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Abstract / Description of output
We present an explicit solution to a classic model of cellpopulation
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 wildtype population is assumed to grow exponentially in a deterministic
fashion. Proportional to the wildtype population size, mutants arrive randomly
and initiate new subpopulations 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 wildtype
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 populationsmall mutation’ limit we recover recent results
of Kessler and Levine (2014 J. Stat. Phys. doi:10.1007/s1095501411433) for a
fully stochastic version of the process.
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 wildtype population is assumed to grow exponentially in a deterministic
fashion. Proportional to the wildtype population size, mutants arrive randomly
and initiate new subpopulations 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 wildtype
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 populationsmall mutation’ limit we recover recent results
of Kessler and Levine (2014 J. Stat. Phys. doi:10.1007/s1095501411433) for a
fully stochastic version of the process.
Original language  English 

Article number  P01011 
Number of pages  29 
Journal  Journal of Statistical Mechanics: Theory and Experiment 
Volume  2015 
DOIs  
Publication status  Published  9 Jan 2015 
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 1 Finished

The emergence of evolution  foundational question in evolutionary biology
1/01/13 → 31/12/14
Project: Research