Schooling fish only pay attention to few neighbours for coordinating their collective movements

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How do fish combine information from multiple neighbours when swimming in a school? Dr Lei Liu and Dr Guy Theraulaz based at the Research Centre on Animal Cognition, in Toulouse, France, used both experiments with live animals, as well as computational and robotic modelling to show that using information about two neighbouring fish is sufficient to establish appropriate collective behaviour. It’s important, however, to pick the most influential neighbours, i.e. the ones that show the biggest impact when choosing the school’s direction of travel.

What do flocks of birds, swarms of insects, herds of wildebeest, schools of fish and even crowds of pedestrians have in common? They can all show collective behaviours that can be quite complex. Individuals can respond to opportunities or threats almost simultaneously giving the impression of operating as a single super-organism. Such coordinated response needs specific interaction rules together with efficient and fast transfer of information among all individuals. However, understanding exactly how this information is shared between neighbours is proving a little elusive.

For example, in a group of hundreds of wild fish, how does each animal determine which neighbours to pay attention to? For researchers, this is the crucial element to understand how these groups of animals can coordinate their movements and how information propagates within these groups.

The thinking has changed over the years to answer this question. The earlier models considered that each fish was influenced by all the neighbours located within a certain distance. In contrast, more modern approaches recognise that the movement of each individual in the group is more likely influenced by a small number of neighbours.

Researchers recognise that fish would need an incredible cognitive ability to continually monitor the movements of a large number of neighbours. It’s easy to see that it’s a lot simpler for these animals to only pay attention to a small number of neighbours.

Dr Lei Liu and Dr Guy Theraulaz based at the Research Centre on Animal Cognition, in Toulouse, France, are keen to disentangle these neighbourly interactions, particularly in fish schools. Recently, the team has proved that fish only need to follow one or two other fish to perform collective U-turns. Now, the researchers want to find out if the same pattern is valid when fish are moving together and not performing joint manoeuvres.

They can limit their attention to a small set of the most influential neighbours, immediately identifying which ones to avoid and move away and which ones to follow.

Swimming around and around

For the researchers, this journey started in a circular tank looking at rummy-nose tetra fish (Hemigrammus rhodostomus) swimming around and around. This species of tropical fish is fascinating to study because they swim in a highly synchronised manner alternating periods of bursts in which each fish accelerates and changes direction with more subtle gliding phases. This intermittent movement is ideal for analysing trajectory as a series of decisions about which direction to take. “Just before these brief accelerations, a fish filters the information coming from its environment and picks its resulting new heading”, explain Dr Liu and Dr Theraulaz.

After hours of observing fish swim either alone or in pairs, the team characterised what clues fish may use and measured how their behaviour changed. On one hand, fish avoid each other when the distance was less than two body lengths, but they also didn’t like it when the distance was higher than six to seven body lengths and actively tried to get closer. For most situations, fish aligned their direction with their group mates, especially when the distance between the fish was a comfortable three body lengths. The influence of a fish on another fish also depends on the direction it is moving in, and especially the “angle of vision” with which it perceives the other fish. Finally, the intensity of social interactions between two fish depends on the direction of their movement with respect to each other. This perception anisotropy leads to asymmetry in what is known as the “social force” exerted on fish A by fish B and that exerted on fish B by fish A.

Photo credit: David Villa ScienceImage/CBI/CNRS, Toulouse

This method may sound simple, but the team determined it was enough to explain how slight changes in direction in a small number of fish could drastically change the whole group. For example, in the wild, fish may be forced to move from travelling in a specific direction (schooling) to adapting a more protective circular swimming (milling) when a predator is detected. The researchers also detected what is known in the fish world as counter-milling behaviour, where occasionally some fish started swimming in the opposite direction to the rest of the group, to ensure that individuals swapped their positions at the front.

In addition, fish reacted to obstacles in their environment. In this case, the tank wall was the obvious barrier. The researchers found that fish quickly changed their direction if heading to the wall at a 45-degree angle, but these animals were happy to swim parallel to the edge.

Strategies for interaction

Over the past few years, and after many experiments following swimming patterns in fish, Dr Liu, Dr Theraulaz and their team developed a general method to extract from tracking data the interactions between fish that are involved in the coordination of their collective movements. They also used this method to develop a computer model to predict the collective behaviours of these animals. Using this model, the researchers tested three different strategies to assess how each individual fish decides which neighbours to pay attention to. The three strategies included selecting the nearest fish, a random fish or the fish that exerted the largest influence on their behaviour.

Dr Liu and Dr Theraulaz were impressed with the results. “The simulation results clearly indicate that group behaviours can be reproduced by our model, not only qualitatively but also quantitatively, provided that individuals interact with at least two of their neighbours at each decision time”. Somewhat counter-intuitively, the researchers found that adding more fish to follow didn’t really improve the results. In fact, it seems that quite the opposite was true. Most interactions needed two neighbours, but for the most influential neighbour, one interaction was enough.

…each fish must acquire a minimal amount of information about the behaviour of its neighbours.

