Moving Animal Groups Research Articles

Confinement-driven state transition and bistability in schooling fish.

We investigate the impact of confinement density (i.e., the number of individuals in a group per unit area of available space) on transitions from the polarized to milling state, using groups of rummy-nose tetra fish (Hemigrammus rhodostomus) under controlled experimental conditions. We demonstrate a continuous state transition controlled by confinement density in a group of live animals. During this transition, the school exhibits a bistable state, wherein both polarization and milling states coexist, with the group randomly alternating between them. A simple two-state Markov process describes the observed transition remarkably well. The confinement density influences the statistics of this bistability, shaping the distribution of transition times between states. Our findings suggest that confinement plays a crucial role in state transitions for moving animal groups. More generally, they provide an experimental benchmark for active matter models of macroscopic, self-propelled, confined agents.

Signatures of criticality in turning avalanches of schooling fish

Moving animal groups transmit information through propagating waves or behavioral cascades, exhibiting characteristics akin to systems near a critical point from statistical physics. Using data from freely swimming schooling fish in an experimental tank, we investigate spontaneous behavioral cascades involving turning avalanches, where large directional shifts propagate across the group. We analyze several avalanche metrics and provide a detailed picture of the dynamics associated with turning avalanches, employing tools from avalanche behavior in condensed-matter physics and seismology. Our results identify power-law distributions and robust scale-free behavior through data collapses and scaling relationships, confirming a necessary condition for criticality in fish schools. We explore the biological function of turning avalanches and link them to collective decision-making processes in selecting a new movement direction for the school. We report relevant boundary effects arising from interactions with the tank walls and influential roles of boundary individuals. Finally, spatial and temporal correlations in avalanches are explored using the concept of aftershocks from seismology, revealing clustering of avalanche events below a designated timescale and an Omori law with a faster decay rate than observed in earthquakes. Published by the American Physical Society 2024

Compromise or choose: shared movement decisions in wild vulturine guineafowl

Shared-decision making is beneficial for the maintenance of group-living. However, little is known about whether consensus decision-making follows similar processes across different species. Addressing this question requires robust quantification of how individuals move relative to each other. Here we use high-resolution GPS-tracking of two vulturine guineafowl (Acryllium vulturinum) groups to test the predictions from a classic theoretical model of collective motion. We show that, in both groups, all individuals can successfully initiate directional movements, although males are more likely to be followed than females. When multiple group members initiate simultaneously, follower decisions depend on directional agreement, with followers compromising directions if the difference between them is small or choosing the majority direction if the difference is large. By aligning with model predictions and replicating the findings of a previous field study on olive baboons (Papio anubis), our results suggest that a common process governs collective decision-making in moving animal groups.

An Alignment-Free Explanation for Collective Predator Evasion in Moving Animal Groups

Moving animal groups consist of many distinct individuals but can operate and function as one unit when performing different tasks. Effectively evading unexpected predator attacks is one primary task for many moving groups. The current explanation for predator evasion responses in moving animal groups require the individuals in the groups to interact via (velocity) alignment. However, experiments have shown that some animals do not use alignment. This suggests that another explanation for the predator evasion capacity in at least these species is needed. Here we establish that effective collective predator evasion does not require alignment, it can be induced via attraction and repulsion alone. We also show that speed differences between individuals that have directly observed the predator and those that have not influence evasion success and the speed of the collective evasion process, but are not required to induce the phenomenon. Our work here adds collective predator evasion to a number of phenomena previously thought to require alignment interactions that have recently been shown to emerge from attraction and repulsion alone. Based on our findings we suggest experiments and make predictions that may lead to a deeper understanding of not only collective predator evasion but also collective motion in general.

Asymmetric Interactions Induce Bistability and Switching Behavior in Models of Collective Motion

Moving animal groups often spontaneously change their group structure and dynamics, but standard models used to explain collective motion in animal groups are typically unable to generate changes of this type. Recently, a model based on attraction, repulsion and asymmetric interactions designed for specific fish experiments was shown capable of producing such changes. However, the origin of the model’s ability to generate them, and the range of this capacity, remains unknown. Here we modify and extend this model to address these questions. We establish that its ability to generate groups exhibiting changes depends on the size of the blind zone parameter β. Specifically, we show that for small β swarms and mills are generated, for larger β polarized groups forms, and for a region of intermediate β values there is a bistability region where continuous switching between milling and polarized groups occurs. We also show that the location of the bistability region depends on group size and the relative strength of velocity alignment when this interaction is added to the model. These findings may contribute to advance the use of self-propelled particle models to explain a range of disruptive phenomena previously thought to be beyond the capabilities of such models.

