Foraging: Behavior and Ecology docx

Foraging

Foraging
Behavior and Ecology
Edited by David W. Stephens,
Joel S. Brown, and
Ronald C. Ydenberg
The University of Chicago Press
Chicago & London
David W. Stephens is Professor of Ecology, Evolution, and Behavior at the University of
Minnesota and author, with J. R. Krebs, of Foraging Theory.
Joel S. Brown is Professor of Biology at the University of Illinois at Chicago and author,
with T. L. Vincent, of Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics.
Ronald C. Ydenberg is Professor in the Behavioral Ecology Research Group and Director of
the Centre for Wildlife Ecology at Simon Fraser University.
The University of Chicago Press, Chicago 60637
The University of Chicago Press, Ltd., London
C

2007 by The University of Chicago
All rights reserved. Published 2007
Printed in the United States of America
16151413121110090807 12345
ISBN-13: 978-0-226-77263-9 (cloth)
ISBN-13: 978-0-226-77264-6 (paper)
ISBN-10: 0-226-77263-2 (cloth)
ISBN-10: 0-226-77264-0 (paper)
Library of Congress Cataloging-in-Publication Data
Foraging : behavior and ecology / [edited by] David W. Stephens, Joel S. Brown &
Ronald C. Ydenberg.

p. cm.
ISBN-13: 978-0-226-77263-9 (cloth : alk. paper)
ISBN-13: 978-0-226-77264-6 (pbk. : alk. paper)
ISBN-10: 0-226-77263-2 (cloth : alk. paper)
ISBN-10: 0-226-77264-0 (pbk. : alk. paper)
1. Animals—Food. I. Stephens, David W., 1955– II. Brown, Joel S. (Joel Steven),
1959– III. Ydenberg, Ronald C.
QL756.5.F665 2007
591.5

3—dc22
2006038724
∞

The paper used in this publication meets the minimum requirements of the American
National Standard for Information Sciences—Permanence of Paper for Printed Library
Materials, ANSI Z39.48-1992.
Contents
Foreword ix
John Krebs and Alex Kacelnik
Acknowledgments xiii
1 Foraging: An Overview 1
Ronald C. Ydenberg, Joel S. Brown, and David W. Stephens
Box 1.1 Prehistory: Before Foraging Met Danger
Peter A. Bednekoff
Box 1.2 Diving and Foraging by the Common Eider
Colin W. Clark
Box 1.3 A Two-Player, Symmetric, Matrix Game
Box 1.4 A Two-Player Continuous Game
part i Foraging and Information Processing

2 Models of Information Use 31
David W. Stephens
3 Neuroethology of Foraging 61
David F. Sherry and John B. Mitchell
Box 3.1 Glossary
Box 3.2 A Nobel Prize in the Molecular Basis of Memory
Box 3.3 Neural Mechanisms of Reward
Peter Shizgal
v
vi Contents
4 Cognition for Foraging 105
Melissa M. Adams-Hunt and Lucia F. Jacobs
Box 4.1 Learning in the Laboratory
part ii Processing, Herbivory, and Storage
5 Food Acquisition, Processing, and Digestions 141
Christopher J. Whelan and Kenneth A. Schmidt
Box 5.1 Modeling Digestive Modulation in
an Ecological Framework
Christopher J. Whelan
Box 5.2 More Than a Matter of Taste
Frederick D. Provenza
6 Herbivory 175
Jonathan Newman
Box 6.1 Herbivory versus Carnivory: Different Means
for Similar Ends
David Raubenheimer
Box 6.2 Animal Farm: Food Provisioning and Abnormal
Oral Behaviors in Captive Herbivores
Georgia Mason
7 Energy Storage and Expenditure 221

Anders Brodin and Colin W. Clark
Box 7.1 Neuroendocrine Mechanisms of Energy Regulation
in Mammals
Stephen C. Woods and Thomas W. Castonguay
Box 7.2 Energy Stores in Migrating Birds
Åke Lindstr
¨
om
Box 7.3 What Current Models Can and Cannot Tell Us
about Adaptive Energy Storage
Alasdair Houston and John McNamara
part iii Modern Foraging Theory
8 Provisioning 273
Ronald C. Ydenberg
Box 8.1 Effects of Social Interactions at Resource Points
on Provisioning Tactics
Box 8.2 Provisioning and Spatial Patterns of
Resource Exploitation
Box 8.3 Variance-Sensitive Provisioning
Contents vii
9 Foraging in the Face of Danger 305
Peter A. Bednekoff
Box 9.1 Allocation of Foraging Effort when Danger Varies
over Time
Box 9.2 Three Models of Information Flow in Groups
10 Foraging with Others: Games Social Foragers Play
331
Thomas A. Waite and Kristin L. Field
Box 10.1 The Ideal Free Distribution
Ian M. Hamilton

