A nim. Behav., 1998, 55, 737–744 Producers, scroungers and the price of a free meal E SA R A N T A *, N I N A P E U H K U R I *, H E I K K I H I R VO N E N * & C H R I ST O P H E R J . BA R N A R D † *Integrative Ecology Unit, Department of Ecology and S ystematics, University of H elsinki †Behaviour and Ecology R esearch Group, S chool of Biology, University of N ottingham ( R eceived 3 December 1996; initial acceptance 31 January 1997; final acceptance 21 July 1997; M S . number: 5404) Abstract. In social foraging, scroungers take a disproportionately large share of the food found relative to their own food-searching efforts, while producers find more food than they manage to monopolize. We present a model of social foraging acknowledging the finder’s advantage and foraging role asymmetries among individuals but incorporating the possibility that producers and scroungers differ in vigilance level and in vulnerability to predators. This allows simultaneous examination of both foraging benefits and anti-predatory aspects of grouping behaviour. Instead of seeking for equal payoff conditions, we first look for groups in which foraging character combinations and anti-predatory properties of producers and scroungers minimize the phenotype-specific predation hazard over food-intake rate, R i /I i, that is, fixed phenotype R i /I i minima. In the second approach, we allow individuals to change their foraging status to achieve lower R i /I i and look for combinations where it no longer pays for either producers or scroungers to change their roles, that is, evolutionarily stable group compositions, ESS. Various character combinations allow the phenotype-specific minima. In most cases, however, producers’ and scroungers’ minima are achievable only in different group compositions. The ESS combinations of producers and scroungers deviate widely from those combinations yielding phenotype-specific minima of R i /I i. If individuals are allowed to be flexible in adopting either a producer or a scrounger role, ESS group compositions will emerge, even though they are more expensive for both producers and scroungers in terms of R i /I i than group compositions yielding the phenotype-specific ? 1998 The Association for the Study of Animal Behaviour R i /I i minima. Both theoretical models and empirical evidence suggest that grouping behaviour is favoured owing to its foraging and anti-predatory benefits to individuals (Bertram 1978; M agurran 1990; Pitcher & Parrish 1993; R anta et al. 1994). F or example, owing to information sharing, the rate of patch finding speeds up and its variance reduces with increasing group size (e.g. Caraco 1981; Clark & M angel 1984; R anta et al. 1993). F urthermore, predation hazard is diluted with an increasing number of individuals in the group (Bertram 1978; F oster & Treherne 1981; M organ & G odin 1985). The probability of detecting a predator also increases with group size because vigilance is Correspondence: E. R anta, D epartment of Ecology and Systematics, D ivision of Population Biology, P.O. Box 17, F IN -00014 U niversity of H elsinki, F inland (email: esa.ranta@helsinki.fi). C. J. Barnard is at the School of Biology, U niversity of N ottingham, N ottingham N G 7 2R D , U .K . 0003–3472/98/030737+ 08 $25.00/0/ar970649 shared among group members (K enward 1978; Caraco 1979; Thompson & Barnard 1983; but see Elgar 1989). Barnard & Sibly (1981) noted that group members may differ in their contribution to food searching. Scroungers are individuals that make disproportionately large use of the food found by others relative to their own food-searching contribution, that is, scroungers exploit the resources found by producers. According to theory, individuals with foraging-role asymmetries are expected to associate together only when foraging payoffs for producing and scrounging individuals match. In such an equal payoff situation individuals of neither phenotype, producer or scrounger, should be more tempted to move to another foraging group (Barnard & Sibly 1981; Parker 1984). The producer–scrounger dichotomy has repeatedly gained attention in studies on social foraging (Barnard & Sibly 1981; Barnard 1984; G iraldeau ? 