Random search with resetting as a strategy for optimal pollination

Abstract

The problem of pollination is unique among a wide scope of search problems, since it requires optimization of benefits for both the searcher (pollinator) and its targets (plants). To address this challenge, we propose a pollination model which is based on a framework of first passage under stochastic restart. We derive equations for the search time and number of visited plants as functions of the distribution of nectar in the plant population and of the probability that a pollinator will leave the plant after examining a flower, thus effectively restarting the search. We demonstrate that nectar variation in plants serves as a driving force for pollination and establish conditions required for optimal pollination, which provides an efficient pollinator search strategy and the maximum number of plants visited by the pollinator.