Box 10.2 Genetic Relatedness and Group Size
Box 10.3 The Rate-Maximizing Producer-Scrounger Game
part iv Foraging Ecology
11 Foraging and Population Dynamics 365
Robert D. Holt and Tristan Kimbrell
Box 11.1 Basic Concepts in Population Dynamics
12 Community Ecology
397
Burt P. Kotler and Joel S. Brown
Box 12.1 Isolegs and Isodars
13 Foraging and the Ecology of Fear
437
Joel S. Brown and Burt P. Kotler
Box 13.1 Stress Hormones and the Predation-Starvation
Trade-off
Vladimir V. Pravosudov
Box 13.2 Giving-up Densities
Joel S. Brown
14 On Foraging Theory, Humans, and the Conservation
of Diversity: A Prospectus
483
Michael L. Rosenzweig
Contributors 503
Literature Cited 507
Index 587

Foreword
On October 1, 1975, JK wrote the following in a letter (no email in those
days!) to Ric Charnov to report the pilot results of the first experimental test
of the “classic” diet model under properly controlled conditions of encounter

rate, handling time, and prey energy content:
Here are the results—read ’em and gloat:
percentage small prey in the diet predicted by:
treatment random foraging prey model observed
1505047
2505037
325 00
450 02
567 09
The last three rows demonstrated the crucial counterintuitive prediction that
small prey would be excluded from the diet, independently of their encounter
rate, if the encounter rate with large prey were above a certain quantifiable
threshold.
Those were heady days! Setting aside the fact that the small prey were not
totally ignored, it seemedasthoughaverysimple,testablemodel,derived from
a few starting assumptions about rate maximization and constraints on forag-
ing,couldactuallypredicthowananimalrespondedinanexperiment.It’shard
to overstate the excitement at the time.
Shortly afterward, Richard Cowie’s quantitative test of the patch model
appeared (Cowie 1977), and the first use of stochastic dynamic modeling
ix
x Foreword
predicted the trade-off between sampling and exploitation of a new environ-
ment (Krebs et al. 1978). It really looked as though a new quantitative the-
oretical framework for behavioral ecology had been born out of the ideas of
MacArthur and Pianka (1966), Emlen (1966), Charnov (1976a, 1976b), and
Parker (1978). By the time Stephens and Krebs published their monograph
on foraging theory in 1986, the optimal foraging industry had been in full
swing for a nearly a decade, and large numbers of laboratory and field studies
seemed to underline the power of the theory.

But by nomeans everyone was convinced. At the Animal Behavior Society
symposium held in Seattle in 1978 (Kamil and Sargent 1981), Reto Zach and
Jamie Smith concluded their article “Optimal Foraging in Wild Birds” as fol-
lows: “Most feeding problems in the wild are complex and it is therefore dif-
ficult todefineoptima. Furthermore, optimal foraging theorycannotbe tested
conclusively. Optimal foraging theory is thus of limited use only. Fortunate-
lythereare otherpromisingapproaches tothe developmentalandcomparative
analysis of foraging skills.”
By 1984, the time of the seminal “Brown Symposium” (Kamil et al. 1987)
(referring of course to the eponymous university, not the color of the re-
sulting book—which was green), not only had the field of optimal foraging
theory become broader, but Russell Gray and John Ollason had developed
excoriating critiques of the whole enterprise. Russell Gray summarized his
views in these terms: “Despite its popularity, OFT faces a long list of serious
problems. . . . These problems are generally downplayed within the OFT lit-
erature and the validity of the optimality assumption is taken on faith. This
faith does not seem to be particularly useful.” John Ollason was equally, if
not more, astringent, commenting that when predictions of OFT and data
coincide, “a labyrinthine tautology has been constructed that is based on
assumption piled on assumption.”
With the benefit of twenty years’ hindsight, who was right? Was it the en-
thusiasticoptimistsor thecynicalcritics? Theansweris, “abitof both.”Onone
hand, there is no doubt that the initial hopes for a simple, all-embracing the-
ory that paid little attention to behavioral mechanisms were soon dashed. On
the other hand, as the research has matured, important insights into behavior
and ecology have been fostered by optimal foraging theory. Indeed, many
important questions have been asked because of optimality thinking, and
asking the right questions is the basis of successful science. Furthermore, the
breadth of impact of foraging theory across many disciplines is remarkable.
This book shows how the field has broadened and deepened. Simplicity

