Dynamic State Variable Models in Ecology: Methods and Applications

302 Pages·2000·14.03 MB·English

by  Colin W. Clark

DYNAMIC STATE
VARIABLE MODELS
IN ECOLOGY
OXFORD SERIES IN ECOLOGY AND EVOLUTION
Edited by Robert M. May and Paul H. Harvey
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Dynamic State Variable Models in Ecology:
Methods and Applications
Colin W. Clark and Marc Mangel
DYNAMIC STATE
VARIABLE MODELS
IN ECOLOGY
Methods and Applications
Colin W. Clark
Marc Mangel
New York Oxford
OXFORD UNIVERSITY PRESS
2000
Oxford University Press
Oxford New York
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Copyright © 2000 by Oxford University Press, Inc.
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Library of Congress Cataloging-in-Publication Data
Clark, Colin Whitcomb, 1931-
Dynamic state variable models in ecology: methods and
applications / Colin W. Clark and Marc Mangel.
p. cm. — (Oxford series in ecology and evolution)
Includes bibliographical references and index.
ISBN 0-19-512266-6; ISBN 0-19-512267-4 (pbk)
1. Animal behavior—Mathematical models. 2. Animal ecology—
Mathematical models. I. Mangel, Marc. II. Title. III. Series.
QL751.65.M3C58 1999
577'.01'5118—dc21 99-12265
1 3 5 7 9 8 6 42
Printed in the United States of America
on acid-free paper
Preface
For discussions and comments about the book, we thank Peter Bednekoff, Jane
Brockman, Anders Brodin, Tim Collier, Reuven Dukas, Shea Gardner, Paul Hart, Pat
Kennedy, Don Ludwig, Barney Luttbeg, Bernie Roitberg, Jay Rosenheim, and Ron
Ydenberg.
Many young scientists contributed to the development of the book by participating
in courses based on early drafts. We thank at the University of California at Santa
Cruz, Edgar Becerra, Melanie Bojanowski, Bret Eldred, Samantha Forde, Eric
Danner, Jennifer Brown, Karen Crow, Diana Steller, Matt Kauffman, Kim Heinemeyer,
Josh Livni, Diane Thomson, Chris Wilcox, and especially Angie Shelton; at Princeton,
Jon Cline, Leila Hadj-Chikh, Tim Kailing, David Smith, Thomas Valqui, and Erika
Zavaleta; at the University of British Columbia, Marty Anderies, Chris Fonnesbeck
and Edward Gregr; and at Simon Fraser University, Sigal Blay, Julian Christians, and
Nick Hughes.
A special vote of thanks goes to Janet Clark, who typeset in T K many drafts, as
E
well as the final published text.
The original research reported on here has been supported by grants to CWC from
the Natural Sciences and Engineering Research Council of Canada, and to MM from
the California Sea Grant Program, the National Science Foundation, and the U. S.
Department of Agriculture.
We were fortunate to be able to review the final draft on the Big Island of Hawaii,
uninterrupted except by omao, yellow tang, and spinner dolphins.
Vancouver, British Columbia C. W. C.
Santa Cruz, California M. M.
August 1999
This page intentionally left blank
Contents
1 The Basics, 3
1.1 Introduction: Biology, constraints and trade-offs, 3
1.2 An example: Formalizing constraints and trade-offs, 4
1.3 A brief digression on probability, 5
1.4 The algorithm of stochastic dynamic programming, 7
1.5 Computer implementation, 9
1.6 Evaluating the fitness of alternative strategies, 18
1.7 Developing a dynamic state variable model, 20
1.8 A model for feeding by the three-spined stickleback, 30
1.9 The role of dynamic state variable models in ecology, 38
1.10 Examples of projects, 40
Appendix: Rate-maximizing theories of diet selection and habitat choice, 45
2 Some Details of Technique, 49
2.1 Linear interpolation, 49
2.2 Sequential coupling, 52
2.3 Forward iteration and Monte Carlo simulation, 54
2.4 The critical level of reserves, 57
2.5 Environmental state variables, 57
2.6 Errors in decisions, 60
2.7 Variable constraints, 61
2.8 Functional forms, 67
3 Using the Model, 71
3.1 Levels of detail in model predictions, 71
3.2 Comparing models and data, 72
3.3 Obtaining and analyzing predictions, 78
3.4 Sensitivity analysis, 80
3.5 Suboptimality analysis, 81
4 Oviposition Behavior of Insect Parasitoids, 82
4.1 Parasitoid life histories, 82
4.2 Fixed clutch models, 86
viii • Contents
4.3 A dynamic but state-independent model, 89
4.4 The proovigenic parasitoid, 95
4.5 The synovigenic parasitoid: Eggs and reserves, 99
4.6 Discussion, 102
5 Winter Survival Strategies, 108
5.1 Foraging and fattening strategies for willow tits, 108
5.2 Social interaction, 118
5.3 Experiments suggested by the model, 121
5.4 Models of hoarding behavior, 122
5.5 Long-term hoarding, 124
5.6 Overwinter foraging by juvenile salmon, 132
5.7 A state variable model for overwinter lipid dynamics, 133
5.8 Empirical test of the predictions, 136
6 Avian Migration, 139
6.1 The energetics of bird migration, 140
6.2 Optimal fuel loads, 144
6.3 A dynamic state variable model of single-flight migration, 147
6.4 Spring migration of western sandpipers, 149
7 Human Behavioral Ecology, 161
7.1 Dynamic discarding in fisheries, 161
7.2 Optimal reproductive strategies in !kung bushmcn females, 167
8 Conservation Biology, 173
8.1 Assessing the fitness consequences of environmental change, 173
8.2 Using fire rotation schemes to maximize the persistence of
midsuccessional species, 176
8.3 Managing a metapopulation, 180
8.4 Some other applications, 188
9 Agroecology, 192
9.1 Behavioral origins of the functional response, 192
9.2 Behavior and population regulation: The behavioral stabilization
of host—parasitoid interactions, 199
9.3 Weed control: Predicting flowering in thistles and other
monocarpic perennials, 206
9.4 Discussion, 209
Contents • ix
10 Population-Level Models, 212
10.1 Ideal free distributions, 212
10.2 Patch choice with frequency-dependent predation risk, 214
10.3 Genetic algorithms as optimization tools, 223
11 Stochasticity, Uncertainty, and Information
as a State Variable, 232
11.1 Ephemeral patches and uncertain food, 232
11.2 A Bayesian foraging model, 238
11.3 Tracking a changing environment, 244
11.4 Discussion, 245
Appendix: Bayesian updating, 246
12 Measures of Fitness, 248
12.1 Nonoverlapping generations, 248
12.2 Overlapping generations, 253
12.3 Fitness measures in dynamic state variable models, 259
Appendix: Programs available at the
OUP Web site, 265
References, 267
Index, 287