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

Disentangling the "many-eyes", "dilution effect", "selfish herd", and "distracted prey" hypotheses in shaping alert and flight initiation distance in a colonial seabird

Group living is thought to have important antipredator benefits for animals, owing to the mechanisms of shared vigilance ("many-eyes" hypothesis), risk dilution ("dilution effect" hypothesis), and relative safety in the center of the group ("selfish herd" hypothesis). However, it can also incur costs since social stimuli, such as conspecific aggression, may distract individuals from anti-predator behavior ("distracted prey" hypothesis). We simultaneously evaluated how these four different hypotheses shape anti-predator behaviors of breeding king penguins (Aptenodytes patagonicus), which aggregate into large colonies, experience frequent aggressive social interactions, and are regularly exposed to predation by giant petrels (Macronectes sp.) and brown skuas (Catharacta loonbergi) when breeding on land. We approached 200 incubating penguins at four different periods of the breeding season across a range of overall increasing colony densities. We measured the distance at which focal birds detected the approaching threat (alert distance: AD), whether birds decided to flee or not, and the distance of flight initiation (flight initiation distance: FID, viz. the bird attempting to walk away with its egg on its feet). We quantified relative local neighbor density, centrality within the colony (rank), and the number of aggressions the focal bird emitted towards neighbors during the approach. We found that birds engaged in aggressive conflicts with neighbors were less likely to flee, and that increasing relative local neighbor density at low and medium overall colony density resulted in a decrease in bird AD, both supporting the "distracted prey" hypothesis. However, at maximal overall colony density, increasing relative local neighbor density resulted in longer AD, supporting the "many-eyes" hypothesis. We found no support for the "dilution effect" and "selfish herd" hypotheses, and no effects of any hypothesis on FID.

School formation characteristics and stimuli based modeling of tetra fish

Self-organizing motion is an important yet inadequately understood phenomena in the field of collective behavior. For birds flocks, insect swarms, and fish schools, group behavior can provide a mechanism for defense against predators, better foraging and mating capabilities and increased hydro/aerodynamic efficiency in long-distance migration events. Although collective motion has received much scientific attention, more work is required to model and understand the mechanisms responsible for school initiation and formation, and information transfer within these groups. Here we investigate schooling of black tetra (Gymnocorymbus ternetzi) fish triggered by startle stimuli in the form of approaching objects. High-speed video and tagging techniques were used to track the school and individual members. We then measured several variables including reaction times, group formation shapes, fish velocity, group density, and leadership within the group. These data reveal three things: (1) information propagates through the group as a wave, indicating that each fish is not reacting individually to the stimulus, (2) the time taken for information to transfer across the group is independent of group density, and (3) information propagates across large groups faster than would be expected if the fish were simply responding to the motion of their nearest neighbor. A model was then built wherein simulated fish have a simple 'stimuli/escape' vector based on a hypothetical field of vision. The model was used to simulate a group of individual fish with initial conditions, size, and stimuli similar to the biological experiments. The model revealed similar behavior to the biological experiments and provide insights into the observed patterns, response times, and wave speeds.

Quantifying the structure and dynamics of fish shoals under predation threat in three dimensions

Detailed quantifications of how predators and their grouping prey interact in three dimensions (3D) remain rare. Here we record the structure and dynamics of fish shoals (Pseudomugil signifer) in 3D both with and without live predators (Philypnodon grandiceps) under controlled laboratory conditions. Shoals adopted two distinct types of shoal structure: “sphere-like” geometries at depth and flat “carpet-like” structures at the water’s surface, with shoals becoming more compact in both horizontal and vertical planes in the presence of a predator. The predators actively stalked and attacked the prey, with attacks being initiated when the shoals were not in their usual configurations. These attacks caused the shoals to break apart, but shoal reformation was rapid and involved individuals adjusting their positions in both horizontal and vertical dimensions. Our analyses revealed that targeted prey were more isolated from other conspecifics, and were closer in terms of distance and direction to the predator compared to non-targeted prey. Moreover, which prey were targeted could largely be identified based on individuals’ positions from a single plane. This highlights that previously proposed 2D theoretical models and their assumptions appear valid when considering how predators target groups in 3D. Our work provides experimental, and not just anecdotal, support for classic theoretical predictions and also lends new insights into predatory–prey interactions in three-dimensional environments.