and coherence have been left behind, but diversity, richness of texture, and
understanding have been gained. The tentacles of foraging theory, in its
broadest sense, have extended to form links with neuroethology, behavioral
Foreword xi
economics, life histories, animal learning, game theory, and conservation
biology.
Perhaps most important of all, the simplistic approach to building and test-
ing models of behavior that characterized some of the early foraging litera-
ture has been replaced by a moresophisticated comparativeanalysisof models.
Take risk sensitivity as anexample. Caraco’s early experimental work (Caraco
et al. 1980) and Stephens’s theoretical formulation (Stephens 1981) provided
a beguilingly simple combination of theory and data: animals should be risk
prone when their expected energybudget is negative and risk averse when itis
positive. Houston and McNamara (1982) subsequently extended Stephens’s
idea, using stochasticdynamicmodels, to predict changes in risksensitivityde-
pendingonbothenergeticstate andtime horizon.The theorybecame moreso-
phisticated, but did not encompass mechanisms of decision making: its predic-
tions were based on arguments about adaptation. But when mechanisms were
considered, it turned out that the purely functional approach embodied in risk
sensitivity theory was not the one that most successfully accounted for the
experimental data.
Kacelnik and Bateson (1997) compared the predictions of four kinds of
models: risk sensitivity theory, short-term rate maximization, scalar utility
theory, and associative learning theory. The first kind of model is based on
functional arguments; the secondis descriptive, predicting choices from regu-
larities previously observed in data; the third derives from the psychophysics
of perception; and the fourth examines the consequences of established prin-
ciples of animal learning.
Althoughsomeof theearly studiesseemedto confirmthe predictionsofrisk
sensitivity theory (namely, experimental animals reversed their preference for

variance depending on manipulations of their energy reserves), this result was
not robust. The single most reliable phenomenon is that, when averages are
equal, animals prefer variable over fixed delays tofoodandfixedovervariable
amountsoffood. Inother words,theyare riskprone fordelayto rewardand risk
averse for amount. Risk sensitivity theory does not explain or predict this ob-
servation, while scalar utility theory predicts both effects at a qualitative level.
None of the theories is fully successful in terms of quantitative predictions:
each predicts some results and fails to predict others. Furthermore, the differ-
ent models are as interesting in the ways in which they fail as they are in their
successes.
This example illustrates several points. First, in its more mature phase,
foraging theory has moved from simply testing the predictions of one kind of
model to comparing the ability of a range of models to explain the data. Sec-
ond, while itisstill important conceptually to distinguishaccountsof behavior
based on functional arguments from those based on causal mechanisms, the
xii Foreword
interplay between these two kinds of explanations benefits both approaches.
On one hand, without the input from functional modeling (as embedded in
risk sensitivity theory), the question of preference for variance would not
have been examined in the light of mechanisms. But on the other hand, if one
of these mechanistic models turns out to be better at predicting behavior, the
functional theory needs to be reexamined. For instance, earlier risk sensitivity
models may have incorrectly identified the selective forces that act on animal
risk taking. The success of scalar utility theory suggests that selection may
have favored a logarithmic encoding of stimulus intensity to allow the animal
to cope with a wide range of stimuli, which leads automatically to preference
for variable delays and fixed amounts.
This excellent volume sets the stage for the next decade of research, as a
result of which the field of foraging will no doubt have evolved and been
transformed again.

