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.     

Schooling properties of an obligate and a facultative fish species

Changes in attraction and repulsion indicators, depending on the species and the group size, were explored under controlled conditions. Two species, displaying different schooling behaviours in the wild were observed: the bigeye scad Selar crumenophthalmus and the barred flagtail Kuhlia mugil . In the bigeye scad, the polarity and speed were high and stable, and the nearest neighbour distance ( D _NN) decreased when the group size increased. In contrast, for the barred flagtail, polarity and speed decreased according to the group size, inducing a loss of cohesion and leading to a disorganized school. The D _NN mean was stable whatever the group size and relatively high. This experiment indicated that the ability to polarize is first a species-specific trait, rather than a property emerging from the group and led by the circumstances.     

Phase diagram of a multiple forces model for animal group formation: marches versus circles determined by the relative strength of alignment and cohesion

Many species of fish, bird, and insect form groups of individuals that move together, called schools, flocks, or swarms, of characteristic shape and speed. Here we study a model that traces movements of many individuals, in which each individual moves at a constant speed, and changes its movement angle in response to its neighbors within a radius of interaction. Outside of a short range of separation (or repulsion), each individual changes moving direction to achieve a similar moving direction as its neighbors (alignment) and to move toward them (cohesion). Between each pair of individuals within an interaction range, both alignment and cohesion are at work simultaneously (multiple forces model). This is different from many other models for animal group formation in which only one of the two forces is at work (single force model), different forces operating in different zones of between-individual distance. Depending on the relative strength of alignment and cohesion, our model produces groups of two distinct patterns: marches and circles. We showed the phase diagram of group patterns depending on the relative strength of alignment and cohesion. As the strength of alignment relative to cohesion increases, the shapes of groups change gradually in the following order: (1) circles, (2) mixture of circles and marches, (3) short marches, (4) long marches, (5) wide marches. We derived a formula for the spatial size of circles, which explains that the radius of circles does not change with the number of individuals, but it increases with moving speed and decreases with the sensitivity of moving direction to neighbors.     

Effects of anisotropic interactions on the structure of animal groups

This paper proposes an agent-based model which reproduces different structures of animal groups. The shape and structure of the group is the effect of simple interaction rules among individuals: each animal deploys itself depending on the position of a limited number of close group mates. The proposed model is shown to produce clustered formations, as well as lines and V-like formations. The key factors which trigger the onset of different patterns are argued to be the relative strength of attraction and repulsion forces and, most important, the anisotropy in their application.     

Japanese Macaques Depend not Only on Neighbours but also on More Distant Members for Group Cohesion

A well‐known behavioural model for group aggregation is that an individual depends on a few neighbouring individuals to adjust its movement, such as departure (repulsion) from and approach (attraction) to neighbours. However, an individual may rely not only on a few closest neighbours, but also on more distant individuals, in a group of stable membership. We measured temporal changes in the local density of individuals around a focal individual and changes in distance to other focal individuals in a group of wild Japanese macaques to determine whether the macaques depended only on a few neighbours or also on more distant individuals for adjustments in cohesiveness. We used simultaneous focal animal sampling, with two observers recording the individuals' locations using a global positioning system (GPS), over three seasons. Numbers of individuals within 20 m from an animal tended to increase after 10 min when there were a small number of individuals around the animal. However, the number tended to decrease when there was a larger number of individuals. It remained similar when there were an intermediate number of individuals. The two focal animals tended to separate after 10 min when the interindividual distance was short. However, they tended to move closer when far apart. They remained a similar distance apart when they were at an intermediate distance. Contact calls, which are suggested to function as locating group members and keeping cohesiveness, were emitted more frequently when the distance between the two focal animals was very large in two seasons. However, the rate of contact calls was not influenced by the number of individuals within 20 m from an animal. These results suggest that individual Japanese macaques do not only rely on a few closest neighbours, but also rely on more distant group members. Japanese macaques may know the general whereabouts of the whole group, and when they stay at the periphery of the group, they may emit contact calls frequently and move towards the central zone so as not to become separated from the group.     