Black-headed gulls synchronise their activity with their nearest neighbours

Animals in groups can benefit from synchronising their behaviour, where multiple individuals conduct similar activities at the same moment in time. Previous studies have demonstrated that some species show synchronisation of vigilance behaviour, but have not explored the mechanism driving this behaviour. Synchronisation could be driven by animals copying their closest neighbours, which would mean that close proximity should lead to increased synchronisation. We simultaneously observed the behaviour of multiple individual black-headed gulls (Chroicocephalus ridibundus) within resting groups, and compared the activity of a focal individual with its two closest neighbours and a randomly selected control individual. Focal individuals were more likely to be synchronised with their closest neighbour. Synchronisation became less likely if individuals were not the closest neighbour. This suggests that synchronisation seen within groups is dependent upon the spatial positions of its members, and black-headed gulls pay more attention to their closest neighbours.

Marginal predation: do encounter or confusion effects explain the targeting of prey group edges?

Marginal predation, also known as the edge effect, occurs when aggregations of prey are preferentially targeted on their periphery by predators and has long been established in many taxa. Two main processes have been used to explain this phenomenon, the confusion effect and the encounter rate between predators and prey group edges. However, it is unknown at what size a prey group needs to be before marginal predation is detectable and to what extent each mechanism drives the effect. We conducted 2 experiments using groups of virtual prey being preyed upon by 3-spined sticklebacks (Gasterosteus aculeatus) to address these questions. In Experiment 1, we show that group sizes do not need to be large for marginal predation to occur, with this being detectable in groups of 16 or more. In Experiment 2, we find that encounter rate is a more likely explanation for marginal predation than the confusion effect in this system. We find that while confusion does affect predatory behaviors (whether or not predators make an attack), it does not affect marginal predation. Our results suggest that marginal predation is a more common phenomenon than originally thought as it also applies to relatively small groups. Similarly, as marginal predation does not need the confusion effect to occur, it may occur in a wider range of predator–prey species pairings, for example those where the predators search for prey using nonvisual sensory modalities.

Evolution of Swarming Behavior Is Shaped by How Predators Attack

Animal grouping behaviors have been widely studied due to their implications for understanding social intelligence, collective cognition, and potential applications in engineering, artificial intelligence, and robotics. An important biological aspect of these studies is discerning which selection pressures favor the evolution of grouping behavior. In the past decade, researchers have begun using evolutionary computation to study the evolutionary effects of these selection pressures in predator-prey models. The selfish herd hypothesis states that concentrated groups arise because prey selfishly attempt to place their conspecifics between themselves and the predator, thus causing an endless cycle of movement toward the center of the group. Using an evolutionary model of a predator-prey system, we show that how predators attack is critical to the evolution of the selfish herd. Following this discovery, we show that density-dependent predation provides an abstraction of Hamilton's original formulation of domains of danger. Finally, we verify that density-dependent predation provides a sufficient selective advantage for prey to evolve the selfish herd in response to predation by coevolving predators. Thus, our work corroborates Hamilton's selfish herd hypothesis in a digital evolutionary model, refines the assumptions of the selfish herd hypothesis, and generalizes the domain of danger concept to density-dependent predation.

The Confinement-Escape Problem of a Defender Against an Evader Escaping from a Circular Region

In this paper, we first formulate the confinement-escape problem of a defender and an evader who attempts escaping from a circular region, which differs from the traditional pursuit-evasion problems. In our setting of the confinement-escape problem, the defender is restricted to move and patrol on the circle, trying to prevent possible escape of the evader who is initially located inside the circle. We describe and characterize some general properties of the problem, and then design two bio-inspired control strategies for the evader and the defender, respectively. In addition, we illustrate some possible motion patterns of the system, investigate the escaping time as a function of the relative-initial-positions of the agents, as well as the winning sets of the two players, respectively, under different system-parameters. To that end, we characterize the contour lines of the winning sets with their gradient properties. Finally, we indicate the abrupt phase transitions between successful confinement and escaping, revealing the strong sensitivity and nonlinearities of the system under critical conditions.

