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The Luria-Delbr{\"u}ck experiment is a cornerstone of evolutionary theory,demonstrating the randomness of mutations before selection. The distribution ofthe number of mutants in this experiment has been the subject of intenseinvestigation during the last 70 years. Despite this considerable effort, mostof the results have been obtained under the assumption of constant growth rate,which is far from the experimental condition. We derive here the properties ofthis distribution for arbitrary growth function, for both the deterministic andstochastic growth of the mutants. The derivation we propose uses the number ofwild type bacteria as the independent variable instead of time. The derivationis surprisingly simple and versatile, allowing many generalizations to be takeneasily into account.

General formulation of Luria-Delbr{\"u}ck distribution of the number of mutants