How the Spatial Position of Individuals Affects Their Influence on Swarms: A Numerical Comparison of Two Popular Swarm Dynamics Models

Schools of fish and flocks of birds are examples of self-organized animal groups that arise through social interactions among individuals. We numerically study two individual-based models, which recent empirical studies have suggested to explain self-organized group animal behavior: (i) a zone-based model where the group communication topology is determined by finite interacting zones of repulsion, attraction, and orientation among individuals; and (ii) a model where the communication topology is described by Delaunay triangulation, which is defined by each individual''s Voronoi neighbors. The models include a tunable parameter that controls an individual''s relative weighting of attraction and alignment. We perform computational experiments to investigate how effectively simulated groups transfer information in the form of velocity when an individual is perturbed. A cross-correlation function is used to measure the sensitivity of groups to sudden perturbations in the heading of individual members. The results show how relative weighting of attraction and alignment, location of the perturbed individual, population size, and the communication topology affect group structure and response to perturbation. We find that in the Delaunay-based model an individual who is perturbed is capable of triggering a cascade of responses, ultimately leading to the group changing direction. This phenomenon has been seen in self-organized animal groups in both experiments and nature.     

Processes affecting size of fish schools in agent-based model

Fish school size varies with several factors, such as environmental conditions, individual size, time of day, and variations between individuals. In this study, we investigate the mean size of fish schools formed in a simple agent-based model, wherein each individual swims at a fixed speed with the direction modified by interactions with the neighbors. If alignment (tendency to swim in their neighbors' direction) is stronger than cohesion (tendency to swim toward the neighbors), then “marches” are formed, in which individuals swim in the same direction. If alignment is weaker than cohesion, then “circles” are formed, in which individuals chase one another and the entire group moves minimally. We analyzed various processes that control the shape and mean size of the schools. The school's shape is primarily affected by the magnitude of alignment, cohesion, and individual noises. In contrast, the mean size of the group is affected by several factors, including the spatial interaction range, initial configuration, individual differences in swimming speed, and sudden encounters with predators.     

Collision avoidance during group evasive manoeuvres: a comparison of real versus simulated swarms with manipulated vision and surface wave detectors

Coordinated group motion has been studied extensively both in real systems (flocks, swarms and schools) and in simulations (self-propelled particle (SPP) models using attraction and repulsion rules). Rarely are attraction and repulsion rules manipulated, and the resulting emergent behaviours of real and simulation systems are compared. We compare swarms of sensory-deprived whirligig beetles with matching simulation models. Whirligigs live at the water''s surface and coordinate their grouping using their eyes and antennae. We filmed groups of beetles in which antennae or eyes had been unilaterally obstructed and measured individual and group behaviours. We then developed and compared eight SPP simulation models. Eye-less beetles formed larger diameter resting groups than antenna-less or control groups. Antenna-less groups collided more often with each other during evasive group movements than did eye-less or control groups. Simulations of antenna-less individuals produced no difference from a control (or a slight decrease) in group diameter. Simulations of eye-less individuals produced an increase in group diameter. Our study is important in (i) differentiating between group attraction and repulsion rules, (ii) directly comparing emergent properties of real and simulated groups, and (iii) exploring a new sensory modality (surface wave detection) to coordinate group movement.     

Scalable rules for coherent group motion in a gregarious vertebrate

Individuals of gregarious species that initiate collective movement require mechanisms of cohesion in order to maintain advantages of group living. One fundamental question in the study of collective movement is what individual rules are employed when making movement decisions. Previous studies have revealed that group movements often depend on social interactions among individual members and specifically that collective decisions to move often follow a quorum-like response. However, these studies either did not quantify the response function at the individual scale (but rather tested hypotheses based on group-level behaviours), or they used a single group size and did not demonstrate which social stimuli influence the individual decision-making process. One challenge in the study of collective movement has been to discriminate between a common response to an external stimulus and the synchronization of behaviours resulting from social interactions. Here we discriminate between these two mechanisms by triggering the departure of one trained Merino sheep (Ovis aries) from groups containing one, three, five and seven naïve individuals. Each individual was thus exposed to various combinations of already-departed and non-departed individuals, depending on its rank of departure. To investigate which individual mechanisms are involved in maintaining group cohesion under conditions of leadership, we quantified the temporal dynamic of response at the individual scale. We found that individuals'' decisions to move do not follow a quorum response but rather follow a rule based on a double mimetic effect: attraction to already-departed individuals and attraction to non-departed individuals. This rule is shown to be in agreement with an adaptive strategy that is inherently scalable as a function of group size.     