Disentangling influence over group speed and direction reveals multiple patterns of influence in moving meerkat groups

Animals that travel together in groups must constantly come to consensus about both the direction and speed of movement, often simultaneously. Contributions to collective decisions may vary among group members, yet inferring who has influence over group decisions is challenging, largely due to the multifaceted nature of influence. Here we collected high-resolution GPS data from five habituated meerkat groups in their natural habitat during foraging and developed a method to quantify individual influence over both group direction and speed. We find that individual influence over direction and speed are correlated, but also exhibit substantial variation. Comparing patterns across social statuses reveals that dominant females have higher influence than other individuals over both group direction and speed. Individuals with high influence also tend to spend more time in the front of the group. We discuss our results in light of meerkat life-history and current literature on influence during group movement. Our method provides a general approach which can be applied to disentangle individual influence over group direction and speed in a wide range of species with cohesive movement, emphasizing the importance of integrating multiple lines of inquiry when inferring influence in moving animal groups.

The impact of individual perceptual and cognitive factors on collective states in a data-driven fish school model.

In moving animal groups, social interactions play a key role in the ability of individuals to achieve coordinated motion. However, a large number of environmental and cognitive factors are able to modulate the expression of these interactions and the characteristics of the collective movements that result from these interactions. Here, we use a data-driven fish school model to quantitatively investigate the impact of perceptual and cognitive factors on coordination and collective swimming patterns. The model describes the interactions involved in the coordination of burst-and-coast swimming in groups of Hemigrammus rhodostomus. We perform a comprehensive investigation of the respective impacts of two interactions strategies between fish based on the selection of the most or the two most influential neighbors, of the range and intensity of social interactions, of the intensity of individual random behavioral fluctuations, and of the group size, on the ability of groups of fish to coordinate their movements. We find that fish are able to coordinate their movements when they interact with their most or two most influential neighbors, provided that a minimal level of attraction between fish exist to maintain group cohesion. A minimal level of alignment is also required to allow the formation of schooling and milling. However, increasing the strength of social interactions does not necessarily enhance group cohesion and coordination. When attraction and alignment strengths are too high, or when the heading random fluctuations are too large, schooling and milling can no longer be maintained and the school switches to a swarming phase. Increasing the interaction range between fish has a similar impact on collective dynamics as increasing the strengths of attraction and alignment. Finally, we find that coordination and schooling occurs for a wider range of attraction and alignment strength in small group sizes.

Bistability and Switching Behavior in Moving Animal Groups

Moving animal groups such as schools of fish and flocks of birds frequently switch between different group structures. Standard models of collective motion have been used successfully to explain how stable groups form via local interactions between individuals, but they are typically unable to produce groups that exhibit spontaneous switching. We are only aware of one model, constructed for barred flagtail fish that are known to rely on alignment and attraction to organize their collective motion, that has been shown to generate this type of behavior in 2D (or 3D). Interestingly, another species of fish, golden shiners, do exhibit switching but have been shown to use attraction and repulsion, not alignment, to coordinate themselves in schools. Suggesting that switching may be explained by attraction and repulsion alone, without an alignment interaction. Here we introduce a model based on attraction and repulsion only and show that groups exhibiting switching similar to that observed in experiments with golden shiners emerges. We also establish that switching occur in two boundary-free extensions of the model. Our work suggests that the bistability and switching behavior observed in golden shiners and other moving animal groups may be explained via attractive and repulsive interactions alone.

