Survival of an evasive prey.
We study the survival of a prey that is hunted by N predators. The predators perform independent random walks on a square lattice with V sites and start a direct chase whenever the prey appears within their sighting range. The prey is caught when a predator jumps to the site occupied by the prey. We analyze the efficacy of a lazy, minimal-effort evasion strategy according to which the prey tries to avoid encounters with the predators by making a hop only when any of the predators appears within its sighting range; otherwise the prey stays still. We show that if the sighting range of such a lazy prey is equal to 1 lattice spacing, at least 3 predators are needed in order to catch the prey on a square lattice. In this situation, we establish a simple asymptotic relation ln P(ev)(t) approximately (N/V)(2)ln P(imm)(t) between the survival probabilities of an evasive and an immobile prey. Hence, when the density rho = N/V of the predators is low, rho << 1, the lazy evasion strategy leads to the spectacular increase of the survival probability. We also argue that a short-sighting prey (its sighting range is smaller than the sighting range of the predators) undergoes an effective superdiffusive motion, as a result of its encounters with the predators, whereas a far-sighting prey performs a diffusive-type motion.
Oshanin
G
G
Laboratory J.-V. Poncelet, Unité Mixte Internationale 2615, Centre National de la Recherche Scientifique, Independent University of Moscow, Bolshoy Vlasyevskiy Pereulok 11, 119002 Moscow, Russia. oshanin@lptmc.jussieu.fr
Vasilyev
O
O
Krapivsky
P L
PL
Klafter
J
J
D000465:Algorithms; D000818:Animals; D001522:Behavior, Animal / Q000502:physiology*; D049628:Body Size; D017753:Ecosystem; D008954:Models, Biological; D015233:Models, Statistical; D008962:Models, Theoretical; D009068:Movement; D011156:Population Density; D011235:Predatory Behavior