The dilemma of the selfish herd: the search for a realistic movement rule

The selfish herd hypothesis predicts that aggregations form because individuals move toward one another to minimize their own predation risk. The "dilemma of the selfish herd" is that movement rules that are easy for individuals to follow, fail to produce true aggregations, while rules that produce aggregations require individual behavior so complex that one may doubt most animals can follow them. If natural selection at the individual level is responsible for herding behavior, a solution to the dilemma must exist. Using computer simulations, we examined four different movement rules. Relative predation risk was different for all four movement rules (p<0.05). We defined three criteria for measuring the quality of a movement rule. A good movement rule should (a) be statistically likely to benefit an individual that follows it, (b) be something we can imagine most animals are capable of following, and (c) result in a centrally compact flock. The local crowded horizon rule, which allowed individuals to take the positions of many flock-mates into account, but decreased the influence of flock-mates with distance, best satisfied these criteria. The local crowded horizon rule was very sensitive to the animal's perceptive ability. Therefore, the animal's ability to detect its neighbors is an important factor in the dynamics of group formation.     

The response of a selfish herd to an attack from outside the group perimeter

According to the selfish herd hypothesis, animals can decrease predation risk by moving toward one another if the predator can appear anywhere and will attack the nearest target. Previous studies have shown that aggregations can form using simple movement rules designed to decrease each animal's Domain of Danger. However, if the predator attacks from outside the group's perimeter, these simple movement rules might not lead to aggregation. To test whether simple selfish movement rules would decrease predation risk for those situations when the predator attacks from outside the flock perimeter, we constructed a computer model that allowed flocks of 75 simulated fiddler crabs to react to one another, and to a predator attacking from 7 m away. We attacked simulated crab flocks with predators of different sizes and attack speeds, and computed relative predation risk after 120 time steps. Final trajectories showed flight toward the center of the flock, but curving away from the predator. Path curvature depended on the predator's size and approach speed. The average crab experienced a greater decrease in predation risk when the predator was small or slow moving. Regardless of the predator's size and speed, however, predation risk always decreased as long as crabs took their flock-mates into account. We conclude that, even when flight away from an external predator occurs, the selfish avoidance of danger can lead to aggregation.     

Mechanisms for aggregation in animals: rule success depends on ecological variables

Under the threat of predation, animals often group tightly together,with all group members benefiting from a reduction in predationrisk through various mechanisms, including the dilution, encounter-dilution,and predator confusion effects. Additionally, the selfish herdhypothesis was first put forward by Hamilton (1971). He proposedthat in order to reduce its risk of predation, an individualshould approach its nearest neighbor, reducing its risk at theexpense of those around it. Despite extensive empirical support,the selfish herd hypothesis has been criticized on theoreticalgrounds: approaching the nearest neighbor does not result inthe observed dense aggregations, and the nearest neighbor inspace is not necessarily the one that can be reached fastest.Increasingly complex movement rules have been proposed, successfullyproducing dense aggregations of individuals. However, no studyto date has made a full comparison of the different proposedmovement rules within the same modeling environment. Further,ecologically relevant parameters, such as the size and densityof a population or group and the time it takes a predator toattack, have thus far been ignored. Here, we investigate thereduction in risk for animals aggregating using different strategiesand demonstrate the importance of ecological parameters on riskreduction in group-living animals. We find that complex rulesare most successful at reducing risk in small, compact populations,whereas simpler rules are most successful in larger, low-densitypopulations, and when predators attack quickly after being detectedby their prey.     