John Krebs
Alex Kacelnik
Oxford, June 2006
Acknowledgments
From the editors:
The editors thank the authors for their patience and good will throughout the
production of this volume. We thank Christie Henry for her advice and as-
sistance, which—quite literally—made this project possible. We thank Todd
Telander, who translated our figures from meaningless scrawls to a coherent
and aestheticallypleasing whole. Finally,wethank NormaRochefor her care-
ful and competent copyediting.
Chapter 1
The overview we present here has been shaped by discussions with many
colleagues over the past several decades. Joel Heath and Grant Gilchrist took
the eider videos to whichthe reader is referred in the openingpassage, and Joel
Heath maintains the Web site on which they are displayed. We thank Dave
Moore and Jon Wright for discussion on particular points.
Chapter 2
I thank Tom Getty, Colleen McLinn, and Ron Ydenberg for comments on
the manuscript. The National Science Foundation (IBN-0235261) and the
National Institute of MentalHealth (RO1-MH64151) supported my research
during the preparation of this manuscript.
Chapter 3
We would like to thank Robert Gegear and Peter Cain for their many helpful
comments on the manuscript and Jennifer Hoshooley for valuable discussion.
Preparation of this chapter was supported by grants from the Natural Sciences
and Engineering Research Council of Canada.
xiii
xiv Acknowledgments
Chapter 4

We would like to thank Al Riley, George Barlow, Seth Roberts,AndySuarez,
Karen Nutt, and the Animal Behavior lunch group for helpful comments and
discussions on early drafts of this manuscript. Thank you also to the editors
of this volume for many helpful comments.
Chapter 5
We thank the editors for inviting our participation and for their constructive
criticisms. Many individuals helped shape our current views on foraging,
especially Joel Brown, Richard Holmes, Robert Holt, William Karasov, Burt
Kotler, Carlos Mart
´
ınez del Rio, Douglas Levey, Timothy Moermond, and
Mary Willson. We especially thankCarlos Mart
´
ınez del Rio, Brenda Molano-
Flores, Dennis Whelan, and Mary Willson for reviewing previous drafts.
Chapter 6
I am deeply grateful to three scientists for all that they have taught me: Tom
Caraco, John Krebs, and Tony Parsons.
Chapter 7
We thank Dave Stephens and Ron Ydenberg for valuable comments and edit-
ing help. AB was supported by a grant from the Swedish Research Council,
VR.
˚
AL warmly acknowledges the ever-inspiring collaboration with Thomas
Alerstam and the Migration Ecology Research Group in Lund.
Chapter 8
I am deeply gratefulto colleagues, friends, and students in theBehavioral Eco-
logy Research Group and the Centre for Wildlife Ecology at Simon Fraser
University for their commitment to collegial scientific inquiry and for their
parts in the parade of ideas, discovery, and natural history that makes working

there so endlessly fascinating.
Chapter 9
I thank Earl Werner, Shannon McCauley, Luis Schiesari, Mara Savacool
Zimmerman, Mike Fraker, Kerry Yurewicz, Steve Lima, Annie Hannan, Uli
Reinhardt, Graeme Ruxton, Tim Caro, Dan Blumstein, Anders Brodin, Will
Cresswell, Ron Ydenberg, and Dave Stephens for helpful comments on the
manuscript, and Robert Gibson and David McDonald for help in locating a
reference.
Acknowledgments xv
Chapter 10
We thank E. A. Marschall, K. M. Passino, R. Ydenberg, D. Stephens, and stu-
dents inourgraduate course inbehavioralecology for comments onthemanu-
script.
Chapter 11
We thank Chris Whelan and the editors for very helpful comments on the
chapter. RDH thanks NSF, NIH, and the University of Florida Foundation
for support, and Burt Kotler, Joel Brown, Tom Schoener, Doug Morris, Per
Lundberg, and John Fryxell for stimulating conversations on foraging. TK
thanks NSF for a graduate research fellowship.
Chapters 12 and 13
We are grateful to our many colleagues and students over the years whose
discussions, ideas, and insights contributed so very much to our own ideas
and worldview. These include Zvika Abramsky, Leon Blaustein, Sasha Dall,
Mike Gaines, Bob Holt, Bill Mitchell, Doug Morris, Ken Schmidt, and Tom
Vincent. We are especially grateful to our teacher and mentor, Mike Rosen-
zweig.
Chapter 14
Thanks to Joel Brown and Dave Stephens for substantive help with the
manuscript. Thanks to Peter Raven and the Missouri Botanical Garden for
sabbatical year hospitality. Thanks to my colleagues Zvika Abramsky, Burt

