Proliferation Model Dependence in Fluctuation Analysis: The Neutral Case

We discuss the evaluation of Luria-Delbrueck 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 bacteria, the suitably normed and centered number of mutants contained in a large culture of bacteria converges to a 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, mutant cells produce the same number of offspring as non-mutant cells.