Mortality, Redundancy, and Diversity in Stochastic Search

Baruch Meerson, S. Redner

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65 Scopus citations

Abstract

We investigate a stochastic search process in one dimension under the competing roles of mortality, redundancy, and diversity of the searchers. This picture represents a toy model for the fertilization of an oocyte by sperm. A population of N independent and mortal diffusing searchers all start at x=L and attempt to reach the target at x=0. When mortality is irrelevant, the search time scales as τD/lnN for lnN 蠑 1, where τD∼L2/D is the diffusive time scale. Conversely, when the mortality rate μ of the searchers is sufficiently large, the search time scales as √τD/μ, independent of N. When searchers have distinct and high mortalities, a subpopulation with a nontrivial optimal diffusivity is most likely to reach the target. We also discuss the effect of chemotaxis on the search time and its fluctuations.

Original languageAmerican English
Article number198101
JournalPhysical Review Letters
Volume114
Issue number19
DOIs
StatePublished - 15 May 2015

Bibliographical note

Publisher Copyright:
© 2015 American Physical Society.

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