How Species Interact: Altering the Standard View on Trophic Ecology

185 Pages·2012·2.36 MB·English

by  Roger Arditi

How Species Interact
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How Species Interact
Altering the Standard View
on Trophic Ecology
Roger Arditi
and
Lev R. Ginzburg

1
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Library of Congress Cataloging-in-Publication Data
Arditi, Roger.
How species interact : altering the standard view on trophic ecology / Roger Arditi and Lev Ginzburg.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-19-991383-1 (hardcover : alk. paper) 1. Predation (Biology)—Mathematical models.
2. Food chains (Ecology)—Mathematical models. I. Ginzburg, Lev R. II. Title.
QL758.A73 2012
591.5′3—dc23 2011034905
1 3 5 7 9 8 6 4 2
Printed in the United States of America
on acid-free paper
Ce qui est simple est toujours faux. Ce qui ne l’est pas est inutilisable.
Paul Valéry, in Mauvaises Pensées et Autres (1942)
[ What is simple is always wrong. What is not is useless.
Paul Valéry, in Bad Th oughts and Others (1942)]
We must learn fr om the mathematician to eliminate and to discard; to keep the type in
mind and leave the single case, with all its accidents, alone; and to fi nd in this sacrifi ce of
what matt ers litt le and conservation of what matt ers much one of the peculiar excellences
of the method of mathematics.
D’Arcy W. Th ompson, in On Growth and Form (1917)
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CONTENTS
Acknowledgments xi
Acronyms and Symbols xiii
Introduction 3
1. Alternative Th eories of Trophic Interaction 8
1.1 Monod versus Contois: Resource-Dependent and
Ratio-Dependent Bacteria 9
1.2 Th e Standard Predator-Prey Model of Ecology 1 4
1.3 Th e Arditi-Ginzburg Ratio-Dependent Model 1 7
1.4 Donor Control and Ratio Dependence 22
1.5 Predator-Dependent Models 24
1.6 What Happens at Low Density? Th e Gradual Interference
Hypothesis 26
1.7 Biomass Conversion 29

2. Direct Measurements of the Functional Response 33
2.1 Insect Predators and Parasitoids, Snails, Fish, and Others:
Laboratory Measurements 35
2.1.1 Manipulating the Consumer Density Alone 35
2.1.2 Measuring Interference in the Presence of a Saturating
Functional Response 3 7
2.1.3 Th e Arditi-Akçakaya Predator-Dependent Model 4 0
2.1.4 Application to Literature Data 4 1
2.1.5 Does Interference Increase Gradually? 4 5
2.2 Wasps and Chrysomelids: A Field Experiment 45
2.3 Wolves and Moose: Field Observations 48
2.3.1 Wolf Social Structure and Spatial Scales 4 9
2.3.2 Model Fitt ing and Model Selection Methods 5 0
2.3.3 Th e Wolf-Moose Functional Response Is
Ratio Dependent 51
2.4 Additional Direct Tests of Ratio Dependence 5 5
2.4.1 Bark Beetles 56
2.4.2 Shrimp 57
2.4.3 Egg Parasitoids 5 7
2.4.4 Benthic Flatworms 5 9
2.5 Identifying the Functional Response in Time Series 60
2.6 Concluding Summary 6 1

3. Indirect Evidence: Food Chain Equilibria 6 2
3 .1 Cascading Responses to Harvesting at the Top of the Food
Chain 63
3 .2 Enrichment Response When the Number of Trophic Levels
is Fixed 6 6
3 .3 Enrichment Response When the Number of Trophic Levels
Increases with Enrichment 7 1
3.4 Why the World is Green 76
3.5 Th e Paradox of Enrichment 7 7
3.6 Donor Control and Stability of Food Webs 80

4. How Gradual Interference and Ratio Dependence Emerge 8 3
4 .1 Experimental Evidence of the Role of Predator Clustering on the
Functional Response 8 4
4.1.1 An Aquatic Microcosm Experiment 85
4.1.2 Predator Aggregations Lead to Ratio Dependence 8 6
4.2 Refuges and Donor Control 89
4.2.1 A Simple Exploratory Th eoretical Model 90
4.2.2 From Donor Control to Ratio Dependence 9 2
4.3 Th e Role of Directed Movements in the Formation of Population
Spatial Structures 9 3
4.3.1 Self-Organization Due to Accelerated Movement 94
4.3.2 Spatially Structured Predator-Prey Systems 9 6
4.3.3 How Ratio Dependence Emerges From
Directed Movement 1 01
4.4 Ratio Dependence and Biological Control 102
4.4.1 Th e Biological Control Paradox 1 02
4.4.2 Trophotaxis and Biological Control 1 03
4.5 Emergence of Gradual Interference: An
Individual-Based Approach 1 08
4.5.1 A Qualitative Model Based on Predator
Home Ranges 1 08
4.5.2 An Individual-Based Model Based on
Trophotaxis 1 11
[ viii ] C ontents
5. Th e Ratio Dependence Controversy 1 15
5.1 Evidence of Ratio Dependence is Oft en Concealed in the
Literature 116
5.2 Th e Paradox of Enrichment and the Cascading Enrichment
Response: Is Th ere Any Evidence Th at Th ey Exist? 1 17
5.3 Th e Fallacy of Instantism 1 20
5 .4 How the Ratio-Dependent Model Serves the Debate on the
Causes of Cyclicity 1 24
5.5 Mechanistic versus Phenomenological Th eories 1 26
5.6 “Th e Truth is Always in the Middle”: How Much Truth is in Th is
Statement? 1 27

6. It Must Be Beautiful 1 29
6.1 Scaling Invariance and Symmetries 130
6.2 Kolmogorov’s Insight 1 35
6.3 Akçakaya’s Ratio-Dependent Model for Lynx-Hare
Cycling 1 37
6.4 Th e Limit Myth 1 39

Appendixes 143
3.A Food Chain Responses to Increased Primary
Production 1 43
3.A.1 Prey-Dependent Four-Level Food Chain 1 43
3.A.2 Ratio-Dependent Th ree-Level Food Chain 145
3.B Cascading Response in the Ratio-Dependent Model 146
6 .A How a Revised Ecology Textbook Could Look 148

References 151
Index 163

Contents [ IX ]