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.
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© 2015 American Physical Society.