Behavioral Ecology Advance Access originally published online on November 27, 2007
Behavioral Ecology 2008 19(1):193-201; doi:10.1093/beheco/arm122
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Mechanisms for aggregation in animals: rule success depends on ecological variables
a Institute of Integrative and Comparative Biology, Faculty of Biological Sciences, University of Leeds, Leeds LS2 9JT, UK b Department of Physics and Centre for Mathematical Biology, University of Bath, Bath BA2 7AY, UK
Address correspondence to L.J. Morell. E-mail: l.j.morrell{at}leeds.ac.uk.
Received 30 August 2007; revised 19 October 2007; accepted 22 October 2007.
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ABSTRACT |
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Under the threat of predation, animals often group tightly together, with all group members benefiting from a reduction in predation risk through various mechanisms, including the dilution, encounter-dilution, and predator confusion effects. Additionally, the selfish herd hypothesis was first put forward by Hamilton (1971)
. He proposed that in order to reduce its risk of predation, an individual should approach its nearest neighbor, reducing its risk at the expense of those around it. Despite extensive empirical support, the selfish herd hypothesis has been criticized on theoretical grounds: approaching the nearest neighbor does not result in the observed dense aggregations, and the nearest neighbor in space is not necessarily the one that can be reached fastest. Increasingly complex movement rules have been proposed, successfully producing dense aggregations of individuals. However, no study to date has made a full comparison of the different proposed movement rules within the same modeling environment. Further, ecologically relevant parameters, such as the size and density of a population or group and the time it takes a predator to attack, have thus far been ignored. Here, we investigate the reduction in risk for animals aggregating using different strategies and demonstrate the importance of ecological parameters on risk reduction in group-living animals. We find that complex rules are most successful at reducing risk in small, compact populations, whereas simpler rules are most successful in larger, low-density populations, and when predators attack quickly after being detected by their prey. Key words: domain of danger, group living, population density, population size, predation risk, selfish herd.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONFUNDINGREFERENCES |
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Group living is a widespread phenomenon in the animal kingdom and has attracted considerable attention in many different contexts (Krause and Ruxton 2002
). One of the explanations for the evolution of animal aggregation behavior is to reduce the risk of predation. By associating closely with others, to form a group, an animal can benefit from a number of mechanisms by which its chance of falling victim to a predator decreases. These include collective vigilance, predator confusion, and the dilution of risk, and all have been shown to be effective mechanisms for reducing predation (reviewed in Krause and Ruxton 2002). The focus of the overwhelming majority of previous work has been to delineate and quantify the costs and benefits of grouping under different conditions. Here we shift the emphasis to consider the mechanisms by which groups might form. Specifically, we are interested in how the individual movement decisions of individuals combine to influence the overall distribution of individuals in space and how this in turn affects predation risk.
In many species, individuals aggregate more closely under threat of predation. Groups of sticklebacks (Gasterosteus aculeatus; Krause and Tegeder 1994), banded killifish (Fundulus diaphanous; Hoare et al. 2004), toad tadpoles (Bufo bufo; Watt et al. 1997; and Bufo maculatus; Spieler and Linsenmair 1999), and ocean skaters (Halobates robustus; Foster and Treherne 1981) all show increased densities after a predator stimulus. The "selfish herd hypothesis," developed by Hamilton (1971) is often used, and widely accepted, as an explanation for this phenomenon.
Hamilton proposed that in order to reduce the risk of predation, an individual should approach its nearest neighbor, thus reducing the area around itself that is closer to it than to all other individuals, known as its domain of danger (DOD). It is assumed that a predator appearing within an individual's DOD can successfully attack the individual; thus, animals should adopt a behavior that gives the greatest possible reduction in DOD size relative to those around it because those with the smallest DOD have the lowest probability of being closest to a randomly appearing predator. DODs are calculated for a group of individuals using Voronoi tessellation (Okabe et al. 1992). In addition to the phenomenon of overall aggregation, the selfish herd hypothesis predicts that individuals that are surrounded by others should have the smallest DODs and, therefore, suffer the lowest levels of predation, and individuals should endeavor to position themselves centrally within a group. Both these predictions have received some empirical support (Krause 1993a, 1993b, Viscido and Wethey 2002).