Group size, grooming and fission in primates: a modeling approach based on group structure

In social animals, fission is a common mode of group proliferation and dispersion and may be affected by genetic or other social factors. Sociality implies preserving relationships between group members. An increase in group size and/or in competition for food within the group can result in decrease certain social interactions between members, and the group may split irreversibly as a consequence. One individual may try to maintain bonds with a maximum of group members in order to keep group cohesion, i.e. proximity and stable relationships. However, this strategy needs time and time is often limited. In addition, previous studies have shown that whatever the group size, an individual interacts only with certain grooming partners. There, we develop a computational model to assess how dynamics of group cohesion are related to group size and to the structure of grooming relationships. Groups’ sizes after simulated fission are compared to observed sizes of 40 groups of primates. Results showed that the relationship between grooming time and group size is dependent on how each individual attributes grooming time to its social partners, i.e. grooming a few number of preferred partners or grooming equally or not all partners. The number of partners seemed to be more important for the group cohesion than the grooming time itself. This structural constraint has important consequences on group sociality, as it gives the possibility of competition for grooming partners, attraction for high-ranking individuals as found in primates’ groups. It could, however, also have implications when considering the cognitive capacities of primates.     

Ion-mediated nucleic acid helix-helix interactions

Salt ions are essential for the folding of nucleic acids. We use the tightly bound ion (TBI) model, which can account for the correlations and fluctuations for the ions bound to the nucleic acids, to investigate the electrostatic free-energy landscape for two parallel nucleic acid helices in the solution of added salt. The theory is based on realistic atomic structures of the helices. In monovalent salt, the helices are predicted to repel each other. For divalent salt, while the mean-field Poisson-Boltzmann theory predicts only the repulsion, the TBI theory predicts an effective attraction between the helices. The helices are predicted to be stabilized at an interhelix distance approximately 26-36 A, and the strength of the attractive force can reach -0.37 k(B)T/bp for helix length in the range of 9-12 bp. Both the stable helix-helix distance and the strength of the attraction are strongly dependent on the salt concentration and ion size. With the increase of the salt concentration, the helix-helix attraction becomes stronger and the most stable helix-helix separation distance becomes smaller. For divalent ions, at very high ion concentration, further addition of ions leads to the weakening of the attraction. Smaller ion size causes stronger helix-helix attraction and stabilizes the helices at a shorter distance. In addition, the TBI model shows that a decrease in the solvent dielectric constant would enhance the ion-mediated attraction. The theoretical findings from the TBI theory agree with the experimental measurements on the osmotic pressure of DNA array as well as the results from the computer simulations.     

Social cohesion in groups of sheep: Effect of activity level, sex composition and group size

We investigated the effects of activity, group size and sex composition on the cohesion of merino sheep (Ovis aries) groups. Mixed-sex (50% of each sex) and single-sex groups of 2, 4, 6 and 8 sheep were placed within 491-m² arenas located in natural pastures and were video recorded during 6 daily hours. The behaviour, orientation and location of each sheep were then extracted from the films at 1-s intervals. We analysed the polarisation of individual orientations, mean inter-individual and nearest neighbours’ distances, as well as the frequency of pairs of nearest neighbours according to their sex within mixed-sex groups. Sheep were more aggregated than predicted under the null hypothesis of random spatial distribution for all group compositions and sizes. Sheep were more spread out and less aligned in half-active than in all-active groups, showing that social cohesion was reduced by a lack of activity synchronisation. The highest proximity between individuals was found in resting groups, yet alignment was low. The polarisation peaked in all-active groups. Mean inter-individual distance did not vary and the nearest neighbour distance decreased as group size increased. When sheep were all-active or all-resting, mixed-sex groups were more spread out than single-sex ones, with a greater distance between opposite than between same-sex individuals. Nearest neighbours of the same sex were also more frequent than random. Our results show that social cohesion can be modulated by activity synchrony but also by social affinity.     

