NDLI: Survival of an evasive prey

Content Provider	PubMed Central
Author	Oshanin, G. Vasilyev, O. Krapivsky, P. L. Klafter, J.
Abstract	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 lnP ev(t) ∼ (N/V)2lnP imm(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.
Related Links	http://dx.doi.org/10.1073/pnas.0904354106
Starting Page	13696
File Format	PDF
ISSN	10916490
e-ISSN	10916490
Journal	Proceedings of the National Academy of Sciences of the United States of America
Issue Number	33
Volume Number	106
Language	English
Publisher	National Academy of Sciences
Publisher Date	2009-08-18
Access Restriction	Open
Rights Holder	National Academy of Sciences
Subject Keyword	Research in Higher Education
Content Type	Text
Resource Type	Article
Subject	Multidisciplinary

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