Behavioral Ecology Advance Access originally published online on August 24, 2005
Behavioral Ecology 2005 16(6):989-993; doi:10.1093/beheco/ari077
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Harvesting resources in groups or alone: the case of renewing patches
a Faculty of Veterinary Medicine, University of Montréal, P.O. Box 5000, St-Hyacinthe, Québec J2S 7C6, Canada, and b Institute of Biomedical Life Sciences, University of Glasgow, Glasgow G12 8QQ, UK
Address correspondence to G. Beauchamp. E-mail: guy.beauchamp{at}umontreal.ca.
Received 4 May 2005; revised 4 July 2005; accepted 14 July 2005.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHE MODELRESULTS AND DISCUSSIONGENERAL DISCUSSIONREFERENCES |
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Group foraging has been proposed to be the most efficient manner with which to exploit habitats with renewing patches as individuals in groups are less likely to revisit patches that have already been exploited recently by others. However, to avoid a group-selection argument, it is necessary to compare the success of solitary and group foraging tactics when each competes with the other. We used a genetic algorithm approach to examine the costs and benefits of exploiting renewing resources in a spatially and temporally explicit habitat, thus controlling the time course of resource renewal and including the time cost of traveling between patches, which may be a significant factor for group foragers that deplete patches more quickly. Results indicate that group foragers fare more poorly than an equivalent number of solitary foragers in the same habitat unless the rate of resource renewal is very low. The low revisitation rate by group foragers allows resources to replenish more fully, thus maintaining the resource level across the habitat at a higher level. In contrast, solitary foragers, who revisit previously exploited patches more often, maintain the same resources at a lower level. Nevertheless, a pure population of group foragers can be readily invaded by solitary foragers even when the rate of renewal is at low levels. We conclude that while group foraging may be an efficient tactic to exploit renewing resources, it is not a stable strategy under the circumstances examined in this model.
Key words: genetic algorithm approach, group foraging, resource renewal, search tactics, travel time.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHE MODELRESULTS AND DISCUSSIONGENERAL DISCUSSIONREFERENCES |
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Many animals exploit resources that are patchily distributed in the environment. Further, these patches are often finite and their exploitation can lead to exhaustion, requiring the forager to abandon a patch in search of another (Charnov et al., 1976
). Renewal of resources in a patch often occurs after abandonment by foragers. For example, leaves and shoots grow back (Watts, 1998), nectar reserves replenish (Kamil, 1978), or prey items can return (Davies and Houston, 1981) after visits by foragers. The problem for an optimal forager is thus to determine the best spatial and temporal pattern of visits to patches in the habitat so as to maximize the intake rate (Bell, 1991). Returning too quickly to a recently exhausted patch leaves little time for a patch to replenish, but returning too late leaves the door open to exploitation of unattended resources by competitors. Optimal solutions have been examined mostly from the point of view of solitary foragers searching for resources independent of one another, although these individuals share an environment and so may compete indirectly for resources (Williams and Thompson, 1998). However, in many species, individuals have the option of foraging in groups. Here, we are concerned with the exploitation of renewing resources by groups of foragers.
Foraging in groups has usually been considered the most efficient manner to exploit renewing resources (Cody, 1971; Miller, 1922; Schoener, 1971). In groups, where all foragers move together from patches to patches, individuals can regulate the timing of access to resources to a greater extent than independent foragers who will often stumble on patches recently exploited by others. This line of reasoning, namely, comparing a population of solitary foragers to a population of group foragers, relies, however, on a group-selection argument; it does not address why foragers join or remain in the group to reap the benefits of communal harvesting and thus fails to consider fitness at the individual level. A similar conceptual problem arises when determining the size of a group that maximizes fitness for all group members. This optimal size has been shown, however, to be unstable because solitary foragers with low fitness are expected to continue joining such a group until the fitness in the group is reduced to the level experienced by solitary individuals (Beauchamp and Fernandez-Juricic, 2005; Giraldeau and Caraco, 2000). The key question, therefore, is how a solitary forager would fare in a habitat dominated by group foragers and vice versa. The evolutionary stability of group harvesting has therefore not been examined (Maynard Smith, 1974).