Quantitative analysis of fiddler crab flock movement: evidence for ‘selfish herd’ behaviour

The selfish herd hypothesis predicts that aggregations form because individuals move towards one another, and that this movement will minimize predation risk as measured by the domain of danger. To test the predictions of the selfish herd hypothesis in the field, we videotaped the movements of sand fiddler crab, Uca pugilator, flocks being attacked by predators. After recording 12 attacks on crabs by shorebird and human attackers, we digitized the video, and determined the positions of crabs before and after being frightened. We estimated the time of panic initiation by the rapid increase in the crabs' velocity. Crab flocks became more cohesive after panic initiation. The frequency distribution of the crabs' domains of danger shifted significantly towards smaller domains after panic initiation. The median domain of danger was significantly lower after panic initiation than beforehand. Two other indices of aggregation also showed statistically significant increases in flock cohesion following panic initiation. We conclude that fiddler crab behaviour is consistent with the selfish herd hypothesis. Therefore, our results support the selfish herd hypothesis as an explanation for gregarious behaviour. Copyright 2002 The Association for the Study of Animal Behaviour. Published by Elsevier Science Ltd. All rights reserved.     

The temporal selfish herd: predation risk while aggregations form

The hypothesis of the selfish herd has been highly influential to our understanding of animal aggregation. Various movement strategies have been proposed by which individuals might aggregate to form a selfish herd as a defence against predation, but although the spatial benefits of these strategies have been extensively studied, little attention has been paid to the importance of predator attacks that occur while the aggregation is forming. We investigate the success of mutant aggregation strategies invading populations of individuals using alternative strategies and find that the invasion dynamics depend critically on the time scale of movement. If predation occurs early in the movement sequence, simpler strategies are likely to prevail. If predators attack later, more complex strategies invade. If there is variation in the timing of predator attacks (through variation within or between individual predators), we hypothesize that groups will consist of a mixture of strategies, dependent upon the distribution of predator attack times. Thus, behavioural diversity can evolve and be maintained in populations of animals experiencing a diverse range of predators differing solely in their attack behaviour. This has implications for our understanding of predator–prey dynamics, as the timing of predator attacks will exert selection pressure on prey behavioural responses, to which predators must respond.     

Contagion of Cooperation in Static and Fluid Social Networks

Cooperation is essential for successful human societies. Thus, understanding how cooperative and selfish behaviors spread from person to person is a topic of theoretical and practical importance. Previous laboratory experiments provide clear evidence of social contagion in the domain of cooperation, both in fixed networks and in randomly shuffled networks, but leave open the possibility of asymmetries in the spread of cooperative and selfish behaviors. Additionally, many real human interaction structures are dynamic: we often have control over whom we interact with. Dynamic networks may differ importantly in the goals and strategic considerations they promote, and thus the question of how cooperative and selfish behaviors spread in dynamic networks remains open. Here, we address these questions with data from a social dilemma laboratory experiment. We measure the contagion of both cooperative and selfish behavior over time across three different network structures that vary in the extent to which they afford individuals control over their network ties. We find that in relatively fixed networks, both cooperative and selfish behaviors are contagious. In contrast, in more dynamic networks, selfish behavior is contagious, but cooperative behavior is not: subjects are fairly likely to switch to cooperation regardless of the behavior of their neighbors. We hypothesize that this insensitivity to the behavior of neighbors in dynamic networks is the result of subjects’ desire to attract new cooperative partners: even if many of one’s current neighbors are defectors, it may still make sense to switch to cooperation. We further hypothesize that selfishness remains contagious in dynamic networks because of the well-documented willingness of cooperators to retaliate against selfishness, even when doing so is costly. These results shed light on the contagion of cooperative behavior in fixed and fluid networks, and have implications for influence-based interventions aiming at increasing cooperative behavior.     

