Putting predators back into behavioral predator prey interactions

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1 70 Opinion 1 Huey, R.B. et al. (1999) Testing the adaptive significance of acclimation: a strong inference approach. Am. Zool. 39, Prosser, C.L. (1991) Environmental and Metabolic Animal Physiology: Comparative Animal Physiology, 4th edn, Wiley Liss 14 Gibert, P. et al. (001) Locomotor performance of Drosophila melanogaster: interactions among developmental and adult temperatures, age, and geography. Evolution 55, Usher, M.L. et al. (1994) Muscle development in Atlantic salmon (Salmo salar) embryos and the effect of temperature on muscle cellularity. J. Fish Biol. 44, Vieira, V.L.A. and Johnston, I.A. (199) Influence of temperature on muscle-fibre development in larvae of the herring Clupea harengus. Mar. Biol. 11, Johnston, I.A. et al. (1998) Embryonic temperature modulates muscle growth characteristics in larval and juvenile herring. J. Exp. Biol. 01, Hoffmann, A.A. and Hewa-Kapuge, S. (000) Acclimation for heat resistance in Trichogramma nr. brassicae: can it occur without costs? 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(1998) Ecological constraints on amphibian metamorphosis: interactions of temperature and larval density with responses to changing food level. Oecologia 115, Thomson, L.J. et al. (001) Field and laboratory evidence for acclimation without costs in an egg parasitoid. Funct. Ecol. 15, Gibbs, A.G. et al. (1998) Effects of cuticular lipids and water balance in a desert Drosophila: is thermal acclimation beneficial? J. Exp. Biol. 01, Woods, H.A. and Harrison, J.F. (001) The beneficial acclimation hypothesis versus acclimation of specific traits: physiological changes in water-stressed Manduca sexta caterpillars. Physiol. Zool. 74, Zwaan, B. et al. (1995) Artificial selection for developmental time in Drosophila melanogaster in relation to the evolution of aging: direct and correlated responses. Evolution 49, Putting predators back into behavioral predator prey interactions Steven L. Lima In the study of behavioral predator prey interactions, predators have been treated as abstract sources of risk to which prey respond, rather than participants in a larger behavioral interaction. When predators are put back into the picture by allowing them to respond strategically to prey behavior, expectations about prey behavior can change. Something as simple as allowing predators to move in response to prey movements might not only (radically) alter standard expectations of prey behavior, but might also reveal new classes of behavioral phenomena that occur at large spatial scales. Similar revelations undoubtedly await many well-studied aspects of the behavioral interaction between predator and prey. Most examples studied to date, both theoretical and empirical, require attention from this predatory perspective. Putting predators back into the picture will be challenging, but doing so might change the way in which biologists think about predator prey interactions in general. Steven L. Lima Dept of Life Sciences, Indiana State University, Terre Haute, IN 47809, USA. S-Lima@indstate.edu Over the past 0 years, the study of behavioral interactions between predator and prey has shed much light on prey behavior, and it is now clear that almost any aspect of prey decision-making (from foraging behavior to mate choice) can be influenced by the risk of predation [1 3]. A growing literature also suggests that nonlethal interactions between predator and prey (those driven by prey avoidance of predation) might be an important component of predator prey interactions in general [4 8]. Work on behavioral predator prey interactions therefore provides an important bridge between the studies of behavior and ecology. In spite of these many advances, our understanding of behavioral predator prey interactions is limited by a simple oversight: we virtually forgot about the behavior of predators! Historically, we have been so focused on prey behavior that we (myself included) became comfortable with treating predators as unresponsive black boxes rather than participants in a behavioral interaction. This oversight has not only led to an incomplete view of behavioral interactions between predators and prey, but has also obscured an entire class of such interactions that occurs at large spatial scales. My goal is to explore some of the insights gained from putting predators back into behavioral predator prey interactions. How were predators removed from the interaction? The removal of predators from the behavioral predator prey interaction is apparent in the ubiquitous fixed-risk assumptions of constant attack rates over time and patch-specific risks of predation (e.g. Ref. [9]); such assumptions imply that predators are not influenced by prey behavior. As few would argue for the strict validity of this assumption, why were predators relegated to the status of unresponsive entities? In many ways, the fixed-risk approach (i.e. the assumption of unresponsive predators) was a sensible starting point. Characterizing predation risk as an environmental constant seemed reasonable given that predators can strike opportunistically and could be anywhere at a given time. Mathematical convenience might have also played a role: models of antipredator decisionmaking are much simpler under an assumption of fixed risk than they are when both predator and prey are allowed to respond to one another. Furthermore, /0/$ see front matter 00 Elsevier Science Ltd. All rights reserved. PII: S (01)0393-X

