Meerson, B.,Redner, S.

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 tau(D) / ln N for ln N >> 1, where tau(D) similar to L-2 / D is the diffusive time scale. Conversely, when the mortality rate mu of the searchers is sufficiently large, the search time scales as root tau(D)/mu, 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.