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collective departure is a decision - making faced by all social species that travel in groups . in this process , an individual generally initiates the movement of the group out of a residence site or towards a new direction . the identity and motivation of this initiator can widely vary according to the social organisation of the considered species @xcite . on the one hand , the leadership is often assumed by a unique or a subset of individuals that monopolise the decisions in hierarchical societies . these individuals can be older @xcite , dominant @xcite or of a specific sex @xcite . these characteristics are generally long - lasting and result in a consistant leadership over time , generally observed in stable and closed groups . on the other hand , the initiators can also be temporarily more motivated due to their physiological state @xcite , level of information @xcite or position in the group @xcite . in these cases , the initiation can be done by any individuals of the group without consistency over time . this mechanism is often present in social species that live in open groups with no consistent membership like bird flocks or fish schools . although each individual can initiate collective movement in these more egalitarian societies , some characteristics may enhance the probability of some members to take the leadership . for example , bold individuals that have a higher tendency to explore new areas will more often lead departures @xcite . similarly , group members with higher nutritional needs will be more motivated to initiate movements towards foraging spots @xcite . therefore , even in non - hierarchical species , leadership can be heterogeneously distributed among the group members . in this context , we studied the distribution of the leadership in the zebrafish _ danio rerio_. in its natural habits , _ danio rerio _ is a gregarious species that live in small groups ( a few to a dozen individuals ) in shallow freshwaters @xcite . it has become a widely studied and well known model organism in genetics and neuroscience @xcite but also in ethology .    in this context , our goal is to evaluate the presence of leaders or their emergence during successive collective departures . to do so , we observe groups of 2 , 3 , 5 , 7 and 10 zebrafish swimming in an experimental arena consisting of two rooms connected by a corridor . our aim is to measure the number of collective departure from one room to the other that are initiated by each fish . then , we put in relation the propensity of the individuals to lead departures to the number of attempts that they made as well as their swimming speed . fish experiments were performed in accordance with the recommendations and guidelines of the buffon ethical committee ( registered to the french national ethical committee for animal experiments # 40 ) after submission to the state ethical board for animal experiments . the fish were reared in housing facilities zebtec and fed two times a day ( special diets services sds-400 scientific fish food ) . we kept fish under laboratory conditions , @xmath0 , 500@xmath1s salinity with a 10:14 day : night light cycle . water ph was maintained at 7 and nitrites ( no@xmath2 ) are below 0.3 mg / l . all zebrafish observed in this study were 6 - 12 months old at the time of the experiments . we observed groups of zebrafish swimming in an arena consisting of two square rooms connected by a corridor starting at one corners of each room placed in 100 x 100 x 30 experimental tank ( fig . [ fig : setup ] ) . the walls of the arena were made of white opaque pmma . the water depth was kept at 6 cm during the experiments in order to keep the fish in nearly 2d to facilitate their tracking . one lamp ( 400w ) was placed on the floor at each edge of the tank which is 60 cm above the floor to provide indirect lightning . the whole setup is confined behind white sheets to isolate experiments and homogenize luminosity . a high resolution camera was mounted 1.60 m above the water surface to record the experiment at a resolution of 2048 x 2048 and at 15 frames per second . we observed 12 groups of two , three , five , seven and ten adult laboratory wild - type zebrafish ( _ danio rerio _ ) ab strain during one hour for a total of 60 experiments . before the trials , the fish were placed with a hand net in a cylindrical arena ( 20 cm diameter ) in one of the two rooms . following a 5 minutes acclimatisation period , the camera started recording and the fish were released and able to swim in the experimental arena . after one hour , the fish were caught by a hand net and replaced in the rearing facilities . the videos were analysed off - line by the idtracker software @xcite . this multi - tracking software extracts specific characteristics of each individual and uses them to identify each fish without tagging throughout the video . this method avoids error propagation and is able to successfully solves crossing , superposition and occlusion problems . however , the tracking system failed to correctly track one experiment with two fish , one experiment with five fish and two experiments with ten fish . therefore , these four experiments were excluded from our analysis . for all other experiments , we obtained the coordinates @xmath3 of all fish at each time step @xmath4 . with these coordinates , we built the trajectories of each fish and computed their position in the arena and their instantaneous speed @xmath5 calculated on three positions and computed as the distance between @xmath6 and @xmath7 divided by 2 time steps .. first , we quantified for all the replicates the total number of collective residence events ( cre ) defined as the whole group resting in one of the two rooms . the number