1998 The Association for the Study of Animal Behaviour 737 738 A nimal Behaviour, 55, 3 et al. 1990, 1994; Vickery et al. 1991; R anta et al. 1996), and evidence shows that foraging individuals indeed assume such foraging role asymmetries (Barnard & Sibly 1981; R ohwer & Ewald 1981; G iraldeau et al. 1990, 1994). Curiously, however, although anti-predatory benefits of group living are evident (e.g. Bertram 1978; Pulliam & Caraco 1984), these aspects have largely been neglected in studies of producer– scrounger relationships. Yet, it is likely that the costs and benefits of group membership depend not only on an individual’s food-intake rate but also on its mortality risk from predation. As several investigations have indicated, animals appear to trade off maximizing energy intake and minimizing predation hazard when making their foraging decisions (Sih 1987; G illiam 1990; G odin 1990; Lima & D ill 1990; Sih & M oore 1990). This could potentially influence the optimal ratio of producer and scrounger phenotypes in a group (Barnard & Thompson 1985). We develop here a producer–scrounger model that simultaneously incorporates both energetic and survival probability aspects. Specifically, after Barnard & Sibly (1981), we assume that producers and scroungers differ in their food-finding ability and in their tendency to exploit the food found by others. We also assume that the patch-finder has priority to some fraction of the food it has found (the finder’s advantage; e.g. M angel 1990). F urthermore, we assume differences in vigilance for, and in vulnerability to, predators between individuals of the two phenotypes. We then examine how these differences influence the two phenotypes’ benefits in varying ratios of producers and scroungers in an environment with patchy food distribution. When investigating this, we follow G illiam & F raser (1987) who assumed that the optimal strategy is the one that minimizes the ratio of mortality rate to feeding rate, given that an individual’s feeding rate exceeds or equals some arbitrary threshold value of needed energy intake. We explore producer–scrounger group structures with both fixed strategies (individuals being either of the two phenotypes) and flexible strategies (individuals being able to adjust their foraging roles). P RO D U CERS , S CRO U N GERS AN D P RED ATIO N RIS K Consider a population where individuals of producer (p) and scrounger (s) phenotypes can be characterized by their tendency to search for food patches, f i, their ability to compete for the food found, ci, their level of vigilance for predators, vi, and their vulnerability to predators, ui. Thus, for any group with individuals of these foraging and anti-predatory characters we denote n= np + ns. To characterize phenotype-specific abilities of food finding and competition we use the model by R anta et al. (1996). The foraging environment consists of randomly dispersed food patches with a given number of food items per patch. Once one individual in the group finds a patch of prey the other group members benefit by gathering around to exploit the prey items. F or the food-finding efficiency of the group we write A (np ,ns)= np f p + ns f s. (1) By definition, we assume f s [0, f p ], and as, after the producer–scrounger theory (Barnard & Sibly 1981), producers should do most of the food searching, we standardize f p = 1. Each individual’s share of the food found depends on its competitive ability, ci = ci(np ,ns). Thus, the food intake for an individual of phenotype i is (R anta et al. 1996): I i = f i(np ,ns)#a+ ci(np ,ns)#(1"a)#A (np ,ns), (2) where a is the finder’s share of the food found (M angel 1990; G iraldeau et al. 1990, 1994; Vickery et al. 1991) and i= p,s. Ever since Barnard & Sibly (1981), the objective in the producer– scrounger game has been, for any given group size n= np + ns, to seek the combination of {np ,ns} that will satisfy the equal payoff condition, I p = I s. R ecently R anta et al. (1996) made an explicit approach by incorporating f i and ci into the search. Our task here is to extend the model to include aspects of anti-predatory behaviour of producers and scroungers and their vulnerability to predation. We do this by assuming that scroungers, by being vigilant for producers, are also more likely than producers to detect predators. It follows that when the proportion of