Despite this empirical support, however, the selfish herd hypothesis has been criticized on various theoretical grounds. First, as pointed out by (Hamilton 1971) himself, a rule of approaching the nearest neighbor does not result in the dense aggregations observed in real systems, instead producing small groups or pairs of animals (Morton et al. 1994). Hamilton (1971) suggested that large aggregations could be formed, if, once animals have reached their nearest neighbor, the resulting small groups could move together to form larger groups, proposing that individuals would see a "common advantage" in moving together toward another group using the same principle as before. Second, in a moving group, the nearest neighbor in space is not necessarily the one that can be reached fastest. Using small fish, Krause and Tegeder (1994) showed that startled individuals approached the closest individual in time rather than space as time spent turning contributed to the time taken to approach a neighbor.
Increasingly complex movement rules have been proposed to account for these difficulties, with the aim of producing compact aggregations. Table 1 summarizes the movement rules proposed to date, which mirror those proposed for attractive and repulsive forces in models of self-organization and collective behavior of groups (Couzin and Krause 2003). Morton et al. (1994) showed that the nearest neighbor (NN) rule represents a significant improvement on random movement, but that including more neighbors into the rule resulted in greater benefits, measured as median change in DOD size, and proportion of individuals decreasing their DOD. Viscido et al. (2002) showed that the most complex averaging rules (utilizing information on the positions of multiple other individuals: such as the local crowded horizon [LCH] rule) produced the densest aggregations when movement ceases and, therefore, the highest decrease in predation risk. Thus, averaging rules appear to be more advantageous than simple or optimal target rules in producing aggregations of animals.
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By definition, the DOD of an animal at the edge of an aggregation is infinite (Morton et al. 1994
): a biologically unrealistic situation. To make analysis of the models tractable, various schemes have been adopted: only central individuals have been considered (Morton et al. 1994), DODs have been bounded in a finite arena (Viscido et al. 2002), or simulations have been run in a world with no edges (a torus; Reluga and Viscido 2005). James et al. (2004) suggest that a more appropriate measure of individual predation risk is the "limited" domain of danger (LDOD). This assumes that a predator can only attack an individual successfully when it is at a limited distance from it, further away, the attack will be unsuccessful, either due to perceptual limitations (Vine 1971; Krause and Ruxton 2002) or finite strike distances (Neill and Cullen 1974) of the predator (James et al. 2004). The LDOD approach has so far only been used to investigate 2 simple movement rules: NN and time minimization (MT).
In addition to the problem of infinite DODs, there are a number of ecologically important factors that have thus far been ignored in models of aggregation behavior. In models of fish shoaling, one factor strongly influencing the emergent properties of the shoal is the size of the population under consideration (Viscido et al. 2005). We can predict, therefore, that group size and density may also have implications for the grouping decisions of the individuals within it. Animals living in small groups may use different aggregation rules to animals that tend to live in larger groups, yet most aggregation models to date have only considered a single population size (Hamilton [1971], N = 100 individuals; Morton et al. [1994], N = 100; Viscido et al. [2001], N = 100; James et al. [2004], N = 100 and N = 20, but see Reluga and Viscido 2005). Furthermore, all modeling thus far investigates DOD size (predation risk) once the DODs have reached equilibrium (Hamilton 1971; Morton et al. 1994; Viscido et al. 2001; James et al. 2004), that is, once the individuals have stopped moving. However, a predation event may commonly occur before this, while individuals are still moving into groups, and before final group sizes have settled. It is unlikely that a predator will wait, once detected by its prey, for the prey animals to maximize their chance of escape.
Here, we aim to address some of these difficulties. We utilize the LDOD approach to investigate the success of both simple and averaging movement rules, under different population sizes and densities. We are interested in how aggregations of animals are formed and how animals can benefit primarily from the encounter-dilution effect associated with group living (Turner and Pitcher 1986). We also investigate how the timing of predation events can influence the success of the different movement rules in reducing predation risk.