Conditions for the Evolution of Gene Clusters in Bacterial Genomes

Genes encoding proteins in a common pathway are often found near each other along bacterial chromosomes. Several explanations have been proposed to account for the evolution of these structures. For instance, natural selection may directly favour gene clusters through a variety of mechanisms, such as increased efficiency of coregulation. An alternative and controversial hypothesis is the selfish operon model, which asserts that clustered arrangements of genes are more easily transferred to other species, thus improving the prospects for survival of the cluster. According to another hypothesis (the persistence model), genes that are in close proximity are less likely to be disrupted by deletions. Here we develop computational models to study the conditions under which gene clusters can evolve and persist. First, we examine the selfish operon model by re-implementing the simulation and running it under a wide range of conditions. Second, we introduce and study a Moran process in which there is natural selection for gene clustering and rearrangement occurs by genome inversion events. Finally, we develop and study a model that includes selection and inversion, which tracks the occurrence and fixation of rearrangements. Surprisingly, gene clusters fail to evolve under a wide range of conditions. Factors that promote the evolution of gene clusters include a low number of genes in the pathway, a high population size, and in the case of the selfish operon model, a high horizontal transfer rate. The computational analysis here has shown that the evolution of gene clusters can occur under both direct and indirect selection as long as certain conditions hold. Under these conditions the selfish operon model is still viable as an explanation for the evolution of gene clusters.     

The Role of Neighbours Selection on Cohesion and Order of Swarms

We introduce a multi-agent model for exploring how selection of neighbours determines some aspects of order and cohesion in swarms. The model algorithm states that every agents'' motion seeks for an optimal distance from the nearest topological neighbour encompassed in a limited attention field. Despite the great simplicity of the implementation, varying the amplitude of the attention landscape, swarms pass from cohesive and regular structures towards fragmented and irregular configurations. Interestingly, this movement rule is an ideal candidate for implementing the selfish herd hypothesis which explains aggregation of alarmed group of social animals.     

An investigation of a nonlocal hyperbolic model for self-organization of biological groups

In this article, we introduce and study a new nonlocal hyperbolic model for the formation and movement of animal aggregations. We assume that the nonlocal attractive, repulsive, and alignment interactions between individuals can influence both the speed and the turning rates of group members. We use analytical and numerical techniques to investigate the effect of these nonlocal interactions on the long-time behavior of the patterns exhibited by the model. We establish the local existence and uniqueness and show that the nonlinear hyperbolic system does not develop shock solutions (gradient blow-up). Depending on the relative magnitudes of attraction and repulsion, we show that the solutions of the model either exist globally in time or may exhibit finite-time amplitude blow-up. We illustrate numerically the various patterns displayed by the model: dispersive aggregations, finite-size groups and blow-up patterns, the latter corresponding to aggregations which may collapse to a point. The transition from finite-size to blow-up patterns is governed by the magnitude of the social interactions and the random turning rates. The presence of these types of patterns and the absence of shocks are consequences of the biologically relevant assumptions regarding the form of the speed and the turning rate functions, as well as of the kernels describing the social interactions.     

A strategy to increase cooperation in the volunteer's dilemma: reducing vigilance improves alarm calls

One of the most common examples of cooperation in animal societies is giving the alarm in the presence of a predator. A reduction in individual vigilance against predators when group size increases (the "group size effect") is one of the most frequently reported relationships in the study of animal behavior, and is thought to be due to relaxed selection, either because more individuals can detect the predator more easily (the "many eyes" effect) or because the risk of predator attack is diluted on more individuals (the "selfish herd" effect). I show that these hypotheses are not theoretically grounded: because everybody relies on someone else to raise the alarm, the probability that at least one raises the alarm declines with group size; therefore increasing group size does not lead to relaxed selection. Game theory shows, instead, that increasing the risk that the predator is not reported (by reducing vigilance) induces everybody to give the alarm more often. The group size effect, therefore, can be due to strategic behavior to improve the production of a public good. This shows how a selfish behavior can lead to a benefit for the group, and suggests a way to solve social dilemmas in the absence of relatedness and repeated interactions.     

