Data-driven discovery of stochastic dynamical equations of collective motion

Coarse-grained descriptions of collective motion of flocking systems are often derived for the macroscopic or the thermodynamic limit. However, the size of many real flocks falls within 'mesoscopic' scales (10 to 100 individuals), where stochasticity arising from the finite flock sizes is important. Previous studies on mesoscopic models have typically focused on non-spatial models. Developing mesoscopic scale equations, typically in the form of stochastic differential equations, can be challenging even for the simplest of the collective motion models that explicitly account for space. To address this gap, here, we take a novel data-driven equation learning approach to construct the stochastic mesoscopic descriptions of a simple, spatial, self-propelled particle (SPP) model of collective motion. In the spatial model, a focal individual can interact withkrandomly chosen neighbours within an interaction radius. We considerk = 1 (called stochastic pairwise interactions),k = 2 (stochastic ternary interactions), andkequalling all available neighbours within the interaction radius (equivalent to Vicsek-like local averaging). For the stochastic pairwise interaction model, the data-driven mesoscopic equations reveal that the collective order is driven by a multiplicative noise term (hence termed, noise-induced flocking). In contrast, for higher order interactions (k > 1), including Vicsek-like averaging interactions, models yield collective order driven by a combination of deterministic and stochastic forces. We find that the relation between the parameters of the mesoscopic equations describing the dynamics and the population size are sensitive to the density and to the interaction radius, exhibiting deviations from mean-field theoretical expectations. We provide semi-analytic arguments potentially explaining these observed deviations. In summary, our study emphasises the importance of mesoscopic descriptions of flocking systems and demonstrates the potential of the data-driven equation discovery methods for complex systems studies.

Individual based models for the simulation of fish movement near barriers: Current work and future directions

River fragmentation is an increasing issue for water managers and conservationists. Barriers such as dams interfere with freshwater fish migration, leading to drastic population declines. While there are a range of widely implemented mitigation approaches, e.g. fish passes, such measures are often inefficient due to suboptimal operation and design. There is increasing need to be able to assess mitigation options prior to implementation. Individual based models (IBMs) are a promising option. IBMs can simulate the fine-scale movement of individual fish within a population as they attempt to find a fish pass, incorporating movement processes themselves. Moreover, IBMs have high transferability to other sites or conditions (e.g. changing mitigation, change in flow conditions), making them potentially valuable for freshwater fish conservation yet their application to the fine-scale movement of fish past barriers is still novel. Here, we present an overview of existing IBMs for fine-scale freshwater fish movement, with emphasis on study species and the parameters driving movement in the models. In this review, we focus on IBMs suitable for the simulation of fish tracks as they approach or pass a single barrier. The selected IBMs for modelling fine-scale freshwater fish movement largely focus on salmonids and cyprinid species. IBMs have many applications in the context of fish passage, such as testing different mitigation options or understanding processes behind movement. Existing IBMs include movement processes such as attraction and rejection behaviours, as reported in literature. Yet some factors affecting fish movement e.g. biotic interactions are not covered by existing IBMs. As the technology available for fine scale data collection continues to advance, such as increasing data linking fish behaviour to hydraulics, IBMs could become a more common tool in the design and implementation of fish bypass structures.

Social competence improves the performance of biomimetic robots leading live fish

Collective motion is commonly modeled with static interaction rules between agents. Substantial empirical evidence indicates, however, that animals may adapt their interaction rules depending on a variety of factors and social contexts. Here, we hypothesized that leadership performance is linked to the leader's responsiveness to the follower's actions and we predicted that a leader is followed longer if it adapts to the follower's avoidance movements. We tested this prediction with live guppies that interacted with a biomimetic robotic fish programmed to act as a 'socially competent' leader. Fish that were avoiding the robot were approached more carefully in future approaches. In two separate experiments we then asked how the leadership performance of the socially competent robot leader differed to that of a robot leader that either approached all fish in the same, non-responsive, way or one that did change its approach behavior randomly, irrespective of the fish's actions. We found that (1) behavioral variability itself appears attractive and that socially competent robots are better leaders which (2) require fewer approach attempts to (3) elicit longer average following behavior than non-competent agents. This work provides evidence that social responsiveness to avoidance reactions plays a role in the social dynamics of guppies. We showcase how social responsiveness can be modeled and tested directly embedded in a living animal model using adaptive, interactive robots.

