Stephens & Foraging - Behavior and Ecology - Chapter 10 pps

10 Foraging with Others: Games Social Foragers Play Thomas A. Waite and Kristin L. Field 10.1 Prologue On a bone-chilling winter night in the far north, a lone wolf travels through theboreal forestlooking forhis nextmeal. Thehalf-dozen pack members in the adjacent home range howl periodically throughout the night. With each chorus, he resists the urge to howl in return. With each chorus, he feels the pull to cross over the ridge, descend into the cedar swamp below, and attempt to join the pack—to give up the soli- tary life. Suddenly, just before daybreak, he happens upon an ancient, arthritic moose. The chase begins. The moose flounders in the deep snow. Within minutes, the wolf subdues the moose, his tenth such suc- cess of the winter. He feeds beyond satiation and then rolls into a ball and sleeps. At first light, ravens arrive, gather around the carcass, and begin to feed. By midday, several dozen ravens are busily engaged in converting the carcass into hundreds of scattered hoards. Later that winter, the same wolf travels through the adjacent home range, having recentlybecome a member of the pack. Again, he happens upon a vulnerable moose. The chase begins. Within minutes, he and his new packmates manage to bring down the moose. As the newcomer in the pack, he must wait for his turn to feed. At first light, ravens begin to gather nearby and wait for their turn at the carcass. At midday, the ravens are still biding their time. 332 Thomas A. Waite and Kristin L. Field 10.2 Embracing the Complexity of Social Foraging The vast majority of carnivores live solitarily. Why, then, do wolves (Canis lupus) live in social groups? Surely, you might think, the advantages of social foraging must favor group living (sociality) in wolves. But the data suggest that wolves live in packs despite suffering reduced foraging payoffs (Vucetich et al. 2004). The data suggest that an individual wolf would often achieve a higher food intake rate if it foraged alone rather than as a member of a pack. So it appears that sociality persists despite negative foraging consequences. Why? Perhaps parents accept a reduction in their own intake rates if the be- neficiaries are their own offspring (Ekman and Rosander 1992). But why would any individual stay in a pack if it could do better on its own? In this chapter, we illustrate some theoretical approaches to analyzing such problems. We show that packs may form through retention of nutritionally dependent offspring, but we cannot readily explain why individuals with de- veloped hunting skills belong to groups. This failure of nepotism as a general explanation prompts further analysis of the foraging payoffs. We incorporate a previously overlookedfeature of wolf foraging ecology, the cost of scaveng- ing by ravens. And voila! Predicted group size increases dramatically. Thus, it appears that benefits of social foraging favor sociality in wolves after all. Throughout this chapter, we describe situations in which foraging payoffs depend not solely on an individual’s own actions, but also on the actions of others. Thiseconomic interdependencemeans that thestudy ofsocial foraging requires game theory(Giraldeau andLivoreil1998). Italso impliesthatanimals may forage socially even if they never interact. Conventional foraging theory (Stephens and Krebs 1986) in effect assumes that foragers are economically independent entities. Until recently, the study of social foraging proceeded without aunified theoretical framework.Fortunately, Giraldeau andCaraco’s (2000) recent book provides a synthesis of game theoretical models of social foraging that remedies this situation. The basic principle of such models is that the best tactic for a forager depends on the tactics used by others. According to the classic patch model from conventional foraging theory (Charnov 1976b; see chap. 1 in this volume), a forager should depart for another patch when its instantaneous rate of gain drops to the habitat-at-large level. To illustrate the difference between conventional and social foraging, we examine how this patch departure threshold differs for solitary versus social foragers. Consider the following scenario (Beauchamp and Giraldeau 1997; Rita et al. 1997): An individual (producer) finds a patch, and forages alone initially, but then other individuals (scroungers) join the producer, ar- riving one at a time (cf. Livoreil and Giraldeau 1997; Sjerps and Haccou 1994). Each scrounger depresses the producer’s intake rate by interfering with the Foraging with Others: Games Social Foragers Play 333 producer’s foraging. If interference is strong, the producer may leave im- mediately when the first scrounger