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 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 optimization 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 their core, models based on optimal foraging theory possess (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 investigate the logic underlying foraging decisions, such as whether an encountered 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 offoraging in debates on philosophical 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 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.
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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 ofthis 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.
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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 explanatory 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 ofthe 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 publication of Stephens and Krebs's book (1986), the range and sophistication of objective functions, choice variables, and constraint sets has expanded. Mathematics has spawned new tools for formulating and solving foraging models. And advances in computing have permitted ever more computationally intensive 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 the biggest 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
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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 seriously; but they treated foraging and danger separately. In the first 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 and Greenwood 1978). The thinking seems to 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 foraging from some kinds of activities. For example, male manakins may spend about 80% of their time at their display courts on leks (Thery 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 graphical models dealt with predation and other aspects of foraging (Rosenzweig 1974; Covich 1976) and one chapter juxtaposed diet choice and antipredator vigilance models, both important contributions made by Pulliam (1976). Although the pieces seem to have been available, 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
v where r is the intrinsic rate of growth for the population, b is current reproduction, and Vis 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 population 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 rule is incomplete for various situations (Ludwig and Rowe 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
(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 andDukas 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 integrated 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 productive 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.
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The wreck had spilled some heavy fuel oil and wildlife had been affected.
The wreck was on the beach, waves were about 12 feet high and it was unlikely we would get a tow wire out to the tug offshore that day.
I had asked a DEP employee to lay out an area of about 200 by 200 feet where we would clear the beach grass and level the area with a bulldozer to use as a staging area for the tow wire. When I arrived that morning, I discovered that the cleared area was 200 by 200 yards, and now I worried that we would be charged for the restoration of an area almost 10 times as large as planned.
I decided to drive back to the hotel where I could update reports and refine some calculations.
On the way back I passed the wildlife rehabilitation center that had been installed at an abandoned salmon hatchery. There was no hurry with the report and decided that maybe there was something to learn about wildlife rehabilitation. Next to the salmon hatchery there was a very impressive semi sized trailer that indicated it was the State Mobile Wildlife Rehabilitation Facility. I got out of my truck, and at that moment somebody came out a door at the salmon hatchery. The women looked at me sternly and asked: “What are you doing here?” I explained that I was one of the salvage people and was curious about the birds. Without hesitation she told me I had to leave because I was disturbing the birds.
I got back in my truck and started to back out of my parking spot. I just started rolling and another woman came out of the trailer. She was standing right next to my open window and she asked if she could help me. I explained that I was a salvor and curious about how the birds were being taken care of, but that I was just told to leave by another person.
She smiled and said: “Volunteers, they are all the same.”
So I asked: “And you are?”
She smiled: “I am the State ornithologist and in charge of this operation, and I think it is great you show interest in our work.”
“I heard there are birds that are covered with oil. How bad is it?”
“That depends on how you look at it. We have found about 100 birds covered with oil, about half were dead and we tried to nurse the others back to health. Of those we have released about 10, about 10 died, and we are hoping for the best for the others.”
“How do you clean the birds and nurse them back?”
“Let me show you,” and I got a tour of the operation. We talked about how the birds were found and the ornithologist explained that while there is an official death count, it is far from clear that the oil caused every bird’s death. Many of the birds were migrating and migration drop outs are very common. In normal conditions those birds would stop flying and would eventually die. But with the oil spill they would become oil covered, be found by volunteers before they died and it would be immediately assumed that their condition was caused by the oil instead of migratory stress. As such, the official count may very well overestimate the number of birds killed by oil. As a matter of fact, some of the birds that would have died during the migration may now get nursed back to health.
But I had heard about these snowy plovers. “Is it really true, the oil spill is exactly in the only remaining nesting area for this exceedingly rare birds?”
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“Yes”, she said, ”It is true. There were only about 10 nesting pairs. We had to catch them, and they are now kept right here in a large cage. Would you like to see them?”
“Well yes. One of the rarest birds in the US? Yes, I would!”
She took to me to a large cage and said: “Now I want you to be quiet, the birds will be sitting on the sand and shell, and they have almost perfect camouflage. So we will quietly get close to the cage and I will point, and then you will just have to look and when you look closely you will see it.”
So we snuck up and she pointed, and after a while I did see this little bird, almost perfectly camouflaged in the sand and shell. I nodded and we walked back. “So why has this bird become so endangered?”
“It is the invasive beach grass that we planted to keep the dunes in place. These birds used to nest on shell and sand and were perfectly camouflaged and were protected against rodents and other egg hunters, because raptors would hunt the rodents. But the beach grass provided cover for rodents against predators, and with increasing rodent populations, the plover nests, which now were surrounded by beach grass, were being raided by the rodents and this resulted in a plover population collapse.”
“So this beach grass is bad for the plovers?”
“Yes”, she said, “actually we are spending a fortune to control it.”
When we got back to my truck, the volunteer came out of the door again and with a beaming smile announced that three birds were ready for release. A few minutes later we released three seagulls and everybody cheered and clapped.
When I got back to the hotel, I found the DEP employee at the bar with the rest of the salvage crowd. I got a beer and ordered one for him too. He thanked me and we took a sip.
I said: “The beach area you cleared is bigger than I thought it would be. Is that going to cost more to restore?”
He waited a second to answer: “Well, we will have to see.”
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“I suppose you are going to have to decide whether you can get away with charging us for not replacing that damn beach grass ……. and then take it out again to protect the plovers?”
He took another sip of his beer and smiled a little and said, “Well, can you blame me for trying?”
Then he looked at me and said: “Ok, so you got me, but now I am wondering. If we pay for the fuel, can we use your bulldozer when you are not using it to clear more of that beach grass?”
“Hell, I can’t think of an idea that would delight me more, and there is no doubt my client would be delighted to pay for the fuel too.”
Cooperation is a beautiful thing. All you need to do is find common ground, and generally you find that by random exploration on the other side of the game.
Pigeons Game Theory Games
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