2 Opinion 71 and perhaps most importantly, prey animals are usually much more amenable to observation and experimentation than are predators, and this has naturally led to more emphasis on the prey. Regardless of the reason, this fixed-risk approach has been a conceptual mainstay from the start [10,11]. In retrospect, predators need not have been excluded from the study of behavioral predator prey interactions for so long. For instance, early papers by Iwasa [1] and Sih [13] challenged (in essence) the fixed-risk paradigm, but this challenge was not appreciated as such at the time. A handful of models on predator prey coevolution [14] also allowed predators to respond to prey (albeit on a different time scale). Furthermore, students of foraging behavior have long known that predators are behaviorally sophisticated [15], yet predators were rendered behaviorally inert in the study of antipredator decision-making, in spite of the fact that many of the first students of antipredator decision-making also studied foraging behavior per se (myself, for instance). In moving away from the assumption of behaviorally inert prey in standard foraging models, we simply transferred, for the sake of tractability, the inertness assumption to predators. Conceptual issues in the return of predators Here, I consider some conceptual issues in bringing predators back into predator prey interactions. Most of these issues center on the surprising consequences of simply allowing predators to move about in search of prey. Predators on the move One of the most important realizations is that predators can move about in search of (patchy) prey and that prey can move to locate resources or to avoid predators. Foraging theory provides a rich body of work on how predators should choose among patches of immobile (and unresponsive) prey [15,16]. All else being equal, a predator should feed preferentially in patches with the highest density of prey. If predators compete for prey, then they might reach an ideal free distribution (IFD) determined, in part, by the distribution of prey items across patches or habitats [17]. A large body of theory also addresses patch choice by mobile prey feeding under a fixed risk of predation imposed by effectively immobile predators [16]. All else being equal, prey should prefer the patch with the lowest risk. Competitive patch choice among prey leads to behavior that is considerably more complex than that described by standard IFD theory, and might involve more than one stable distribution of prey in a given setting [18]. What happens when predator and prey can move simultaneously? We can expect that predators will go where prey are more dense, and that prey will simultaneously avoid areas where there are more predators. Both predator and prey have options that can potentially thwart the other, but the consequences of these options are not intuitively obvious. Mathematical game theory provides a natural framework within which to analyse these issues that surround putting predators back into predator prey interactions. Predator prey games of patch or habitat choice actually date back to Iwasa s [1] model of diel vertical migration by zooplankton and predatory fish. These game models typically assume a threetrophic-level system in which a predator species feeds on a prey species, which in turn feeds on its (nonresponsive) resource [19,0]. Predator and prey are free to move to any patch in the system. These models have a similar message: intuitive expectations are sometimes altered radically in a game of predator prey patch choice (Box 1). Under some circumstances, predators might appear to ignore prey and distribute themselves according to the distribution of the resource of the prey. Prey might appear to ignore their resource and base their distribution mainly on the risk imposed by predators [19 1]. Note that these results do not imply that prey decision-making is unresponsive to the risk of predation under some circumstances. Prey responses to risk are, in fact, an integral part of the equations determining evolutionarily stable behavior. Bouskila et al. [] add to the above theme of unintuitive expectations in their model of ontogenetic habitat shifts in developing larvae. These (generic) larval prey must decide at what time or size to shift from their natal habitat to a more dangerous but more energetically favorable habitat. Standard theory (fixed risk and unresponsive predators) suggests that the timing of the shift will be determined by a tradeoff between growth and mortality [4]. However, when predators can move between both habitats, prey might often maximize fitness simply by choosing the habitat that yields the highest growth rate. In essence, predator movement might negate the antipredator benefit of delaying the habitat switch. Conceptually, the most important message in this game theoretical work is the idea that risk is not a fixed property of a particular location when predators can move among patches. Our typical experimental and conceptual paradigm of fixed-risks and unresponsive predators allows us to see only the prey half of the overall interaction. One could question some of the assumptions in these simple game models, and it seems probable that more realistic assumptions (prey that interact socially in thwarting predators, state-dependent behavior, etc.) would change some of these topsy-turvy expectations. Nevertheless, the results are certainly cause for thought. Predators on the move over large areas Predators usually move over areas that are much larger than those typically considered in studies of behavioral predator prey interactions (which are generally on the scale at which individual predator

