Emergence of Oblong School Shape: Models and Empirical Data of Fish

Interrelationship among spatial cohesion, aggression rate, counter-aggression and female dominance in three lemur species

Abstract

How social and ecological factors are associated with variation in dominance style across species of animals has been studied frequently, but the underlying processes are often not addressed. Theoretical research indicates that stronger spatial cohesion among individuals in a group causes a higher frequency of fighting and, thus, through the self-reinforcing effects of winning and losing fights, a stronger differentiation of the dominance hierarchy and dominance of females over more males. Our aim in the present paper is to study whether the same interrelationship among processes may underlie differences in dominance style among three species of lemur that differ in their degree of despotism: Lemur catta, Propithecus verreauxi and Eulemur rufifrons. We investigated their agonistic interactions and spatial cohesion based on 2752 h of observational data of 20 wild groups of these three species. We determined dominance style using the proportion of counter-aggression, with a lower proportion indicating a more despotic dominance style. We found that stronger spatial cohesion among individuals is associated with a higher rate of aggression, stronger despotism and dominance of females over more males. The results of our study emphasise the general importance of spatial cohesion in determining dominance style.

Significance statement

Theoretical studies have shown that the spatial configuration of individuals in a group influences the dominance style. In an agent-based model, DomWorld, individuals are guided by simple rules of grouping and fighting and emergent patterns of behaviour switch between resembling those of despotic or egalitarian primates depending on the degree of cohesion in groups. Yet this link has seldom been studied empirically. We, therefore, examine the relevance of spatial cohesion on patterns of behaviour of individuals in groups of three species of lemur. We confirm the predictions from the model and show that stronger spatial cohesion results in more frequent aggression, a more despotic dominance style and stronger female dominance over males. In light of this, we urge future research of animal dominance to include measures of cohesion.

Follow the straggler: zebrafish use a simple heuristic for collective decision-making

Animal groups often make decisions sequentially, from the front to the back of the group. In such cases, individuals can use the choices made by earlier ranks, a form of social information, to inform their own choice. The optimal strategy for such decisions has been explored in models which differ on, for example, whether or not agents take into account the sequence of observed choices. The models demonstrate that choices made later in a sequence are more informative, but it is not clear if animals use this information or rely instead on simpler heuristics, such as quorum rules. We show that a simple rule 'copy the last observed choice', gives similar predictions to those of optimal models for most likely sequences. We trained groups of zebrafish to choose one arm of a Y-maze and used them to demonstrate various sequences to naive fish. We show that the naive fish appear to use a simple rule, most often copying the choice of the last demonstrator, which results in near-optimal choices at a fraction of the computational cost.

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

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

Local interactions and their group-level consequences in flocking jackdaws

As one of nature's most striking examples of collective behaviour, bird flocks have attracted extensive research. However, we still lack an understanding of the attractive and repulsive forces that govern interactions between individuals within flocks and how these forces influence neighbours' relative positions and ultimately determine the shape of flocks. We address these issues by analysing the three-dimensional movements of wild jackdaws ( Corvus monedula) in flocks containing 2-338 individuals. We quantify the social interaction forces in large, airborne flocks and find that these forces are highly anisotropic. The long-range attraction in the direction perpendicular to the movement direction is stronger than that along it, and the short-range repulsion is generated mainly by turning rather than changing speed. We explain this phenomenon by considering wingbeat frequency and the change in kinetic and gravitational potential energy during flight, and find that changing the direction of movement is less energetically costly than adjusting speed for birds. Furthermore, our data show that collision avoidance by turning can alter local neighbour distributions and ultimately change the group shape. Our results illustrate the macroscopic consequences of anisotropic interaction forces in bird flocks, and help to draw links between group structure, local interactions and the biophysics of animal locomotion.

Inferring collective behaviour from a fossilized fish shoal

Collective motion by animal groups can emerge from simple rules that govern each individual's interactions with its neighbours. Studies of extant species have shown how such rules yield coordinated group behaviour, but little is known of their evolutionary origins or whether extinct group-living organisms used similar rules. Here, we report evidence consistent with coordinated collective motion in a fossilized group of the extinct fish Erismatopterus levatus, and we infer possible behavioural rules that underlie it. We found traces of two rules for social interaction similar to those used by extant fishes: repulsion from close individuals and attraction towards neighbours at a distance. Moreover, the fossilized fish showed group-level structures in the form of oblong shape and high polarization, both of which we successfully reproduced in simulations incorporating the inferred behavioural rules. Although it remains unclear how the fish shoal's structure was preserved in the fossil, these findings suggest that fishes have been forming shoals by combining sets of simple behavioural rules since at least the Eocene. Our study highlights the possibility of exploring the social communication of extinct animals, which has been thought to leave no fossil record.