Kotler, and Yaron Ziv for continual intellectual stimulation.
1
Foraging: An Overview
Ronald C. Ydenberg, Joel S. Brown, and David W. Stephens
1.1 Prologue
Hudson Bay in winter is frozen and forbidding. But, at a few special
places where strong tidal currents are deflected to the surface by ridges
on the seafloor, there are permanent openings in the ice, called polyn-
yas, that serve as the Arctic equivalent of desert oases. Many polynyas
are occupied by groups of common eiders. When the current in the po-
lynya slackens between tide changes, these sea ducks can forage, and they
take advantageofthe opportunity by divingmanytimes. With vigorous
wing strokes they descend to the bottom, where they search though the
jumbled debris, finding and swallowing small items, and occasionally
bringing a large item such as an urchin or a mussel clump to the surface,
where they handle itextensively before eating or discarding it. (Readers
can take an underwater look at a common eider diving in a polynya at
www.sfu.ca/eidervideo/. These videos were made by Joel Heath and
Grant Gilchrist at the Belcher Islands in Hudson Bay.)
This foraging situation presents many challenges. Eiders must con-
sume a lot of preyduringa short period to meet the high energy demand
of a very cold climate. Most available prey are bulky and of low qual-
ity, and the ducks must process a tremendous volume of material to
extract the energy and nutrients they need. They must also keep an eye
on the clock, for the strong currents limit the available foraging time.
2 Ronald C. Ydenberg, Joel S. Brown, and David W. Stephens
Throughout the winter, individual ducks may move among several widely
separated polynyas or visit leads in the pack ice when the wind creates open-
ings. Foxes haunting the rim of the polynyas and seals in the water below

create dangers that require constant wariness. In this unforgiving environ-
ment, the eider must meet all these challenges, for in the Arctic winter, a
hungry eider is very soon a dead eider.
1.2 Introduction
Twenty years ago, Dave Stephens and John Krebs opened their book Foraging
Theory (1986) with an example detailing the structure of a caddisfly web. The
example showed how the web could be analyzed as a trap carefully construct-
ed to capture prey. The theme of the book was that foraging behavior could
also be looked at as “well-designed.” In it, they reviewed the basic theoretical
models and quantitative evidence that had been published since 1966. In that
year, a single issue of The American Naturalist carried back-to-back papers that
may fairly be regarded as launching “optimal foraging theory.” The first, by
Robert MacArthur and Eric Pianka, explored prey selection as a phenomenon
in its own right, while the second, by John Merritt Emlen, was focused on
the population and community consequences of such foraging decisions. This
book gives an overview of current research into foraging, including the off-
spring of both these lines of investigation.
The reader will discover that foraging research has expanded and matured
over the past twenty years. The challenges facing common eiders in Hudson
Bay symbolize how the study of foraging has progressed. Some of these
problems will be familiar to readers of Foraging Theory (which items to eat?),
but their context (diving) requires techniques that have been developed since
1986. Eiders work harder when they are hungry, so their foraging is state-
dependent. The digestive demand created by bulky prey and the periodicity
in prey availability mean that their foraging decisions are time-dependent
(dynamic). Predators are an ever-present menace, and eiders may employ
variance-sensitive tactics to help meet demand. Furthermore, the intense for-
aging of a hundred eiders throughout an Arctic winter in a small polynya
must have a strong influence on the benthic community as these prey organ-
isms employ their own strategies to avoid becoming food for eiders.

All these topics have been developed greatly since 1986. This book argues
that foraging has grown into a basic topic in biology, worthy of investigation
in its own right. Emphatically, it is not a work of advocacy for a particular
approach or set of models. The enormous diversity of interesting foraging
Foraging: An Overview 3
problems across all levels of biological organization demands many different
approaches, and our aim here is to articulate a pluralistic view. However, for-
aging research was originally motivated by and organized around optimality
models and the ideas of behavioral ecology, and for that reason, we take
Stephens and Krebs’s 1986 book as our starting point. We aim to show that
the field has diversified enormously, expanding its purview to look at topics
ranging from lipids to landscapes.
A colleague recently asked when we would finally be able to stop testing
the patch model. Our answer was that there is no longer a single patch model,
any more than there is a single model of enzyme kinetics. The patchmodel and
the way it expresses the concept of diminishing returns is so useful that it plays
a role in working through the logic of countless foraging contexts. Hence, it
often helps in developing hypotheses—which is what we are really interested
in testing. In exactly analogous ways, working scientists everywhere use the
conceptual structure of their discipline to develop and test hypotheses. If their
discipline is healthy, it expands the concepts and methods it uses, just as we
feel has been happening in foraging research.
We have aimed the text at a hypothetical graduate student at the outset of
her career, someone reading widely to choose and develop a research topic.
This book is best used in an introductory graduate seminar or advanced under-
graduate reading course, but should be useful to any biologist aiming to increase
his familiarity with topics in which foraging research now plays a role. We
begin with a chapter-by-chapter comparison with Stephens and Krebs (1986)
to give a brief overview of how the field of foraging research has developed
over the past two decades, identify the main advances, and introduce students

