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We study the degree of success of a single predator hunting a herd of prey ona two dimensional square lattice landscape. We explicitly consider the selfvolume of the prey restraining their dynamics on the lattice. The movement ofboth predator and prey is chosen to include an intelligent, decision makingstep based on their respective sighting ranges, the radius in which they candetect the other species (prey cannot recognise each other besides the selfvolume interaction): after spotting each other the motion of prey and predatorturns from a nearest neighbour random walk into direct escape or chase,respectively. We consider a large range of prey densities and sighting rangesand compute the mean first passage time for a predator to catch a prey as wellas characterise the effective dynamics of the hunted prey. We find that theprey's sighting range dominates their life expectancy and the predator profitsmore from a bad eyesight of the prey than from his own good eye sight. Wecharacterise the dynamics in terms of the mean distance between the predatorand the nearest prey. It turns out that effectively the dynamics of thisdistance coordinate can be captured in terms of a simple Ornstein-Uhlenbeckpicture. Reducing the many-body problem to a simple two-body problem byimagining predator and nearest prey to be connected by a Hookean bond, allfeatures of the model such as prey density and sighting ranges merge into theeffective binding constant.

A single predator charging a herd of prey: effects of self volume and predator-prey decision-making