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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., Competing Interests: We declare we have no competing interests.

While a rich variety of self-propelled particle models propose to explain the collective motion of fish and other animals, rigorous statistical comparison between models and data remains a challenge. Plausible models should be flexible enough to capture changes in the collective behaviour of animal groups at their different developmental stages and group sizes. Here, we analyse the statistical properties of schooling fish ( Pseudomugil signifer ) through a combination of experiments and simulations. We make novel use of a Boltzmann inversion method, usually applied in molecular dynamics, to identify the effective potential of the mean force of fish interactions. Specifically, we show that larger fish have a larger repulsion zone, but stronger attraction, resulting in greater alignment in their collective motion. We model the collective dynamics of schools using a self-propelled particle model, modified to include varying particle speed and a local repulsion rule. We demonstrate that the statistical properties of the fish schools are reproduced by our model, thereby capturing a number of features of the behaviour and development of schooling fish., Competing Interests: We declare we have no competing interests.

The exceptional reactivity of animal collectives to predatory attacks is thought to be owing to rapid, but local, transfer of information between group members. These groups turn together in unison and produce escape waves. However, it is not clear how escape waves are created from local interactions, nor is it understood how these patterns are shaped by natural selection. By startling schools of fish with a simulated attack in an experimental arena, we demonstrate that changes in the direction and speed by a small percentage of individuals that detect the danger initiate an escape wave. This escape wave consists of a densely packed band of individuals that causes other school members to change direction. In the majority of cases, this wave passes through the entire group. We use a simulation model to demonstrate that this mechanism can, through local interactions alone, produce arbitrarily large escape waves. In the model, when we set the group density to that seen in real fish schools, we find that the risk to the members at the edge of the group is roughly equal to the risk of those within the group. Our experiments and modelling results provide a plausible explanation for how escape waves propagate in nature without centralized control.