Dynamics of collective motion across time and species

Most studies of collective animal behaviour rely on short-term observations, and comparisons of collective behaviour across different species and contexts are rare. We therefore have a limited understanding of intra- and interspecific variation in collective behaviour over time, which is crucial if we are to understand the ecological and evolutionary processes that shape collective behaviour. Here, we study the collective motion of four species: shoals of stickleback fish (Gasterosteus aculeatus), flocks of homing pigeons (Columba livia), a herd of goats (Capra aegagrus hircus) and a troop of chacma baboons (Papio ursinus). First, we describe how local patterns (inter-neighbour distances and positions), and group patterns (group shape, speed and polarization) during collective motion differ across each system. Based on these, we place data from each species within a 'swarm space', affording comparisons and generating predictions about the collective motion across species and contexts. We encourage researchers to add their own data to update the 'swarm space' for future comparative work. Second, we investigate intraspecific variation in collective motion over time and provide guidance for researchers on when observations made over different time scales can result in confident inferences regarding species collective motion. This article is part of a discussion meeting issue 'Collective behaviour through time'.

Randomness in the choice of neighbours promotes cohesion in mobile animal groups

Classic computational models of collective motion suggest that simple local averaging rules can promote many observed group-level patterns. Recent studies, however, suggest that rules simpler than local averaging may be at play in real organisms; for example, fish stochastically align towards only one randomly chosen neighbour and yet the schools are highly polarized. Here, we ask-how do organisms maintain group cohesion? Using a spatially explicit model, inspired from empirical investigations, we show that group cohesion can be achieved in finite groups even when organisms randomly choose only one neighbour to interact with. Cohesion is maintained even in the absence of local averaging that requires interactions with many neighbours. Furthermore, we show that choosing a neighbour randomly is a better way to achieve cohesion than interacting with just its closest neighbour. To understand how cohesion emerges from these random pairwise interactions, we turn to a graph-theoretic analysis of the underlying dynamic interaction networks. We find that randomness in choosing a neighbour gives rise to well-connected networks that essentially cause the groups to stay cohesive. We compare our findings with the canonical averaging models (analogous to the Vicsek model). In summary, we argue that randomness in the choice of interacting neighbours plays a crucial role in achieving cohesion.

Collective predator evasion: Putting the criticality hypothesis to the test

According to the criticality hypothesis, collective biological systems should operate in a special parameter region, close to so-called critical points, where the collective behavior undergoes a qualitative change between different dynamical regimes. Critical systems exhibit unique properties, which may benefit collective information processing such as maximal responsiveness to external stimuli. Besides neuronal and gene-regulatory networks, recent empirical data suggests that also animal collectives may be examples of self-organized critical systems. However, open questions about self-organization mechanisms in animal groups remain: Evolutionary adaptation towards a group-level optimum (group-level selection), implicitly assumed in the "criticality hypothesis", appears in general not reasonable for fission-fusion groups composed of non-related individuals. Furthermore, previous theoretical work relies on non-spatial models, which ignore potentially important self-organization and spatial sorting effects. Using a generic, spatially-explicit model of schooling prey being attacked by a predator, we show first that schools operating at criticality perform best. However, this is not due to optimal response of the prey to the predator, as suggested by the "criticality hypothesis", but rather due to the spatial structure of the prey school at criticality. Secondly, by investigating individual-level evolution, we show that strong spatial self-sorting effects at the critical point lead to strong selection gradients, and make it an evolutionary unstable state. Our results demonstrate the decisive role of spatio-temporal phenomena in collective behavior, and that individual-level selection is in general not a viable mechanism for self-tuning of unrelated animal groups towards criticality.

