2014/04/09 by David A. Kessler, Kessler, David A., Herbert Levine +1
Biochemistry, Genetics and Molecular Biology · Environmental Science · Physics and Astronomy · #Bacteriophages and microbial interactions #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Physical sciences #Populations and Evolution (q-bio.PE) #Protein Structure and Dynamics #Spectroscopy and Quantum Chemical Studies #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.1404.2407
openalex publication_date 2014/04/09 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
One of the most popular models for quantitatively understanding the emergence\nof drug resistance both in bacterial colonies and in malignant tumors was\nintroduced long ago by Luria and Delbr "uck. Here, individual resistant mutants\nemerge randomly during the birth events of an exponentially growing sensitive\npopulation. A most interesting limit of this process occurs when the population\nsize N is large and mutation rates are low, but not necessarily small\ncompared to 1/N. Here we provide a scaling solution valid in this limit,\nmaking contact with the theory of Levy \α-stable distributions, in\nparticular one discussed long ago by Landau. One consequence of this\nassociation is that moments of the distribution are highly misleading as far as\ncharacterizing typical behavior. A key insight that enables our solution is\nthat working in the fixed population size ensemble is not the same as working\nin a fixed time ensemble. Some of our results have been presented previously in\nshortened form.\n