Attraction vs. Alignment as Drivers of Collective Motion

Moving animal groups exhibit a range of fascinating behaviors. The standard explanation for how these groups form and function is that the individual animals interact via attraction, repulsion, and alignment, where alignment is proposed to drive the collective motion. However, it has been shown both experimentally and theoretically that alignment interactions are not required to induce group level alignment. In particular, via the use of self-propelled particle models it has been established that several other mechanisms induce group level alignment (aka polarization) in combination with attraction alone. However, no systematic comparison of these mechanisms among themselves, or with explicit alignment, has been presented and it remains unclear how, or even if, they can be distinguished at the collective level. Here, we introduce two previously unreported mechanisms, burst-and-glide and burst-and-stop, and show via simulation that they also induce polarization in combination with attraction alone. Then, we compare the polarization inducing characteristics of six mechanisms; asymmetric interactions, asynchrony, anticipation, burst-and-glide, burst-and stop, and explicit alignment. We show that the mechanisms induce polarization in different parts of the attraction parameter space, that the route to polarization from uniformly random initial conditions, as well as repolarization following strong perturbations, is markedly different among the mechanisms. In particular, we find that alignment based and non-alignment based mechanisms can be distinguished via their polarization and repolarization processes. These findings further challenge the current alignment based theory of collective motion and may contribute to a more versatile theory of collective motion across scales.

Collective close calling mediates group cohesion in foraging meerkats via spatially determined differences in call rates

During group movements, many socially living and group-foraging animals produce contact calls. Contact calls typically function to coordinate and maintain cohesion among group members by providing receivers with information on the callers' location or movement-related motivation. Previous work suggests that meerkats, Suricata suricatta, also produce short-range contact calls, so-called ‘close calls’, while foraging to maintain group cohesion. Yet, the underlying mechanism of how meerkats coordinate cohesion via close calling is unclear. Using a combination of field observations and playback experiments we here show that foraging meerkats adjusted the call rates of their continuously produced close calls depending on their spatial position to group members. Specifically, meerkats called at higher rates when foraging at a closer distance to and when surrounded by conspecifics; however, the number of calling individuals or their call rates did not affect a subject's close call rate. Overall, close call playbacks elicited a call response in receivers and attracted them to the sound source. Our results suggest that differences in individual close call rates are determined by a meerkat's proximity to other group members, being assessed through their vocal interactions. We discuss how local differences in individual call rates may extrapolate to the group level, where emerging ‘vocal hotspots’ indicate areas of high individual density, in turn attracting and potentially guiding group members' movements. Hence, the described pattern illustrates a so far undocumented call mechanism where local differences in the call rates of continuously produced close calls can generate a group level pattern that mediates the cohesion of progressively moving animal groups.

A statistical method for identifying different rules of interaction between individuals in moving animal groups.

The emergent patterns of collective motion are thought to arise from application of individual-level rules that govern how individuals adjust their velocity as a function of the relative position and behaviours of their neighbours. Empirical studies have sought to determine such rules of interaction applied by 'average' individuals by aggregating data from multiple individuals across multiple trajectory sets. In reality, some individuals within a group may interact differently from others, and such individual differences can have an effect on overall group movement. However, comparisons of rules of interaction used by individuals in different contexts have been largely qualitative. Here we introduce a set of randomization methods designed to determine statistical differences in the rules of interaction between individuals. We apply these methods to a case study of leaders and followers in pairs of freely exploring eastern mosquitofish (Gambusia holbrooki). We find that each of the randomization methods is reliable in terms of: repeatability of p-values, consistency in identification of significant differences and similarity between distributions of randomization-based test statistics. We observe convergence of the distributions of randomization-based test statistics across repeat calculations, and resolution of any ambiguities regarding significant differences as the number of randomization iterations increases.

Anticipation Induces Polarized Collective Motion in Attraction Based Models

Moving animal groups are prime examples of natural complex systems. In most models of such systems each individual updates its heading based on the current positions and headings of its neighbors. However, recently, a number of models where the heading update instead is based on the future anticipated positions/headings of the neighbors have been published. Collectively these studies have established that including anticipation may have drastically different effects in different models. In particular, anticipation inhibits polarization in alignment-based models and in one alignment-free model, but promotes polarization in another alignment-free model. Indicating that our understanding of how anticipation affects the behavior of alignment-free models is incomplete. Given that attraction is a component of many alignment-free models we include anticipation in an attraction only model here to investigate. We establish that anticipation induces polarized collective motion and inhibits swarming and milling in combination with attraction alone. We also show that anticipation orients milling groups when attraction is sufficiently strong, but not otherwise. Finally, we derive an explicit heading update formula for this model with anticipation that allows for a simple heuristic explanation of its polarization inducing capacity. Due to the biological plausibility of both attraction and anticipation we believe that utilizing these components to explain collective motion in animal groups may be advantageous in some cases.

A data-driven method for reconstructing and modelling social interactions in moving animal groups.

