Mutant number distribution in an exponentially growing population

Peter Keller, Tibor Antal

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We present an explicit solution to a classic model of cell-population
growth introduced by Luria and Delbr¨uck (1943 Genetics 28 491–511) 70 years
ago to study the emergence of mutations in bacterial populations. In this model
a wild-type population is assumed to grow exponentially in a deterministic
fashion. Proportional to the wild-type population size, mutants arrive randomly
and initiate new sub-populations of mutants that grow stochastically according
to a supercritical birth and death process. We give an exact expression for
the generating function of the total number of mutants at a given wild-type
population size. We present a simple expression for the probability of finding no
mutants, and a recursion formula for the probability of finding a given number of
mutants. In the ‘large population-small mutation’ limit we recover recent results
of Kessler and Levine (2014 J. Stat. Phys. doi:10.1007/s10955-014-1143-3) for a
fully stochastic version of the process.
Original languageEnglish
Article numberP01011
Number of pages29
Journal Journal of Statistical Mechanics: Theory and Experiment
Publication statusPublished - 9 Jan 2015


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