A ligand-gated association between cytoplasmic domains of UNC5 and DCC family receptors converts netrin-induced growth cone attraction to repulsion.

Netrins are bifunctional: they attract some axons and repel others. Netrin receptors of the Deleted in Colorectal Cancer (DCC) family are implicated in attraction and those of the UNC5 family in repulsion, but genetic evidence also suggests involvement of the DCC protein UNC-40 in some cases of repulsion. To test whether these proteins form a receptor complex for repulsion, we studied the attractive responses of Xenopus spinal axons to netrin-1, which are mediated by DCC. We show that attraction is converted to repulsion by expression of UNC5 proteins in these cells, that this repulsion requires DCC function, that the UNC5 cytoplasmic domain is sufficient to effect the conversion, and that repulsion can be initiated by netrin-1 binding to either UNC5 or DCC. The isolated cytoplasmic domains of DCC and UNC5 proteins interact directly, but this interaction is repressed in the context of the full-length proteins. We provide evidence that netrin-1 triggers the formation of a receptor complex of DCC and UNC5 proteins and simultaneously derepresses the interaction between their cytoplasmic domains, thereby converting DCC-mediated attraction to UNC5/DCC-mediated repulsion.     

Chimeric axon guidance receptors: the cytoplasmic domains of slit and netrin receptors specify attraction versus repulsion.

Frazzled (Fra) is the DCC-like Netrin receptor in Drosophila that mediates attraction; Roundabout (Robo) is a Slit receptor that mediates repulsion. Both ligands are expressed at the midline; both receptors have related structures and are often expressed by the same neurons. To determine if attraction versus repulsion is a modular function encoded in the cytoplasmic domain of these receptors, we created chimeras carrying the ectodomain of one receptor and the cytoplasmic domain of the other and tested their function in transgenic Drosophila. Fra-Robo (Fra's ectodomain and Robo's cytoplasmic domain) functions as a repulsive Netrin receptor; neurons expressing Fra-Robo avoid the Netrin-expressing midline and muscles. Robo-Fra (Robo's ectodomain and Fra's cytoplasmic domain) is an attractive Slit receptor; neurons and muscle precursors expressing Robo-Fra are attracted to the Slit-expressing midline.     

Interindividual distances in mixed-species groups of ants: an estimation of cohesion in social groups

Spatial organization was estimated in mixed-species groups of ants with interindividual distance measures as a function of: (1) the age of the workers when associated; and (2) the presence of the brood. Workers ofManica rubida (Myrmicinae) andFormica selysi (Formicinae) were reared in single-species groups (control) or in artificial, mixed-species groups, created 5 h, 12 h or 22 h after emergence, with or without brood. By recording the location of each individual in the nest during the 10 days following the creation of the groups, we evaluated the spatial organization and the interindividual distances between homocolonial or allospecific workers, and between workers and homocolonial or allospecific brood. The cohesion of the group, depend on the age of the workers when associated: the younger the individuals are when the groups are created, the smaller are the interindividual distances. Moreover, homocolonial individuals aggregated with brood, when present, which improves the overall cohesion of the group. However, in mixed groups, both species associated preferentially with members of their own species. This suggests that newly-emerged ants do not depend totally on the odors of their nestmates to construct their recognition template and that they also possess an innate, specific template.     

Evidence for sexual attraction pheromones released by male tropical donkey's ear abalone (Haliotis asinina), (L.)

