORAL MODELLING AND RESOURCE MANAGEMENT •••••••••••••••••• • • • • • • • • • • • 11
Colin W. Clark .
MODELING FOR BIOLOGICAL RESOURCE MANAGEMENT ••••••• • • • • • • • • • • • • • • • • • • • • • •• 22
Wayne M. Getz
OPTIMAL HARVEST POLICIES FOR FISHERIES WITH 43
UNCERTAIN STOCK SIZES
G.P. Kirkwood
ANALYSIS OF ENVIRONMENTAL INFLUENCES ON 54
POPULATION DYNAMICS
Louis W. Botsford
IDENTIFICATION AND CONTROL OF STOCHASTIC 66
LINEAR MULTISPECIES ECOSYSTEM MODELS
Yosef Cohen
AN EVOLUTIONARY RESPONSE TO HARVESTING 80
Thomas L. Vincent and
Joel S. Brown
DENSITY-DEPENDENT HABITAT SELECTION: A TOOL FOR 98
MORE EFFECTIVE POPULATION MANAGEMENT
Michael L. Rosenzweig
PART II CONTROLS/TECHNIQUES
APPROACHES TO ADAPTIVE POLICY DESIGN FOR ................................. 114
HARVEST MANAGEMENT
Carl J. Walters
COMPUTER-INTENSIVE METHODS FOR FISHERIES •••••••••••••••••••••••••••••••• 125
STOCK ASSESSMENT
Donald Ludwig
VARIABILITY IN ECOSYSTEM MODELS: ••••••••••••••••••••••••••••••••••••••• 139
A DETERMINISTIC APPROACH
Michael E. Fisher
VIII
CONTENTS (continued)
GENERATING REACHABLE SET BOUNDARIES FOR 152
DISCRETE-TIME SYSTEMS
Walter J. Grantham and
Michael E. Fisher
UNCERTAIN DYNAMICAL SYSTEMS: AN APPLICATION TO •••.•••••••••••••••••.••••• 167
RIVER POLLUTION CONTROL
C.S. Lee and G. Leitmann
REAL TIME MANAGEMENT OF A RESOURCE ••••••••.••••.•••..•.•••.•••••.••...• 186
CONSUMPTION MODEL
G. Bojadziev and J. Skowronski
CONTROL PROBLEMS IN IRRIGATION MANAGEMENT 195
R.J. Stonier
A DIFFERENTIAL GAME BETWEEN TWO PLAYERS 207
HARVESTING FROM A DIVIDED FISHERY
Brodie Nicol
PART III MANAGEMENT/REAL PROBLEMS
GROUNDWATER-BASED AGRICULTURE IN THE ARID •••••••••••••••.••••••.••••••••• 222
AMERICAN WEST: MODELING THE TRANSITION TO
A STEADY-STATE RENEWABLE RESOURCE ECONOMY
Robert McKel vey
GREAT LAKES FISHERIES: ARE EXPLICIT ••••••••••••••.•••..••.•.••.•••..••• 236
CONTROLS NECESSARY?
George R. Spangler
SAMPLING HIGHLY AGGREGATED POPULATIONS WITH •••.•••••••••.•••.•••••••••••. 247
APPLICATION TO CALIFORNIA SARDINE-MANAGEMENT
Marc Mangel
THE STRUCTURE OF FISHING SYSTEMS AND THE ••••••••.••••.•••.•••••••••••••• 264
IMPLEMENTATION OF MANAGEMENT POLICY
Susan S. Hanna
SPATIAL MODELS OF TUNA DYNAMICS IN THE WESTERN •••••••••.•••••••••••••.••• 276
PACIFIC: IS INTERNATIONAL MANAGEMENT NECESSARY?
Ray Hil born
EXAMINATION OF INSTITUTIONAL STRUCTURES IN MULTIPLE •••••••••••••••••••••••. 287
RESOURCE, MULTIPLE MANAGEMENT SYSTEMS: A CONTROL
THEORETIC APPROACH
Ann Lowes Blackwell
OPTIMAL HARVESTING OF A YEAR-CLASS OF PRAWNS ••••••••••••••••••.•••••••••• 304
Phil ip R. Sl uczanowski
PART I
MODELLING/BIOLOGY