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METHODS |
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General model
We use the modeling framework described by James et al. (2004)
as the basis for our simulation model of aggregation behavior. N agents are placed in a 2-dimensional circular arena of radius R after a random uniform distribution. Throughout this paper, spatial dimensions are measured in meters, although the model is applicable to any unit. We focus our investigation on polar, rather than point-like agents, as most group-living animals have a front, a rear, and a preferred direction of locomotion. Thus, our agents must turn in order to move in a particular direction. The initial orientation of agents is also generated from a random uniform distribution. Each agent is surrounded by a 2-dimensional LDOD in the shape of a circle of radius rd, with a maximum area Amax = 
r
. Only isolated individuals (those at least 2rd from any others) have an LDOD area of Amax. For other individuals, the circular LDOD is reduced by any bisector generated by an agent within a distance of 2rd. In each simulation, agents are allocated one on several possible movement rules (see below). All agents are allocated the same movement rule within a simulation. The start of the simulation represents the point at which the agents begin moving. This may be because they have detected a hidden predator or been startled in some other way. We assume that the agents possess no information on the location of the potential predator, only that it has appeared in the vicinity (following Hamilton 1971).
In each time step t, until a maximum tmax, each agent identifies its target location, based on the movement rule it is following, and then rotates and moves toward its target location. We use empirically derived values for rotation speed and movement speed, based on the finding of Krause and Tegeder (1994). When startled, three-spine sticklebacks move toward the target by first rotating at a rate of 110 degrees per second and then swim at a speed of 0.15 m/s. Within each time step, each agent first rotates in order to face its target. If any time is remaining, it begins to move in the direction of the target. If further rotation is necessary, this occurs during subsequent time steps. If no rotation is needed (i.e., the agent is already facing in the direction of the target), it moves directly to the target. All individuals move simultaneously, as is likely to occur in nature, and thus each agent updates its target location and direction in every time step. Each time step in our simulations lasts 0.1 s, during which an agent can rotate up to 11° or swim 0.015 m, or about a third of a body length for a typical adult stickleback. LDOD areas are calculated after every time step and for every individual. All simulations were run in C. Resulting data were analyzed using Matlab R2006b (Mathworks 2006) and R version 2.2.1 (R Development Core Team 2006).
Movement rules
In line with Hamilton's (1971) original ideas, agents do not receive any directional information regarding the predator's approach direction (the "hiding lion", which can be heard but not seen). The incorporation of directional cues, using the LDOD approach, as seems more likely in the majority of natural systems, is a line for future enquiry (but see Viscido et al. 2001). Additionally, the habitat is assumed to be homogenous, with no areas of cover that could potentially be used for protection. Thus, movement directions are determined solely by the positions of other agents in the simulation. The rules are outlined in Table 1.
All simulations were identical apart from the movement rule. We ran 100 simulations for each rule, using different randomly chosen starting positions and orientations for each replicate simulation. However, we standardized the starting positions between movement rules, such that for each movement rule, the 100 simulations were run with the same set of starting positions and orientations.
Ecological parameters
We investigate the impact of population size and initial density on the simulation results, by altering the values of N (number of agents) and R (radius of the arena). Population density, d, is described by N/R2. We present results for 3 different population sizes and 3 different initial densities to illustrate the types of outcome that the model predicts (Figures 2–4). Finally, we investigate the effect of altering the LDOD radius rd, which can be thought of as the distance from which a predator can successfully detect or attack an individual (Figure 5). The predator appears in any part of the arena of size R2, if the predator appears within the LDOD of an individual, then it is assumed to predate that individual.
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All models so far have considered the reduction in DOD area once simulations have reached equilibrium. Here, we investigate the success of the rules at different time steps of the simulation (which can be thought of as differing predator attack times). We present the results of our simulations in 3 ways. First, as in Figure 1, we show how the mean normalized LDOD area (such that Amax = 1) changes as a function of time for simulations using each rule. In Figure 2, we show the length of time for which the mean normalized LDOD area of individuals following the NN rule (the least successful at equilibrium, Figure 1) is less than that of equivalent individuals using the LCH rule (the most successful at equilibrium, remembering that each run of the model using LCH has the same set of starting locations and orientations as each run of the model using NN). To reduce the complexity of subsequent results presented (Figures 3–5
), we also chose 2 times to inspect the data: when a predator attacks rapidly after movement begins (chosen as being after 2 s) and when the predator attacks after a greater delay (after 10 s). These points are illustrated in Figure 1 by vertical dashed lines. Second, we investigate the proportion of individuals for which LDOD area has decreased (Figure 3), again at 2 and 10 s after the simulation begins (Morton et al. 1994; Viscido et al. 2002).