Previous work has also neglected an important cost of group foraging, namely, travel time between patches (Cody, 1971; Schoener, 1971; Zemel and Lubin, 1995). Groups exploit resources in a patch more quickly than solitary foragers, leading to faster patch depletion. As a consequence, individuals in groups often spend more time searching for patches than solitary foragers during a foraging episode, at the expense of long-term intake rate (e.g., Gillespie and Chapman, 2001; Glück, 1987; Tsubaki and Kitching, 1982). It is therefore not immediately obvious how the balance of costs and benefits will be struck for solitary and group foragers exploiting renewing resources.
The case where patches do not recover after exploitation has been investigated recently (Beauchamp, 2005). This previous study investigated the proposal that increased avoidance of food patches exploited by others would be an adaptive benefit to group foraging. However, results demonstrated that this benefit was always outweighed by the increased time cost of searching for new patches caused by a group of foragers depleting a patch of given size quicker than a single individual. Hence, it appears that group foraging would not lead to higher mean reward rates when patches do not renew.
Here, we extend the model to renewing resources and also examine for the first time the stability of each strategy as foragers using the alternative strategy intrude in the habitat. Using a genetic algorithm approach (Huse et al., 1999), we examined the costs and benefits of exploiting renewing resources in a spatially and temporally explicit habitat. We could thus control the time course of depletion and subsequent renewal of resources and also include the time cost of traveling between patches. We pitted the foraging success of a group of foragers against that of the same number of foragers searching for the same resources but independent of one another. We then examined the stability of the two strategies by allowing invasion of a pure population by individuals using the alternative foraging strategy.
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THE MODEL |
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TOPABSTRACTINTRODUCTIONTHE MODELRESULTS AND DISCUSSIONGENERAL DISCUSSIONREFERENCES |
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We consider a population of M (M = 20) foragers. Throughout a generation, each forager has a fixed strategy (S = solitary foraging or G = group foraging). The differences between these strategies will be explained below.
The environment is an N x N grid of possible positions (N = 30). At the start of the first generation, the M foragers are distributed randomly throughout the habitat. At the start of the simulation, P (P = 90) food patches are distributed randomly around the habitat, subject to the restriction that no two patches can occupy the same site. Each food patch initially contains f (f = 50) food units. Patches can be exhausted by foragers, leaving no food behind, but an exhausted patch can also recover after the foragers have abandoned it. The combination of 20 foragers exploiting 90 food patches each containing 50 food units ensures that exhaustion of a given patch can occur so that foragers can encounter several patches during the duration of a generation. In addition, the number of foragers has to be sufficiently large to create indirect competition for food patches when individuals forage solitarily. We explored below the consequences of using different parameter values.
After abandonment, the patch is shifted to another randomly selected position on the grid that does not currently contain a patch. This patch-movement rule was adopted to prevent immediate and therefore wasteful return of foragers to a just-exhausted patch. Such a premature return is clearly ecologically unrealistic because the foragers are expected to remember, at the very least, the positions of their most recent patch choices. However, the random-walk strategy described below does not include a memory factor,and so the patch-movement rule has been introduced to achieve the same ends. The patch then recovers over time, with the food present on the patch F being a function of the number of time steps since the patch was exhausted (
), according to the equation
 | (1) |
A generation lasts for T (T = 400) time steps. During a time step, a forager that is on a location containing food consumes R (R = 1) food units. Foragers not able to forage at the current time step, because their current location holds food values less than R, move to one of the four orthogonal nearest neighbor patches chosen at random. All the group foragers at a given position without food are constrained, however, to select the same nearest neighbor position; groups of gregarious individuals remain together once they have aggregated by chance. All gregarious foragers remain in a patch with food until no food is left.
At the end of the generation, M new foragers are created for the next generation replacing each member of the older cohort. Each new forager selects a single parent randomly and independently from the top 50% of foragers in the preceding generation. Each forager at the end of a generation is ranked according to the intake rate defined as the number of food items collected over one generation divided by T. Each new forager begins the new generation at the spatial position at which their parent finished the preceding generation and takes the same state (G or S) as their parent subject to a small mutation rate µ (µ = 0.005). That is, with probability µ they take the opposite state to their parent, otherwise they take their parent's state. This process was repeated for 100 generations, which was sufficient to obtain steady-state behavior in all cases examined here. This steady-state behavior represents a unique solution to the problem.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONTHE MODELRESULTS AND DISCUSSIONGENERAL DISCUSSIONREFERENCES |
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If we set µ = 0 and start with all individuals in the same state, then we can explore the performance of a population made up entirely of similar individuals. We call the two possibilities pure G and pure S. We compare the effect of the two different strategies by starting with either 20 S or 20 G individuals and exploring how the mean intake rate of individuals is affected by the rate of patch recovery. Mean intake rate is defined as the mean intake of individuals per generation averaged over generations 20–100. We ignored the first 20 generations to remove the effect of the initial conditions in order to better capture equilibrium behavior. For the default values, solitary individuals are able to achieve a much higher intake rate than group foragers (Figure 1a). However, if patch recovery rate is reduced by reducing the value of y, the intake rate of solitary individuals is affected more drastically than that of group foragers. Indeed, when y is reduced to extremely low values, intake can actually be higher for the group foragers than for a population with the same number of solitary individuals (Figure 1b).