to the basics.
1.3 A Brief History of Optimal Foraging Theory
Interest by ecologists in foraging grew rapidly after the mid-1960s. Scientists
in areas such as agricultural and range research already had long-standing
interests in the subject (see chap. 6 in this volume). Entomologists, wildlife
biologists, naturalists, and others had long been describing animal diets. So
what was new? What generated the excitement and interest among ecologists?
We believe that the answer to this question is symbolized by a paper
published by the economist Gordon Tullock in 1971, entitled “The coal tit as
a careful shopper.” Tullock had read the studies of Gibb (1966) on foraging by
small woodland birds on insects, and he suggested in his paper that one could
apply microeconomic principles to understand what they were doing. (We
4 Ronald C. Ydenberg, Joel S. Brown, and David W. Stephens
do not mean to suggest that Tullock originated this approach, merely that
his paper clearly expressed what many ecologists were thinking.) The idea of
using an established concept set to investigate the foraging process from first
principles animated many ecologists. This motivation fused with developing
notions about natural selection (Williams 1966) and the importance of energy
in ecological systems to give birth to “optimal foraging theory” (OFT). The
new idea of optimal foraging theory was that feeding strategies evolved by
natural selection, and it was a natural next step to use the techniques of opti-
mization models.
Although the terminology differs somewhat among authors, the elements
of a foraging model have remained the same since the publication of Stephens
and Krebs’s book. At theircore, models based on optimal foraging theory pos-
sess (1) an objective function or goal (e.g., energy maximization or starvation
minimization), (2) a set of choice variables or options under the control of the
organism, and (3) constraints on the set of choices available to the organism
(set by limitations based on genetics, physiology, neurology, morphology,
and the laws of chemistry and physics). In short, foraging models generally

take the form, “Choose the option that maximizes the objective, subject
to constraints.” A specific case may be matched with a detailed model (e.g.,
Beauchamp et al. 1992), or a model may conceptualize general principles to in-
vestigate the logic underlying foraging decisions, such as whether an encoun-
tered item should be eaten or passed over in favor of searching for a better item.
We now regard the rubric “optimal foraging theory,” used until the mid-
1980s, as unfortunate. Although optimality models were important, they
were not the only component of foraging theory, and the term emphasized
the wrong aspects of the problem. “Optimality” became a major focus and
entangled those interested in the science of foraging in debates on philosoph-
ical perspectives and even political stances, which, needless to say, did more
to obscure than to illuminate the scientific questions. A few key publications
will enable the reader to appreciate this history and the intensity of debate.
Stephens and Krebs(1986)reviewed the issues up to 1986(seePykeet al. 1977;
Kamil and Sargent 1981; and Krebs et al. 1983 for earlier reviews). Perry
and Pianka (1997) provided a more recent review, and showed that while the
titles of published papers dropped the words “optimal” and “theory” after the
mid-1980s, foraging remained an active area of research. Sensing opprobrium
from their colleagues, scientists evidently began to shy away from identifying
with optimal foraging theory. If the reader doubts that this was a real factor,
he or she should read the article by Pierce and Ollason (1987) entitled “Eight
reasons why optimal foraging theory is a complete waste of time.” In a more
classic (and subtle) vein, Gould and Lewontin (1979) criticized the general
idea of optimality in their famous paper entitled “The spandrels of San Marco
Foraging: An Overview 5
and the Panglossian paradigm: A critique of the adaptationist programme”
(later lampooned by Queller [1995] in a piece entitled “The spaniels of St.
Marx”). Many other publications have addressed these and related themes.
A persistent source of confusion has been just what “optimality” refers
to. Critics assert that it is unreasonable to view organisms as “optimal,”