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RESULTS |
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Figure 1 shows 2 examples of how LDOD area changes over time. We present the normalized LDOD area, such that Amax = 1. In Figure 1a, we use a population of N = 50 individuals in an arena R = 1.0 m (so d = 15.9 animals per square meter) and an LDOD radius rd = 0.2 m. It is clear that individuals following the more complex averaging rules reduce their DOD more rapidly, and to a smaller final size, than individuals following other simple rules. In Figure 1b, however, we show an example where the population exists at a lower density (N = 50 in an arena R = 1.995 m (so d = 4 animals per square meter) and an LDOD radius rd = 0.2 m). In this example, simpler rules such as MT and NN result in the most rapid decrease in LDOD area, although averaging rules result in a greater decrease in risk if movement continues over the longer term. In line with other studies, random movement presents no benefit to the individuals in either situation and, in fact, results in an increase in LDOD area as individuals move further apart.
In Figure 2, we investigate all possible combinations of 3 population sizes (N = 10, 20, and 50) and 3 different starting densities (d = 2, 4, and 10 animals per square meter) and look only at 2 of the possible strategies: NN (the simplest rule) and LCH (the most complex rule). First, as population size increases, the length of time for which animals using NN are safer than animals using LCH increases. Second, as density increases, the mean normalized LDOD areas of animals using the NN rule are smaller than those using the LCH rule only for a very short period of time.
In Figures 3 and 4, we investigate the impact on population size and density on the success of different movement rules. In each figure, we present the results of the model for 2 possible population sizes (N = 20 or 50) and 3 possible population densities (d = 2, 4, or 10 animals per square meter) to give 6 panels. In Figure 3, we show the proportion of individuals that successfully decrease their LDOD area. For each run of the model, we calculate the proportion of individuals for which their LDOD area is smaller after 2 s than it was at the start of the simulation and the proportion for which it is smaller after 10 s, as indicated by the dashed lines on Figure 1. We present the mean of these over 100 replicate runs. In Figure 4, we present the mean percentage change in the mean normalized LDOD area. Mean normalized LDOD area is calculated separately for each run of the model (as the mean LDOD area for all individuals in that particular simulation run). These means are then used to calculate the mean percentage change for the 2 time steps specified above. These times were arbitrarily selected to represent a predator that attacks rapidly after it has been detected by the prey, giving them little time to move (2 s), and a predator that attacks later, giving time for the prey to move to their preferred target location before attacking (10 s), reflecting previous modeling work on aggregation and selfish herd behavior (Morton et al. 1994; Viscido et al. 2002; James et al. 2004).
From Figures 3 and 4, it is immediately clear that population size and density have a strong influence on the relative success of the different movement rules. Using a random movement rule, the majority of individuals do not decrease their LDOD area. However, following any of the simple or averaging rules, more than half the individuals successfully reduce their LDOD area after 2 s of movement, and almost all individuals reduce their LDOD area after 10 s (Figure 3). At low densities (Figure 3a,b), a higher proportion of individuals decrease their LDOD areas by following simple (MT or NN) rules than by following averaging rules (5NN or LCH) after 2 s of movement. After 10 s, however, there is little difference between the movement rules, although in larger populations, simple rules may be slightly more beneficial (Figure 3b). As population density increases, the differences between the success of simple and averaging rules become smaller (Figure 3c,d), and in high-density populations (Figure 3e,f), more individuals reduce their LDOD area by following averaging rules (LCH, nNN) than by following simple rules (NN, MT), regardless of whether we consider risk reduction at 2 or 10 s. However, in high-density populations, following simple movement rules, fewer individuals decrease their LDOD area even after 10 s.
Slightly different patterns are seen in Figure 4, where we consider the size of the LDODs, rather than the proportion of individuals that decrease their LDOD area. When the population density is low (d = 2 or 4 animals per square meter, panels a–d), the simplest movement rules (NN and MT) show the greatest percentage decrease in LDOD area after 2 s. This pattern is even more pronounced in larger populations of 100 individuals where densities of 10 individuals per square meter produce similar patterns (data not shown). However, if prey are allowed to move for a longer time before the predator attacks, the averaging rules (nNN, LCH) do best. At higher population densities (Figure 4e), averaging rules are better at reducing risk even in the short term, unless population sizes are large (Figure 4f). Thus, although there may be little difference between movement rules in the proportion of individuals that decrease their risk (e.g., Figure 4c), the mean reduction in risk may still differ (e.g., Figure 4c).