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However, the recovery rate needs to be very low for this to occur. A y value of 0.004 implies that an exhausted patch has only recovered to 10% of its maximum value after 800 time steps (two full generations) and takes five generations to recover to 94% of its maximum value. This advantage to a pure G population occurs because the way the group foragers exploit the environment decreases the likelihood that a patch will be revisited before it has fully recovered and so allows them to maintain a higher food standing stock in the environment (Figure 2). This difference in standing crop can be sufficiently large to compensate for the less efficient way that the G individuals harvest a given food resource. Less efficient harvest occurs here because group foragers deplete patches quickly and thus must return quickly to searching for another patch. However, when patch regeneration is fast (i.e., high values of y), then the standing stock of food is similar for both the pure G and pure S populations, and so the pure S individuals do better because G individuals pay a competition price for being in a big group on a patch but do not find patches any quicker than a single individual.
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We now introduce the possibility of frequency-dependent competition, by introducing a nonnegligible mutation rate (µ = 0.005), thus allowing S and G individuals to coexist in the same population. When frequency-dependent competition is introduced, the evolutionary trajectory converges to a population dominated by S individuals, with irregular small outbreaks of G individuals occurring as a result of mutation events no matter the starting conditions. Not surprisingly, this is true under the conditions where a population of pure S foragers could do better than a population of pure G foragers. However, the same is true for low y values, where a pure G population would do better than a pure S population. A pure G population can be successfully invaded by S individuals who then come to dominate the population, and although small outbreaks of G continue to occur through mutation, these outbreaks are contained in size (Figure 3, where y = 0.004).
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These general results are robust to changes in the parameter values, in that it is possible to find parameter values where a pure G population can obtain higher mean intake rates than a pure S population. Such situations are characterized by the pure G population being able to maintain a considerably higher standing stock of food in the environment than the pure S population. However, under all parameter value combinations, if S individuals arise by mutation, then the S strategy can invade a pure G population and dominate from then on, with only small isolated outbursts of the G strategy being driven by mutation.
If we reduce the number of foragers, competition decreases and so mean intake rates increase (compare Figure 4 with Figure 1b). Competition is more of a problem for group foragers, and so reducing the population size has a more beneficial effect on the pure G population than on the pure S. This can be seen by comparing the mean intake rates at high y values in Figures 1b and 4. Conversely, the smaller number of foragers means that patches are likely to have more time to recover before being rediscovered, and so the advantage of pure G populations at low y values is less when populations are lower. This explains why even lower y values are needed for the pure G strategy to have higher mean intake rates than the pure S strategy when there are 10 individuals (Figure 4) than when there are 20 individuals (Figure 1b). Reducing the number of patches or the size of patches, of course, reduces intake rates but has little effect on the relative effectiveness of the pure G and pure S strategies (Figure 4). This is because changing the number of food patches or the size of food patches does influence the availability of food and the rate at which patches are rediscovered, but in qualitatively similar ways for both types of foragers.
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GENERAL DISCUSSION |
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TOPABSTRACTINTRODUCTIONTHE MODELRESULTS AND DISCUSSIONGENERAL DISCUSSIONREFERENCES |
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Results from the genetic algorithm model indicate that group foragers fare more poorly than an equivalent number of solitary foragers in the same habitat unless the rate of resource renewal is very low. The low revisitation rate by group foragers allows resources to replenish more fully, thus maintaining the resource level across the habitat at a higher level. In contrast, solitary foragers, who revisit previously exploited patches more often, maintain those same resources at a lower level, slowing down renewal. Nevertheless, a pure population of group foragers can readily be invaded by solitary foragers even when the rate of renewal is at low levels. Sensitivity analyses revealed that this conclusion is robust with respect to population size and patch characteristics.
