 First, I would like to thank the organizers for the invitation. This has been a very stimulating week. And I think I would like to thank all the organizers that have been involved in this nice meeting, and in particular, Asia, Irene, water Dario, and Yen, and also Antonio. So I will focus my talk. A very simple example of collective behavior that happen in fish schools when they have to decide collectively and spontaneously to change their direction of motion. This is probably not as spectacular as many other forms of collective behavior that can be observed in nature that have been presented in this meeting. But at least it can be investigated quantitatively in control condition. And I hope you will see that we can learn a lot about the way individuals interact with each other and how collective decisions emerge from these interactions. Indeed, one of the fundamental questions in this field of collective animal behavior studies is how groups make decisions collectively. And this comes down to understanding the mechanisms by which individual influence each other and how these interactions are combined and integrated at the collective level. And earlier this week, Andrea Giovanni Reina presented one of a very famous example of collective decision based on direct interactions between individuals during the process of nest site selection in Hollybees. So in this situation, you have hundreds of scoots, bees that explore the environment for potential nest site. And these scoots bring back to the swarm some information about potential nest sites and they share this information with the other scoots by the means of these waggled ends. And the strengths of these waggled ends is directly proportional to the site quality. So that the scoots that are committed to high quality site execute much more vigorous dances. And as a consequence, they have a higher probability to convince other scoots to visit their site. And although they abandon their own site more slowly than the scoots that are committed to lower quality site. So there is a form of competition of information at the collective level and the information that succeed to grow faster than the others will determine in the end the final choice of the swarm. And all this story has been nicely described by Tom Sile in his book, On a Bee Democracy. And in that particular case, in fact, the entire decision making process requires sometimes the dance activity of the scoots can last several days. But in many other situations, animal groups must take a decision on a shorter time scale. For instance, when a predator is detected in the environment, in the neighborhood. And when this happens, for instance, in fish schools and bird flocks, the danger is generally detected. The video is not working. I don't know why. OK. So the danger is detected by only a small number of individuals that change their direction and speed. And this leads to the formation of an escape wave that propagate across the entire group. As you can see here, when the flock of starlings is reacting to an attack by a peregrine falcon. So this ability to rapidly and coherently react to a perturbation certainly brings some important benefits to the individual as it can provide them an advantage of detecting the predator faster. And there are also many other situations in which the perturbation is not triggered by the presence of an external threat in the environment. A group may change its collective behavior spontaneously, simply the consequence of stochastic changes that affect the behavior of a single or few individual in the group. And these behavioral changes then propagate within the group. And they lead all individuals to adopt, for instance, a new direction of motion here, for instance, in Locust, or a new form of collective motion, for instance, here in this work by the group of Hien-Ku Xin. So these situations are quite interesting because they can be analyzed and used. They can be used, in fact, to analyze in undisturbed condition how these behavioral fluctuations arise at the individual scale. And then how this information propagates within the group and determine the change in the collective behavior. So in the end, we expect to get a better understanding about how individual interact with each other during these events and how these dynamics of interactions can lead to a collective decision. And the first important step to do this kind of investigation is first to find both a species and a situation in which we can observe, in control conditions, such spontaneous change in collective behavior. And the species that we have studied is this one. It's Romino stetra, emigramus rhodostomus, which is a small tropical fish species that exhibit a strong schooling behavior, and in which that can be handled, in fact, very easily in control condition. And the average body length of these species is about 30 millimeters. And we found that when groups of these fish frame swilly in a ring-shaped term, they regularly change their direction of motion from clockwise to anticlockwise and vice versa. So with this experimental setup, we can record a very large number of these collective view terms, and by tracking the position and the heading of each individual within a group, we can also analyze the interactions between fish during these collective view terms and how the information propagates within the group. So here is the experimental setup that we use for this series of experiment. You see that it is protected from the outside with white curtain. And so there were no external visual cues that can influence the behavior of the fish. And we filled the arena with the limited depth of seawater so that the motion of fish was mostly in two dimensions. Then we tracked the position of fish with ID tracker. And here is an example of collective view terms in a group of four fish. And you can see the corresponding trajectories of each individual during the new term and also the degree of alignment of the fish with the role, which goes from minus one to plus one when the fish is swimming counterclockwise after the new term. And on each of these events, we can then identify the time of turning of each individual. So when the degree of alignment with the role equals zero and also the position of the individual when