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Collective movement can be achieved when individuals respond to the local movements and positions of their neighbours. Some individuals may disproportionately influence group movement if they occupy particular spatial positions in the group, for example, positions at the front of the group. We asked, therefore, what led individuals in moving pairs of fish (Gambusia holbrooki) to occupy a position in front of their partner. Individuals adjusted their speed and direction differently in response to their partner's position, resulting in individuals occupying different positions in the group. Individuals that were found most often at the front of the pair had greater mean changes in speed than their partner, and were less likely to turn towards their partner, compared to those individuals most often found at the back of the pair. The pair moved faster when led by the individual that was usually at the front. Our results highlight how differences in the social responsiveness between individuals can give rise to leadership in free moving groups. They also demonstrate how the movement characteristics of groups depend on the spatial configuration of individuals within them.

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.

The escape trajectories animals take following a predatory attack appear to show high degrees of apparent 'randomness' - a property that has been described as 'protean behaviour'. Here we present a method of quantifying the escape trajectories of individual animals using a path complexity approach. When fish (Pseudomugil signifer) were attacked either on their own or in groups, we find that an individual's path rapidly increases in entropy (our measure of complexity) following the attack. For individuals on their own, this entropy remains elevated (indicating a more random path) for a sustained period (10 seconds) after the attack, whilst it falls more quickly for individuals in groups. The entropy of the path is context dependent. When attacks towards single fish come from greater distances, a fish's path shows less complexity compared to attacks that come from short range. This context dependency effect did not exist, however, when individuals were in groups. Nor did the path complexity of individuals in groups depend on a fish's local density of neighbours. We separate out the components of speed and direction changes to determine which of these components contributes to the overall increase in path complexity following an attack. We found that both speed and direction measures contribute similarly to an individual's path's complexity in absolute terms. Our work highlights the adaptive behavioural tactics that animals use to avoid predators and also provides a novel method for quantifying the escape trajectories of animals., Comment: 9 pages