Group-living organisms that collectively migrate range from cells and bacteria to human crowds, and include swarms of insects, schools of fish, and flocks of birds or ungulates. Unveiling the behavioural and cognitive mechanisms by which these groups coordinate their movements is a challenging task. These mechanisms take place at the individual scale and can be described as a combination of interactions between individuals and interactions between these individuals and the physical obstacles in the environment. Thanks to the development of novel tracking techniques that provide large and accurate datasets, the main characteristics of individual and collective behavioural patterns can be quantified with an unprecedented level of precision. However, in a large number of studies, social interactions are usually described by force map methods that only have a limited capacity of explanation and prediction, being rarely suitable for a direct implementation in a concise and explicit mathematical model. Here, we present a general method to extract the interactions between individuals that are involved in the coordination of collective movements in groups of organisms. We then apply this method to characterize social interactions in two species of shoaling fish, the rummy-nose tetra (Hemigrammus rhodostomus) and the zebrafish (Danio rerio), which both present a burst-and-coast motion. From the detailed quantitative description of individual-level interactions, it is thus possible to develop a quantitative model of the emergent dynamics observed at the group level, whose predictions can be checked against experimental results. This method can be applied to a wide range of biological and social systems. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Predators attacking virtual prey reveal the costs and benefits of leadership

A long-standing assumption in social behavior is that leadership incurs costs as well as benefits, and this tradeoff can result in diversified social roles in groups. The major cost of leadership in moving animal groups is assumed to be predation, with individuals leading from the front of groups being targeted more often by predators. Nevertheless, empirical evidence for this is limited, and experimental tests are entirely lacking. To avoid confounding effects associated with observational studies, we presented a simulation of virtual prey to real fish predators to directly assess the predation cost of leadership. Prey leading others are at greater risk than those in the middle of groups, confirming that any benefits of leading may be offset by predation costs. Importantly, however, followers confer a net safety benefit to leaders, as prey leading others were less likely to be attacked compared with solitary prey. We also find that the predators preferentially attacked when solitary individuals were more frequent, but this effect was relatively weak compared with the preference for attacking solitary prey during an attack. Using virtual prey, where the appearance and behavior of the prey can be manipulated and controlled exactly, we reveal a hierarchy of risk from solitary to leading to following social strategies. Our results suggest that goal-orientated individuals (i.e., potential leaders) are under selective pressure to maintain group cohesion, favoring effective leadership rather than group fragmentation. Our results have significant implications for understanding the evolution and maintenance of different social roles in groups.

Speed-mediated properties of schooling.

Collectively moving animals often display a high degree of synchronization and cohesive group-level formations, such as elongated schools of fish. These global patterns emerge as the result of localized rules of interactions. However, the exact relationship between speed, polarization, neighbour positioning and group structure has produced conflicting results and is largely limited to modelling approaches. This hinders our ability to understand how information spreads between individuals, which may determine the collective functioning of groups. We tested how speed interacts with polarization and positional composition to produce the elongation observed in moving groups of fish as well as how this impacts information flow between individuals. At the local level, we found that increases in speed led to increases in alignment and shifts from lateral to linear neighbour positioning. At the global level, these increases in linear neighbour positioning resulted in elongation of the group. Furthermore, mean pairwise transfer entropy increased with speed and alignment, implying an adaptive value to forming faster, more polarized and linear groups. Ultimately, this research provides vital insight into the mechanisms underlying the elongation of moving animal groups and highlights the functional significance of cohesive and coordinated movement.

The milling pattern in animal groups and its dependence on the density and on the number of particles

Moving animal groups often exhibit aggregation behavior. In many species, the collective behavior invariably depends on local interactions among individuals. In such groups, the mechanism of group formation require that interaction rules be followed by all members, and as consequence, animal aggregates such as schools of fish, flocks of birds, and swarms of locusts exhibit a variety of dynamical behavior patterns. In this paper we investigated only the milling pattern. Of particular interest to us is to analyze its dependence on the density and on the number of particles. We found that the milling formation depends of these two physical quantities.

Social conformity and propagation of information in collective U-turns of fish schools.