of cre decreases with the size of the groups with a median number of 233 cre for 2 fish to 131 cre for groups of 10 fish ( fig . [ fig : ndepartures]a ) . moreover , we counted the total number of collective departures events ( cde ) defined as the whole group leaving one of the resting sites for the corridor towards the other one . the number of cde also decreases with the size of the group but with a stronger difference between the groups ( from a median number of 212 for two zebrafish to 16 cde for groups of 10 zebrafish ( fig . [ fig : ndepartures]b ) . these observations show that 90% of the cre were followed by a collective departure in groups of 2 fish while only 12% were in groups 10 fish . thus , larger groups were more likely to split into subgroups during departures while small groups of fish swam together most of the time . thanks to the individual tracking of the fish , we were able to determine the identity of the first fish that left a room for all collective departures . thus , for all groups , we computed the proportion of collective departure initiated by each fish and ranked the group members according to the proportion of departure that they led . to characterise the distribution of the leadership among the group members , we ranked each individual according to the proportion of collective departures that they have initiated and compared the distributions of the ranks with two theoretical ones . on the one hand , we simulated a situation where all fish have the same probability ( @xmath8 ) to initiate a departure . on the other hand , we simulated a despotic configuration with a fish that has a 0.9 probability to initiate collective movement while the others have only a @xmath9 chance to start a departure . the experimental data lay between these two extreme scenarios ( fig . [ fig : rankedinitiation ] for 5 fish ) . in groups of five fish , the 1@xmath10 ranked fish initiated 45% of the collective departures on average . this value is largely below the 90% observed in the despotic simulation but also higher than the 25% of the uniform repartition . these results highlight an heterogeneous distribution of leadership among group members , some fish have a higher tendency to start departure than others . we observed similar results for groups of 2 , 3 , 7 and 10 fish .    ) while the despotic distribution assumed that one fish has a higher probability ( @xmath11 ) to initiate collective departure while other have a small probability to do so ( @xmath12 ) . the results show that the frequency of initiation in groups of zebrafish differs from both simulated distribution highlighting a distributed leadership . ]    to determine whether this distributed leadership was related to a different success rate or the number of initiation attempts , we measured the number of time that each fish was the first to exit a resting site independently of its success to be followed by the other group members ( i.e. an _ attempt _ ) . the intra - group proportion of attempts made by each fish shows a continuum from an egalitarian to a more despotic distribution for all group sizes ( fig . [ fig : prop_attempt ] ) . for each group , we compared the distribution of the total number of attempts made by each fish with a theoretical homogeneous distribution . for two fish , 4 dyads out of 11 did not significantly differ from the homogeneous distribution ( @xmath13 test , see table for details ) . in groups of three fish , the hypothesis of homogeneous distribution was not rejected in only one trio . finally , all groups of 5 , 7 and 10 fish significantly differ from the equal distribution of the number of attempts . thus , like the distribution of initiations , the attempts are also heterogeneously distributed among the fish of the group . then , we checked for a potential correlation between the number of initiations and the number of attempts made by each fish . a linear regression shows that the number of initiation is linearly correlated to the number of attempts perform by the fish and that the coefficient of this correlation depends on the group size ( fig . [ fig : attempts]a ) . for groups of two fish , 92% of the attempts made by a fish resulted in a collective departure of the whole group . moreover , the linear relation between the numbers of attempts and initiations highlights that this high success rate is shared by all fish . therefore , the fish leading the largest number of departures were the more active fish . in addition , the proportion of initiation led is proportional to the proportion of attempts performed by each fish ( fig . [ fig : attempts]b ) . these results highlight that all fish have the same success rate in starting a collective departure when they attempt it . thus , the higher status of initiator of some fish is not related to a higher influence on other fish or a better success but on a higher tendency to exit the resting sites . the results for other group sizes are qualitatively similar but differ quantitatively : while the linear relation persists , the success rate for each attempt decrease when the group size increases ( 90% for 3 fish , 66% for 5 fish , 53% for 7 fish and 26% for 10 fish ) . next , we studied the temporal distribution of the leading event to highlight a potential succession of temporary leaders . to do so , we computed the probability of a fish to perform two successive initiations and compared this probability to the proportion of cde that the fish has led . a temporal segregation of the initiators would results in a high probability of successive initiations compared to the proportion of led cde while homogeneously distributed initiations would give similar probabilities of successive initiations and led cde . for all group sizes , we observed a linear correlation