It should be noted that in these simulations, movement was terminated at 10 s and not allowed to continue until equilibrium LDOD sizes had been reached. Thus, individuals are still moving. In our observations of longer simulations and in situations where equilibrium is approached or reached (Figures 3e 4), averaging rules are superior at equilibrium, and LCH proves to be the most successful at producing the greatest decrease in individual risk. However, we argue that predators may not wait until equilibrium is reached, and so our findings have biological significance.
When predators are able to attack successfully from a greater distance (rd = 0.5 m; Figure 5b), averaging rules most quickly reduce LDOD area and therefore predation risk in comparison to shorter attack distances (rd = 0.2 m; Figure 5a). At high LDOD radii, the LDOD for any individual will overlap with many of the LDODs of its neighbors, resulting in a situation similar to the unlimited DOD models. Thus, we demonstrate that population size, population density, the distance from which a predator is able to successfully attack, and the time it takes for the predator to attack after being detected all have an impact on the relative success of the different movement rules at reducing risk.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONFUNDINGREFERENCES |
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Previous models of aggregation have concluded that the more complex rules are the most successful at generating compact aggregations and therefore reducing the risk of predation. We considered 2 measures of risk reduction: the proportion of individuals decreasing their individual risk (previously used to analyze rule effectiveness (Viscido et al. 2002
; Figure 3)) and also the mean percentage decrease in LDOD area (Figures 2, 4, and 5). Both these measures are biologically relevant: the aim of each individual is to reduce its own level of risk (as in the selfish herd), but in doing so, individuals reduce the total area in which they as a group can be detected by predators, each individual thereby benefiting from the encounter-dilution effect (Krause and Ruxton 2002). We have demonstrated that ecological variables are critically important to the success of these movement rules. Predator attack speed, population size, and population density have strong influences on which movement rules provide the best protection from predators.
Animals in the wild differ in the size and density of the groups in which they live. Group sizes vary dramatically between species, but there is also variation in group size within a species (Krause and Ruxton 2002). By considering only a single population size, previous models of aggregation behavior (Hamilton 1971; Morton et al. 1994; Viscido et al. 2002) have not included this natural variation. We show that differences in group sizes may influence the most successful behavior for an individual to adopt in the face of immediate predation risk. We show that the density of a group also influences optimal risk reduction behavior, and again, different species and populations may demonstrate differences in interindividual distances (Pitcher and Parrish 1993), impacting on the most successful risk reduction behavior. Our modeling predicts that simpler rules are likely to be more prevalent in larger, lower density populations.
However, in smaller populations of moderate to high density, more complex movement rules do prove the most successful at quickly reducing individual risk and result in the most compact groups of animals. Unfortunately, these averaging rules have already been criticized as being too complex for animals to follow (Morton et al. 1994; Viscido et al. 2002), and without empirical investigation of real animals, it is impossible to tell whether this is the case. One can imagine that in order to escape rapidly from a predator, an animal must make a decision as to its movement direction in a split second. For complex averaging rules to work, the animal must already be in possession of or very quickly be able to establish the position of several of its nearest neighbors. A precise calculation of an optimal target position may be unlikely, but animals may be able to make an approximate and almost instantaneous guess at where that target location ought to be.
Unfortunately, there has been very little empirical investigation of the movement rules determining aggregation behavior, particularly when under predation threat. However, interest is growing in the self-organized behavior of animal groups (Couzin and Krause 2003) with a particular research focus on shoaling behavior in fish (Parrish et al. 2002; Kunz and Hemelrijk 2003; Viscido et al. 2005; Zheng et al. 2005). In normal shoaling behavior, Tien et al. (2004) found that chub (Semotilus atromaculatus) and dace (Rhinichthys atratulus) appear to react to the presence of only one neighbor, whereas other studies suggest that fish may react to more individuals than this (Partridge 1981; Parrish and Turchin 1997) but with nearest neighbors having the greatest influence (Partridge 1981). This suggests that under normal shoaling behavior, animals may be aware of the locations of multiple neighbors and could therefore use this information to aggregate more tightly under the threat of predation. Only a single study has investigated aggregation rules under the risk of predation: in sticklebacks, aggregation behavior is more consistent with MT than NN rules (Krause and Tegeder 1994). Other, more complex, rules remain untested in an experimental setting.