arrives, even if it must spend a long time traveling to the next patch. Thus,a scrounger’s arrival can lead a social forager to leave a patch much sooner than a solitary forager would. This scenario (see also box 10.1) emphasizes the basic theme that the economic interdependence of foraging payoffs shapes the decision making of social foragers. BOX 10.1 The Ideal Free Distribution Ian M. Hamilton The Ideal Free Distribution (IFD; Fretwell and Lucas 1969) predicts the effects of competition for resources on the distribution of foragers between patchesdiffering inquality,assuming that foragersare“ideal” (able togauge perfectly the quality of all patches) and “free” (able to move among patches at no cost). The original IFD model assumed continuous input of prey and scramble competition. Undercontinuous input, resourcescontinuously arrive and are instantlyremoved by foragers.Assuming equalcompetitiveabilities and no foraging costs, the payoff of foraging in patch i is the rate of renewal of the resource, Q i , shared among N i foragers in the patch. At equilibrium, foragers will be distributed so that none can improve its payoff by unilater- ally switching patches. In the original model, the ratio of forager densities between two patches at equilibrium matches that of the rates of resource input intothe patches(i.e., N i /N j =Q i /Q j ). Thismatch inratios isknown as the input matching rule. At equilibrium, the fitness payoff to foragers is also equal in all patches. The input matching rule holds even for predators that do not immediately consume prey upon its arrival, so long as the only source of prey mortality is consumption by the predators (Lessells 1995). There have been numerous modifications of the original model. Re- laxing the ideal and free assumptions of the original model can result in undermatching, or lower use of high-quality patches than expected based on resource distribution (Fretwell 1972; Abrahams 1986). Undermatching is a common finding in tests of the IFD (Kennedy and Gray 1993; but see Earn and Johnstone 1997). Other modifications include changing the form of competition and the currency assumed in the model. In this box I briefly review these ideas. Extensive reviews of IFD models and empirical tests can be found in Parker and Sutherland (1986), Milinski and Parker (1991), Kennedy and Gray (1993), Tregenza (1995), Tregenza et al. (1996), van der Meer and Ens (1997), and Giraldeau and Caraco (2000). (Box 10.1 continued) Continuous Input, Unequal Competitors If forager phenotypesdifferin theirabilitiesto compete forprey,and iftheir relative abilities remain the same in all patches, then there are an infinite number of stable distributions of phenotypes between patches (Sutherland and Parker 1985). However, all of these distributions are consistent with competitive-weight matching. If each individual is weighted by its competitive ability, the ratio of the summed competitive weights in each patch matches the ratio of resource input rates. At equilibrium, the mean intake rates are equal across patches. If relative competitive abilities differ among patches, a truncated pheno- type distribution is predicted (Sutherland and Parker 1985). Foragers with the highest competitive abilities aggregate in patches where competitive differences have the greatest effect on fitness payoffs, and those with the lowest competitive abilities are found where competitive differences have the smallest effect. Average intake rate is higher for better competitors. Interference Continuous input prey dynamics are rare in nature (Tregenza 1995). Inter- ference models applywhen preydensities areconstantor graduallydecrease over time and when the quality of patches to foragers reversibly decreases with increasing competitor density. There are several ways to model in- terference, which lead to different predicted distributions (reviewed in Tregenza 1995; van der Meer and Ens 1997). The simplest of these is the addition of an “interference constant,” m (Hassell and Varley 1969), to the effects of forager density on patch quality, so that the payoff for choos- ing patch i is Q i /N i m (Sutherland and Parker 1985). When m < 1, more competitors use the high-quality patch than expected based on the ratio of patch qualities. When m> 1, the opposite is predicted. When phenotypes differ in competitive ability, this model predicts a truncated phenotype distribution. Kleptoparasitism One form of interference that has been extensively investigated is klep- toparasitism, in which some individuals steal resources acquired by others. If kleptoparasitism does not change the average intake rate, but simply reallocates food from subordinates to dominants, no stable distribution is predicted (Parker and Sutherland 1986). (Box 10.1 continued) Models based onthe transition of foragers among behavioral states,such as searching, handling, and fighting, have also been used to investigate the influence of kleptoparasitism on forager distributions (Holmgren 1995; Moody and Houston 1995; Ruxton and Moody 1997; Hamilton 2002). These models reach stable equilibria and predict greater than expected use of high-quality patches by all foragers when competitors are equal (Moody and Houston 1995; Ruxton and Moody 1997) and by dominant foragers (Holmgren 1995) or kleptoparasites (Hamilton 2002) when competitors are not equal. Changing Currencies The previous models all use net intake rate as the currency on which de- cisions are based. The IFD has also provided fertile ground for models ex- ploring how animals balance energetic gain and safety (Moody et al. 1996; Grand and Dill 1999) and for empirical studies seeking to measure the energetic equivalence of predation risk (Abrahams and Dill 1989; Grand and Dill 1997; but see Moody et al. 1996). Hugie and Grand (2003) have shownhow such “non-IFD”considerationsasavoidingpredators or search- ing for mates affect the distribution of unequal competitors (see above), resulting in a unique, stable equilibrium. Some authors have also used IFD models to examine the interaction between predatordistributions and those of theirprey whenboth can move (Hugie and Dill 1994; Sih 1998; Heithaus 2001). These models predict that predators tend to aggregate in patches that are rich in resources used by their prey. If patches also differ in safety, prey tend to aggregate in safer patches, even when these patches are relatively poor in resources. A recent model by Hughes and Grand (2000) used growth rate, rather than intakerate, asthe fitnesscurrency inan unequal-competitors, continu- ous-input model of the distribution of fish. In fish, like other ectotherms, growth rate isstrongly influencedby temperature, andthis model predicted temperature-based segregation ofcompetitive types(bodysizes) whenpatches differed in temperature. This scenario also shows how social foraging can have both positive and negative consequences.Individuals may benefitfrom foragingsocially because groups discover more food or experience less predation. In general, individ- uals may benefit by joining others who have already discovered a resource. 336 Thomas A. Waite and Kristin L. Field However, joining represents a general cost of social foraging. “Whenever some animals exploit the finds of others, all members of the group do worse than if no exploitation had occurred. The almost inevitable spread of scroung- ing behavior within groups and its necessary lowering of average foraging rate may be considered a cost of group foraging” (Vickery et al. 1991, 856). Recent work has revealed that foragers may sacrifice their intake rate to stay close to conspecifics (Delestrade 1999; Vasquez and Kacelnik 2000; see also Beauchamp et al. 1997). Other work has shown that social foragers may ac- quire poor information (i.e., about a circuitous, costly route to food) (Laland and Williams 1998). In the extreme, joining can lead to an individual’s demise through tissue fusion (see section 10.5).These examples highlight the intrinsic complexity of social foraging. This chapter reviews theoretical and empirical developments in the study of social foraging. Throughout, we explore joining decisions: When should a solitary individual join a foraging group? When should a group member join another member’s food discovery? When should an individual join another through fusion of their peripheral blood vessels? We begin by exploring the economic logic of group membership. Next, we review producer-scrounger games, in which individuals must decide how to allocate their time between searching for food (producing) and joining other individuals’ discoveries (scrounging). Finally, we review work on cooperative foraging. 10.3 Group Membership Predicting Group Size Stable Group Size Often Exceeds Rate-Maximizing Group Size Many animals find themselves in a so-called aggregation economy, in which individuals in groups experience higher foraging payoffs than solitary individuals (e.g., Baird and Dill 1996; review by Beauchamp 1998). Peaked fitness functions are the hallmark of such economies (fig. 10.1; Clark and Mangel 1986; Giraldeau and Caraco 2000). By contrast, animals in a disper- sion economy experience maximal foraging payoffs when solitary and strictly diminishing payoffs withincreasing groupsize (e.g., B ´ elisle 1998). Inan aggre- gation economy, theper capita rate of intake increases initiallywith increasing group size G. However, because competition also increases with group size