Scale dependence of sex ratio in wild plant populations: implications for social selection

Social context refers to the composition of an individual''s social interactants, including potential mates. In spatially structured populations, social context can vary among individuals within populations, generating the opportunity for social selection to drive differences in fitness functions among individuals at a fine spatial scale. In sexually polymorphic plants, the local sex ratio varies at a fine scale and thus has the potential to generate this opportunity. We measured the spatial distribution of two wild populations of the gynodioecious plant Silene vulgaris and show that there is fine‐scale heterogeneity in the local distribution of the sexes within these populations. We demonstrate that the largest variance in sex ratio is among nearest neighbors. This variance is greatly reduced as the spatial scale of social interactions increases. These patterns suggest the sex of neighbors has the potential to generate fine‐scale differences in selection differentials among individuals. One of the most important determinants of social interactions in plants is the behavior of pollinators. These results suggest that the potential for selection arising from sex ratio will be greatest when pollen is shared among nearest neighbors. Future studies incorporating the movement of pollinators may reveal whether and how this fine‐scale variance in sex ratio affects the fitness of individuals in these populations.     

Behavior pattern (innate action) of individuals in fish schools generating efficient collective evasion from predation

The schooling of fishes is one typical animal social behavior. One primary function of fish school is to protect members when attacked by predators. One main way that the school reduces the predator's chance of making a successful kill is to confuse the predator as it makes its strike. This may be accomplished by collective evasion behaviors organized through integration of motions of individual fish made based on their innate actions (behavior patterns). In order to investigate what kind of behavior pattern of individuals can generate the efficient collective evasion of a school, we present a model of evasion behavior pattern which consists of three component behavior patterns, schooling, cooperative escape, and selfish escape behavior patterns and the rule for choice of one among them with proper timing. Each fish determines its movement direction taking into account simultaneously three kinds of elemental motions, mimicking its neighbors, avoiding collisions with its nearest neighbors, and escaping from an approaching predator. The weights of three elemental motions are changed depending on which component behavior pattern the fish carries out. The values of the weights for three component behavior patterns can be definitively determined under the condition that the collective evasion of the school becomes the most efficient, that is, the probability that any member is eaten by the predator becomes minimum.     

Geometry for mutualistic and selfish herds: the limited domain of danger

We present a two-dimensional individual-based model of aggregation behaviour in animals by introducing the concept of a "limited domain of danger", which represents either a limited detection range or a limited attack range of predators. The limited domain of danger provides a suitable framework for the analysis of individual movement rules under real-life conditions because it takes into account the predator's prey detection and capture abilities. For the first time, a single geometrical construct can be used to analyse the predation risk of both peripheral and central individuals in a group. Furthermore, our model provides a conceptual framework that can be equally applied to aggregation behaviour and refuge use and thus presents a conceptual advance on current theory that treats these antipredator behaviours separately. An analysis of individual movement rules using limited domains of danger showed that the time minimization strategy outcompetes the nearest neighbour strategy proposed by Hamilton's (J. Theor. Biol. 31 (1971) 295) selfish herd model, whereas a random strategy confers no benefit and can even be disadvantageous. The superior performance of the time minimization strategy highlights the importance of taking biological constraints, such as an animal's orientation relative to its neighbours, into account when searching for efficient movement rules underlying the aggregation process.     

A Spatially Explicit Model of Synchronization in Fiddler Crab Waving Displays

Fiddler crabs (Uca spp., Decapoda: Ocypodidae) are commonly found forming large aggregations in intertidal zones, where they perform rhythmic waving displays with their greatly enlarged claws. While performing these displays, fiddler crabs often synchronize their behavior with neighboring males, forming the only known synchronized visual courtship displays involving reflected light and moving body parts. Despite being one of the most conspicuous aspects of fiddler crab behavior, little is known about the mechanisms underlying synchronization of male displays. In this study we develop a spatially explicit model of fiddler crab waving displays using coupled logistic map equations. We explored two alternative models in which males either direct their attention at random angles or preferentially toward neighbors. Our results indicate that synchronization is possible over a fairly large region of parameter space. Moreover, our model was capable of generating local synchronization neighborhoods, as commonly observed in fiddler crabs under natural conditions.     