Given the sparseness of empirical investigation into selfish herd movement rules, there is little evidence to either support or contradict the higher order rules. On one hand, fish show a preference for larger shoals over smaller ones, and this preference is stronger when perceived predation risk is high (Hager and Helfman 1991; Krause and Godin 1994; Svensson et al. 2000), suggesting the ability to distinguish and respond to large groups of conspecifics. However, shoal choice is random if the time permitted for assessment is short (Krause et al. 1997), and sticklebacks show a trade-off between the distance and number of individuals in stimulus shoals, preferring small nearby shoals over more distant, larger shoals (Tegeder and Krause 1995). These authors argue that shoal choice decisions are constrained by an apparent perceptual limit (numerosity effect), and fish are unable to distinguish accurately between shoal sizes above a certain size, providing some evidence for lower order rules. There is a clear need for further empirical investigation of the movement rules used by animals, perhaps matching observed movement patterns to the predictions of models.
Any decrease in the DOD of an individual represents an increase in safety for that individual. In previous work, the proportion of individuals decreasing their DOD was used as a measure of the success of any given movement rule (Morton et al. 1994; Viscido et al. 2002). We found that in some cases, the majority of individuals reduced their LDOD area, regardless of the movement rule they were following and suggesting that all rules were successful at generating aggregations of animals (Figure 3). If all individuals decrease their DOD, this does not necessarily represent an increase in safety through the selfish herd effect, as it is the decrease relative to others that is important, and selfish herds require that movement is at the expense of others (Hamilton 1971). However, the average LDOD area of all individuals fell more for one movement rule than for another (Figure 4). This means that the total area in which predators are able to detect or attack the group is reduced—known as the encounter-dilution effect (Turner and Pitcher 1986) and often stated as one of the benefits of group living (Krause and Ruxton 2002). Thus, although 2 individuals moving together have the same relative risk regardless of how far apart they are, by moving together they may reduce the chance that a randomly appearing predator encounters them in the first instance. As mentioned in the Introduction, one criticism of the simple rules is that although they reduce predation risk, they do not produce the types of dense aggregation seen in the wild, producing small clusters instead of single compact herds. As we have simply investigated existing rules here, this issue remains: simple rules result in small clusters, and more complex rules result in dense aggregations. However, the small clusters can form much more rapidly than single dense aggregations and may provide protection from predation in this way.
We assumed here that predators attack the closest individual, but this is not necessarily the case. Predators may use an attack strategy that is most likely to be successful, such as attacking isolated individuals (to combat the confusion effect, Tosh et al. 2006) or target phenotypically conspicuous individuals (the oddity effect, Landeau and Terborgh 1986). Such predator strategies may influence the success of different movement rules. We also find that the size of the LDOD influences the success of the different movement rules. Large, overlapping LDODs mean that complex movement rules are most successful. We consider the LDOD to be a measure of the perceptual limit of the predator (Vine 1971). A randomly appearing predator knows that the prey are nearby, but it does not know their exact location until it launches an attack. Thus, predators may appear in areas that are not within any individual's LDOD.
Here, we considered movement rules in isolation—all individuals in a population used the same rule. James et al. (2004) considered the performance of mutant strategies within a population using a single movement rule, finding that although a population using the NN rule could be invaded by a population using MT, the reverse case was not true: MT was stable against invasion by NN, suggesting that MT is evolutionarily stable while NN is not (James et al. 2004). Reluga and Viscido (2005) used an evolutionary approach to demonstrate how the LCH rule could evolve from simple rules and found that the population evolved to take account of increasing number of neighbors, resulting in tighter aggregations and greater reductions in risk for centrally positioned individuals (peripheral individuals had infinite domains of danger). However, the criticism raised by previous authors that taking account of multiple neighbors may be too complex remains a problem (Viscido et al. 2002). Using an evolutionary approach to modeling 2-dimensional swarming behavior, Wood and Ackland (2007) found that under the risk of predation the zone of orientation around an individual (individuals align themselves with others in this zone) evolves to be either large or small, resulting in different flock dynamics and suggesting that either averaging or simple rules could evolve.
