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Optimal Foraging: Some Theoretical Explorations OPTIMAL FORAGING: SOME THEORETICAL EXPLORATIONS by Eric L. Charnov † Center for Quantitative Science University of Washington, Seattle, WA 98195 and Institute of Animal Resource Ecology University of British Columbia Vancouver 8, Canada and Gordon H. Orians Department of Zoology University of Washington, Seattle, WA 98195 1973 † Present Address: Department of Biology, University of Utah, Salt Lake City, UT INTRODUCTION This book had its genesis in a rather disorganized and poorly conceived lecture on optimal foraging theory that one of us (GHO) gave to an advanced ecology class during the winter of 1971. The deficiencies in that treatment, combined with the obvious potential of an improved conceptual- ization and analysis of the problem, led to the formation of a small seminar on optimal foraging theory attended by Charles Fowler, Nolan Pearson and ourselves. This seminar, which extended over two academic quarters, produced the basic fine-grained foraging models and some hints about wider applications of the results. We both found ourselves independently stimulated to explore the implications of the ideas we had conceived for a wide range of ecological problems and these pre- liminary explorations, carried out while we were physically widely separated, were sufficiently rewarding that we decided to collaborate to produce the present work. We have individually brought to this effort very different skills and experiences and much of what there is of value in this book is the result of the mutual interplay of these contrasting abilities. One of us (ELC) has been primarily responsible for the mathematical formulations appearing in the following chapters, while the other (GHO) has provided a larger share of biological insights. Nevertheless we are quite unable to trace the genesis of most of our original ideas and we are both keenly aware that neither of us alone could have produced anything remotely resembling the present work. TABLE OF CONTENTS PART 1 INTRODUCTION AND OBJECTIVES ............................ 1 Chapter 1 Natural Selection and Foraging Processes . 1 Chapter 2 Optimality Models for Foraging .................................... 5 2.1 General Considerations ........................................... 5 2.2 A Foraging Hierarchy ............................................ 7 2.3 Fitness as a Life History Concept ................................... 9 2.4 Some Thoughts on Hypothesis Testing . 13 Chapter 3 Characteristics of Predators and their Prey . 15 3.1 Filter (Suspension) Feeders ....................................... 17 3.2 Detritivores (Deposit Feeders) .................................... 18 3.3 Parasitoids and Parasites ......................................... 19 3.4 Typical Predators ............................................... 20 3.5 Herbivores ................................................... 20 3.6 Mutualistic Foragers ............................................ 21 PART II SOME SPECIFIC OPTIMALITY MODELS . 23 Chapter 4 Fine-grained Foraging Models for a Typical Predator . 24 4.1 Handling Time of a Prey Item .................................... 25 4.2 Food Value of a Prey Item........................................ 28 4.3 A Fine-grained Foraging Model ................................... 29 4.3.1 A Fundamental Theorem of Optimal Foraging (FT) (31); 4.3.2 A Second Theorem (35) 4.4 A Special Case for a Single Prey Type . 38 4.5 Tests of Some Hypotheses on the Fine-grained Use of Prey . 39 4.5.1 Ivlev’s Laboratory Experiments with Fish (39); 4.5.2 Holling’s Laboratory Experiments with the Mantid, Hierodula crassa (41); 4.5.3 The Spider Philodromus rufus with a Single Prey Type (48) Chapter 5 Use of a Patchy Habitat by a Typical Predator . 50 5.1 A General Model............................................... 50 5.1.1 The Fundamental Theorem Applied to Patches (54); 5.1.2 A Useful Algebraic Identity (56) 5.2 Tests of Patch Use .............................................. 57 5.2.1 Foraging by Blackbirds (57); 5.2.2 Patch Use by Rainbow Trout (59); 5.2.3 The Concept of “Giving-Up Time” (59); 5.2.4 Gibb’s Data (61) 5.3 Central Place Foraging .......................................... 62 Chapter 6 The Theoretical Literature in Optimal Foraging . 68 6.1 Emlen, J.M. 1966. The role of time and energy in food preference. American Naturalist 100:611-617 ......................................... 68 6.2 Emlen, J.M. 1973. Ecology: An Evolutionary Approach, Addison-Wesley . 70 6.3 MacArthur, R.H. and E.R. Pianka. 1966. On optimal use of a patchy environment. American Naturalist 100:603-9......................... 71 6.4 MacArthur, R.H. 1972. Geographical Ecology, Harper and Row . 