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Swarming behaviours in animals have been extensively studied owing to their implications for the evolution of cooperation, social cognition and predator-prey dynamics. An important goal of these studies is discerning which evolutionary pressures favour the formation of swarms. One hypothesis is that swarms arise because the presence of multiple moving prey in swarms causes confusion for attacking predators, but it remains unclear how important this selective force is. Using an evolutionary model of a predator-prey system, we show that predator confusion provides a sufficient selection pressure to evolve swarming behaviour in prey. Furthermore, we demonstrate that the evolutionary effect of predator confusion on prey could in turn exert pressure on the structure of the predator's visual field, favouring the frontally oriented, high-resolution visual systems commonly observed in predators that feed on swarming animals. Finally, we provide evidence that when prey evolve swarming in response to predator confusion, there is a change in the shape of the functional response curve describing the predator's consumption rate as prey density increases. Thus, we show that a relatively simple perceptual constraint-predator confusion-could have pervasive evolutionary effects on prey behaviour, predator sensory mechanisms and the ecological interactions between predators and prey. © 2013 The Author(s) Published by the Royal Society. All rights reserved.