they make their new terms. Then we have investigated how these collective view terms arise in different group size from single individuals up to 20 individuals. And for each group size, we have recorded a very large number of this event that you can see here. We have more than 5,000 events in total. And as you can see here on this graph, in fact, the size of the group strongly affects the ability of a group to spontaneously perform a new term. Indeed, in groups of 10 fish, the average time interval between two successive view terms is about 20 minutes, while it's about 12 seconds in a group of two fish. So you can see that the average time interval between two successive view terms increases by two order of magnitudes when the group size is five times bigger. And the decrease in the number of collective view terms, in fact, is mainly a consequence of the fact that the probability of a fish to initiate and propagate a new term, decrease as group size increases. So individual fish tend to adopt the behavior of the majority of the group members and this tendency, in fact, inhibit the initiation of view terms. Now who are these individuals that initiate collective view terms and under what condition does it happen? In fact, in all group size that we have investigated, we found that collective view terms were usually initiated by the fish that were located at the front of the school. And once a fish has decided to make a new term, the change of the swimming direction propagates toward the rear of the group. As you can see here, when we plot the average position of individual according to their rank of turning when the U-turn is initiated. And we also found that all collective view terms are preceded by a period during which the school slows down and, in fact, as the fish speed decrease, the school is in a state close to a transition between a schooling state which is characterized by a strong alignment between fish and a swarming state which is characterized by a weak alignment. And in a previous work, we have shown that when a school is close to this transition between these two states, the swarming and the schooling, the fluctuation in the swimming direction of the fish increases, but also the school has a hole, becomes very sensitive to a perturbation that may affect the behavior of a single fish. So this may explain why all the U-turns occurs after the group has collectively slowed down in our experiments because the school is in a state near this transition between these two states. Then how does the U-turn propagate within a school once it has been initiated? So if we look at the average time interval between the successive turn of individuals, we can see that it is almost constant in a given group size. So we found no evidence for the existence of a dampening or an amplification of information as fish adapt the new direction of motion. There is no amplification like that. And moreover, on average, the turning information propagates faster in larger groups, as you can see here on the right. And this happens to be a consequence of just the increase of the swimming speed with the group size, which requires that individual react faster. And you can see indeed on the right that the reaction time of individual decreases with group size. And if we normalize the time interval between the successive turns of individual by the average speed of the group, you can see that all curves now collapse on the same curves, which suggests that the shorter reaction time, which is observed in larger groups, is mostly due to their faster swimming speed. So once the U-turn has been initiated, the wave of turning propagates in a sequential way. And this is similar to a chain of following dominoes in which the time interval between two successive folds is constant without any positive feedback. So what does it tell us exactly about the underlying phenomenon? This phenomenon suggests that, in fact, each fish mainly copied the behavior of a small number of its neighbors. Now how does this fish copy the behavior of their neighbors? And what are the interactions between individuals? We have recently characterized and modeled the functional form of this interaction from experimental data. So this hemigrammous species perform this kind of swimming, the burst and ghost type of swimming, which is characterized by a sudden sequence of sudden increase in speed, followed by mostly passive gliding period. And if we look at the variation of the velocity with time, you can clearly see this succession of short acceleration phase followed by a gliding phase in which the velocity decreases. So we call this event during which the fish changes its velocity and its direction of motion a kick. And most changes in fish heading occurs exactly at the onset of the acceleration phases. So we can analyze the fish trajectories as a series of discrete behavioral decision in time and space. And we can describe the trajectory as a succession of segments and angular changes between the segments. And here in our experiments, we found that the average duration between kicks was close to 0.5 seconds when both fish were swimming either alone or in pair. And the mean length covered between two successive kicks was about 70 millimeters, which is a little bit more than two body lengths. But the main interest of this burst and glide swimming mode is that we can use the spatial location where the kick have been performed by the fish to identify the potential stimuli or the potential information in the neighborhood that could have elicited their behavioral response. For instance, in this situation, when a fish is swimming alone, the information which is used by the fish can be, for instance, the distance to the wall or its orientation with regard to the wall. So we can measure the behavioral response of fish, which is the amplitude of the angular change when they detect the wall. And what we observe is that a fish mainly avoids the wall when it comes close to the wall. He performs a kick that sends him away from the wall. And this curve, in fact, corresponds to the intensity of the avoidance reaction of the fish as a function of the distance to the wall. Here the fish is close to the wall. Here it's far. And you can see that the range of interaction of that wall