scroungers in a group decreases, the overall level of vigilance for predators levels off, especially if producers direct most of their time and activity towards finding prey patches. F or the phenotype-specific vigilance vi we assume vp [0,vs], and, as above, for scroungers we standardize vs = 1. The overall vigilance, as a R anta et al.: Producers and scroungers 739 function of the group composition, thus has the general form V (np ,ns)= np vp + nsvs. (3) Analogously, for the vulnerability we write U(np ,ns)= np up + nsus. (4) Producers and scroungers may match in vulnerability, up = us, (ui = 1) or they may differ, up > us, (us = 1) or up < us, (up = 1). Vulnerability here refers to some character that may increase the likelihood that a predator attacks an individual of one phenotype more frequently than an individual of the other phenotype. F or example, if producers, while searching for prey, are more active than scroungers, they may attract a predator’s attention more than scroungers. There is experimental evidence that the presence of one or a few deviating individuals among matching ones increases the overall interest of a predator towards the entire group (Landeau & Terborgh 1986), which hence justifies an approach like equation (4). We assume that the benefit of the pooled vigilance of the group, V (np ,ns), will be shared equally among all the members of the group, regardless of their phenotypes. Assuming that vigilant individuals gain more from the vigilance, although a realistic addition (e.g. F itzG ibbon 1989; Lima 1994; K rause & G odin 1996), would affect only the level of the predation hazard to intake ratio R i /I i in favour of the more vigilant phenotype, not the p and s combinations where the R i /I i minima are found. The pooled vulnerability, U(np ,ns), will be weighted by the phenotype-specific vulnerabilities, ui (np ,ns). Thus, the phenotype-specific risk of being killed by the predator has the form G illiam & F raser (1987) suggested that individuals should minimize the ratio of mortality risk to food intake. When the idea of minimizing risk over food intake is applied to the producer– scrounger problem, one should seek not the combination of {np ,ns} {f p ,f s} and {cp ,cs} that will satisfy the equal payoff condition, I p = I s, but rather the combination of {np ,ns} {f p ,f s} {cp ,cs} {vp ,vs} and {up ,us} that will satisfy In the following, we examine whether groups of producers and scroungers exist that satisfy equation (6). We include both fixed and flexible strategies. With fixed strategies individuals are either producers or scroungers, while the flexible strategy allows individuals to switch between the two strategies whenever they can thereby reducing their R i /I i ratio. We set out to solve equation (6) for both producers and scroungers by using equation (2) for phenotype-specific food-intake rates and equation (5) for the risk of being killed by the predator. In principle, after the simplifications listed below, we were seeking for the character combinations f i, ci, vi, ui and n= np + ns that would minimize the phenotype-specific predation risk over foodintake rate. F irst, for scroungers the f s values ranged from 0 to 1, from no food seeking to food seeking matching that of producers. Similarly, for producers the vigilance vp ranged from 0 to 1. After R anta et al. (1996), the competitive ability ci of the worse competitor was set to 1, and that of the better competitor was set to ci > 1. H ence, for the matching pair we have cp = cs; otherwise cp = 1 and cs > 1, or cp > 1 and cs = 1. The same rationale was followed for phenotype-specific vulnerability ui to predators. We used the following feasible parameter combinations for up , us, cp and cs: up = us, cp = cs; up = us, cp < cs; up = us, cp > cs; up < us, cp = cs; up < us, cp < cs; up < us, cp > cs; up > us, cp = cs; up > us, cp < cs; and up > us, cp > cs. In half of the runs we let the producers’ vigilance vp change from 0 to 1 in steps of 0.1; in the other half, the scroungers’ food searching f s was allowed to vary similarly. This yielded 99 parameter combinations for both cases. All the results presented here are for groups of 10 individuals, as experiments indicated that the conclusions are not sensitive to the foraging group