3 7 Opinion Box 1. The strange world of multitrophic-level games of habitat choice What happens when both predator and prey can move in response to resources and to each other? A few game-theoretical models have addressed this question in varying contexts. Although simplified in many ways, these models provide the clearest available picture of the potential consequences of putting predators back into predator prey interactions. Iwasa [a] first addressed this question in a three-trophic-level system composed of fish, their zooplanktonic prey, and (spatially fixed) phytoplankton. The fish and zooplankton were free to move between a surface habitat (dangerous for zooplankton but phytoplankton-rich) and a deep-water habitat (safe but phytoplankton-poor). His model suggested that zooplankton should base their distribution on the risk imposed by fish across habitat types, rather than on phytoplankton densities. However, phytoplankton densities should influence the distribution of fish, even though fish do not consume phytoplankton. This basic result was duplicated many years later in studies of adaptive predator aggregation and its effects on predator prey population dynamics [b,c]. Many of these topsy-turvy expectations were formalized in a general model by Hugie and Dill [d]. In addition to the predator prey interaction between trophic levels (once again, with a fixed resource for prey), their model included competition within predator and prey populations, as well as interference among predators. Their analysis suggested that the relative distribution of prey across two habitats (1 and ) will be as in Eqn I: N N 1 Here, N 1 and N are the densities of prey in habitats 1 and, P i is the density of predators, and c i is a coefficient of predator interference. Habitat riskiness is given by α i, which represents the joint effect of search rate and the probability of prey capture. For the predator, the relative distribution across habitat types is given by Eqn II: P ar1 mn1 = P ar mn 1 α = α ( 1+ c1p 1) ( 1+ c P ) 1 where R i is the productivity of the prey s resource in habitat i, a is the energy available to prey after subtracting foraging and processing costs, and m is the metabolic rate of the prey. These equations suggest that the relative riskiness of the two habitats will have a strong effect on the distribution of prey, and that the predators will be strongly influenced by the productivity of the prey s resource. Note that with little predator interference (c 0), and relatively low prey metabolic costs (m 0), Eqn I and II reduce to the case where prey match the inverse of habitat riskiness and predators match the productivity of prey resources: N 1 /N α /α 1 and P 1 /P R 1 /R. These counterintuitive matching expectations might also apply in a system with intraguild predation in which the predator can feed on both the prey and on the prey s [I] [II] resource [e]. However, the existence of an alternative resource for predators (unavailable to the prey in question) might result in a nearly fixed-risk situation for prey [e]. Sih [f] extended Hugie and Dill s model still further by incorporating variable degrees of intraspecific competition in both predator and prey populations. His model suggests that both prey and predator distributions might respond strongly to the productivity of the prey s resources across patches. However, the degree to which prey and predators match the resource productivity depends strongly on the degree of intraspecific competition in each trophic level. Generally speaking, weak predator competition favors the strong undermatching of resources by prey (i.e. they tend to avoid the rich patch). Strong predator competition tends to favor overmatching (i.e. stronger preference for the richer patch) by both predator and prey. Some results from earlier models emerge as special cases of Sih s model depending on the degree of intraspecific competition in the prey or predator populations. Finally, intuitive expectations fail again in Bouskila s [g] matrix-game analysis of a one prey two predator system involving snakes, owls and a desert rodent. The rodents and snakes can choose to be in a brushy microhabitat or in the open, whereas owls are found only in the open (owls do not participate directly in the game). Snakes are more effective in the brushy habitat than in the open, and are not themselves subject to predation. One might expect rodents to shift into the open habitat under conditions of no moonlight, increased food availability in the open, and increased dilution of risk in the open. However, Bouskila s analysis suggests that the distribution of rodents will nevertheless be (apparently) insensitive to such factors in the game scenario. However, these same factors cause the snakes to shift into the open habitat, much as one might have expected in the rodents. Some aspects of rodent behavior in the Mojave desert corroborate these basic expectations [h]. References a Iwasa, Y. (198) Vertical migration of zooplankton: a game between predator and prey. Am. Nat. 10, b van Baalen, M. and Sabelis, M.W. (1993) Coevolution of patch selection strategies of predator and prey and the consequences for ecological stability. Am. Nat. 14, c van