We show that group foraging, while providing higher fitness under some circumstances, is not a stable strategy with evolution leading to the emergence of solitary foraging where all individuals achieve lower fitness. This is reminiscent of other foraging games, such as producer and scrounger, where individuals using the scrounger tactic, which involves no search for food, can invade a group of producers searching for resources independently, bringing the foraging success of everyone down (Giraldeau and Beauchamp, 1999). Explicit consideration of the evolutionary stability of group foraging tactics thus indicates generally that the benefits generated by group living can be exploited successfully by selfish individuals.
Earlier work with solitary foragers harvesting renewing resources indicates that systematic foraging strategies, such as traplining where returns to previously exploited patches are timed more precisely, are generally more efficient than stochastic movement strategies that fail to use any information from previous patch encounters (Cody, 1971; Kamil, 1978; Ohashi and Thompson, 2005; Possingham, 1989). In our model, we adopted a random-walk strategy for both solitary and group foragers with explicit avoidance of the last visited food patch only. While this allowed us to compare the fitness of the two strategies in the same habitat using the same rules of movements, one wonders whether group foragers, who could regulate visits to patches more easily than solitary foragers, might have enjoyed a higher intake rate using a more systematic search strategy. We believe that this is not the case. In fact, the more systematic the search, the more likely solitary foragers could track the movement of a group and time patch visits so as to arrive just before the group foragers.
Our modified random walk is one of the simplest search tactics available to explore a habitat, and obviously, more complex search tactics involving more memory of recently visited patches and different turning probabilities are available to exploit renewing resources (Higgins and Strauss, 2004). It would remain interesting to examine the success of solitary and group foragers using different search tactics. There is also the possibility that solitary and group foragers could use different search tactics and that different search tactics are more suited for groups of different sizes (Smith, 1977; Wheal, 1996).
Group foragers have also been thought to regulate not only the quantity but also the quality of renewing resources. For instance, periodical returns to browsing patches may maximize food quality for certain herbivores because quality of the sward may vary with the amount of previous browsing (Fox and Kahlert, 2003; McNaughton, 1984). Our model ignored changes in food quality but only focused on the amount of food present in a patch. Including changes in food quality through time would probably increase the range of values over which group foraging provides an advantage over solitary foraging. However, the fact that a population of group foragers can be invaded by solitary foragers would be problematic whether or not resources vary in quality with time since the last visit.
In a habitat with renewing resources, we believe group foraging could be useful in two contexts: (1) when the foraging benefits of solitary foraging are offset by higher fitness costs and (2) when group foragers can defend a joint territory. In the first scenario, the higher fitness costs of solitary foraging will prevent individuals from leaving groups. For instance, predation risk usually decreases with group size, placing a premium on solitary individuals to join a group (Krause and Ruxton, 2002). This may be the case for some species of birds, such as geese (Fox and Kahlert, 2003; Prins et al., 1980; Rowcliffe et al., 1995), finches (Cody, 1971), or plovers (Barnard and Thompson, 1985), efficiently timing their returns to renewing patches with apparently little losses to solitary foragers. In the second scenario, a group defends a territory and thus wards off intrusions by other foragers. Efficient exploitation of renewing resources has already been documented for solitary territorial foragers (Davies and Houston, 1981; Kamil, 1978; Thompson, 1996). Moving together, individuals in a territorial group could also regulate more effectively returns to previously exploited patches with little competition. This may be the case for primates with extensive home ranges (Janson, 1998; Watts, 1998) returning to previously exploited areas in their home range after a delay. These possibilities could be explored more fully in future extensions of the model.
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ACKNOWLEDGEMENTS |
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We thank M. Hauber and two anonymous referees for useful comments on the paper.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONTHE MODELRESULTS AND DISCUSSIONGENERAL DISCUSSIONREFERENCES |
|---|
Barnard CJ, Thompson DBA, 1985. Gulls and plovers: the ecology and behaviour of mixed-species feeding groups. London: Croom Helm.
Beauchamp G, 2005. Does group foraging promote efficient exploitation of resources? Oikos (in press).
Beauchamp G, Fernandez-Juricic E, 2005. The group-size paradox: effects of learning and patch departure rules. Behav Ecol 16:352–357.
Bell WJ, 1991. Searching behaviour. London: Chapman & Hall.