Guppies Prefer to Follow Large (Robot) Leaders Irrespective of Own Size

Body size is often assumed to determine how successfully an individual can lead others with larger individuals being better leaders than smaller ones. But even if larger individuals are more readily followed, body size often correlates with specific behavioral patterns and it is thus unclear whether larger individuals are more often followed than smaller ones because of their size or because they behave in a certain way. To control for behavioral differences among differentially-sized leaders, we used biomimetic robotic fish (Robofish) of different sizes. Live guppies (Poecilia reticulata) are known to interact with Robofish in a similar way as with live conspecifics. Consequently, Robofish may serve as a conspecific-like leader that provides standardized behaviors irrespective of its size. We asked whether larger Robofish leaders are preferentially followed and whether the preferences of followers depend on own body size or risk-taking behavior ("boldness"). We found that live female guppies followed larger Robofish leaders in closer proximity than smaller ones and this pattern was independent of the followers' own body size as well as risk-taking behavior. Our study shows a "bigger is better" pattern in leadership that is independent of behavioral differences among differentially-sized leaders, followers' own size and risk-taking behavior.

Stress-induced changes in group behaviour

Testing animals in groups can provide valuable data for investigating behavioural stress responses. However, conventional measures typically focus on the behaviour of individual animals or on dyadic interactions. Here, we aimed to determine metrics describing the behaviour of grouping animals that can reveal differences in stress responses. Using zebrafish (Danio rerio) as a model, we observed replicated shoals both immediately and 24 hours after exposure to a novel environment, as an assessment of temporal change in response to an acute stressor. We quantified various standard behavioural measures in combination with metrics describing group structure, including different proximity, social, and spatial metrics. Firstly, we showed a high collinearity between most of the analysed metrics, suggesting that they describe similar aspects of the group dynamics. After metric selection, we found that under acute stress shoals had significantly higher shoal densities, a lower variation in nearest neighbour distances and were in closer proximity to the walls compared to the same groups tested 24 hours later, indicating a reduction in acute stress over time. Thus, the use of group metrics could allow for the refinement of behavioural protocols carried out in a range of research areas, by providing sensitive and rich data in a more relevant social context.

Towards a framework for collective behavior in growth-driven systems, based on plant-inspired allotropic pairwise interactions

A variety of biological systems are not motile, but sessile in nature, relying on growth as the main driver of their movement. Groups of such growing organisms can form complex structures, such as the functional architecture of growing axons, or the adaptive structure of plant root systems. These processes are not yet understood, however the decentralized growth dynamics bear similarities to the collective behavior observed in groups of motile organisms, such as flocks of birds or schools of fish. Equivalent growth mechanisms make these systems amenable to a theoretical framework inspired by tropic responses of plants, where growth is considered implicitly as the driver of the observed bending towards a stimulus. We introduce two new concepts related to plant tropisms: point tropism, the response of a plant to a nearby point signal source, and allotropism, the growth-driven response of plant organs to neighboring plants. We first analytically and numerically investigate the 2D dynamics of single organs responding to point signals fixed in space. Building on this we study pairs of organs interacting via allotropism, i.e. each organ senses signals emitted at the tip of their neighbor and responds accordingly. In the case of local sensing we find a rich state-space. We describe the different states, as well as the sharp transitions between them. We also find that the form of the state-space depends on initial conditions. This work sets the stage towards a theoretical framework for the investigation and understanding of systems of interacting growth-driven individuals.

Self-organized traffic via priority rules in leaf-cutting ants

Ants, termites and humans often form well-organized and highly efficient trails between different locations. Yet the microscopic traffic rules responsible for this organization and efficiency are not fully understood. In previous experimental studies with leaf-cutting ants (Atta colombica), a set of local priority rules were isolated and it was proposed that these rules govern the temporal and spatial organization of the traffic on the trails. Here we introduce a model based on these priority rules to investigate whether they are sufficient to produce traffic similar to that observed in the experiments on both a narrow and a wider trail. We establish that the model is able to reproduce key characteristics of the traffic on the trails. In particular, we show that the proposed priority rules induce de-synchronization into clusters of inbound and outbound ants on a narrow trail, and that priority-type dependent segregated traffic emerges on a wider trail. Due to the generic nature of the proposed priority rules we speculate that they may be used to model traffic organization in a variety of other ant species.

