Survival of an evasive prey

G. Oshanin, O. Vasilyev, P. L. Krapivskye, J. Klafter

Research output: Contribution to journalArticlepeer-review


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 Pev(t) ∼ (N/V)2 ln Pimm(t) between the survival probabilities of an evasive and an immobile prey. Hence, when the density ρ = N/V of the predators is low, ρ ≪ 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.

Original languageEnglish
Pages (from-to)13696-13701
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number33
StatePublished - 18 Aug 2009


  • Chase
  • Diffusion
  • First-passage times
  • Pursuit
  • Superdiffusion


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