Stephens & Foraging - Behavior and Ecology - Chapter 1 ppt

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 advantageof theopportunity bydiving manytimes. Withvigorous 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 prey during a shortperiod to meet the highenergy 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 thanthere is asingle 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 bookis best used in an introductory graduate seminar or advancedunder- 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 their core, models based onoptimal 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 andKrebs (1986)reviewed theissues up to1986 (seePyke etal. 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 onboth sides. Ourview is thatmost of thisdebate misses thepoint 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 advancesin computing havepermitted evermore 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. Someof 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 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; butthey treated foragingand dangerseparately. Inthe firstedition 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 (Harveyand Greenwood 1978).Thethinking seemstohave 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 graphical modelsdealtwithpredationand other 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 rule isincompletefor various situations(Ludwigand Rowe 1990; Houston etal. 1993),it issurprisingly 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 Foraging: An Overview 9 listed above, one can find recent reviews of the published tests of these models in Sih and Christensen (2001; 134 published studies of the diet model) and Nonacs (2001; 26 studies of the patch model). The significance of these two models lies in the types of decisions analyzed. The terms “diet” and “patch” are misnomers in the sense that the decisions are more general than choices about food items or patch residence time. Stephens and Krebs (1986) termed these models the “attack” and “exploitation” models to underscore this point, but these terms have never caught on. The diet model analyzes the decision to attack or not to attack. The items attacked are types of prey items, and the forager decides whether to spend the necessary time “handling” and eating an item or to pass it over to search for something else. The model identifies the rules for attack that maximize the long-term rate of energy gain. Specifically, the model predicts that foragers should ignore low-profitability prey types when more profitable items are sufficiently common, because using the time that would be spent handling low-profitability items to search for more profitable items gives a higher rate of energy gain. The diet model introduced the principle of lost opportunity to ecologists, who have since used the concept in many other settings (e.g., “optimal escape”; Ydenberg and Dill 1986). The diet model considers energy gain, but the same rules apply in non-foraging situations of choice among items that vary in value and involvement time. The patch model asks how much time a forager should invest in exploiting a resourcethat offers diminishingreturns beforemoving on tofind and exploit the next such resource. The “patches” are localized concentrations of prey between which the predator must travel, and the rule that maximizes the overall rate of energy gain is to depart when more can be obtained by moving on. In this sense, the patch model also considers lost opportunity, but its real value was to introduce the notion of diminishing returns. If the capture rate in a patch falls as the predator exploits it—a general property of patches— then the maximum “long-term” rate of gain (i.e., over many patch visits) is that patch residence time at which the “marginal value” (i.e., the intake rate expected over the next instant) is equal to the long-term rate of gain using that patch residence rule. Because diminishing returns are ubiquitous, this so-called “marginal value theorem” (Charnov 1976b) can be used in many situations. For example, we can think of eiders as “loading” oxygen into their tissues prior to a dive. The rate at which they can do so depends on the dif- ference in partial pressure between the tissues and the atmosphere, and hence the process mustinvolve diminishing returns. How much oxygen they should load depends on the situation, and the “patch” model gives usa way to analyze the problem (Box 1.2). BOX 1.2 Diving and Foraging by the Common Eider Colin W. Clark Common eiders and other diving birds capture prey underwater during “breath-hold” diving. During pauses on the surface between dives, they “dump” the carbon dioxide that has accumulated in their tissues and “load” oxygen in preparation for the next dive. (Heat loss may also be a significant factor in some systems, but is not considered here.) Figure 1.2.1 schemat- ically portrays a complete dive cycle. This graph shows a slightly offbeat version of the marginal value theorem. Figure 1.2.1. The relationship between dive time (composed of round-trip travel time to the bottom plus feeding time on the bottom) and the total amount of time required for a dive plus subsequent full recovery (pause time). The relationship accelerates because increasingly lengthy pauses are required to recover after longer dives. Small prey are consumed at rate c during the feeding portion of the dive. The problem is to adjust feeding time (t d − t t ) to maximize the rate of intake over the dive as a whole. The tangent construction in the figure shows the solution. The reader can check the central prediction of this model by redrawing the graph to portray dives in deeper water (i.e., make travel time longer). The repositioned tangent will show that dives should increase in length if energy intake is to be maximized. A dive consists of round-trip travel time to the bottom (t t ) and time on the bottom spent finding and consuming small mussels (feeding time). Travel time is a constraint, and it is longer in deeper water or, as in the eider example in the prologue, faster currents. Dive time (t d ) consists of travel time plus feeding time. Dive-cycle time consists of dive time plus the pause time on the surface between dives (t s ). How should an eider organize its dives to maximize the feeding rate? [...]