Familiarity affects collective motion in shoals of guppies (Poecilia reticulata)

The coordinated and synchronized movement of animals in groups often referred to as collective motion emerges through the interactions between individual animals within the group. Factors which affect these interactions have the potential to shape collective movement. One such factor is familiarity, or the tendency to bias behaviour towards individuals as a result of social recognition. We examined the effect of familiarity on the expression of collective motion in small shoals of female guppies (Poecilia reticulata). Groups comprising familiar individuals were more strongly polarized than groups of unfamiliar individuals, particularly when in novel surroundings. The ability to form more strongly polarized shoals potentially promotes information transfer and enhances the anti-predator benefits of grouping.

Analysis of topological relationships and network properties in the interactions of human beings

In the animal world, various kinds of collective motions have been found and proven to be efficient ways of carrying out some activities such as searching for food and avoiding predators. Many scholars research the interactions of collective behaviors of human beings according to the rules of collective behaviors of animals. Based on the Lennard-Jones potential function and a self-organization process, our paper proposes a topological communication model to simulate the collective behaviors of human beings. In the results of simulations, we find various types of collective behavior and fission behavior and discover the threshold for the emergence of collective behavior, which is the range five to seven for the number of topology K. According to the analysis of network properties of the model, the in-degree of individuals is always equal to the number of topology. In the stable state, the out-degrees of individuals distribute around the value of the number of topology K, except that the out-degree of a single individual is approximately double the out-degrees of the other individuals. In addition, under different initial conditions, some features of different kinds of networks emerge from the model. We also find the leader and herd mentality effects in the characteristics of the behaviors of human beings in our model. Thus, this work could be used to discover how to promote the emergence of beneficial group behaviors and prevent the emergence of harmful behaviors.

Curvature controlled defect dynamics in topological active nematics

We study the spatiotemporal patterns that emerge when an active nematic film is topologically constraint. These topological constraints allow to control the non-equilibrium dynamics of the active system. We consider ellipsoidal shapes for which the resulting defects are 1/2 disclinations and analyze the relation between their location and dynamics and local geometric properties of the ellipsoid. We highlight two dynamic modes: a tunable periodic state that oscillates between two defect configurations on a spherical shape and a tunable rotating state for oblate spheroids. We further demonstrate the relation between defects and high Gaussian curvature and umbilical points and point out limits for a coarse-grained description of defects as self-propelled particles.

Local interactions and global properties of wild, free-ranging stickleback shoals

Collective motion describes the global properties of moving groups of animals and the self-organized, coordinated patterns of individual behaviour that produce them. We examined the group-level patterns and local interactions between individuals in wild, free-ranging shoals of three-spine sticklebacks, Gasterosteus aculeatus. Our data reveal that the highest frequencies of near-neighbour encounters occur at between one and two body lengths from a focal fish, with the peak frequency alongside a focal individual. Fish also show the highest alignment with these laterally placed individuals, and generally with animals in front of themselves. Furthermore, fish are more closely matched in size, speed and orientation to their near neighbours than to more distant neighbours, indicating local organization within groups. Among the group-level properties reported here, we find that polarization is strongly influenced by group speed, but also the variation in speed among individuals and the nearest neighbour distances of group members. While we find no relationship between group order and group size, we do find that larger groups tend to have lower nearest neighbour distances, which in turn may be important in maintaining group order.

Collective behaviour in vertebrates: a sensory perspective

Collective behaviour models can predict behaviours of schools, flocks, and herds. However, in many cases, these models make biologically unrealistic assumptions in terms of the sensory capabilities of the organism, which are applied across different species. We explored how sensitive collective behaviour models are to these sensory assumptions. Specifically, we used parameters reflecting the visual coverage and visual acuity that determine the spatial range over which an individual can detect and interact with conspecifics. Using metric and topological collective behaviour models, we compared the classic sensory parameters, typically used to model birds and fish, with a set of realistic sensory parameters obtained through physiological measurements. Compared with the classic sensory assumptions, the realistic assumptions increased perceptual ranges, which led to fewer groups and larger group sizes in all species, and higher polarity values and slightly shorter neighbour distances in the fish species. Overall, classic visual sensory assumptions are not representative of many species showing collective behaviour and constrain unrealistically their perceptual ranges. More importantly, caution must be exercised when empirically testing the predictions of these models in terms of choosing the model species, making realistic predictions, and interpreting the results.

