Progress of a half century in the study of the Luria-Delbrück distribution

DOI10.1016/S0025-5564(99)00045-0zbMath0947.92024OpenAlexW2014268112WikidataQ33806584 ScholiaQ33806584MaRDI QIDQ1969229

Qi Zheng

Publication date: 16 March 2000

Published in: Mathematical Biosciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0025-5564(99)00045-0

zbMATH Keywords

probability generating functionreviewPoisson-stopped-sum distributionfiltered Poisson processLuria-Delbrück modelBartlett formulationestimation of mutation rateLea-Coulson algorithmphenotypic delay

Mathematics Subject Classification ID

Problems related to evolution (92D15) Signal detection and filtering (aspects of stochastic processes) (60G35) Genetics and epigenetics (92D10)

Related Items (38)

Cellular replication limits in the Luria-Delbrück mutation model ⋮ Mutation frequencies in a birth-death branching process ⋮ Giant number fluctuations in microbial ecologies ⋮ General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks ⋮ Proliferation model dependence in fluctuation analysis: The neutral case ⋮ Somatic mosaicism and cancer: inference based on a conditional Luria-Delbrück distribution ⋮ Mean field mutation dynamics and the continuous Luria-Delbrück distribution ⋮ Fast maximum likelihood estimation of mutation rates using a birth-death process ⋮ A note on a universal random variate generator for integer-valued random variables ⋮ Sampling HIV intrahost genealogies based on a model of acute stage CTL response ⋮ Cell population growth kinetics in the presence of stochastic heterogeneity of cell phenotype ⋮ Statistics for the Luria-Delbrück distribution ⋮ Fluctuation analysis on mutation models with birth-date dependence ⋮ Genetic composition of an exponentially growing cell population ⋮ First-passage properties of the Pólya urn process ⋮ Mutant number distribution in an exponentially growing population ⋮ A new discrete distribution induced by the Luria–Delbrück mutation model ⋮ On Haldane's formulation of Luria and Delbrück's mutation model ⋮ Universal asymptotic clone size distribution for general population growth ⋮ New approaches to mutation rate fold change in Luria-Delbrück fluctuation experiments ⋮ The fixed-size Luria-Delbrück model with a nonzero death rate ⋮ Global solutions to an equation for mutation process in bacteria and its preservation of positive supports ⋮ On the probability of random genetic mutations for various types of tumor growth ⋮ The coalescence of intrahost HIV lineages under symmetric CTL attack ⋮ Letter to the Editor ⋮ Large population solution of the stochastic Luria–Delbrück evolution model ⋮ On an unbiased and consistent estimator for mutation rates ⋮ Accumulation of neutral mutations in growing cell colonies with competition ⋮ On Bartlett's formulation of the Luria-Delbrück mutation model ⋮ Estimation of Spontaneous Mutation Rates ⋮ The fractional birth process with power-law immigration ⋮ A modified fluctuation test for elucidating drug resistance in microbial and cancer cells ⋮ New algorithms for Luria-Delbrück fluctuation analysis ⋮ A generalized Luria-Delbrück model ⋮ Gestational mutations and carcinogenesis ⋮ Scaling solution in the large population limit of the general asymmetric stochastic Luria-Delbrück evolution process ⋮ Mean field dynamics of interaction processes with duplication, loss and copy ⋮ Statistical and algorithmic methods for fluctuation analysis with SALVADOR as an implementation

Uses Software

• Mathematica

Cites Work

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• On a compartmental analysis result
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• Mathematical models for estimating mutation rates in cell populations
• A population birth-and-mutation process, I: explicit distributions for the number of mutants in an old culture of bacteria
• Asymptotics of the Luria-Delbrück distribution via singularity analysis
• Interconnected birth and death processes

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