  A swarm of preys when attacked by a predator is known to rely on their
cooperative interactions to escape. Understanding such interactions of
collectively moving preys and the emerging patterns of their escape
trajectories still remain elusive. In this paper, we investigate how the range
of cooperative interactions within a prey group affects the survival chances of
the group while chased by a predator. As observed in nature, the interaction
range of preys may vary due to their vision, age, or even physical structure.
Based on a simple theoretical prey-predator model, here, we show that an
optimality criterion for the survival can be established on the interaction
range of preys. Very short range or long range interactions are shown to be
inefficient for the escape mechanism. Interestingly, for an intermediate range
of interaction, survival probability of the prey group is found to be maximum.
Our analysis also shows that the nature of the escape trajectories strongly
depends on the range of interactions between preys and corroborates with the
naturally observed escape patterns. Moreover, we find that the optimal survival
regime depends on the prey group size and also on the predator strength.