is about two body lengths. And the color dots that you can see here corresponds, in fact, to the experimental data that we have gathered in different arena size. And you can see that the reaction of fish, in fact, do not depend on the size of the tank. And the pink curve that you can see here, in fact, is just the fitted function to this data that we can use in the model. What we can also observe is that the intensity of the fish reaction is strongly reduced when a fish is parallel to the wall. Here it's minus 90 degrees or 90 degrees. So this is interesting because when the fish is parallel to the wall, in fact, it seems to be not really interact with the wall. And when the fish is far from the wall, it no longer interact with that wall. And you can see that in this situation, in fact, the distribution of angular changes between two successive kick is a narrow Gaussian, which is peak on zero. And this Gaussian distribution introduce a kind of directional inertia in the fish movement. Now, what about the interaction between fish? Here are the results that we have obtained. I'm not going into the detail about the way we extract this interaction function, but we can go back to this paper to have all the detail. It's a little bit technical. And what we found is that there is a continuous combination of attraction and alignment interaction whose intensity depends on the distance, on the angular position, and on the relative orientation of individuals. So the strengths of these attraction and alignment behavior depend on three parameters. And this makes very difficult the use of simple 2D behavioral maps to characterize and then model the functional form of this interaction between fish. So first, if we look at the influence of the distance between fish on the intensity of the alignment of attraction, you can see when the distance of fish is less than 30 millimeters, which correspond to one body length, there is a short range repulsion. This is the attraction. You can see here it's a negative attraction, so it's a repulsion. And then at the distance between the fish increases, the attraction here in red becomes more important and reaches a maximum value around 200 millimeters, which corresponds about to six to seven body lengths. We also found that the alignment interactions dominates the attraction up to 2.5 body lengths while the attraction becomes more dominant for larger distance. And as the distance between the fish increases even more, attraction, the attraction must of course decrease, something like that. But we have not been able to measure this effect because of the limited size of the experimental tanks and also because of the lack of data, because we do not have a lot of situation when the two fish were far away from each other. And the full line that you can see here in fact correspond to the functional forms of the attraction and alignment interaction that can be fit to the experimental data. We can also clearly see that the behavioral response of fish are strongly modulated by the anisotropic perception of their environment and this leads to an asymmetry of the interactions between fish, depending on their relative position in particular. You can see that the maximum amplitude of the alignment interaction here in blue is when a neighboring fish is located either on the front right or on the front left and then you can see that it decreases as the focal fish, as the neighbors move toward the back of the focal fish. So the social force which is exerted by the fish J on a fish I is much more important than the social force which is exerted by the fish I on fish J when J is in front of I. And this asymmetry of the interactions may explain also why the U-turns are mostly initiated by the fish that are located at the front of the group. And indeed at this position, the individual experience a weaker influence from the other fish. So this frontal individual are much, they are much subject to heading fluctuation especially when the speed of the group decrease and at the consequence they are less inhibited to initiate a U-turn. Then we have checked that the implementation of these interaction functions in a burst and glide model qualitatively and quantitatively reproduce the movements of pair of fish in a circular arena. You can see that the fish tend to stay close to the wall and also close to each other but the temporary leader which is in the front is much more closer than the temporary follower. So we find a very good agreement between the model and the experiments if we consider the distance between the fish but also the distribution of the orientation of fish with regard to the wall. But the big question is to understand how a fish integrate multiple interactions with the other fish and how the combination of these interactions affects its behavior. So to better understand the combined effect, the combined impact of the tendency of a fish to adopt the behavior of a few of its neighbors, what we call social conformity, of the asymmetry of interaction between fish and also the impact of group size on the propagation of information during collective U-turns. We build an easy type spin model. It's a very simple model. So in this model each fish is represented by an agent that can only move in two directions, either clockwise or anti-clockwise. When it moves clockwise, its direction is minus one when it moves and plus one when it moves anti-clockwise. And in the model, the relative position of individual and the interaction networks are kept fixed here, you can see, which is obviously a simplification. However, one can justify this simplification because during the very few seconds before a U-turn, the topological structure of the group doesn't change much in particular for the fish which is located at the front of the group. So the agents are positioned in staggered row that correspond to the fact that when group size is increasing, the shape of the group becomes more elongated. And in this configuration, each agent in the model can only interact with a small number of their direct neighbors between one and two. And the strength of the interaction between an agent I and its neighbor J only depends on two parameters. The first one, J, control the strength of social conformity. So the strengths with