between the two proportions ( fig . [ fig : samelead ] ) . thus , the probability of a fish to initiate a cde was not dependent on its status of initiator or follower during the previous cde . finally , we looked at a potential link between the motion characteristics of the individual and the number of attempts that they have made . in particular , we measured the average linear speed of all individual as an indicator of their motility . there is a positive correlation between the average speed of the individual and the number of attempts that they performed . however , this correlation is only significant for groups of 5 , 7 and 10 fish ( fig . [ figure4]a - f ) . we also compared the intra - group ranking of the fish for the number of initiation with their intra - group ranking for the linear speed . we used the kendall s @xmath14 coefficient to measure the association between the two rankings . the intra - group ranking for the initiation is positively correlated to the intro - group ranking for the linear speed ( fig . [ figure4]c ) for groups of 3 , 5 , 7 and 10 fish . thus , the fish with a highest average speed of its group is more likely to also be the fish that has started the largest number of departures , except for dyads . these results show that the initiation of collective movements is related to the motility of the fish , particularly in large groups . the initiation of collective movement in fish is often reported as a distributed process in which each fish can potentially lead a departure . this distribution of the leadership is particularly suited for large schools of hundreds or thousands of fish that have to detect and avoid attacks from predator coming potentially from any direction . thus , the first fish to spot a predator can start an escaping manoeuvre that will be propagated from neighbour to neighbour in the whole school . in these conditions , it is difficult to imagine a permanent leader monopolising the initiation of collective movement . however , the situation can be quite different in smaller groups of fish . while they still have to avoid predators , the inter - individual differences can be more marked due to the small number of group members . therefore , a heterogeneous distribution of the leadership due to individual characteristic is more likely to appear .    here , we showed that the initiation of collective departure is a distributed process among the group members in zebrafish . however , the role of initiator is not homogeneously distributed , with some individuals leading more departures than others . by also measuring the number of attempt made by each fish , we highlighted that this heterogeneous distribution was not the result of a higher success rate of some individual that could have a higher tendency to be followed . on the contrary , the success of the fish to trigger a collective departure was linearly correlated to their number of attempt . therefore , the best initiators do not seem to occupy a particular hierarchical status in the group but are the most motivated individuals to exit the room . in addition , we showed that the initiation process was not temporarily organised with a fish leading the group during a particular time period before being relayed by another fish , but a distributed status during the whole experimental time . finally , we showed that the motility of the fish is a predictor of the tendency of the fish to initiate collective departure . indeed , the intra - group ranking of the fish for average speed of the fish was correlated to its intra - group ranking for departure attempts . thus , these results provide evidence that the emergence of specific initiator of collective movement in zebrafish is more related to individual characteristics of the group members than to a particular status in the group . all authors declare having no competing interests . b.c . performed the data analysis , ran the simulations and wrote the manuscript . a.s . and y.c . performed the experiments and collected the experimental data . l.c . developed the video treatment and tracking system . designed , conceived , coordinated the study and revised the manuscript . all authors gave final approval for publication . this work was supported by european union information and communication technologies project assisibf , ( fp7-ict - fet n. 601074 ) . the funders had no role in study design , data collection and analysis , decision to publish , or preparation of the manuscript .
for animals living in groups , one of the important questions is to understand what are the decision - making mechanisms that lead to choosing a motion direction or leaving an area while preserving group cohesion . here , we analyse the initiation of collective departure in zebrafish _ 
 danio rerio_. in particular , we observed groups of 2 , 3 , 5 , 7 and 10 zebrafish swimming in a two resting sites arena and quantify the number of collective departure initiated by each fish . 
 while all fish initiated at least one departure , the probability to be the first one to exit a resting site is not homogeneously distributed with some individuals leading more departures than others . 
 we show that this number of initiation is linearly proportional to the number of attempts performed and that all fish have the same success rate to lead the group out of a resting sites after an attempt . 
 in addition , by measuring the average swimming speed of all fish , we highlight that the intra - group ranking of a fish for its proportion of initiation is correlated to its intra - group ranking in average speed . 
 these results highlight that the initiation of collective departure in zebrafish is a heterogeneously distributed process , even if all individual have the same success rate after attempting a departure .