Abstract

The tropical donkey's ear abalone (Haliotis asinina) is routinely collected in many parts of the Indo-Pacific and has significant potential for commercial aquaculture. Although its reproductive cycle has been investigated, no studies have reported the use of chemical signals to coordinate reproduction and spawning. Using a bioassay designed with one caged individual, whilst the other is free to roam, we investigated the presence of attraction pheromones released from mature individuals. Only mature females were attracted to caged mature males with all other treatments showing no significant attraction. Those mature females also took significantly less time to reach the mature males than other pairings. Temperature influenced the response with the maximum number of positives occurring between 25 and 31°C, which coincides with the optimum physiological temperatures and the spawning times for this species. We have also shown that the attraction pheromone is present in mature male testes and induces stereotypical pre-spawning behaviours (sweeping epipodial and cephalic tentacles) as well as attracting females. Some individuals also moved towards the surface of the water, this may also be a pre-spawning behaviour. This is the first time that a sexual attraction pheromone has been reported for any haliotid species and is likely to have a critical function in the synchronization of spawning in the wild between sexes.     

Social spacing in the mormyrid fish Gnathonemus petersii (Pisces): A multisensory approach

The sensory basis of group cohesion in the weak-electric fish Gnathonemus petersii was investigated in a circular tank with groups of four fish each, interacting through a wide-meshed plastic screen with intact or operated conspecifics, or with other stimulus objects. We confined these stimuli to one or two peripheral holding compartments. The response measures were obtained from the free swimming fish and included (1) the time the fish spent together as a group, (2) the time they spent in front of the holding compartments, (3) the circular distribution of the fish's positions, and (4) the mean nearest neighbour distances. Under empty compartment conditions, four different groups were tested, consisting of either (1) intact, electrically active fish, or (2) electrically ‘silent’ fish (with their electric organ surgically rendered inoperative), or (3) blind, or (4) ‘silent’ and blind animals. The loss of either sensory modality, vision or feedback from electric organ discharge, led to changes of comparable size, decreasing the time spent as a group and increasing the mean nearest neighbour distance. In fish lacking both modalities, group cohesion was further impaired. With stimuli present in one or both holding compartments, the strength of social attraction depended on the nature of the stimulus: the more intact stimulus conspecifics were present, the more densely did the fish group in front of the stimulus compartment. ‘Wired-in’ electric organ discharges (simulating waveform and intensity) and electrically ‘silent’ fish were equally attractive, but only half as attractive as intact fish. Blind free swimming fish aggregated with intact and also with ‘silent’ conspecifics. Under dim light conditions, group cohesion was predominantly, though not exclusively, affected by electrosensory feedback from the electric organ discharge and visual input. Mechanical and olfactory cues may also be involved.     

The function of loud calls (Hoot Series) in wild western gorillas (Gorilla gorilla)

The use of loud vocal signals to reduce distance among separated social partners is well documented in many species; however, the underlying mechanisms by which the reduction of spacing occurs and how they differ across species remain unclear. Western gorillas (Gorilla gorilla) offer an opportunity to investigate these issues because their vocal repertoire includes a loud, long‐distance call (i.e., hoot series) that is potentially used in within‐group communication, whereas mountain gorillas use an identical call exclusively during intergroup encounters. First, we tested whether the hoot series functions as a contact/separation call. Second, we examined which individuals were more likely to reply and which party was more responsible for decreasing distance to identify the underlying mechanisms and cognitive implications of hoot series. We collected behavioral, spatial, and acoustic data on five adult gorillas over 15 months at the Mondika Research Center (Republic of Congo and CAR). Hoot series are individually distinct calls and given by both male and female gorillas when separated from each other. Following hooting, the distance between separated group members decreased significantly; thus we concluded that western gorillas use this call to reestablish group cohesion. The way in which proximity was achieved depended upon listeners replying or not to the caller. Replies may indicate a conflict between callers about intended travel direction, with vocal interchanges serving to negotiate a consensus. Although the acoustic features of vocal signals are highly constrained in closely related species, our results demonstrate that the function and usage of particular calls can be flexible. Am J Phys Anthropol 155:379–391, 2014. © 2014 Wiley Periodicals, Inc.