G, intake rate peaks (at G ∗ ) and then falls with further increases in group size. Clearly, this situation favors group foraging, but can we predict group size? It might seem that the observed group size G should match the intake- maximizing groupsize G ∗ , atwhich each groupmember maximizesits fitness. Foraging with Others: Games Social Foragers Play 337 Figure 10.1. Hypothetical relationship between group size G and an unspecified surrogate for fitness (e.g., net rate of energy intake). This general peaked function is characteristic of an aggregation economy, in which individuals gain fitness with increasing G, at least initially. G ∗ (= 3) is the intake-maximizing group size. G may exceed G ∗ because a solitary individual would receive a fitness gain by joining the group. G may continue to grow until it reaches ˆ G (= 6), the largest size at which each individual would do better to be in the group than to be solitary. G is not expected to exceed ˆ G because a joiner that increases G to ˆ G + 1 would achieve greater fitness by remaining solitary. Many studies,however, havefound thatG oftenexceeds G ∗ (Giraldeau 1988). This mismatch is notunexpected. With a peak inthe fitness function at G ∗ (see fig. 10.1), the intake-maximizing group is unstable because a solitary forager can benefit from joining the group. A group of size G ∗ will grow as long as foragers dobetter in thatgroup than ontheir own, butit should notexceed the largest possibleequilibrium group size ˆ G. Atthat point, solitaryindividuals do better to continue foraging alone than to join such a large group. Equilibrium group size may be as small as the intake-maximizing group size G ∗ and as large as the largest possible equilibrium size ˆ G, depending on whether the individual or the group controlsentry and on the degree of geneticrelatedness between individuals (box 10.2). Thanks to the development of this theory, it is no longer paradoxical to find animals in groups larger than the intake-maximizing group size G ∗ . Yet the role of foraging payoffs in the maintenance of groups of large carnivores remains contentious (see Packer et al. 1990 for a fascinating case study). The wolves discussed in the prologue present a paradox, because pack size routinely exceeds the apparently largest possible equilibrium size ˆ G.Why would a wolf belong to a pack when it could forage more profitably on its own? Here we attempt to resolve this paradox while reviewing the theory on group membership. BOX 10.2 Genetic Relatedness and Group Size Giraldeau and Caraco (1993) analyzed the effects of genetic relatedness on group membership decisions. Consider a situation in which individuals benefit from increasing group size, and in which all individuals are related by a coefficient r. According to Hamilton’s rule, kin selection favors an altruistic act (e.g., allowing an individual to join the group) when rB−C > 0, where B is the net benefit for all relatives at which the act is directed and C is the cost of the act to the performer. In the context of group membership decisions, both effects on others (E R ) and effects on self (E S ) can be either positive or negative, so we rewrite Hamilton’s rule as rE R + E S > 0. (10.1.1) Group-Controlled Entry In some social foragers, group members decide whether to permit solitaries to join the group. Such groups should collectively repel a potential group member (i.e., keep the group at size G) when Hamilton’s rule is satisfied. Here E R is the effect of repelling the intruder on the intruder: E R = (1) − (G + 1), (10.1.2) and E S is the effect of repelling the intruder on the group: E s = G[(G) − (G + 1)], (10.1.3) where (1) is the direct fitness of the solitary intruder, (G) is the direct fitness of each of G individuals in the current group, and (G + 1) is the direct fitness of each individual if the group decides not to repel the intruder. (As we highlight below, the group-level decision is based on the selfish interests of the individual group members.) Substituting these expressions for the effects of repelling the intruder on the intruder [E R ; eq. (10.1.2)] and on the group [E S ; eq. (10.1.3)] into equation (10.1.1) and dividing all terms by G, we see that selection favors repelling a prospective joiner when  r G  [(1) − (G + 1)] + [(G) − (G + 1)] > 0, (10.1.4) where we express both the indirect fitness (first term on the left-hand side) and the direct fitness (second term) of group members on a per capita basis. By extension, group members should evict an individual from the group when rE R + E S > 0. Here the effect on the evicted individual E R is Foraging with Others: Games Social Foragers Play 339 (Box 10.2 continued) (1) − (G), and the effect on the remaining group