size (provided the groups are large enough). RES U LTS U nder the current model of food finding, equation (2), producer–scrounger combinations that would minimize the phenotype-specific predation risk over food-intake ratios, R p /I p and R s /I s, are attainable in mixed foraging groups of producers and scroungers. F igure 1 shows examples of R p /I p and R s /I s functions (with some combinations of A nimal Behaviour, 55, 3 740 Scrounger's food searching, fs 1.0 Producer's vigilance, vp u p = u s, c p = c s, fs = 0.1 v p = 0.1 u p = u s, c p < c s, fs = 0.1 v p = 0.1 u p < u s, c p < c s, fs = 0.7 v p = 0.7 u p > u s, c p < c s, fs = 0.7 v p = 0.7 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 Risk/Intake, R i/I i 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 0:10 5:5 10:0 0:10 5:5 10:0 Figure 1. Examples of predation hazard over food intake rate for producers (.) and scroungers (-) in a group of foragers (n= 10). All possible producer:scrounger combinations are shown. M inima for phenotype-specific predation risk:food-intake ratios R i /I i are indicated for producers (0) and scroungers (5) as well as the evolutionarily stable strategy group composition (*). The selected parameter values are indicated in the left-hand panels (when vulnerability to predators up = us and competitive ability cp = cs the value is 1, when up > us or cp > cs, or the other way round, the smaller value is 1, the larger 2). R anta et al.: Producers and scroungers up , us, cp , cs and f s and vp ) for a group of n= 10 individuals. F or example, in F ig. 1, with up = us, cp = cs and f s = 0.1, the fixed-phenotype R i /I i minimum for producers is met with np = ns = 5, while for scroungers it is np = 6, ns = 4. The R s /I s function with these character combinations is above the R p /I p function. Thus, when a flexible switch in foraging status is enabled, scrounging individuals will switch to being producers until an evolutionarily stable strategy (ESS) group composition np = 7, ns = 3 is reached and no one can gain by changing foraging status. Similarly, the ESS foraging group structure with flexible switching of foraging roles can be assessed for all the up , us, cp , cs and f s and vp values evaluated (examples in F ig. 1). We found that in the majority of the cases examined the minima of R p /I p and R s /I s were achievable with different combinations of np and ns in the foraging group (cf. F ig. 1). The group composition matched for R p /I p and R s /I s minima in two cases out of 99 when we evaluated the effect of scrounger food-finding ability f s on the balanced number of producers and scroungers in the foraging group. The corresponding number of cases was five when we varied producer vigilance vp . Another notable feature is that when the fixed strategy is contrasted with the flexible strategy they rarely agree (as already suggested in the examples of F ig. 1), group composition usually evolving away from the phenotype-specific R i /I i minima even if these are attained at the same group composition. H owever, if R p /I p and R s /I s minima are reached at the same group composition and with equal minimum values, the group composition at the shared minimum point is an ESS composition. When we tally the ESS group composition in terms of the number of producers (number of cases in parentheses) we get the following frequencies: 0(69), 1(6), 2(6), 3(3), 4(4), 5(4), 6(4), 7(5), 8(6), 9(5), 10(86). That is, the ESS combination was met in 78% of cases in all-producer or all-scrounger groups. In the all-producer groups, producers tend to be more vigilant than in mixed foraging groups (0.56 versus 0.45; t 97 = 2.31, P = 0.023); in scrounger-only groups, scroungers also tend to have a higher level of food finding than in mixed groups (0.586 versus 0.378; t 97 = 3.50, P = 0.007) With the fixed strategy, assuming that producers tolerate the presence of scroungers only when 741 the combination of np + ns yields the minimum of R p /I p , the risk over intake cost for scroungers at that group composition can be calculated. This is the difference between the minimum of R s /I s and R s /I s at the minimum of R p /I p . Similarly, when the combination of np + ns is such that the minimum of R s /I s is reached, the risk over intake cost can