Understanding how animal groups achieve coordinated movement

Moving animal groups display remarkable feats of coordination. This coordination is largely achieved when individuals adjust their movement in response to their neighbours' movements and positions. Recent advancements in automated tracking technologies, including computer vision and GPS, now allow researchers to gather large amounts of data on the movements and positions of individuals in groups. Furthermore, analytical techniques from fields such as statistical physics now allow us to identify the precise interaction rules used by animals on the move. These interaction rules differ not only between species, but also between individuals in the same group. These differences have wide-ranging implications, affecting how groups make collective decisions and driving the evolution of collective motion. Here, I describe how trajectory data can be used to infer how animals interact in moving groups. I give examples of the similarities and differences in the spatial and directional organisations of animal groups between species, and discuss the rules that animals use to achieve this organisation. I then explore how groups of the same species can exhibit different structures, and ask whether this results from individuals adapting their interaction rules. I then examine how the interaction rules between individuals in the same groups can also differ, and discuss how this can affect ecological and evolutionary processes. Finally, I suggest areas of future research.

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.

A stochastic vision-based model inspired by zebrafish collective behaviour in heterogeneous environments

Collective motion is one of the most ubiquitous behaviours displayed by social organisms and has led to the development of numerous models. Recent advances in the understanding of sensory system and information processing by animals impels one to revise classical assumptions made in decisional algorithms. In this context, we present a model describing the three-dimensional visual sensory system of fish that adjust their trajectory according to their perception field. Furthermore, we introduce a stochastic process based on a probability distribution function to move in targeted directions rather than on a summation of influential vectors as is classically assumed by most models. In parallel, we present experimental results of zebrafish (alone or in group of 10) swimming in both homogeneous and heterogeneous environments. We use these experimental data to set the parameter values of our model and show that this perception-based approach can simulate the collective motion of species showing cohesive behaviour in heterogeneous environments. Finally, we discuss the advances of this multilayer model and its possible outcomes in biological, physical and robotic sciences.

Locust Collective Motion and Its Modeling

Over the past decade, technological advances in experimental and animal tracking techniques have motivated a renewed theoretical interest in animal collective motion and, in particular, locust swarming. This review offers a comprehensive biological background followed by comparative analysis of recent models of locust collective motion, in particular locust marching, their settings, and underlying assumptions. We describe a wide range of recent modeling and simulation approaches, from discrete agent-based models of self-propelled particles to continuous models of integro-differential equations, aimed at describing and analyzing the fascinating phenomenon of locust collective motion. These modeling efforts have a dual role: The first views locusts as a quintessential example of animal collective motion. As such, they aim at abstraction and coarse-graining, often utilizing the tools of statistical physics. The second, which originates from a more biological perspective, views locust swarming as a scientific problem of its own exceptional merit. The main goal should, thus, be the analysis and prediction of natural swarm dynamics. We discuss the properties of swarm dynamics using the tools of statistical physics, as well as the implications for laboratory experiments and natural swarms. Finally, we stress the importance of a combined-interdisciplinary, biological-theoretical effort in successfully confronting the challenges that locusts pose at both the theoretical and practical levels.

Diffusion and topological neighbours in flocks of starlings: relating a model to empirical data

Moving in a group while avoiding collisions with group members causes internal dynamics in the group. Although these dynamics have recently been measured quantitatively in starling flocks (Sturnus vulgaris), it is unknown what causes them. Computational models have shown that collective motion in groups is likely due to attraction, avoidance and, possibly, alignment among group members. Empirical studies show that starlings adjust their movement to a fixed number of closest neighbours or topological range, namely 6 or 7 and assume that each of the three activities is done with the same number of neighbours (topological range). Here, we start from the hypothesis that escape behavior is more effective at preventing collisions in a flock when avoiding the single closest neighbor than compromising by avoiding 6 or 7 of them. For alignment and attraction, we keep to the empirical topological range. We investigate how avoiding one or several neighbours affects the internal dynamics of flocks of starlings in our computational model StarDisplay. By comparing to empirical data, we confirm that internal dynamics resemble empirical data more closely if flock members avoid merely their single, closest neighbor. Our model shows that considering a different number of interaction partners per activity represents a useful perspective and that changing a single parameter, namely the number of interaction partners that are avoided, has several effects through selforganisation.