using biological arguments such as the claim that natural selection is a coarse
mechanism that rarely has enough time to perfect traits, or that important
features of organisms may originate as by-products of selection for other
traits. These arguments graded into ideological stances, such as claims that use
of “optimality” promotes a worldview that justifies profound socioeconomic
inequalities. It is difficult to disentangle useful views in this literature from
overheated rhetoric, a problem exacerbated by careless terminology and glib
applications on both sides. Our view is that most of this debate misses the point
that “optimality” should not be taken to describe the organisms or systems
investigated. “Optimality” is properly viewed as an investigative technique
that makes use of an established set of mathematical procedures. Foraging
research uses this and many other experimental, observational, and modeling
techniques.
Nor does optimality reasoning require that animals perform advanced
mathematics. As an analogue, a physicist can use optimality models to analyze
the trajectories that athletes use to catch a pass or throw to a target. However,
no one supposes that any athlete is performing calculus as he runs down a
well-hit ball (see section 1.10 below).
The word “theory” was also a stumbling block for many ecologists, who
regarded it as a sterile pursuit with little relevance to the rough-and-tumble
reality of the field. Early foraging models were very simple, and their ex-
planatory power in field situations may have been oversold (see, e.g., Schluter
1981). Ydenberg (chap. 8 in this volume), for example, makes clear the
limitations of the basic central place foraging model put forward in 1979.
But, informed by solid field studies (e.g., Brooke 1981), researchers identified
the holes in the model and developed theoretical constructs to address them
(e.g., Houston 1987). Errors in the formulation of the basic model were soon
corrected (Lessells and Stephens 1983; Houston and McNamara 1985). This
historical perspective shows how misrepresentative are oft-repeated claims
such as, “Empirical studies of animal foraging developed more slowly than

theory” (Perry and Pianka 1997). As in most other branches of scientific
inquiry, theory and empirical studies proved, in practice, to be synergistic
partners. Their partnership is flourishing in foraging research, and theory and
empiricism in both laboratory and field are important parts of this volume.
If the basics of foraging models have remained unchanged since the pub-
lication of Stephens and Krebs’s book (1986), the range and sophistication of
6 Ronald C. Ydenberg, Joel S. Brown, and David W. Stephens
objective functions, choice variables, and constraint sets has expanded. Math-
ematics has spawned new tools for formulating and solving foraging models.
And advances in computing havepermittedevermore computationally inten-
sive models. The emphasis of modeling has expanded from analytic solutions
to include numerical and simulation techniques that require mind-boggling
numbers of computations. The last two decades have seen a pleasing lockstep
among empirical, modeling, mathematical, and computational advances.
New concepts have also emerged. Some of thebiggest conceptual advances
in foraging theory have come from the realization that foragers must balance
food and safety (see chaps. 9, 12, and 13 in this volume), an idea that ecologists
had just begun to consider when Stephens and Krebs published their book in
1986. Box 1.1 outlines the history of this important idea.
BOX 1.1 Prehistory: Before Foraging Met Danger
Peter A. Bednekoff
The theory of foraging under predation danger took time to formulate.
Broadly speaking, students of foraging hardly ever addressed the effects of
predation during the 1970s, but they gave increasing attention to predation
in the 1980s, and predation enjoyed unflagging interest through the 1990s.
From the start, behavioral ecologists took the danger of predation seri-
ously; buttheytreated foraging anddanger separately. In thefirst edition of
Behavioral Ecology (Krebs and Davies 1978), the chapter on foraging (Krebs
1978) is immediately followed by one dealing with predators and prey
(Bertram 1978), with another chapter on antipredator defense strategies not

far behind(Harvey andGreenwood 1978). Thethinking seemsto have been
that these phenomena operated on different scales, such that danger might
determine where and when animals fed, but energy maximization ruled
how they fed (Charnov and Orians 1973; Charnov 1976a, 1976b). This
was a useful scientific strategy: it was important to test whether energetic
gain affected foraging decisions before testing whether energetic gain and
danger jointly affected foraging decisions. We probably can separate forag-
ing from some kinds of activities. For example, male manakins may spend
about 80% of their time at their display courts on leks (Th
´
ery 1992). Male
manakins probably need to secure food as rapidly as possible when off the
lek and to display as much as possible when on the lek. Therefore, foraging
and displaying are separate activities. Survival, however, is a full-time job.
Animals cannot afford to switch off their antipredator behavior. Because
(Box 1.1 continued)
trade-offs between danger and foraging gain can occur at all times and on
all scales, the effects of danger can enrich all types of foraging problems.
A more subtle difficulty may have delayed the integration of foraging
and danger: the two models that dominated early tests of foraging theory,
the diet and patch models, do not readily suggest ways to integrate danger
(see Lima 1988b; Gilliam 1990; Houston and McNamara 1999 for later
treatments).Several graphicalmodels dealtwith predationandother aspects
of foraging (Rosenzweig 1974; Covich 1976) and one chapter juxtaposed
diet choice and antipredator vigilance models, both important contribu-
tions made by Pulliam (1976). Although the pieces seem to have been avail-
able, integration did not happen quickly. Even the early experimental tests
treated danger as a distraction rather than a matter of life and death (Milin-
ski and Heller 1978; Sih 1980). These studies would have reached similar
conclusions if they had considered competitors rather than predators.