Baalen, M. and Sabelis, M.W. (1999) Nonequilibrium population dynamics of ideal and free prey and predators. Am. Nat. 154, d Hugie, D.M. and Dill, L.M. (1994) Fish and game: a game theoretic approach to habitat selection by predators and prey. J. Fish Biol. 45, e Heithaus, M.R. (001) Habitat selection by predators and prey in communities with asymmetrical intraguild predation. Oikos 9, f Sih, A. (1998) Game theory and predator prey response races. In Advances in Game Theory and the Study of Animal Behavior (Dugatkin, L.A. and Reeve, H.K., eds), pp. 1 38, Oxford University Press g Bouskila, A. (001) A habitat selection game of interactions between rodents and their predators. Ann. Zool. Fennici 38, h Bouskila, A. (1995) Interactions between predation risk and competition: a field study of kangaroo rats and snakes. Ecology 76, and prey encounter one another). This simple realization raises an interesting question: is prey decision-making influenced by predator movement over the larger ecological landscape? I suspect that there are many behavioral phenomena that emerge as a result of large-scale predator movement (Box ). The common thread in such phenomena is that predator movement acts to link the behavior of prey across the home range of a predator; this linked behavior might, in turn, affect the behavior of the

4 Opinion 73 Box. Some possible large-scale behavioral predator prey interactions Large-scale behavioral interactions are driven fundamentally by the movement of predators across relatively large areas, and can manifest themselves in several ways. Here are three examples of large-scale phenomena that have received scattered attention. Predator prey shell games Predator prey shell games occur when predators search for elusive prey, and prey stay on the move to remain elusive. The possibility of such shell games is generally unrecognized, although the basic idea has been mentioned sporadically [a,b]. This view of prey movement is in marked contrast to the present consensus that movement and activity in general is dangerous for prey [c,d]. Note that predator prey shell games emerge only at a relatively large spatial scale at which prey and predator have many options for feeding sites. Furthermore, shell game movements are evolutionarily stable only when predators have a good spatial memory, and when prey have a reasonable chance of escaping attack; otherwise, movement might actually enhance the risk of predation for prey [e]. Predator prey shell games imply that the risk of predation experienced by prey at a given feeding location is directly related to the degree to which they are predictably at that location. Hence the exclusive patch preferences (i.e. spatially predictable foraging behavior) predicted by many models are unlikely under the shell game scenario; prey might bias their visitation towards the best feeding patches, but still spend a good deal of time foraging in lesser patches. Such partial preferences for patches are presently viewed mainly as the result of state-dependent foraging decisions [f]. The predator pass-along effect The predator pass-along effect is driven by predator movement that is induced by unsuccessful attacks following an unsuccessful attack, a predator s best option should often be to move on in search of other prey rather than pursue further attacks. Thus, an animal that successfully evades an attack simply passes the predator along to other prey individuals. The net result of this predator pass-along is an enhanced level of antipredator behavior in the prey population [g]. This effect implies that mortality per se might be a poor predictor of risk perceived. More fundamentally, the pass-along effect suggests that seemingly isolated prey (or groups of prey) interact indirectly via the (prey-induced) movement of the predator. This effect also suggests that the numerical dilution of risk experienced by a socially feeding animal depends not only on the size of its group, but also on the behavior of other groups in the area. Predator management of prey behavior Predators might manage the antipredator behavior of the prey in their home range in a way that leaves prey easier to capture. In essence, a predator might spread the risk over its many hunting sites to manage its prey s behavior (and the resulting pass-along effect) and its long-term energy intake rate. This idea of risk management (in one form or another) goes all the way back to Charnov et al. [h], and has been alluded to in various modeling contexts [g,i], but it has yet to be explored either theoretically or empirically. Prey management by a predator could be a kind of prudent predation if a predator has no competitors within its home range [h]. More generally, avoiding frequent attacks at a given location might simply be the best strategy for a predator. In any case, prey management requires stable prey and predator home ranges and the spatial and temporal cognitive abilities necessary to remember what has transpired at a particular site. Prey management might also modify the shell game by allowing prey to feed more predictably in their better feeding patches. References a Sonerud, G.A. (1985) Brood movements in grouse and waders as defence against win stay search in their predators. Oikos 44, b Greenberg, R. (000) Birds of many feathers: the formation and structure of mixed-species flocks of forest birds. In On the Move: How and Why Animals Travel in Groups (Boinski, S. and Garber, P.A., eds), pp , University of Chicago Press c