title: Mortality, redundancy, and diversity in stochastic search.
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 τ_{D}/lnN for lnN≫1, where τ_{D}~L^{2}/D is the diffusive time scale. Conversely, when the mortality rate μ of the searchers is sufficiently large, the search time scales as sqrt[τ_{D}/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.
authors.affiliation: Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
authors.forename: Baruch
authors.initials: B
authors.lastname: Meerson
authors.affiliation: Department of Physics, Boston University, Boston, Massachusetts 02215, USA and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
authors.forename: S
authors.initials: S
authors.lastname: Redner