Takeover Times of Noisy Non-Generational Selection Rules that Undo Extinction

The takeover time of some selection method is the expected number of iterations of this selection method until the entire population consists of copies of the best individual under the assumption that the initial population consists of a single copy of the best individual. We consider a class of nongenerational selection rules that run the risk of loosing all copies of the best individual with positive probability. Since the notion of a takeover time is meaningless in this case these selection rules are modi ed in that they undo the last selection operation if the best individual gets extinct from the population. We derive exact results or upper bounds for the takeover time for three commonly used selection rules via a random walk or Markov chain model. The takeover time for each of these three selection rules is O(n logn) with population size n.