Our results suggest that simple rules do not necessarily need to be discarded in favor of more complex ones as they may benefit individuals using them in different ways. The rules presented here need not represent the full spectrum of possibilities. Hierarchical rules, where individuals follow one rule until a certain criteria has been met and then follow another (such as Hamilton's [1971] suggestion that individuals move to form small groups, then move together as a group to merge with other groups) have yet to be investigated. Alternatively, movement rules may differ between individuals. Decisions may be state dependent (Rands et al. 2004) if an individual bases its movement decision on its perceived level of risk, for example. Habitat heterogeneity is another factor that may influence escape decisions, if animals use habitat features as cover. Finally, individuals may take directional cues from the predator while it is still too far away to attack (Romey 1996; Viscido et al. 2001), which can result in increased group cohesiveness. However, any movement rule needs to be realistic at the level of the individual, as well as producing the phenomenon of interest (Morton et al. 1994; Parrish and Edelstein-Keshet 1999; Viscido et al. 2002) and further empirical work is clearly needed.
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FUNDING |
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Natural Environment Research Council Postdoctoral Fellowship (NE/D008921/1 to L.J.M.)
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ACKNOWLEDGEMENTS |
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Paul Bennett wrote the original program on which this work is based. We would like to thank Jens Krause for useful discussions and Graeme Ruxton and 2 anonymous referees for insightful comments on the manuscript.
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REFERENCES |
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Couzin ID, Krause J. Self-organization and collective behavior in vertebrates. Adv Study Behav (2003) 32:1–75.[CrossRef]
Foster WA, Treherne JE. Evidence for the dilution effect in the selfish herd from fish predation on a marine insect. Nature (1981) 293:466–467.[CrossRef][Web of Science]
Hager MC, Helfman GS. Safety in numbers: shoal size choice by minnows under predatory threat. Behav Ecol Sociobiol (1991) 29:271–276.[CrossRef][Web of Science]
Hamilton WD. Geometry for the selfish herd. J Theor Biol (1971) 31:295–311.[CrossRef][Web of Science][Medline]
Hoare DJ, Couzin ID, Godin JGJ, Krause J. Context-dependent group size choice in fish. Anim Behav (2004) 67:155–164.[CrossRef][Web of Science]
James R, Bennett PG, Krause J. Geometry for mutualistic and selfish herds: the limited domain of danger. J Theor Biol (2004) 228:107–113.[CrossRef][Web of Science][Medline]
Krause J. The effect of ‘Schreckstoff’ on the shoaling behaviour of the minnow: a test of Hamilton's selfish herd theory. Anim Behav (1993a) 45:1019–1024.[CrossRef][Web of Science]
Krause J. Positioning behaviour in fish shoals: a cost-benefit analysis. J Fish. Biol (1993b) 43(Suppl A):309–314.[Web of Science]
Krause J, Godin JGJ. Shoal choice in the banded killifish (Fundulus diaphanus, Teleostei, Cyprinodontidae): effects of predation risk, fish size, species composition and size of shoals. Ethology (1994) 98:128–136.[Web of Science]
Krause J, Rubenstein D, Brown D. Shoal choice behaviour in fish: the relationship between assessment time and assessment quality. Behaviour (1997) 134:1051–1062.[CrossRef]
Krause J, Ruxton GD. Living in groups. (2002) Oxford: Oxford University Press.
Krause J, Tegeder RW. The mechanism of aggregation behaviour in fish shoals: individuals minimize approach time to neighbours. Anim Behav (1994) 48:353–359.[CrossRef][Web of Science]
Kunz H, Hemelrijk CK. Artificial fish schools: collective effects of school size, body size, and body form. Artif Life (2003) 9:237–253.[CrossRef][Web of Science][Medline]
Landeau L, Terborgh J. Oddity and the confusion effect in predation. Anim Behav (1986) 34:1372–1380.[CrossRef][Web of Science]
Mathworks. In: Matlab 2006b (2006) Natick (MA): Mathworks Inc.
Morton TL, Haefner JW, Nugala V, Decino RD, Mendes L. The selfish herd revisited: do simple movement rules reduce relative predation risk. J Theor Biol (1994) 167:73–79.[CrossRef][Web of Science]
Neill SRS, Cullen JM. Experiments on whether schooling by their prey affects hunting behavior of cephalopods and fish predators. J Zool (1974) 172:549–569.[Web of Science]
Okabe A, Boots BN, Sugihara K. Spatial tessellations: concepts and applications of voronoi diagrams. (1992) Chichester (UK): Wiley.