'Selfish herds' of guppies follow complex movement rules, but not when information is limited

Under the threat of predation, animals can decrease their level of risk by moving towards other individuals to form compact groups. A significant body of theoretical work has proposed multiple movement rules, varying in complexity, which might underlie this process of aggregation. However, if and how animals use these rules to form compact groups is still not well understood, and how environmental factors affect the use of these rules even less so. Here, we evaluate the success of different movement rules, by comparing their predictions with the movement seen when shoals of guppies (Poecilia reticulata) form under the threat of predation. We repeated the experiment in a turbid environment to assess how the use of the movement rules changed when visual information is reduced. During a simulated predator attack, guppies in clear water used complex rules that took multiple neighbours into account, forming compact groups. In turbid water, the difference between all rule predictions and fish movement paths increased, particularly for complex rules, and the resulting shoals were more fragmented than in clear water. We conclude that guppies are able to use complex rules to form dense aggregations, but that environmental factors can limit their ability to do so.

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.

Pattern formation in prey-taxis systems

In this paper, we consider spatial predator-prey models with diffusion and prey-taxis. We investigate necessary conditions for pattern formation using a variety of non-linear functional responses, linear and non-linear predator death terms, linear and non-linear prey-taxis sensitivities, and logistic growth or growth with an Allee effect for the prey. We identify combinations of the above non-linearities that lead to spatial pattern formation and we give numerical examples. It turns out that prey-taxis stabilizes the system and for large prey-taxis sensitivity we do not observe pattern formation. We also study and find necessary conditions for global stability for a type I functional response, logistic growth for the prey, non-linear predator death terms, and non-linear prey-taxis sensitivity.

COSTS AND BENEFITS OF WITHIN‐GROUP SPATIAL POSITION: A FEEDING COMPETITION MODEL

An animal's within-group spatial position has several important fitness consequences. Risk of predation, time spent engaging in antipredatory behavior and feeding competition can all vary with respect to spatial position. Previous research has found evidence that feeding rates are higher at the group edge in many species, but these studies have not represented the entire breadth of dietary diversity and ecological situations faced by many animals. In particular the presence of concentrated, defendable food patches can lead to increased feeding rates by dominants in the center of the group that are able to monopolize or defend these areas. To fully understand the tradeoffs of within-group spatial position in relation to a variety of factors, it is important to be able to predict where individuals should preferably position themselves in relation to feeding rates and food competition. A qualitative model is presented here to predict how food depletion time, abundance of food patches within a group, and the presence of prior knowledge of feeding sites affect the payoffs of different within-group spatial positions for dominant and subordinate animals. In general, when feeding on small abundant food items, individuals at the front edge of the group should have higher foraging success. When feeding on slowly depleted, rare food items, dominants will often have the highest feeding rates in the center of the group. Between these two extreme points of a continuum, an individual's optimal spatial position is predicted to be influenced by an additional combination of factors, such as group size, group spread, satiation rates, and the presence of producer-scrounger tactics.

Dynamics of prey-flock escaping behavior in response to predator's attack

The dynamic behavior of prey-flock in response to predator's attack was investigated by using molecular dynamics (MD) simulations in a two-dimensional (2D) continuum model. By locally applying interactive forces between prey individuals (e.g. attraction, repulsion, and alignment), a coherently moving state in the same direction was obtained among individuals in prey-flock. When a single predator was introduced to the prey population, the prey-flock was correspondingly deformed by the predator's continuous attacks towards the prey-flock's center. In response to the predator's attack, three regimes in the flock size (compression (Regime I), expansion (Regime II), compression (Regime III)) were revealed if the predator's attack speed (kappa) was comparatively low to the escape speed of prey-flock. If noise was added to the predator's attacking course, a higher degree of variation was observed in the patterns of compression and expansion in the prey-flock size. However, the scaling behavior in the changes in prey-flock size was present in different levels of noise with the increase in predation risk (R) when kappa takes an appropriately low value. During the procedure of escaping, order breaking in alignment (phi) of prey population was observed, while the degree of alignment was dependent upon the changes in parameters of kappa and R.