Active swarms on a sphere

We show that coupling to curvature nontrivially affects collective motion in active systems, leading to motion patterns not observed in flat space. Using numerical simulations, we study a model of self-propelled particles with polar alignment and soft repulsion confined to move on the surface of a sphere. We observe a variety of motion patterns with the main hallmarks being polar vortex and circulating band states arising due to the incompatibility between spherical topology and uniform motion-a consequence of the "hairy ball" theorem. We provide a detailed analysis of density, velocity, pressure, and stress profiles in the circulating band state. In addition, we present analytical results for a simplified model of collective motion on the sphere showing that frustration due to curvature leads to stable elastic distortions storing energy in the band.

Ordering dynamics in collectively swimming Surf Scoters

One striking feature of collective motion in animal groups is a high degree of alignment among individuals, generating polarized motion. When order is lost, the dynamic process of reorganization, directly resulting from the individual interaction rules, provides significant information about both the nature of the rules, and how these rules affect the functioning of the collective. By analyzing trajectories of collectively swimming Surf Scoters (Melanitta perspicillata) during transitions between order and disorder, I find that individual speed and polarization are positively correlated in time, such that individuals move more slowly in groups exhibiting lower alignment. A previously validated zone-based model framework is used to specify interactions that permit repolarization while maintaining group cohesion and avoiding collisions. Polarization efficiency is optimized under the constraints of cohesion and collision-avoidance for alignment-dominated propulsion (versus autonomous propulsion), and for repulsion an order of magnitude larger than attraction and alignment. The relative strengths of interactions that optimize polarization also quantitatively recover the speed-polarization dependence observed in the data. Parameters determined here through optimizing polarization efficiency are essentially the same as those determined previously from a different approach: a best-fit model for polarized Surf Scoter movement data. The rules governing these flocks are therefore robust, accounting for behavior across a range of order and structure, and also highly responsive to perturbation. Flexibility and efficient repolarization offers an adaptive explanation for why specific interactions in such animal groups are used.

Influence of the number of topologically interacting neighbors on swarm dynamics

Recent empirical and theoretical works on collective behaviors based on a topological interaction are beginning to offer some explanations as for the physical reasons behind the selection of a particular number of nearest neighbors locally affecting each individual's dynamics. Recently, flocking starlings have been shown to topologically interact with a very specific number of neighbors, between six to eight, while metric-free interactions were found to govern human crowd dynamics. Here, we use network- and graph-theoretic approaches combined with a dynamical model of locally interacting self-propelled particles to study how the consensus reaching process and its dynamics are influenced by the number k of topological neighbors. Specifically, we prove exactly that, in the absence of noise, consensus is always attained with a speed to consensus strictly increasing with k. The analysis of both speed and time to consensus reveals that, irrespective of the swarm size, a value of k ~ 10 speeds up the rate of convergence to consensus to levels close to the one of the optimal all-to-all interaction signaling. Furthermore, this effect is found to be more pronounced in the presence of environmental noise.

Schools of fish and flocks of birds: their shape and internal structure by self-organization

Models of self-organization have proved useful in revealing what processes may underlie characteristics of swarms. In this study, we review model-based explanations for aspects of the shape and internal structure of groups of fish and of birds travelling undisturbed (without predator threat). Our models attribute specific collective traits to locomotory properties. Fish slow down to avoid collisions and swim at a constant depth, whereas birds fly at low variability of speed and lose altitude during turning. In both the models of fish and birds, the 'bearing angle' to the nearest neighbour emerges as a side-effect of the 'blind angle' behind individuals and when group size becomes larger, temporary subgroups may increase the complexity of group shape and internal structure. We discuss evidence for model-based predictions and provide a list of new predictions to be tested empirically.

