Frank, S. A. 2022. The number of neutral mutants in an expanding Luria-Delbrück population is approximately Fréchet. F1000Research 11:1254.

A growing population of cells accumulates mutations. A single mutation early in the growth process carries forward to all descendant cells, causing the final population to have a lot of mutant cells. When the first mutation happens later in growth, the final population typically has fewer mutants. The number of mutant cells in the final population follows the Luria-Delbrück distribution. The mathematical form of the distribution is known only from its probability generating function. In practice, one typically uses computer simulations to estimate the distribution. This article shows that the Fréchet distribution provides a good approximation for the Luria-Delbrück distribution for neutral mutations, which do not cause a growth rate change relative to the original cells. The Fréchet distribution apparently provides a good match through its description of extreme value problems for multiplicative processes such as exponential growth.