On Bartlett's formulation of the Luria-Delbrück mutation model

Current knowledge of microbial mutation rates was accumulated largely by means of fluctuation experiments. A mathematical model describing the cell dynamics in a fluctuation experiment is indispensable to the estimation of mutation rates through fluctuation experiments. In almost six decades the model formulated by Lea and Coulson dominated in research and application, although the model formulated by Bartlett is generally believed to describe the cell dynamics more faithfully. The neglect of the Bartlett formulation was mainly due to mathematical difficulties. The present investigation overcomes some of these difficulties, thereby paving the way for the application of the Bartlett formulation in estimating mutation rates. Specifically, the article offers an algorithm for computing the distribution function of the number of mutants under the Bartlett formulation. The article also provides algorithms for computing point and interval estimates of mutation rates that are based on the maximum-likelihood principle. In addition, the article examines and compares the asymptotic behavior of the distributions of the number of mutants under the two formulations.