Banks, P.B. et al. (000) Non-linearity in the predation risk of prey mobility. Proc. R. Soc. London B Biol. Sci. 67, d Boinski, S. et al. (000) A critical evaluation of the influence of predators on primates: effects on group travel. In On the Move: How and Why Animals Travel in Groups (Boinski, S. and Garber, P.A., eds), pp. 43 7, University of Chicago Press e Mitchell, W.A. and Lima, S.L. Predator prey shell games: large-scale movement and its implications for decision-making by prey. Oikos (in press) f Houston, A.I. and McNamara, J.M. (1999) Models of Adaptive Behavior, Cambridge University Press g Lima, S.L. (1990) Evolutionarily stable antipredator behavior among isolated foragers: on the consequences of successful escape. J. Theor. Biol. 143, h Charnov, E.L. et al. (1976) The ecological implications of resource depression. Am. Nat. 110, i Brown, J.S. et al. (1999) The ecology of fear: optimal foraging, game theory, and trophic interactions. J. Mammal. 80, predators. Some of these phenomena might change the way in which behavioral ecologists think about predator prey interactions at all spatial scales. Predators do more than move One can imagine predator prey games played out in a variety of behavioral contexts: predators can certainly do more than move in response to the behavior of their prey. Nevertheless, very few of these possibilities have been investigated theoretically, and the available models deal mainly with prey activity. The temporal activity of prey should respond to temporal changes in predation risk [3,4]. However, just as patch-specific predation risk reflects a behavioral interaction between predator and prey (Box 1), so too should predation risk over time. Brown et al. [5] make this point nicely in a model of the temporal activity of predator and prey, in which a top predator feeds on a prey species that consumes a depleting resource. Both predator and prey are allowed to be active at any time in response to the activity of the other. The results represent a kind of temporal analog of the results in Box 1: predator activity tends to mirror the level of the resource of the prey, whilst the proportion of active prey remains constant over time. Models that assume constant or

5 74 Opinion fixed predator behavior [3,4] cannot capture these effects. The issue of when to resume activity following an encounter with a predator has been partially analysed by Johansson and Englund [6], who suggest that evolutionary stability might not be a general feature of such interactions (see also Ref. [7]). In addition, predator prey games of activity figure prominently in some recent models that translate behavioral decisions to population-level phenomena [8,5,8]. Empirical studies where do we stand? We stand on shaky ground. As mentioned before, much is known about the behavior of predators feeding on unresponsive prey, and that of prey feeding under a fixed risk of predation. However, empirically, almost nothing is known about the kinds of predator prey interactions outlined above. Surprisingly, even the straightforward and provocative game theoretical analyses of patch choice (Box 1) remain untested (but see Refs [13,1,9]). As for large-scale interactions (Box ), no empirical information exists beyond a few suggestive anecdotes [30,31]. More generally, how much is known about the way in which predator and prey react to each other s behavioral options? These mutual responses form the basis of the game theoretical models. Here again, we come up largely empty-handed. For example, in the study of pursuit-deterrence signaling by prey to predator [3], the crux of the interaction is that predators are indeed deterred from attacking by honest signals of the ability to escape. We nevertheless know surprisingly little about the effects that such signaling has on predators [33]. Similarly, an understanding of the tactics of predator attack (and how they relate to prey behavior) could greatly alter our interpretation of vigilance behavior [34,35]. In spite of decades of research on vigilance [36], only two studies provide any such information [37,38]. Finally, consider the small bird in winter research paradigm, in which small birds must survive the rigors of winter and the onslaught of the hawks: in light of the conceptual prominence of this paradigm in the study of antipredator decision-making [3], the predatory behavior of Accipiter hawks is virtually unstudied [39]. This empirical focus on prey behavior has had other unintended effects. First, our lack of attention to predators leaves us with little information on the effectiveness of antipredator decision-making in reducing predation. Thus, it is troubling that a recent well-worked example suggests that refuging behavior in a stream-dwelling salamander species is an ineffective defense against their main predator [40]. Nevertheless, I suspect that such decision-making is generally effective at lowering the risk of predation, but more confirmation of this suspicion [39,41,4] is certainly desirable. Second, our lack of attention to predators has left us with little understanding of antipredator behavior in a multipredator environment. Because predators were usually treated as unresponsive abstractions, they were effectively lumped together as a single abstract entity. Hence, we have lost sight of the fact that most environments harbor many different types of predators. The behavioral ramifications of a multipredator environment are thus largely unexplored [43 45]. Where do