Abstract
The collective dynamics of self-organised systems emerge from the decision rules agents use to respond to each other and to external forces. This is evident in groups of animals under attack from predators, where understanding collective escape patterns requires evaluating the risks and rewards associated with particular social rules, prey escape behaviour, and predator attack strategies. Here, we find that the emergence of the 'fountain effect', a common collective pattern observed when animal groups evade predators, is the outcome of rules designed to maximise individual survival chances given predator hunting decisions. Using drone-based empirical observations of schooling sardine prey (Sardinops sagax caerulea) attacked by striped marlin (Kajikia audax), we first find the majority of attacks produce fountain effects, with the dynamics of these escapes dependent on the predator's attack direction. Then, using a spatially-explicit agent-based model of predator-prey dynamics, we show that fountain manoeuvres can emerge from combining an optimal individual prey escape angle with social interactions. The escape rule appears to prioritise maximising the distance to the predator and creates conflict in the effectiveness of predators' attacks and the prey's avoidance, explaining the empirically observed predators' attack strategies and the fountain evasions produced by prey. Overall, we identify the proximate and ultimate explanations for fountain effects and more generally highlight that the collective patterns of self-organised predatory-prey systems can be understood by considering both social escape rules and attack strategies.