The first mature theory of foraging and predation concentrated on
habitat choice and did not consider the details of foraging within habitats
(Gilliam 1982). This theory assumed that animals grew toward a set size
with no time limit. It showed that animals should always choose the
habitat that offers the highest ratio of growth rate, g, to mortality rate,
M. In order to avoid potentially dividing by zero, Gilliam expressed his
solution in terms of minimizing the mortality per unit of growth, so we
call this important result the mu-over-g rule. Departures from the basic
assumptions lead to modifications of the M/g rule. This rule is a special
case of a more general minimization of
M + r −
b
v
g
,
where r is the intrinsic rate of growth for the population, b is current re-
production, and V is expected future reproduction (Gilliam 1982; Werner
and Gilliam 1984). The familiar special case applies to juveniles in a stable
population: juveniles are not yet reproducing, so b is zero, and the popu-
lation is stable, so its growth rate, r, is also zero (Gilliam 1982; Werner and
Gilliam 1984). Gilliam never published this work from his dissertation, but
Stephens and Krebs (1986) cogently summarized the special case. Although
the M/g ruleis incompletefor varioussituations(Ludwig andRowe 1990;
Houston et al.1993),it is surprisingly robust (see Werner and Anholt 1993).
Modified versions may be solutions for problems that do not superficially
8 Ronald C. Ydenberg, Joel S. Brown, and David W. Stephens
(Box 1.1 continued)
resemble the one analyzed by Gilliam (Houston et al. 1993), and Gilliam’s
M/g criterion may reappear from analysis of specific problems (e.g., Clark
and Dukas 1994; see also Lima 1998, 221–222, and chap. 9 in this volume).

In hindsight, we can see that various studies in the early 1980s pointed
to the pervasive effects of danger on foraging (e.g., Mittelbach 1981; Dill
and Fraser 1984; Kotler 1984), but these effects were not immediately in-
tegrated into the body of literature on foraging. Besides Gilliam’s studies,
Stephens and Krebs mentioned only one other study of foraging under
predation danger, which found that black-capped chickadees sacrifice their
rate of energetic gain in order to reduce the amount of time spent exposed
at a feeder (Lima 1985a). This influential book seems to have just preceded
a flood of results. In the mid-1980s, students of foraging found that danger
influences many details of foraging and other decisions made by animals
(Lima and Dill 1990). The general framework has continued to be produc-
tive and currently shows no sign of slowing its expansion (see Lima 1998).
A second profoundly important concept is “state dependence,” the idea
that the tactical choices of a forager might depend on state variables, such as
hunger or fat reserves. This concept developed in ecology in the late 1970s
and 1980s and is described in sections 1.8 and 1.9 below. Stephens and Krebs
(1986) used the idea of state dependence in two chapters and anticipated the
still-growing impact of this concept.
A third important conceptual advance not considered at all in Stephens and
Krebs (1986) lies in social foraging games and the consequences of foraging as
a group. Foraging games between predator and prey represent an extension
of both game theory and foraging theory. Here the objective function of the
prey takes into account its own behavior as well as that of the predator, and
the predator’s objective function considers the consequences of its behavior
and that of its prey. We anticipate that these models will find application in a
variety of basic and applied settings.
1.4 Attack and Exploitation Models
The second chapter of Stephens and Krebs (1986) develops the foundational
models of foraging, the so-called “diet” and “patch” models. The treatment
is clear and rigorous, and the beginning student is encouraged to use their

chapter as an excellent starting point. In addition to the classic review articles