Moving animal groups such as schools of fishes or flocks of birds often undergo sudden collective changes of their travelling direction as a consequence of stochastic fluctuations in heading of the individuals. However, the mechanisms by which these behavioural fluctuations arise at the individual level and propagate within a group are still unclear. In this study, we combine an experimental and theoretical approach to investigate spontaneous collective U-turns in groups of rummy-nose tetra (Hemigrammus rhodostomus) swimming in a ring-shaped tank. U-turns imply that fish switch their heading between the clockwise and anticlockwise direction. We reconstruct trajectories of individuals moving alone and in groups of different sizes. We show that the group decreases its swimming speed before a collective U-turn. This is in agreement with previous theoretical predictions showing that speed decrease facilitates an amplification of fluctuations in heading in the group, which can trigger U-turns. These collective U-turns are mostly initiated by individuals at the front of the group. Once an individual has initiated a U-turn, the new direction propagates through the group from front to back without amplification or dampening, resembling the dynamics of falling dominoes. The mean time between collective U-turns sharply increases as the size of the group increases. We develop an Ising spin model integrating anisotropic and asymmetrical interactions between fish and their tendency to follow the majority of their neighbours nonlinearly (social conformity). The model quantitatively reproduces key features of the dynamics and the frequency of collective U-turns observed in experiments.

Inferring influence and leadership in moving animal groups.

Collective decision-making is a daily occurrence in the lives of many group-living animals, and can have critical consequences for the fitness of individuals. Understanding how decisions are reached, including who has influence and the mechanisms by which information and preferences are integrated, has posed a fundamental challenge. Here, we provide a methodological framework for studying influence and leadership in groups. We propose that individuals have influence if their actions result in some behavioural change among their group-mates, and are leaders if they consistently influence others. We highlight three components of influence (influence instances, total influence and consistency of influence), which can be assessed at two levels (individual-to-individual and individual-to-group). We then review different methods, ranging from individual positioning within groups to information-theoretic approaches, by which influence has been operationally defined in empirical studies, as well as how such observations can be aggregated to give insight into the underlying decision-making process. We focus on the domain of collective movement, with a particular emphasis on methods that have recently been, or are being, developed to take advantage of simultaneous tracking data. We aim to provide a resource bringing together methodological tools currently available for studying leadership in moving animal groups, as well as to discuss the limitations of current methodologies and suggest productive avenues for future research.This article is part of the theme issue 'Collective movement ecology'.

Crimson Spotted Rainbowfish (Melanotaenia duboulayi) Change Their Spatial Position according to Nutritional Requirement.

Decision making in moving animal groups has been shown to be disproportionately influenced by individuals at the front of groups. Therefore, an explanation of state-dependent positioning of individuals within animal groups may provide a mechanism for group movement decisions. Nutritional state is dynamic and can differ between members of the same group. It is also known to drive animal movement decisions. Therefore, we assayed 6 groups of 8 rainbowfish foraging in a flow tank. Half of the fish had been starved for 24h and half had been fed 1h prior to experimental start. Groups were assayed again one week later but individuals were allocated to the opposite nutritional treatment. During the assay the positions of individually identified fish were recorded as were the number of food items they each ate and the position within the group they acquired them from. Food-deprived fish were more often found towards the front of the shoal; the mean weighted positional score of food-deprived fish was significantly larger than that of well-fed fish. Individuals were not consistent in their position within a shoal between treatments. There was a significant positive correlation between mean weighted positional score and number of food items acquired which displays an obvious benefit to front positions. These results suggest that positional preferences are based on nutritional state and provide a mechanism for state-dependent influence on group decision-making as well as increasing our understanding of what factors are important for group functioning.

The shape and dynamics of local attraction

Moving animal groups, such as flocks of birds or schools of fish, exhibit a varity of self-organized complex dynamical behaviors and shapes. This kind of flocking behavior has been studied using self-propelled particle models, in which the “particles” interact with their nearest neighbors through repulsion, attraction and alignment responses. In particular, it has been shown that models based on attraction alone can generate a range of dynamic groups in 2D, with periodic boundary conditions, and in the absence of repulsion. Here we investigate the effects of changing these conditions on the type of groups observed in the model. We show that replacing the periodic boundary conditions with a weak global attaction term in 2D, and extending the model to 3D does not significantly change the type of groups observed. We also provide a description of how attraction strength and blind angle determine the groups generated in the 3D version of the model. Finally, we show that adding repulsion do change the type of groups oberved, making them appear and behave more like real moving animal groups. Our results suggest that many biological instances of collective motion may be explained without assuming that animals explicitly align with each other. Instead, complex collective motion is explained by the interplay of attraction and repulsion forces.