Charnov EL, Orians GH, Hyatt K, 1976. Ecological implications of resource depression. Am Nat 110:247–259.[CrossRef]
Cody ML, 1971. Finch flocks in the Mojave Desert. Theor Popul Biol 2:142–158.[CrossRef][Medline]
Davies NB, Houston AI, 1981. Owners and satellites: the economics of territory defence in the pied wagtail, Motacilla alba. J Anim Ecol 50:157–180.
Fox AD, Kahlert J, 2003. Repeated grazing of a salt marsh grass by moulting greylag geese Anser anser—does sequential harvesting optimise biomass or protein gain? J Avian Biol 34:89–96.[CrossRef]
Gillespie TR, Chapman CA, 2001. Determinants of group size in the red colobus monkey (Procolobus badius): an evaluation of the generality of the ecological-constraint model. Behav Ecol Sociobiol 50:329–338.[CrossRef]
Giraldeau L-A, Beauchamp G, 1999. Food exploitation: searching for the optimal joining policy. Trends Ecol Evol 14:102–106.[CrossRef][Medline]
Giraldeau L-A, Caraco T, 2000. Social foraging theory. Princeton: Princeton University Press.
Glück E, 1987. Benefits and costs of social foraging and optimal flock size in goldfinches (Carduelis carduelis). Ethology 74:65–79.
Higgins CL, Strauss RE, 2004. Discrimination and classification of foraging paths produced by search-tactic models. Behav Ecol 15:248–254.
Huse G, Strand E, Giske J, 1999. Implementing behaviour in individual-based models using neural networks and genetic algorithms. Evol Ecol 13:469–483.[CrossRef]
Janson CH, 1998. Experimental evidence for spatial memory in foraging wild capuchin monkeys, Cebus apella. Anim Behav 55:1229–1243.[CrossRef][Web of Science][Medline]
Kamil AC, 1978. Systematic foraging for nectar by the amakihi (Loxops virens). J Comp Psychol 92:388–396.[CrossRef]
Krause J, Ruxton GD, 2002. Living in groups. Oxford: Oxford University Press.
Maynard Smith J, 1974. The theory of games and the evolution of animal conflicts. J Theor Biol 47:209–221.[CrossRef][Web of Science][Medline]
McNaughton SJ, 1984. Grazing lawns: animals in herds, plant form and coevolution. Am Nat 124:863–886.[CrossRef]
Miller RC, 1922. The significance of the gregarious habit. Ecology 3:122–126.[CrossRef]
Ohashi K, Thompson JD, 2005. Efficient harvesting of renewing resources. Behav Ecol 16:592–605.
Possingham HP, 1989. The distribution and abundance of resources encountered by a forager. Am Nat 133:42–60.[CrossRef]
Prins HHT, Ydenberg R, Drent R, 1980. The interaction of brent geese Branta bernicla and sea plantain Plantago maritima during spring staging: field observations and experiments. Acta Bot Neerl 29:585–596.
Rowcliffe JM, Watkinson AR, Sutherland WJ, Vickery JA, 1995. Cyclic winter grazing patterns in Brent Geese and the regrowth of salt-marsh grass. Funct Ecol 9:931–941.[CrossRef]
Schoener TW, 1971. Theory of feeding strategies. Annu Rev Ecol Syst 2:369–404.[CrossRef]
Smith JNM, 1977. Feeding rates, search paths, and surveillance for predators in great-tailed grackle flocks. Can J Zool 55:891–898.
Thompson JD, 1996. Trapline foraging by bumblebees. I. Persistence of flight-path geometry. Behav Ecol 7:158–164.
Tsubaki Y, Kitching RI, 1982. Group feeding as a strategy for exploiting food resources in the burnet moth Pryeria sinica. Oecologia 55:12–20.[CrossRef]
Watts DP, 1998. Long-term habitat use by mountain gorilla (Gorilla gorilla beringei). II. Reuse of foraging areas in relation to resource abundance, quality and depletion. Int J Primatol 19:681–702.[CrossRef]
Wheal M, 1996. Movement patterns of honeyeaters foraging alone and in flocks for nectar of Astroloma conostephioides in Hale Conservation Park, South Australia. Emu 96:55–61.
Williams NM, Thompson JD, 1998. Trapline foraging by bumble bees. III. Temporal patterns of visitation and foraging success at single plants. Behav Ecol 9:612–621.
Zemel A, Lubin Y, 1995. Inter-group competition and stable group sizes. Anim Behav 50:485–488.[CrossRef]
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