Simulated evolution of selfish herd behavior

Single species aggregations are a commonly observed phenomenon. One potential explanation for these aggregations is provided by the selfish herd hypothesis, which states that aggregations result from individual efforts to reduce personnel predation risk at the expense of group-mates. Not all movement rules based on the selfish herd hypothesis are consistent with observed animal behavior. Previous work has shown that herd-like aggregations are not generated by movement rules limited to local interactions between nearest neighbors. Instead, rules generating realistic herds appear to require delocalized interactions. To date, it has been an open question whether or not the necessary delocalization can emerge from local interactions under natural selection. To address this question, we study an individual-based model with a single quantitative genetic trait that controls the influence of neighbors as a function of distance. The results indicate that predation-based selection can increase the influence of distant neighbors relative to near neighbors. Our results lend support for the idea that selfish herd behavior can arise from localized movement rules under natural selection.

State-dependent foraging rules for social animals in selfish herds

Many animals gain benefits from living in groups, such as a dilution in predation risk when they are closely aggregated (referred to as the 'selfish herd'). Game theory has been used to predict many properties of groups (such as the expected group size), but little is known about the proximate mechanisms by which animals achieve these predicted properties. We explore a possible proximate mechanism using a spatially explicit, individual-based model, where individuals can choose to rest or forage on the basis of a rule-of-thumb that is dependent upon both their energetic reserves and the presence and actions of neighbours. The resulting behaviour and energetic reserves of individuals, and the resulting group sizes, are shown to be affected both by the ability of the forager to detect conspecifics and areas of the environment suitable for foraging, and by the distribution of energy in the environment. The model also demonstrates that if animals are able to choose (based upon their energetic reserves) between selecting the best foraging sites available and moving towards their neighbours for safety, then this also has significant effects upon individuals and group sizes. The implications of the proposed rule-of-thumb are discussed.

Mutual interactions, potentials, and individual distance in a social aggregation

We formulate a Lagrangian (individual-based) model to investigate the spacing of individuals in a social aggregate (e.g., swarm, flock, school, or herd). Mutual interactions of swarm members have been expressed as the gradient of a potential function in previous theoretical studies. In this specific case, one can construct a Lyapunov function, whose minima correspond to stable stationary states of the system. The range of repulsion (r) and attraction (a) must satisfy r < a for cohesive groups (i.e., short range repulsion and long range attraction). We show quantitatively how repulsion must dominate attraction ( Rr(d+1) > cAa(d+1) where R, A are magnitudes, c is a constant of order 1, and d is the space dimension) to avoid collapse of the group to a tight cluster. We also verify the existence of a well-spaced locally stable state, having a characteristic individual distance. When the number of individuals in a group increases, a dichotomy occurs between swarms in which individual distance is preserved versus those in which the physical size of the group is maintained at the expense of greater crowding.

Computer algebra in the life sciences

This note (1) provides references to recent work that applies computer algebra (CA) to the life sciences, (2) cites literature that explains the biological background of each application, (3) states the mathematical methods that are used, (4) mentions the benefits of CA, and (5) suggests some topics for future work.

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.

A predator's selection of an individual prey from a group

This paper examines the mechanisms by which a predator selects an individual target from a group of prey. In a predatory situation, both the group of prey and the predator move around in a two-dimensional space. The predator has to select one individual among these prey to catch. For the mathematical treatment of such a selection, this paper introduces priority functions. Three different priority functions, labeled Strategies N, P and S, are then defined to indicate selection of the Nearest victim, the Peripheral victim or the Split victim (an individual separated from the group), respectively. It is found that, from the predator's standpoint, Strategy P is the best of the three regardless of how the prey group moves in reaction to an attack. Such reaction motions are classified into three types: ordered, partially disordered and fully disordered motion. Of the three types of motion, partially disordered motion is the most difficult type, as it confuses the predator in selecting and tracking a target individual.