Using field data to test locust migratory band collective movement models

Wingless locust nymphs can form massive migratory groups known as bands, whose coordinated movement results from local interactions. We analysed the spatial distribution of locusts within naturally occurring bands and compared them with computer simulations to infer which interaction rules are used by individuals. We found that the empirical radial distribution of neighbours around a focal individual was isotropic, indicating a tendency for locusts to interact with neighbours all around them, rather than a bias towards pursuing individuals ahead or escaping from the ones following behind. By using maps of neighbour densities and pair correlation functions, we found evidence for a short-range repulsion force, balanced by a clustering force, presumably alignment and/or attraction, at a distance of around 3 cm. These results were similar to those observed when using a 'zonal' self-propelled particles model where repulsion/alignment/attraction forces are delimited by concentric circular zones of set radii. However, the profiles obtained either by using different combinations of forces, limiting the number of neighbours involved in interactions, or by varying the range of some zones, all appeared to produce similar results, thereby limiting the ability to more precisely determine the rules underlying locust interactions.

From social network (centralized vs. decentralized) to collective decision-making (unshared vs. shared consensus)

Relationships we have with our friends, family, or colleagues influence our personal decisions, as well as decisions we make together with others. As in human beings, despotism and egalitarian societies seem to also exist in animals. While studies have shown that social networks constrain many phenomena from amoebae to primates, we still do not know how consensus emerges from the properties of social networks in many biological systems. We created artificial social networks that represent the continuum from centralized to decentralized organization and used an agent-based model to make predictions about the patterns of consensus and collective movements we observed according to the social network. These theoretical results showed that different social networks and especially contrasted ones--star network vs. equal network--led to totally different patterns. Our model showed that, by moving from a centralized network to a decentralized one, the central individual seemed to lose its leadership in the collective movement's decisions. We, therefore, showed a link between the type of social network and the resulting consensus. By comparing our theoretical data with data on five groups of primates, we confirmed that this relationship between social network and consensus also appears to exist in animal societies.

Quantifying the interplay between environmental and social effects on aggregated-fish dynamics

Demonstrating and quantifying the respective roles of social interactions and external stimuli governing fish dynamics is key to understanding fish spatial distribution. If seminal studies have contributed to our understanding of fish spatial organization in schools, little experimental information is available on fish in their natural environment, where aggregations often occur in the presence of spatial heterogeneities. Here, we applied novel modeling approaches coupled to accurate acoustic tracking for studying the dynamics of a group of gregarious fish in a heterogeneous environment. To this purpose, we acoustically tracked with submeter resolution the positions of twelve small pelagic fish (Selar crumenophthalmus) in the presence of an anchored floating object, constituting a point of attraction for several fish species. We constructed a field-based model for aggregated-fish dynamics, deriving effective interactions for both social and external stimuli from experiments. We tuned the model parameters that best fit the experimental data and quantified the importance of social interactions in the aggregation, providing an explanation for the spatial structure of fish aggregations found around floating objects. Our results can be generalized to other gregarious species and contexts as long as it is possible to observe the fine-scale movements of a subset of individuals.

Some causes of the variable shape of flocks of birds

Flocks of birds are highly variable in shape in all contexts (while travelling, avoiding predation, wheeling above the roost). Particularly amazing in this respect are the aerial displays of huge flocks of starlings (Sturnus vulgaris) above the sleeping site at dawn. The causes of this variability are hardly known, however. Here we hypothesise that variability of shape increases when there are larger local differences in movement behaviour in the flock. We investigate this hypothesis with the help of a model of the self-organisation of travelling groups, called StarDisplay, since such a model has also increased our understanding of what causes the oblong shape of schools of fish. The flocking patterns in the model prove to resemble those of real birds, in particular of starlings and rock doves. As to shape, we measure the relative proportions of the flock in several ways, which either depend on the direction of movement or do not. We confirm that flock shape is usually more variable when local differences in movement in the flock are larger. This happens when a) flock size is larger, b) interacting partners are fewer, c) the flock turnings are stronger, and d) individuals roll into the turn. In contrast to our expectations, when variability of speed in the flock is higher, flock shape and the positions of members in the flock are more static. We explain this and indicate the adaptive value of low variability of speed and spatial restriction of interaction and develop testable hypotheses.