73 6.5 Werner, E.E. 1972. On the Breadth of Diet in Fishes M.S.................. 74 6.6 Schoener, T.W. 1969. Models of optimal size for solitary predators. American Naturalist 103:277-313 ......................................... 75 Schoener, T.W. 1971. Theory of feeding strategies. Annual Review of Ecology and Systematics II:369-404........................................... 75 6.7 Rapport, D.J. 1971. An optimization model of food selection. American Naturalist 105:575-87 .......................................... 78 Chapter 7 Stochastic Models for a “Typical Predator” . 80 Chapter 8 Herbivores ................................................... 87 8.1 Foraging Patterns Among Small Herbivores . 89 8.1.1 Predictions for Small Herbivores (92); 8.1.2 Foraging of Small Herbivores (94) 8.2 Foraging Patterns Among Large Herbivores . 95 8.2.1 Predictions for Large Herbivores (98); 8.2.2 Foraging of Large Herbivores (100) Chapter 9 Mutualistic Foraging ........................................... 101 9.1 Exploitation of Nectar and Pollen ................................. 102 9.2 Production of Nectar and Pollen .................................. 107 9.3 Exploitation of Fruits .......................................... 113 9.4 Production of Fruits ........................................... 114 PART III THE EVOLUTION OF OPTIMAL FORAGING . 117 Chapter 10 Evolution of the Characteristics of Predators . 118 10.1 Evolution of Habitat Selection ................................... 118 10.2 Evolution of Searching Mode .................................... 119 10.3 Changes in Predator Behavior with Changes in Prey Density . 124 10.4 Predator Behavior in a Featured Environment . 128 10.5 Response of Predators to Changing Rates of Prey Recruitment . 130 10.6 Evolution of Information Gathering Ability . 132 Chapter 11 Evolution of the Characteristics of Prey . 136 11.1 Factors Affecting the Fitness Prey . 136 11.2 Evolution of Toxic Prey......................................... 138 11.3 Evolution of Müllerian Mimicry Systems . 140 11.4 Aspect Diversity of Prey ........................................ 142 Chapter 12 Some Concluding Remarks...................................... 144 LITERATURE CITED ...................................................... 147 APPENDIX A Glossary of Terms ........................................... 155 PART 1. INTRODUCTION AND OBJECTIVES Chapter 1. Natural Selection and Foraging Processes Ideas about predation have played a significant role in biological thought. No such thing as a “predation theory” exists but several theories have been developed around questions asked about predators and their activities. They have a key role in concepts of population regulation (Holling 1965, Huffaker 1971), although some have challenged the basic ideas (Errington 1946, 1963). Productivity studies have made use of the notions of predation or trophic efficiencies, and some ecologists have believed that productivity is a major factor to be explained by ecological theory (Warren 1971, Ivlev 1961). Ecological genetics, indeed the development of the concept of natural selection itself, relies heavily on field work related to predation. Frequency dependent selection and mimicry are two outstanding examples (Ford 1964). Theories of learning are based on assumptions and data about the behavior of predators (Krebs 1973), and there is a large literature on the regula- tion of food intake and the feedback processes involved (Handbook of Physiology 1967). This list is very incomplete and is intended only to point out that predators have been consider- ed in many ways, with the questions of interest determining the appropriate type of theory. In this book we explore one type of question about predation, the matter of “prudence” on the part of individual predators, and then examine some of its consequences. This perspective is not new (Elton 1927), but statements in the older literature are often anecdotal and usually lack the conciseness necessary to qualify as testable hypotheses. An example is Elton’s view that any predator is restricted to a certain size range of prey because the big prey are difficult to capture, while the small ones are not worth the effort. Foraging behavior should be molded by natural selection because the kinds of 1 choices made by a predator will influence (a) survival during periods of food shortage, if and when they occur, (b) the rate of accumulation of energy reserves for reproduction and, hence, the number of offspring that can be provisioned, (c) and the amount of time that must be allocated to foraging activities. This, in turn, influences the amount of time available for other activities, which also con- tribute to fitness. In addition, there may be risks associated with foraging, and selection can be expected to mold behavior in the direction of minimizing these risks, whether they are time-related or event-related. It is
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