General formulation of LuriaDelbrück distribution of the number of mutants
Abstract
The LuriaDelbrück experiment is a cornerstone of evolutionary theory, demonstrating the randomness of mutations before selection. The distribution of the number of mutants in this experiment has been the subject of intense investigation during the past 70 years. Despite this considerable effort, most of the results have been obtained under the assumption of constant growth rate, which is far from the experimental condition. We derive here the properties of this distribution for arbitrary growth function for both the deterministic and stochastic growth of the mutants. The derivation we propose uses the number of wildtype bacteria as the independent variable instead of time. The derivation is surprisingly simple and versatile, allowing many generalizations to be taken easily into account.
 Publication:

Physical Review E
 Pub Date:
 July 2015
 DOI:
 10.1103/PhysRevE.92.012719
 arXiv:
 arXiv:1505.06108
 Bibcode:
 2015PhRvE..92a2719H
 Keywords:

 87.23.Kg;
 05.40.a;
 02.50.Ey;
 Dynamics of evolution;
 Fluctuation phenomena random processes noise and Brownian motion;
 Stochastic processes;
 Physics  Biological Physics;
 Physics  Data Analysis;
 Statistics and Probability;
 Quantitative Biology  Populations and Evolution