Robots vs fish

To complement this computational approach, Dr Liu and Dr Theraulaz also used robots to check if they could get robust collective movements as the model predicted, when physical constraints are present and when each robot must control their speed to avoid collision with other robots. Similarly to the computer model, the group of robots remained close and cohesive by interacting with their most influential neighbour. In contrast, the group lost all kind of coordinated behaviour by picking the nearest neighbour instead. In this case, using at least two neighbours improved their behaviour, but it was only when robots interacted with three of their nearest neighbours that this strategy produced a highly cohesive and coordinated group. Remarkably, it is possible to obtain group cohesion and coherent collective motion over long periods of time even when swarm robots only interact with one most influential neighbour.

Finally, Dr Liu and Dr Theraulaz wanted to compare the predictions of the computer models and robot swarms with the experiments conducted under the same conditions with groups of live fish. “Overall, and even more convincingly than in the case of the fish model”, said the researchers, “the most influential strategy leads to the best overall agreement when fish focused on one or two neighbours”. Remarkably, it was possible to obtain group cohesion and coherent collective motion over long periods of time even when the robots only interact with their most influential neighbour. On the other end of the scale, picking the nearest fish didn’t boost group coordination for only one neighbour, and had only marginal improvements for two neighbours.

Combining computational and robotic approaches to investigate the impact of different strategies for a fish to interact with its neighbours on collective swimming in groups of rummy-nose tetra fish.
Photo credit: David Villa ScienceImage/CBI/CNRS, Toulouse.

Getting inside the fish brain

In all vertebrates – and in particular in fish – the midbrain and the forebrain are heavily involved in processing visual information and selecting which external stimulus should be the focus of attention. The midbrain continuously monitors the environment for clues. This is the primary location where information coming from neighbours is collected and then passed on to the forebrain, which is responsible for picking the best stimuli on which the fish must focus their attention.

Using this cognitive mechanism, fish can be very good at filtering relevant information from their surroundings. They can limit their attention to a small set of the most influential neighbours, immediately identifying which ones to avoid and move away and which ones to follow. These neighbours which trigger and immediate action – can set in motion a larger response than other neighbours, making the concept of most influential neighbours easy to understand.

All combined, Dr Liu’s and Dr Theraulaz’s results show that fish typically interact with their two most influential neighbours. This selection reduces the amount of information that needs to be processed in the brain and avoids cognitive overload. “Our study thus suggests that each fish must acquire a minimal amount of information about the behaviour of its neighbours for coordination to emerge at the group level”, concluded the researchers, “thus allowing fish to avoid information overload when they move in large groups. Besides our findings will benefit to the design of autonomous swarms of micro-robots”.

Excitingly, these findings can be exploited as a source of inspiration to coordinate the actions of artificial systems, such as swarms of drones that in the future might become increasingly used for search and rescue operations, environmental and wildlife monitoring.

Can the same methods be applied to other animals that study their collective behaviour, like insects or birds?

The general methodology and the procedures that we used in fish can be similarly applied on any set of trajectories of other organisms, including humans to measure social interactions between individuals. Understanding how the interactions between individuals in swarms of insects, schools of fish, flocks of birds, herds of ungulates, or human crowds give rise to the ‘collective level’ properties requires the development of mathematical models. Our methodology ultimately leads to concise and explicit models that can be exploited to understand and explain diverse experimental features and various forms of collective behaviour and that have a predictive power.



  • Lei L, Escobedo R, Sire C, Theraulaz G. (2020). Computational and robotic modeling reveal parsimonious combinations of interactions between individuals in schooling fish. PLoS Comput Biol 16: e1007194.
  • Escobedo R, Lecheval V, Papaspyros V, Bonnet F, Mondada F, Sire C, & Theraulaz G. (2020). A data-driven method for reconstructing and modelling social interactions in animal groups. Philosophical Transactions of the Royal Society of London – Serie B., 375, 20190380.
  • Calovi DS, Litchinko A, Lecheval V, Lopez U, Pérez Escudero A, Chaté H, Sire C & Theraulaz G. (2018). Disentangling and modeling interactions in fish with burst and coast swimming reveal distinct alignment and attraction behaviors. Plos Computational Biology 14: e1005933.

Research Objectives

Lei Liu and Guy Theraulaz’s research interests include swarm intelligence in natural and artificial systems, self-organisation in biological and robotic systems, collective behaviours and collective intelligence in animal and human societies, computational and systems biology.


Liu Lei was supported by a grant from the Natural Science Foundation of Shanghai under Grant No.17ZR1419000 and Visiting Fund of Shanghai Education Commission.

Guy Theraulaz gratefully acknowledges the Indian Institute of Science to serve as Infosys visiting professor at the Centre for Ecological Sciences in Bengaluru.


Ramon Escobedo (CRCA/CBI/CNRS), Clément Sire (Laboratoire de Physique Théorique, CNRS and Université de Toulouse).


Lei Liu is a USST associate professor. He is specialised in complex systems control, such as collective motion in swarms of robots, intelligent transportation systems.


Guy Theraulaz is a research director at CNRS. He is an expert in the study of collective animal behaviours and a leading researcher in the field of swarm intelligence.

Liu Lei
University of Shanghai for Science and Technology (USST), Shanghai, China

Guy Theraulaz
Centre de Recherches sur la Cognition Animale, Centre de Biologie Intégrative, Centre National de la Recherche Scientifique (CNRS),
Université de Toulouse—Paul Sabatier (UPS), Toulouse, France

Dr Liu

Dr Guy Theraulaz

Twitter: @GTheraulaz

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