Random sequential addition simulations of animal aggregations provide null models of group structure

Apparent structure in animal aggregations such as fish and Antarctic krill schools may result from the tight packing of these elongated animals. This geometrical structure may be difficult to differentiate from behavior-induced structure resulting from individuals preferentially taking up certain positions relative to conspecifics to gain an adaptive advantage such as reduced locomotive cost. Here we use random sequential addition (RSA) simulations to quantify the effect of animal shape, aggregation organization, and aggregation density on 2D school structure. This technique allows for the generation of a null model for nearest neighbor distance and nearest neighbor position angle for a specific body shape and aggregation density, thus isolating the effect of geometry from that of behavior. We further identify a shape-specific aggregation density threshold above which the animal shape affects the spatial distribution of nearest neighbors. Nearest neighbor distance data of fish schools with densities above and below the threshold are found to agree well with nearest neighbor statistics found from RSA-generated schools.

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.

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.

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.

Emergence of a coherent and cohesive swarm based on mutual anticipation

Collective behavior emerging out of self-organization is one of the most striking properties of an animal group. Typically, it is hypothesized that each individual in an animal group tends to align its direction of motion with those of its neighbors. Most previous models for collective behavior assume an explicit alignment rule, by which an agent matches its velocity with that of neighbors in a certain neighborhood, to reproduce a collective order pattern by simple interactions. Recent empirical studies, however, suggest that there is no evidence for explicit matching of velocity, and that collective polarization arises from interactions other than those that follow the explicit alignment rule. We here propose a new lattice-based computational model that does not incorporate the explicit alignment rule but is based instead on mutual anticipation and asynchronous updating. Moreover, we show that this model can realize densely collective motion with high polarity. Furthermore, we focus on the behavior of a pair of individuals, and find that the turning response is drastically changed depending on the distance between two individuals rather than the relative heading, and is consistent with the empirical observations. Therefore, the present results suggest that our approach provides an alternative model for collective behavior.

Mathematical analysis and validation of an exactly solvable model for upstream migration of fish schools in one-dimensional rivers

Upstream migration of fish schools in 1-D rivers as an optimal control problem is formulated where their swimming velocity and the horizontal oblateness are taken as control variables. The objective function to be maximized through a migration process consists of the biological and ecological profit to be gained at the upstream-end of a river, energetic cost of swimming against the flow, and conceptual cost of forming a school. Under simplified conditions where the flow is uniform in both space and time and the profit to be gained at the goal of migration is sufficiently large, the optimal control variables are determined from a system of algebraic equations that can be solved in a cascading manner. Mathematical analysis of the system reveals that the optimal controls are uniquely found and the model is exactly solvable under certain conditions on the functions and parameters, which turn out to be realistic and actually satisfied in experimental fish migration. Identification results of the functional shapes of the functions and the parameters with experimentally observed data of swimming schools of Plecoglossus altivelis (Ayu) validate the present mathematical model from both qualitative and quantitative viewpoints. The present model thus turns out to be consistent with the reality, showing its potential applicability to assessing fish migration in applications.

A Measurement Method for Speed Distribution of Collective Motion with Optical Flow and Its Applications to School of Fish

We propose a measurement method for the mean speed distribution of collective motions of highly dense groups with optical flow based on our previous work. This measurement is fundamental for ecological investigations and mathematical modeling of collective animal behaviors. Our method is applicable to highly dense homogeneous groups wherein individual movements are approximately uniform locally. To measure speed distributions, we partition a group into regions and estimate mean speeds in each region by extracting only flows that are relevant to collective motions and averaging them over a period of time. We apply our method to schools of sardines to measure a kind of speed distribution called rotation curve (RC). As experiments, we first performed simulations and found that our method can estimate flows and RCs accurately. We then performed experiments with videos of real fish. The RCs estimated by our method and ones by manual tracking were approximately equal. We applied our method to a longer video and confirmed that time series of RCs can be estimated automatically. In addition, we detected noticeable events by two features derived from flows. We also applied our method to a school of anchovies. The results indicate that our method is practically useful.

Collective response to perturbations in a data-driven fish school model

Fish schools are able to display a rich variety of collective states and behavioural responses when they are confronted by threats. However, a school's response to perturbations may be different depending on the nature of its collective state. Here we use a previously developed data-driven fish school model to investigate how the school responds to perturbations depending on its different collective states, we measure its susceptibility to such perturbations, and exploit its relation with the intrinsic fluctuations in the school. In particular, we study how a single or a small number of perturbing individuals whose attraction and alignment parameters are different from those of the main population affect the long-term behaviour of a school. We find that the responsiveness of the school to the perturbations is maximum near the transition region between milling and schooling states where the school exhibits multistability and regularly shifts between these two states. It is also in this region that the susceptibility, and hence the fluctuations, of the polarization order parameter is maximal. We also find that a significant school's response to a perturbation only happens below a certain threshold of the noise to social interactions ratio.