members E S is (G − 1)[(G − 1) − (G)]. Equation (10.1.4)indicates that repelling is neverfavored when1 < G < G ∗ , where G ∗ is the group size at which individual fitness is maximized, but repelling is always favored when G> ˆ G, where ˆ G is the largest group size at which the individual fitness of group members exceeds that of a solitary. Thus, equilibrium (stable) group size must fall within the interval G ∗ <G< ˆ G. Under group-controlled entry, the effect of increasing genetic relatedness is toincrease theequilibriumgroup size.By contrast, ifpotential joiners can freely enter the group, genetic relatedness has the opposite effect. Free Entry Under free entry, group members do not repel potential joiners; thus, potential joiners make group membership decisions. Any such individual should join a group when Hamilton’s rule is satisfied, where E R is the combined effect of joining on all the joiner’s relatives: E R = (G −1)[(G) − (G − 1)], (10.1.5) and E S is the effect of joining on the joiner: E S = (G) − (1). (10.1.6) Substituting, we see that joining a group of size (G−1) is favored when r (G − 1)[(G) − (G − 1)] + [(G) − (1)] > 0. (10.1.7) An analysis of equation (10.1.7) reveals that, under free entry, the effect of increasing genetic relatedness is to decrease equilibrium group size. (For derivation of the expressions for equilibrium group size under both entry rules, see Giraldeau and Caraco 2000.) Rate-Maximizing Foraging and Group Size In wolf packs, group members control entry. Thus, pack size should fall somewhere between the intake-maximizing group size G ∗ and the largest possible equilibrium size ˆ G (see box 10.2). The data show that a group size of two maximizes net per capita intake rate and that individuals would do worse in a larger group than alone (i.e., G ∗ = ˆ G = 2; see fig. 3 in Vucetich et al. 2004). Thus, this initial analysis cannot explain pack living. 340 Thomas A. Waite and Kristin L. Field Variance-Sensitive Foraging and Group Size Our initial attempt might have failed for lack of biological realism. We assumed that each individual would obtain the mean payoff for its group size. However, in nature, the realized intake rate of an individual might deviate widely from the average rate. In principle, a reduction in intake rate variation with increasing group size could translate into a reduced risk of energetic shortfall. However, a variance-sensitive analysis indicates that an individual will have the best chance to meet its minimum requirement if it forages with just one other wolf (see fig. 4 in Vucetich et al. 2004). Its risk of shortfall will be higher in a group of three or more than alone. Thus, once again, foraging models fail to explain pack living. Genetic Relatedness and Group Size So far, foraging-based explanations seem unable to account for the mis- match between group size predictions and observations. Kin selection would seem to provide a satisfactory explanation (e.g., Schmidt and Mech 1997). Af- ter all, wolf packs form, in part, through the retention of offspring. However, kin-directed altruism (parental nepotism) does not account for the observa- tion that pack size routinely exceeds the largest possible equilibrium group size ˆ G. Although we expect group size to increase with genetic relatedness when groups control entry (see box 10.2), theory predicts that equilibrium group size cannot exceed ˆ G, even in all-kin groups (Giraldeau and Caraco 1993). Recalling that for wolves, the largest possible equilibrium group size ˆ G = 2, kin selection cannot explain pack living. This does not mean, however, that group size should never exceed two. Consider immature wolves, which cannot forage independently. If evicted, they would presumably achieve an intake rate of virtually zero. Under this assumption, Hamilton’s (1964) rule (see box 10.2) predicts group membership for nutritionally dependent first- order relatives (i.e., offspring or full siblings). However, individuals that can achieve the average intake rate of a solitary adult should not belong to groups, even all-kin groups (fig. 10.2). Thus, while kin selection offers an adequate explanation for packs comprising parents and their immature offspring, we still have not provided a general explanation for wolf sociality. How do we account for packs that include unrelated immigrants and mature individuals? Is there an alternative foraging-based explanation that has evaded us? Kleptoparasitism and Group Size Inclusion of a conspicuous feature of wolf foraging ecology, loss of food to ravens(Corvuscorax), increasesthepredicted groupsize dramatically (fig.10.3). Both rate-maximizing (fig. 10.3) and variance-sensitive currencies predict large pack sizes, even for small amounts of raven kleptoparasitism. Why does [...]