Mean field mutation dynamics and the continuous Luria-Delbr\"uck distribution
Mathematical Physics
2011-12-14 v1 math.MP
Probability
Populations and Evolution
Abstract
The Luria-Delbr\"uck mutation model has a long history and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using some mathematical tools from nonlinear statistical physics. Starting from the classical formulations we derive the corresponding differential models and show that under a suitable mean field scaling they correspond to generalized Fokker-Planck equations for the mutants distribution whose solutions are given by the corresponding Luria-Delbr\"uck distribution. Numerical results confirming the theoretical analysis are also presented.
Cite
@article{arxiv.1112.2836,
title = {Mean field mutation dynamics and the continuous Luria-Delbr\"uck distribution},
author = {Eugene Kashdan and Lorenzo Pareschi},
journal= {arXiv preprint arXiv:1112.2836},
year = {2011}
}