which a fish adopt the behavior of its neighbor. And as a consequence, this parameter here control the stiffness of the group behavior. And the second parameter, alpha, controls the anisotropic perception of the fish and the asymmetry of interaction. So this parameter accounts for the fact that the fish reacts stronger to a frontal stimuli. So when J is in front of I, alpha, I, J equal one plus epsilon. And when J is behind hind, it equal one minus epsilon. And epsilon is a coefficient of asymmetry that is kept constant for all group size. So at a given moment, we can compute the propensity of an individual to make a U-turn. And this propensity only depends on its current direction and the direction of its neighbor and the strengths of the interaction. And this propensity to make a U-turn reflects in some way the level of discomfort of an individual that can be expressed in the following way. You can see that the level of discomfort, the discomfort of a fish I is minimum when all its neighbors are locally aligned and maximum when the fish, in fact, is in opposite direction of all its neighbors. So when a fish flip, then we can compute the change of its discomfort, which is associated with a probability to accept the turn and the strengths of the social conformity, a J, as you can see here, controls the nonlinearity of the acceptance probability. And you can see that for how high value of J, if the turn would increase the discomfort of the agent, the probability to accept the turn is very low. And on the contrary, if the turn would, in fact, decrease the level of discomfort, you can see that the probability to accept the turn is very high. So we use this model to explore both the impact of J and epsilon on the collective dynamics. And we found a couple of values for these parameters that lead to a fair agreement between the simulation result and the experimental data for all group size. In particular, the model here in red quantitatively reproduced the effect of group size on the dynamics of collective U-turns. So the number of collective U-turns decreases as collective U-turn increases. And we also find in the model that the tendency of individuals to initiate U-turn and move in the opposite direction of the other fish decreases with group size here. The model also reproduced quite well the impact of group size of the probability to initiate a U-turn. And the simulation of the model also reproduced quite well the sequential propagation of information both in space and time. And in particular here, you can see on this graph the crucial impact of the anisotropic perception of fish, which is controlled by epsilon here. So this is in gray. This is when there is no anisotropy. So you can see that, in fact, the information, the U-turn can be initiated both at the front and at the back of the school. There is no more asymmetry. And in the model, in fact, this individual that initiates a U-turn are located at the boundaries of the group. And since these individuals have the same probability to initiate a U-turn, you can see that when there is no asymmetry, in fact, there is no particular direction. No particular direction is favored. And the U-turn can propagate from the front to the back or to the back and to the front. So the anisotropic perception of fish impose a directionality to the propagation wave. The model also reproduces creatively well the linear propagation of information at the individual scale. So how do U-turn propagate within the group? And we find in the model the same domino-like propagation of direction of motion across the group that we have observed in the experiments. And finally, the model predicts that once we scale by the U-turn duration, in fact, the average swimming direction profile doing a collective U-turn is independent of the group size. So you can see that despite the fact that we have only two free parameters in our model, G and epsilon, that we have also fixed apological configuration and only nearest neighbor interaction, you can see that the model is able to reproduce quite well the chains of turning decision and also the main features of the experiment of the experiments. So to summarize our results, you have seen that the detail quantitative analysis of the propagation of information within a group during these collective U-turns, both at the individual and collective scale, I showed that the speed decrease facilitated the amplification of fluctuation in the heading of the group, which can trigger the U-turn. And this observation is in agreement with our previous theoretical prediction. We have seen that there is a linear propagation of information in all group size, and that the time between two successive individual performing U-turns doesn't decrease with the number of fish that have already performed a U-turn. This means that there is no amplification of the individual tendency to perform a U-turn. And the fact that we observe this linear propagation also suggests that each fish only interact with a small number of their neighbors, typically one and two. And we get, in fact, a similar result using a different kind of analysis, based this time on short-term correlation, direction correlation, that also show that the movement choice of a fish are affected only by one or two influential neighbors. And the fish regularly shift from one neighbor to the others. And we have also seen that a simple model that integrates this effect of social conformity that is the nonlinear tendency of individuals to imitate the behavior of a small number of its close neighbor and that also integrate the asymmetric interactions between fish, reproduce the sequential propagation of information within the group, and at least for the group size that we have studied in the experiment. And also, the main features are the dynamics that we observe in our experiments. Finally, I would like to thank all these people that have been involved in this work in the past five years. So Valentin Lecheval, Daniel Kalovi, Alexandra Lechinko, Lee Jung, and Piattici in my group, in Toulouse. Also, Charlotte M. Reich, who co-supervised Piagetisus, Valentin Lecheval, Hucchati from the French Atomic Energy Commission, and Clemenci from the theoretical physics lab in Toulouse. Thank you very much. Thank you, Guy.