... modeled the producer-scrounger situation as both a rate-maximizing (Vickery et al 1991) and a variance-sensitive game (Caraco and Giraldeau 1991; reviewed by Giraldeau and Livoreil 1998; Giraldeau and Caraco 2000) In the rate-maximizing game, the predicted equilibrium frequency of scrounging q decreases as a function of the finder’s share of the ˆ food items (see box 10. 3) In the variance-sensitive game,... predicted rate-maximizing behavior (After Giraldeau and Beauchamp 1999; originally described in Giraldeau and Livoreil 1998; see also Giraldeau and Caraco 2000.) Foraging with Others: Games Social Foragers Play producing and scrounging as the rate-maximizing producer-scrounger game predicts However, this study, like all previous studies, has several shortcomings It failed to establish that producing and scrounging... Kristin L Field 10. 7 Suggested Readings Giraldeau and Caraco (2000) offer an excellent, timely, and comprehensive synthesis of social foraging theory Galef and Giraldeau (2001) review how social environment influences foraging by biasing individual learning processes Crespi (2001) considers the evolutionary ecology of social behavior, including cooperative foraging, in microorganisms Sober and Wilson (1998)... shortfall (Caraco 1981, 1987; Caraco and Giraldeau 1991) To evaluate this possibility, Koops and Giraldeau (1996) exploited the fact that rate-maximizing and variance-sensitive producer-scrounger models make different predictions about the effect of patch encounter rate λ (and hence patch density) on equilibrium scrounger frequency q As box 10. 3 shows, ˆ the rate-maximizing model predicts that patch... review these approaches and recent experiments that have tested them (see reviews by Giraldeau and Livoreil 1998; Giraldeau and Beauchamp 1999; Giraldeau and Caraco 2000) Information-Sharing versus Producer-Scrounger Models Information-sharing (IS) models assume that each group member concurrently searches for food and monitors opportunities to join the discoveries of others (Clark and Mangel 1984; Ranta... A/n)] (10. 2.2) Setting these two expressions equal to each other and rearranging yields an expression for the equilibrium frequency of the scrounger tactic: ˆ q =1− 1 a + , F G (10. 2.3) which implies that individuals should adjust their proportional use of foraging tactics in response to the finder’s share (a/F) and the size of the group This rate-maximizing PS model [eq (10. 2.3)] predicts that an Foraging. .. scrounging behavior is a pervasive feature of group foraging (Giraldeau and Beauchamp 1999) But should individuals always join others’ discoveries? Doesn’t scrounging become unprofitable if everyone does it? What is the optimal scrounging policy, and what factors affect the decision? Behavioral ecologists have analyzed these questions using two antagonistic approaches, information-sharing (IS) and producer-scrounger... finder’s share and the potential joiner’s ˆ energetic requirement The following discussion describes experimental tests of these two games Testing the Rate-Maximizing Producer-Scrounger Game The rate-maximizing producer-scrounger game predicts that the proportional use of the scrounger tactic q increases with group size G and decreases as the ˆ finder’s share increases (see box 10. 3) Giraldeau and his colleagues... scroungers, this manipulation generated two predicted producer-scrounger equilibria that Mottley and Giraldeau could explore in a follow-up experiment Converging on Predicted Equilibria To test whether group -foraging spice finches would converge on the predicted equilibria, Mottley and Giraldeau modified their apparatus to allow movement between the producer and scrounger compartments Their results show that subjects.. .Foraging with Others: Games Social Foragers Play Immature kin (r=0.5) mature kin (r=0.5) 3 rER + ES 2 1 ESS is to repel 0 ESS is not to repel -1 -2 -3 2 4 6 8 10 12 14 16 18 Pack size, G Figure 10. 2 The application of Hamilton’s rule to predict whether mature and immature solitary wolves should be allowed in packs of various sizes . models and empirical tests can be found in Parker and Sutherland (1986), Milinski and Parker (1991), Kennedy and Gray (1993), Tregenza (1995), Tregenza et al. (1996), van der Meer and Ens (1997), and. predation risk (Abrahams and Dill 1989; Grand and Dill 1997; but see Moody et al. 1996). Hugie and Grand (2003) have shownhow such “non-IFD”considerationsasavoidingpredators or search- ing for mates affect. on which de- cisions are based. The IFD has also provided fertile ground for models ex- ploring how animals balance energetic gain and safety (Moody et al. 1996; Grand and Dill 1999) and for empirical