Proliferation model dependence in fluctuation analysis: the neutral case.

We discuss the evaluation of Luria-Delbrück fluctuation experiments under Bellman-Harris models of cell proliferation. It is shown that under certain very natural assumptions concerning the life-time distributions and the offspring distributions of mutant and non-mutant cells, the suitably normed and centered number of mutants contained in a large culture of bacteria (or the like) converges to a certain stable random variable with index 1. The result obtains under the assumption that the mutation under consideration is "neutral" in the sense that on average and in the long run, mutant cells produce the same number of offspring as non-mutant cells.