be calculated for producers, and the R i /I i values reached in the ESS combinations can be compared with those of the phenotype-specific R i /I i minima. We summarized such differences over the three scenarios of predator vulnerability (up = us; up > us; up < us) and competition (cp = cs; cp > cs; cp < cs) both for varying scrounger’s food finding and for varying producer’s vigilance explorations (F ig. 2). D eviations from the phenotype-specific minima of R i /I i were often larger for scroungers than for producers. H owever, a striking outcome is that the R i /I i ratios in the ESS groups are systematically higher than those of the fixed-strategy minima. This is especially true for the scrounging strategy (F ig. 2). D IS CU S S IO N Barnard & Sibly (1981) and R anta et al. (1996) looked for group compositions enabling equal payoffs, or matching food-intake rates, for producers and scroungers in mixed foraging groups. H owever, while feeding, individuals are often faced with the risk of being preyed upon by predators. To behave adaptively, individuals should be sensitive to this hazard and take it into account when making foraging decisions (e.g. Lima & D ill 1990). In consequence, when it comes to choosing a foraging group, not only the foodintake rate but also the risk of predation in a given group should be of importance. We have thus enriched the producer–scrounger model with aspects of anti-predatory behaviour and differences between producers and scroungers in their vulnerability to predation. G illiam & F raser (1987) modelled individuals’ selection of foraging habitat in terms of minimizing the ratio of mortality risk from predation to food intake, with different levels of predation hazard and food abundance. M inimizing such a currency, R i /I i, was proposed as an alternative to maximizing net energy gain when predation hazard differed between food patches (G illiam & F raser 1987). We applied the min(R i /I i) rule to the A nimal Behaviour, 55, 3 742 Scrounger's food searching fs [0,1] (a) Producer's vigilance vp [0,1] (b) Vulnerability 1.5 1 0 up = us up > us up < us up = us up > us up < us up = us up > us up < us up = us up > us up < us 1.5 (c) (d) Competition Relative difference 0.5 1 0.5 0 cp = cs cp > cs cp < cs ESS cp = cs cp > cs cp < cs cp = cs cp > cs cp < cs Min(R i/l i) ESS cp = cs cp > cs cp < cs Min(R i/l i) Figure 2. R elative difference (X &95% confidence interval) between the predation risk:food-intake ratio R i /I i and R i /I i minimum for producers (scroungers) when the producer:scrounger combination is such that it yields scrounger’s (producer’s) R i /I i minimum. The differences for the ESSs are calculated by comparing the R i /I i at the ESS group compositions with those in the phenotype-specific minima. The differences are evaluated for phenotype-specific predator vulnerabilities (ui) (a, b) and differences in competitive ability (ci) (c, d) by averaging over the scrounger’s food-searching gradient (a, c) and the producer’s vigilance gradient (b, d). .: Scroungers; /: producers. producer–scrounger context to look for combinations of foraging and anti-predatory characters that would minimize the ratio of predation hazard to food intake for producers and scroungers. Since there is some experimental evidence that the finder of the food patch gets some of the prey in the patch before the others arrive to take their share (e.g. G iraldeau et al. 1990, 1994) we included the finder’s advantage in the model. N ote that we do not expect the min(R i /I i) rule to hold in exceptional situations, for example, when almost certain death is traded off by extremely high food-intake rate. We checked that this was not the case in the current analyses. It turned out that the phenotype-specific minima of R i /I i for producers and scroungers can be attained in mixed-phenotype groups. F or example, producers may allow the invasion of scroungers and the following decrease in rate of food intake if, by doing this, they can decrease their predation hazard, for example, via the dilution of hazard or increased group vigilance. Evidence for the latter has emerged from interspecific producer–scrounger relationships in mixed-species flocks of birds (Thompson & Barnard 1983; M unn 1986). Scroungers may thus pay for