Parrish JK, Edelstein-Keshet L. Complexity, pattern, and evolutionary trade-offs in animal aggregation. Science (1999) 284:99–101.
Parrish JK, Turchin P. Individual decisions, traffic rules, and emergent patterns in schooling fish. In: Animal groups in three dimensions—Parrish JK, Hamner WM, eds. (1997) Cambridge (UK): Cambridge University Press.
Parrish JK, Viscido SV, Grunbaum D. Self-organized fish schools: an examination of emergent properties. Biol Bull (2002) 202:296–305.
Partridge BL. Internal dynamics and the interrelations of fish in schools. J Comp Physiol (1981) 144:313–325.[CrossRef]
Pitcher TJ, Parrish JK. Functions of shoaling behaviour in teleosts. In: Behaviour of teleost fishes—Pitcher TJ, ed. (1993) London: Chapman and Hall.
R Development Core Team. R: a language and environment for statistical computing [Internet]. (2006) Vienna (Austria): R Foundation for Statistical Computing. Available from: http://www.R-project.org. Accessed 13 Nov 2007.
Rands SA, Pettifor RA, Rowcliffe JM, Cowlishaw G. State-dependent foraging rules for social animals in selfish herds. Proc R Soc Lond B Biol Sci (2004) 271:2613–2620.[Medline]
Reluga TC, Viscido S. Simulated evolution of selfish herd behavior. J Theor Biol (2005) 234:213–225.[CrossRef][Web of Science][Medline]
Romey WL. Individual differences make a difference in the trajectories of simulated schools of fish. Ecol Modell (1996) 92:65–77.[CrossRef][Web of Science]
Spieler M, Linsenmair KE. Aggregation behaviour of Bufo maculatus tadpoles as an antipredator mechanism. Ethology (1999) 105:665–686.[CrossRef][Web of Science]
Svensson PA, Barber I, Forsgren E. Shoaling behaviour of the two-spotted goby. J Fish Biol (2000) 56:1477–1487.[CrossRef][Web of Science]
Tegeder RW, Krause J. Density dependence and numerosity in fright stimulated aggregation behaviour of shoaling fish. Philos Trans R Soc Lond B Biol Sci (1995) 350:381–390.
Tien JH, Levin SA, Rubenstein DI. Dynamics of fish shoals: identifying key decision rules. Evol Ecol Res (2004) 6:555–565.
Tosh CR, Jackson AL, Ruxton GD. The confusion effect in predatory neural networks. Am Nat (2006) 167:E52–E65.[CrossRef][Web of Science][Medline]
Turner GF, Pitcher TJ. Attack abatement: a model for group protection by combined avoidance and dilution. Am Nat (1986) 128:228–240.[CrossRef][Web of Science]
Vine I. Risk of visual detection and pursuit by a predator and selective advantage of flocking behaviour. J Theor Biol (1971) 30:405–422.[CrossRef][Web of Science][Medline]
Viscido SV, Miller M, Wethey DS. The response of a selfish herd to an attack from outside the group perimeter. J Theor Biol (2001) 208:315–328.[CrossRef][Web of Science][Medline]
Viscido SV, Miller M, Wethey DS. The dilemma of the selfish herd: the search for a realistic movement rule. J Theor Biol (2002) 217:183–194.[CrossRef][Web of Science][Medline]
Viscido SV, Parrish JK, Grunbaum D. The effect of population size and number of influential neighbors on the emergent properties of fish schools. Ecol Modell (2005) 183:347–363.[CrossRef][Web of Science]
Viscido SV, Wethey DS. Quantitative analysis of fiddler crab flock movement: evidence for ‘selfish herd’ behaviour. Anim Behav (2002) 63:735–741.[CrossRef][Web of Science]
Watt PJ, Nottingham SF, Young S. Toad tadpole aggregation behaviour: evidence for a predator avoidance function. Anim Behav (1997) 54:865–872.[CrossRef][Web of Science][Medline]
Wood AJ, Ackland GJ. Evolving the selfish herd: emergence of distinct aggregating strategies in an individual-based model. Proc R Soc Lond B Biol Sci (2007) 274:1637–1642.[Medline]
Zheng M, Kashimori Y, Hoshino O, Fujita K, Kambara T. Behavior pattern (innate action) of individuals in fish schools generating efficient collective evasion from predation. J Theor Biol (2005) 235:153–167.[CrossRef][Web of Science][Medline]
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