What determines the attack distance of a stalking predator?

Stalking predation has been identified in many different taxa of animals. A lthough previous studies have identified environmental conditions that affe ct hunting success, we still lack a theory that explains diverse stalking p atterns on the basis of these conditions. Here, I present an optimization m odel of a stalking hunt based on a predator's multi-stage decision-making. This incorporates the essential feature of stalking predation: as the preda tor attacks at a shorter distance and when it attacks before the prey notic es it, its hunting success is enhanced. At each step of a hunt, the predato r chooses either to shorten the distance by stalking with a risk of being n oticed or to attack immediately. Major conclusions are as follows: (1) The predator attains its maximum expected hunting success just by following a s imple rule: keep stalking for as long as the merit of proximity exceeds the risk of losing the merit of surprise. (2) The predator attacks at a greate r distance as the environmental conditions enhance the risk of losing the m erit of surprise compared to the merit of proximity. (3) The optimal attack distance is neither affected by the distance where the predator starts its hunt nor by the previous stalking success as long as the merit of proximit y is sufficiently large. This constancy of the optimal attack distance can be used to test if a stalking predator follows the above simple decisionmak ing rule.