Mean field mutation dynamics and the continuous Luria-Delbrück distribution

2011/12/13 by Kashdan, Eugene, Pareschi, Lorenzo
#FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Populations and Evolution (q-bio.PE) #Probability (math.PR)

paper · doi:10.48550/arxiv.1112.2836

Abstract

The Luria-Delbrück 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-Delbrück distribution. Numerical results confirming the theoretical analysis are also presented.

Related

• The kinetic theory of mutation rates
• Scaling solution in the large population limit of the general asymmetric\n stochastic Luria-Delbr "uck evolution process
• Criticality in the Luria-Delbrück model with an arbitrary mutation rate
• General formulation of Luria-Delbrück distribution of the number of mutants
• Mutation frequencies in a birth-death branching process