A plant-capture approach for achieving complete coverage of a population

Sightings of any member of a target population of unknown size occur according to a homogeneous Poisson process. The Poisson processes are independent and have a common rate. Individuals are tagged when first sighted. The population is augmented by the insertion of known number of planted individuals who have already been tagged and whose behaviour is identical to that of the other members. Consideration is given to two stopping rules for determining, within a specified error probability, when all members of the target population have been seen. A comparison is made of the average time to termination under these two rules. It is shown that, when the target population is small, the use of plants can provide a useful reduction in the average time taken to achieve complete coverage within the specified error probability.