their apparently free meal by lowering the predation hazard of producers. H owever, with most of the R anta et al.: Producers and scroungers character combinations examined here, the minima of R i /I i for producers and scroungers were achieved at different group compositions (np + ns). H ence, with fixed foraging strategies a stable coexistence of producers and scroungers in a group is restricted to just a few character combinations, individuals in most cases being tempted to change foraging groups to try to find a better option. This temptation to leave the current group can be expected to be more pronounced with scroungers as they seemed to bear a larger cost in terms of R i /I i if the group composition was at the producers’ R i /I i minimum than did producers when the group composition was at the scroungers’ R i /I i minimum. Producing and scrounging can also be seen as foraging behaviours that individual foragers assume depending on prevailing conditions. F or example, Giraldeau & Lefebvre (1986) have experimentally shown that producer and scrounger roles of feral pigeons, Columba livia, are exchangeable depending on the food-patch type and group composition. In the present context, flexibility in foraging strategy would enable individuals to change their status whenever, by doing so, they could reduce their own R i /I i ratio in the foraging group. When it no longer pays for anyone to switch from scrounging to producing, or vice versa, an ESS group composition is reached. It is a rather striking feature, if producing and scrounging are seen as flexible strategies, that the R i /I i found in ESS groups are far off the mark compared with the phenotype-specific R i /I i minima. If individuals were to obey the min(R i /I i) rule they might thus lose in terms of R i /I i when adopting a flexible foraging strategy rather than the fixed strategy. A rather interesting feature in the current model was that the group composition evolved in 78% of all the cases examined to an ESS group of either producers or scroungers. In such groups producers were usually vigilant for predators and scroungers did some food searching. That is, even if individuals may change from one foraging role to another, no food searching at all is not likely to be favoured when playing scrounger, nor is producing without paying attention to the whereabouts of predators. ACKN O WLED GM EN TS We thank N eil M etcalfe for his persistence in promoting the ‘minimizing of the predation 743 hazard over food intake’ principle in producer– scrounger context. Comments by two referees, Luc-Alan G iraldeau and G raeme R uxton, were of great value. REFEREN CES Barnard, C. J. 1984. The evolution of food-scrounging strategies within and between species. In: Producers and S croungers: S trategies of Ex ploitation and Parasitism (Ed. by C. J. Barnard), pp. 95–126. London: Croom H elm. Barnard, C. J. & Sibly, R . M . 1981. Producers and scroungers: a general model and its application to captive flocks of house sparrows. A nim. Behav., 29, 543–550. Barnard, C. J. & Thompson, D . B. A. 1985. Gulls and Plovers: the Ecology and Behaviour of M ix ed-species Feeding Groups. N ew York: Columbia U niversity Press. Bertram, B. C. R . 1978. Living in groups: predators and prey. In: Behavioural Ecology. A n Evolutionary A pproach (Ed. by J. R . K rebs & N . B. D avies), pp. 64–96. Oxford: Blackwell Scientific Publications. Brockmann, H . J. & Barnard, C. J. 1979. K leptoparasitism in birds. A nim. Behav., 27, 487–514. Caraco, T. 1979. Time budgeting and group size: a test of theory. Ecology, 60, 618–627. Caraco, T. 1981. R isk-sensitivity and foraging groups. Ecology, 63, 527–531. Clark, C. W. & M angel, M . 1984. F oraging and flocking strategies: information in an uncertain environment. A m. N at., 123, 626–641. Elgar, M . 1989. Predator vigilance and group size among mammals and birds: a critical review of the evidence. Biol. R ev., 64, 13–34. F itzG ibbon, C. D . 1989. A cost to individuals with reduced vigilance in groups of Thomson’s gazelles hunted by cheetahs. A nim. Behav., 37, 508–510. F oster, W. A. & Treherne, J. E. 1981. Evidence for the dilution effect in the selfish herd from fish predation on a marine insect. N ature, L ond., 293, 466–467. G illiam, J. F . 