we go from here? Almost all aspects of putting predators back into behavioral predator prey interactions need attention. Theoretically, even the most well-studied aspects of such interactions have only rarely been explored as games between predator and prey. Particularly fruitful might be explorations of predator prey games in the context of classic optimal foraging theory. For example, some failures of standard optimal diet theory [46] might be explicable in terms of a predator prey game. We also need to think big and explore large-scale behavioral phenomena (Box ). Further elaboration of existing game theory should also prove rewarding. One-on-one games between individual predator and prey (e.g. how long should a predator pursue prey during an encounter) demand more attention especially as they relate to conditions favoring the existence of an evolutionary stable strategy. Further refinements of multitrophiclevel games of patch choice (Box 1) could perhaps consider the kinds of information that animals might have available to them (which might vary with the scale of the physical system in question). Such considerations not only add a degree of realism to models, but might also significantly alter current theoretical expectations [47,48] and their implications for population dynamics [8,49]. Empirically, there is even more to be done. In particular, game-theoretical models (Box 1) must be tested. In a related issue, we need much more information on the way in which predator and prey respond to the behavior of the other. Particularly useful will be techniques that are designed to reveal the response of predators to behaviors that prey would not normally use in a given situation or vice versa. Krause and Godin [38] provide a nice example of such a technique in which a large fish (behind a two-way mirror) was allowed to watch smaller fish as the latter fed completely unaware of the former; certain prey feeding postures consistently invoked attacks by the predator, revealing why these postures are rarely used in the presence of predators. This sort of information can help characterize the behavioral dynamics underlying predator prey games. Furthermore, large-scale behavioral phenomena are virtually unexplored and thus in much need of empirical attention. This large-scale work could, in part, address the question of whether prey have large-scale information about predator behavior and that of other prey in the area, or whether large-scale phenomena emerge simply as a consequence of

6 Opinion 75 Acknowledgements I thank William Mitchell, Timothy Roth, Todd Steury and three anonymous reviewers for helpful comments. Mart Gross provided valuable help during the early stages of this project. small-scale decision making. At any scale of study, it might often be necessary to study the natural history of a predator before the finer points of behavioral predator prey interactions can be addressed. Finally, future work will need to confront some difficult questions raised by game theory. For instance, in multitrophic-level games of patch choice (Box 1), will perceptually constrained animals approach the behavioral equilibria suggested by simple game theory? Are there simple behavioral rules-of-thumb [50] that will allow predator and prey to approach Nash equilibria even if prey know little about the behavior of predators and vice versa? What can prey really know about predator behavior in ecological time (beyond the instinctual knowledge of the prey)? Not only are these interesting behavioral questions, but the answers might ultimately also dictate the precision with which simple game theoretical models can predict behavior [48]. In conclusion, there is much to be gained from putting predators back into behavioral predator prey interactions. This task will not be an easy one, especially at larger spatial scales, but the behavioral and ecological insights gained from doing so will be well worth the effort. Can one expect a sweeping revolution in our view of these behavioral interactions? I would not go that far. I do expect, however, that a greater emphasis on the behavior of predators might change the way in which we think about predator prey interactions in general. References 1 Sih, A. (1994) Predation risk and the evolutionary ecology of reproductive behaviour. J. Fish Biol. 45, Kats, L.B. and Dill, L.M. (1998) The scent of death: chemosensory assessment of predation risk by prey animals. Ecoscience 5, Lima, S.L. 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(1978) Influence of a predator on the optimal foraging behaviour of sticklebacks (Gasterosteus aculeatus L.). Nature 75, Mangel, M. and Clark, C.W. (1988) Dynamic Modeling in Behavioral Ecology, Princeton University Press 1 Iwasa, Y. (198) Vertical migration of zooplankton: a game between predator and prey. Am. Nat. 10, Sih, A. (1984) The behavioral response race between predator and prey. Am. Nat. 13, Abrams, P.A. (000) The evolution of predator prey interactions: theory and evidence. Annu. Rev. Ecol. Syst. 31, Stephens, D.W. and Krebs, J.R. (1986) Foraging Theory, Princeton University Press 16 Houston, A.I. and McNamara, J.M. (1999) Models of Adaptive Behavior, Cambridge University Press 17 Sutherland, W.J. (1996) From Individual Behaviour to Population Ecology, Oxford University Press 18 Moody, A.L. et al. (1996) Ideal free distributions under predation risk. Behav. Ecol. Sociobiol. 38, Hugie, D.M. and Dill, L.M. 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