Inherent noise appears as a Lévy walk in fish schools

Recent experimental and observational data have revealed that the internal structures of collective animal groups are not fixed in time. Rather, individuals can produce noise continuously within their group. These individuals' movements on the inside of the group, which appear to collapse the global order and information transfer, can enable interactions with various neighbors. In this study, we show that noise generated inherently in a school of ayus (Plecoglossus altivelis) is characterized by various power-law behaviors. First, we show that individual fish move faster than Brownian walkers with respect to the center of the mass of the school as a super-diffusive behavior, as seen in starling flocks. Second, we assess neighbor shuffling by measuring the duration of pair-wise contact and find that this distribution obeys the power law. Finally, we show that an individual's movement in the center of a mass reference frame displays a Lévy walk pattern. Our findings suggest that inherent noise (i.e., movements and changes in the relations between neighbors in a directed group) is dynamically self-organized in both time and space. In particular, Lévy walk in schools can be regarded as a well-balanced movement to facilitate dynamic collective motion and information transfer throughout the group.

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.

Model flocks in a steady vortical flow

We modify the standard Vicsek model to clearly distinguish between intrinsic noise due to imperfect alignment between organisms and extrinsic noise due to fluid motion. We then consider the effect of a steady vortical flow, the Taylor-Green vortex, on the dynamics of the flock, for various flow speeds, with a fixed intrinsic particle speed. We pay particular attention to the morphology of the flow, and quantify its filamentarity. Strikingly, above a critical flow speed there is a pronounced increase in the filamentarity of the flock, when compared to the zero-flow case. This is due to the fact that particles appear confined to areas of low vorticity; a familiar phenomena, commonly seen in the clustering of inertial particles in vortical flows. Hence, the cooperative motion of the particles gives them an effective inertia, which is seen to have a profound effect on the morphology of the flock, in the presence of external fluid motion. Finally, we investigate the angle between the flow and the particles direction of movement and find it follows a power-law distribution.

Emergent runaway into an avoidance area in a swarm of soldier crabs

Emergent behavior that arises from a mass effect is one of the most striking aspects of collective animal groups. Investigating such behavior would be important in order to understand how individuals interact with their neighbors. Although there are many experiments that have used collective animals to investigate social learning or conflict between individuals and society such as that between a fish and a school, reports on mass effects are rare. In this study, we show that a swarm of soldier crabs could spontaneously enter a water pool, which are usually avoided, by forming densely populated part of a swarm at the edge of the water pool. Moreover, we show that the observed behavior can be explained by the model of collective behavior based on inherent noise that is individuals’ different velocities in a directed group. Our results suggest that inherent noise, which is widely seen in collective animals, can contribute to formation and/or maintenance of a swarm and that the dense swarm can enter the pool by means of enhanced inherent noise.

The EMO-model: an agent-based model of primate social behavior regulated by two emotional dimensions, anxiety-FEAR and satisfaction-LIKE

Agent-based models provide a promising tool to investigate the relationship between individuals' behavior and emerging group-level patterns. An individual's behavior may be regulated by its emotional state and its interaction history with specific individuals. Emotional bookkeeping is a candidate mechanism to keep track of received benefits from specific individuals without requiring high cognitive abilities. However, how this mechanism may work is difficult to study in real animals, due to the complexity of primate social life. To explore this theoretically, we introduce an agent-based model, dubbed EMO-model, in which we implemented emotional bookkeeping. In this model the social behaviors of primate-like individuals are regulated by emotional processes along two dimensions. An individual's emotional state is described by an aversive and a pleasant dimension (anxiety and satisfaction) and by its activating quality (arousal). Social behaviors affect the individuals' emotional state. To implement emotional bookkeeping, the receiver of grooming assigns an accumulated affiliative attitude (LIKE) to the groomer. Fixed partner-specific agonistic attitudes (FEAR) reflect the stable dominance relations between group members. While the emotional state affects an individual's general probability of executing certain behaviors, LIKE and FEAR affect the individual's partner-specific behavioral probabilities. In this way, emotional processes regulate both spontaneous behaviors and appropriate responses to received behaviors, while emotional bookkeeping via LIKE attitudes regulates the development and maintenance of affiliative relations. Using an array of empirical data, the model processes were substantiated and the emerging model patterns were partially validated. The EMO-model offers a framework to investigate the emotional bookkeeping hypothesis theoretically and pinpoints gaps that need to be investigated empirically.