Sharks shape the geometry of a selfish seal herd: experimental evidence from seal decoys

Many animals respond to predation risk by forming groups. Evolutionary explanations for group formation in previously ungrouped, but loosely associated prey have typically evoked the selfish herd hypothesis. However, despite over 600 studies across a diverse array of taxa, the critical assumptions of this hypothesis have remained collectively untested, owing to several confounding problems in real predator–prey systems. To solve this, we manipulated the domains of danger of Cape fur seal (Arctocephalus pusillus pusillus) decoys to provide evidence that a selfish reduction in a seals'' domain of danger results in a proportional reduction in its predation risk from ambush shark attacks. This behaviour confers a survival advantage to individual seals within a group and explains the evolution of selfish herds in a prey species. These findings empirically elevate Hamilton''s selfish herd hypothesis to more than a ‘theoretical curiosity’.     

Facilitative interactions among the pelagic community of temperate migratory terns,tunas and dolphins

We studied habitat and behavioral interactions among the marine community of top pelagic predators over the Atlantic continental shelf, observed from shipboard surveys off the northeastern United States. We hypothesized that foraging seabirds, specifically common terns Sterna hirundo and roseate terns S. dougallii, associate positively with the distribution and abundance of large, easily‐detected subsurface marine predators, as a result of facilitative interactions. Few rigorous tests examine the effect of interspecific interactions on seabird distributions, though many papers note the importance of environmental influences. Fewer, still, assess facilitation, defined as positive interactions among multiple taxa (birds, fish, mammals), where individuals use foraging neighbors for improved prey detection or enhanced prey availability. Our use of spatiotemporal‐structured Bayesian hierarchical models allowed us to test for fine‐scale associations of common and roseate terns with aggregations of tunas and cetaceans, and with standard oceanographic parameters. High tern abundance was linked to relatively high tuna densities and low dolphin densities, as well as high sea surface temperatures, shallow water, and proximity to shore. The fact that terns foraged when in the presence of tunas or relatively dense dolphin pods supports our hypothesis that the mechanism behind this spatial association involves positive interspecific interactions (attraction), a phenomenon that has been described but rarely quantified. This study reveals that community structure depends on static and dynamic covariates alike, ranging from bathymetry to the movement of other guild members. To improve the efficacy of predictive modeling, ecosystem approaches to applied conservation management should integrate not only habitat, but also behavior and community factors into analyses, especially in the case of marine spatial planning.     

Antipredator defense as a limited resource: unequal predation risk in broods of an insect with maternal care

The allocation of parental investment is a potential sourceof conflict within broods whenever offspring are able obtaindifferential access to the parental resource. Unlike the provisioningof food, parental antipredator behavior is usually considereda resource that benefits all offspring simultaneously. In thethornbug treehopper (Umbonia crassicornis), offspring formaggregations in exposed positions on host-plant stems. Theyare subject to intense predation, and maternal defense is theirprimary means of protection. I examined the distribution ofrisk within these offspring groups, using natural variationin the outcome of more than 500 predation attempts (324 recordedon videotape) by vespid wasps (Pseudopolybia compressa) on18 U. crassicornis aggregations. I found three influences onan individual offspring's risk of predation. The first wasthe presence of a defending female: as expected, offspringwere much more likely to survive contact with a wasp if thefemale was present than if the female had disappeared. Thesecond influence was position relative to other offspring: when wasps were successful in removing an individual, they almostalways removed it from the edge of the group. The third influencewas distance from the female: the closer an offspring was tothe female at the time it was contacted by a wasp, the higherits likelihood of survival. The distribution of risk is determinedlargely by the behavior of defending females and the prey-searchingbehavior of wasps. The nature of risk within these aggregations sets the stage for two forms of sibling rivalry: selfish herdbehavior and competition for access to maternal defense. Italso raises the question of how a parent should allocate defenseamong offspring when it is unable to defend them all simultaneously.     