... and they may perform poorly in other contexts Students of foraging (e.g., Stephens and Anderson 20 01) offer a view of rationality that is based on evolution and plausible natural decision problems faced by foraging animals (see section 1. 5 above) Economists, psychologists, and cognitive scientists (Gigerenzer and Selten 20 01; Simon 19 56; Tversky and Kahneman 19 20 Ronald C Ydenberg, Joel S Brown, and. .. foraging and its relation to ecological communities An organism needs energy and materials to reproduce, grow, and stave off death In turn, these processes influence the distribution and abundance of species (chapter 11 ) Population interactions and species composition and diversity form the core of community ecology Foraging shapes the intensity, quality, and form of community interactions and consequent... physiological and morphological traits This, then, is the domain of foraging ecology Foraging ecology considers the population, community, and evolutionary consequences of animals’ feeding behaviors Feeding behaviors are central to ecological and evolutionary feedbacks between an individual and its environment As such, they can offer behavioral indicators of a species’ prospects In chapter 14 , Mike Rosenzweig... in significant changes in the elk’s feeding behaviors and ecology (Laundre et al 20 01) Chapter 14 goes beyond the utility of foraging behavior for conservation It proposes using the principles of foraging theory to understand human perspectives and goals In this light, foraging theory provides a framework for incorporating human resource acquisition activities and their ecological consequences ... authoritative compilation entitled Behavioural Ecology (Krebs and Davies 19 78) devoted an entire chapter to dynamic optimization (McCleery 19 78), as did Stephens and Krebs (19 86), but behavioral ecologists avoided or ignored dynamic optimization because of the difficulty and mathematical abstruseness of the subject This all changed quite suddenly in the mid -1 9 80s with the development of what are now called... Ydenberg, Joel S Brown, and David W Stephens 1. 9 Variance-Sensitive Foraging In nature, random variation in prey size, handling time, the time between successive encounters with prey, and other components of the foraging process combine to create variance around the expected return of a particular foraging strategy Stephens and Krebs treated this concept in their chapter 7 Naively, one might think that... food and safety) in a common currency When Foraging Theory was published in 19 86, the “differing currencies” problem seemed formidable indeed 15 16 Ronald C Ydenberg, Joel S Brown, and David W Stephens The most satisfactory solution to the trade-off problem came from rethinking the structure of optimization problems In fact, Stephens and Krebs hinted at this solution in a section entitled “Trade-offs and. .. limitations and shortfalls of the basic models have been recognized and left behind, and students of foraging have developed new ideas and techniques to conquer problems that seemed very thorny in 19 86 The field has matured and expanded beyond the set of topics Stephens and Krebs considered in 19 86 To paraphrase Mark Twain, reports of the death of foraging theory have been greatly exaggerated! In the remainder... strikes and kills a kangaroo rat—a common event in desert landscapes (see chaps 12 and 13 in this volume)—much of the action of classic foraging models ends, but in fact the snake’s job has just begun The kill begins an elaborate and time-consuming process of consumption and processing The snake, as many will know, must manage to swallow its prey whole and uses 25 26 Ronald C Ydenberg, Joel S Brown, and. .. None of these “post-kill” phenomena are well integrated with conventional foraging theory, yet they are surely important to any complete understanding of foraging Part 2 of this book (chapters 5, 6, and 7) deals with three themes that begin where conventional foraging models end In chapter 5, Chris Whelan and Ken Schmidt review issues of food acquisition, processing, and digestion The chapter explains . in ecology in the late 19 70s and 19 80s and is described in sections 1. 8 and 1. 9 below. Stephens and Krebs (19 86) used the idea of state dependence in two chapters and anticipated the still-growing. history and the intensity of debate. Stephens andKrebs (19 86)reviewed theissues up to1986 (seePyke etal. 19 77; Kamil and Sargent 19 81; and Krebs et al. 19 83 for earlier reviews). Perry and Pianka (19 97). Lima 19 88b; Gilliam 19 90; Houston and McNamara 19 99 for later treatments).Several graphical modelsdealtwithpredationand other aspects of foraging (Rosenzweig 19 74; Covich 19 76) and one chapter