On the duality between interaction responses and mutual positions in flocking and schooling

Recent research in animal behaviour has contributed to determine how alignment, turning responses, and changes of speed mediate flocking and schooling interactions in different animal species. Here, we propose a complementary approach to the analysis of flocking phenomena, based on the idea that animals occupy preferential, anysotropic positions with respect to their neighbours, and devote a large amount of their interaction responses to maintaining their mutual positions. We test our approach by deriving the apparent alignment and attraction responses from simulated trajectories of animals moving side by side, or one in front of the other. We show that the anisotropic positioning of individuals, in combination with noise, is sufficient to reproduce several aspects of the movement responses observed in real animal groups. This anisotropy at the level of interactions should be considered explicitly in future models of flocking and schooling. By making a distinction between interaction responses involved in maintaining a preferred flock configuration, and interaction responses directed at changing it, our work provides a frame to discriminate movement interactions that signal directional conflict from interactions underlying consensual group motion.

Interaction rules underlying group decisions in homing pigeons

Travelling in groups gives animals opportunities to share route information by following cues from each other's movement. The outcome of group navigation will depend on how individuals respond to each other within a flock, school, swarm or herd. Despite the abundance of modelling studies, only recently have researchers developed techniques to determine the interaction rules among real animals. Here, we use high-resolution GPS (global positioning system) tracking to study these interactions in pairs of pigeons flying home from a familiar site. Momentary changes in velocity indicate alignment with the neighbour's direction, as well as attraction or avoidance depending on distance. Responses were stronger when the neighbour was in front. From the flocking behaviour, we develop a model to predict features of group navigation. Specifically, we show that the interactions between pigeons stabilize a side-by-side configuration, promoting bidirectional information transfer and reducing the risk of separation. However, if one bird gets in front it will lead directional choices. Our model further predicts, and observations confirm, that a faster bird (as measured from solo flights) will fly slightly in front and thus dominate the choice of homing route. Our results explain how group decisions emerge from individual differences in homing flight behaviour.

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.

The modelling cycle for collective animal behaviour

Collective animal behaviour is the study of how interactions between individuals produce group level patterns, and why these interactions have evolved. This study has proved itself uniquely interdisciplinary, involving physicists, mathematicians, engineers as well as biologists. Almost all experimental work in this area is related directly or indirectly to mathematical models, with regular movement back and forth between models, experimental data and statistical fitting. In this paper, we describe how the modelling cycle works in the study of collective animal behaviour. We classify studies as addressing questions at different levels or linking different levels, i.e. as local, local to global, global to local or global. We also describe three distinct approaches—theory-driven, data-driven and model selection—to these questions. We show, with reference to our own research on species across different taxa, how we move between these different levels of description and how these various approaches can be applied to link levels together.

Bidirectional sorting of flocking particles in the presence of asymmetric barriers

We demonstrate numerically bidirectional sorting of flocking particles interacting with an array of V-shaped asymmetric barriers. Each particle aligns with the average swimming direction of its neighbors according to the Vicsek model and experiences additional steric interactions as well as repulsion from the fixed barriers. We show that particles preferentially localize to one side of the barrier array over time and that the direction of this rectification can be reversed by adjusting the particle-particle exclusion radius or the noise term in the equations of motion. These results provide a conceptual basis for isolation and sorting of single-cell and multicellular organisms that move collectively according to flocking-type interaction rules.

Better safe than sorry--socio-spatial group structure emerges from individual variation in fleeing, avoidance or velocity in an agent-based model

In group-living animals, such as primates, the average spatial group structure often reflects the dominance hierarchy, with central dominants and peripheral subordinates. This central-peripheral group structure can arise by self-organization as a result of subordinates fleeing from dominants after losing a fight. However, in real primates, subordinates often avoid interactions with potentially aggressive group members, thereby preventing aggression and subsequent fleeing. Using agent-based modeling, we investigated which spatial and encounter structures emerge when subordinates also avoid known potential aggressors at a distance as compared with the model which only included fleeing after losing a fight (fleeing model). A central-peripheral group structure emerged in most conditions. When avoidance was employed at small or intermediate distances, centrality of dominants emerged similar to the fleeing model, but in a more pronounced way. This result was also found when fleeing after a fight was made independent of dominance rank, i.e. occurred randomly. Employing avoidance at larger distances yielded more spread out groups. This provides a possible explanation of larger group spread in more aggressive species. With avoidance at very large distances, spatially and socially distinct subgroups emerged. We also investigated how encounters were distributed amongst group members. In the fleeing model all individuals encountered all group members equally often, whereas in the avoidance model encounters occurred mostly among similar-ranking individuals. Finally, we also identified a very general and simple mechanism causing a central-peripheral group structure: when individuals merely differed in velocity, faster individuals automatically ended up at the periphery. In summary, a central-peripheral group pattern can easily emerge from individual variation in different movement properties in general, such as fleeing, avoidance or velocity. Moreover, avoidance behavior also affects the encounter structure and can lead to subgroup formation.

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.