Escaping parasitism in the selfish herd: age, size and density-dependent warble fly infestation in reindeer

It has been suggested that animals may escape attack from mobile parasites by aggregating in selfish herds. A selfish herd disperses the risk of being attacked among its members and the per individual risk of parasite infection should therefore decrease with increasing animal density through the encounter–dilution effect. Moreover, in a selfish herd, dominant and agile animals should occupy the best positions and thereby receive fewer attacks compared to lower ranked animals at the periphery. We tested these predictions on reindeer ( Rangifer tarandus tarandus ) parasitized by warble flies ( Hypoderma tarandi ). Warble flies oviposit their eggs on reindeer during summer and induce strong anti-parasitic behavioural responses in the herds. In this period, reindeer are sexually segregated; females and calves form large and dense herds while males are more solitary. After hatching, the warble fly larvae migrate under the skin of their host where they encyst. In the present study encysted larvae were counted on newly slaughtered hides of male calves and 1.5 year old males from 18 different reindeer herds in Finnmark, northern Norway with large contrasts in reindeer density. In reindeer, body mass is correlated with fitness and social status and we hypothesized that individual carcass mass reflected the animal's ability to occupy the best positions within the herd. Larval abundance was higher among the 1.5 year old males than among the calves. For calves we found in accordance with the selfish herd hypothesis a negative relationship between larval abundance and animal density and between larval abundance and body mass. These relationships were absent for the 1.5 year old males. We suggest that these differences were due to different grouping behaviour where calves and females, but not males, aggregated in selfish herds where they escaped parasitism.     

Natural selection of cooperation and degree hierarchy in heterogeneous populations

One of the current theoretical challenges to the explanatory powers of Evolutionary Theory is the understanding of the observed evolutionary survival of cooperative behavior when selfish actions provide higher fitness (reproductive success). In unstructured populations natural selection drives cooperation to extinction. However, when individuals are allowed to interact only with their neighbors, specified by a graph of social contacts, cooperation-promoting mechanisms (known as lattice reciprocity) offer to cooperation the opportunity of evolutionary survival. Recent numerical works on the evolution of Prisoner's Dilemma in complex network settings have revealed that graph heterogeneity dramatically enhances the lattice reciprocity. Here we show that in highly heterogeneous populations, under the graph analog of replicator dynamics, the fixation of a strategy in the whole population is in general an impossible event, for there is an asymptotic partition of the population in three subsets, two in which fixation of cooperation or defection has been reached and a third one which experiences cycles of invasion by the competing strategies. We show how the dynamical partition correlates with connectivity classes and characterize the temporal fluctuations of the fluctuating set, unveiling the mechanisms stabilizing cooperation in macroscopic scale-free structures.     

The fitness benefits of germinating later than neighbors

Premise of the Study

Phenology, the seasonal timing of development, can alter biotic interactions. Emergence from dormant or quiescent stages often occurs earlier when neighbors are present, which may reduce the neighbors' competitive effects. Delayed emergence in response to neighbors also has been observed, but the potential benefits of such delays are unclear. Further, emergence time may respond to neighbors experienced by parents, which may predict future competition in offspring.

Methods

In the annual plant Arabidopsis thaliana (Brassicaceae), we quantified seed germination responses to neighbors in parental and offspring (seed) environments. To examine how observed changes in germination affect interactions with neighbors, we performed an outdoor experiment using neighbors of different sizes to represent different germination times.

Key Results

Seeds were more likely to germinate if their parent had neighbors, but they were less likely to germinate if they themselves experienced a neighbor cue (canopy). As seeds lost dormancy over time, they gained the ability to germinate under a canopy, which suggests that they germinate later in the presence of neighbors. Neighbors of both sizes reduced growth, survival to reproduction, fecundity, and total fitness, but large neighbors increased seedling survival. Smaller neighbors provided no such benefit and had stronger negative effects.

Conclusions

Delayed germination in response to neighbors can reduce negative interactions and promote positive ones if it occurs late enough to expose seedlings to larger neighbors. By altering relative phenologies and, in turn, the outcomes of biotic interactions, phenological responses to environmental change may influence species interactions and community dynamics.