1990. H unting by the hunted: optimal prey selection by foragers under predation hazard. In: Behavioural M echanisms of Food S election (ed. by R . N . H ughes), pp. 797–819. Berlin: Springer Verlag. G illiam, J. F . & F raser, D . F . 1987. H abitat selection under predation hazard: test of a model with foraging minnows. Ecology, 68, 1856–1862. G iraldeau, L.-A. & Lefebvre, L. 1986. Exchangeable producer and scrounger roles in a captive flock of feral pigeons: a case for the skill pool effect. A nim. Behav., 34, 797–803. G iraldeau, L.-A., H ogan, J. A. & Clinchy, M . J. 1990. The payoffs to producing and scrounging: what happens when patches are divisible? Ethology, 85, 132– 146. G iraldeau, L.-A., Soos, C. & Beauchamp, G . 1994. A test of the producer-scrounger foraging game in captive flocks of spice finches, L onchura punctulata. Behav. Ecol. S ociobiol., 34, 251–256. 744 A nimal Behaviour, 55, 3 G odin, J.-G . J. 1990. D iet selection under the risk of predation. In: Behavioural M echanisms of Food S election (Ed. by R . N . H ughes), pp. 739–769. Berlin: Springer Verlag. K enward, R . E. 1978. H awks and doves: factors affecting success and selection in goshawk attacks on woodpigeons. J. A nim. Ecol., 47, 449–460. K rause, J. & G odin, J.-G . J. 1996. Influence of prey foraging posture on flight behavior and predation risk: predators take advantage of unwary prey. Behav. Ecol., 7, 264–271. Landeau, L. & Terborgh, J. 1986. Oddity and the ‘confusion effect’ in predation. A nim. Behav., 34, 1372–1380. Lima, S. L. 1994. On the personal benefits of antipredatory vigilance. A nim. Behav., 48, 734–736. Lima, S. L. & D ill, L. M . 1990. Behavioral decisions made under the risk of predation: a review and prospectus. Can. J. Z ool., 68, 619–640. M agurran, A. E. 1990. The adaptive significance of schooling as an anti-predator defence in fish. A nn. Z ool. Fenn., 27, 51–66. M angel, M . 1990. R esource divisibility, predation and group formation. A nim. Behav., 39, 1163–1172. M organ, M . J. & G odin, J.-G . J. 1985. Antipredator benefits of schooling behaviour in a cyprinodontid fish, the banded killifish (Fundulus diaphanus). Z . T ierpsychol., 70, 236–246. M unn, C. A. 1986. Birds that ‘cry wolf’. N ature, L ond., 319, 143–145. Parker, G . A. 1984. Evolutionary stable strategies. In: Behavioural Ecology: A n Evolutionary A pproach. 2nd edn (Ed. by J. R . K rebs & N . B. D avies), pp. 30–61. Oxford: Blackwell Scientific Publications. Pitcher, T. J. & Parrish, J. K . 1993. F unctions of shoaling behaviour in teleosts. In: T he Behaviour of T eleost Fishes (Ed. by T. J. Pitcher), pp. 363–440. London: Croom H elm. Pulliam, H . R . & Caraco, T. 1984. Living in groups: is there an optimal group size? In: Behavioural Ecology: A n Evolutionary A pproach. 2nd edn (Ed. by J. R . K rebs & N . B. D avies), pp. 122–147. Oxford: Blackwell Scientific Publications. R anta, E., R ita, H . & Lindström, K . 1993. Competition versus co-operation: success of individuals foraging alone and in groups. A m. N at., 142, 42–58. R anta, E., Peuhkuri, N . & Laurila, A. 1994. A theoretical exploration of antipredatory and foraging factors promoting phenotype-assorted fish schools. Ecoscience, 1, 99–106. R anta, E., Peuhkuri, N ., Laurila, A., R ita, H . & M etcalfe, N . B. 1996. Producers, scroungers and foraging group structure. A nim. Behav., 51, 171–175. R ohwer, S. & Ewald, P. W. 1981. The cost of dominance and advantage of subordination in a badge signaling system. Evolution, 35, 441–454. Sih, A. 1987. Predator and prey lifestyles: an evolutionary and ecological overview. In: Predation, Direct and Indirect Impacts on A quatic Communities (Ed. by W. C. K erfoot & A. Sih), pp. 203–224. H anover: U niversity Press of N ew England. Sih, A. & M oore, R . D . 1990. Interacting effects of predator and prey behavior in determining diets. In: Behavioural M echanisms of Food S election (Ed. by R . N . H ughes), pp. 771–796. Berlin: Springer Verlag. Thompson, D . B. A. & Barnard, C. J. 1983. Antipredator responses in mixed species associations of lapwings, golden plovers and gulls. A nim. Behav., 31, 585–593. Vickery, W. L., G iraldeau, J.-A., Templeton, J. J., K ramer, D . L. & Chapman, C. A. 1991. Producers, scroungers, and group foraging. A m. N at., 137, 847– 863.