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

Luria, 1943, Mutations of bacteria from virus sensitivity to virus resistance, Genetics, 28, 491, 10.1093/genetics/28.6.491

Li, 1985, A deterministic approach for the estimation of mutation rates in cultured mammalian cells, Mutation Res., 149, 127, 10.1016/0027-5107(85)90017-X

Kendal, 1988, Pitfalls and practice of Luria–Delbrück fluctuation analysis: a review, Cancer Res., 48, 1060

Lea, 1949, The distribution of the numbers of mutants in bacterial populations, J. Genetics, 49, 264, 10.1007/BF02986080

P. Armitage, The statistical theory of bacterial populations subject to mutation, J. Royal Statist. Soc. B 14 (1952) 1 (with discussion on pp. 34–40)

Kendall, 1952, On the choice of a mathematical model to represent normal bacterial growth, J. Royal Statist. Soci. B, 14, 41

Kendall, 1952, Les processus stochastique de croissance en biologie, Ann. Inst. Henri Poincaré, 13, 43

Mandelbrot, 1974, A population birth-and-mutation process I: Explicit distributions for the number of mutants in an old culture of bacteria, J. Appl. Prob., 11, 437, 10.2307/3212688

Bartlett, 1955

Bartlett, 1978

Bailey, 1964

Crump, 1974, Mathematical models for estimating mutation rates in cell populations, Biometrika, 61, 237, 10.1093/biomet/61.2.237

Koch, 1982, Mutation and growth rates from Luria–Delbrück fluctuation tests, Mutation Res., 95, 129, 10.1016/0027-5107(82)90252-4

Cairns, 1988, The origin of mutants, Nature, 335, 142, 10.1038/335142a0

Lenski, 1989, Mutation and selection in bacterial populations: alternatives to the hypothesis of directed mutation, Proc. Nat. Acad. Sci. USA, 86, 2775, 10.1073/pnas.86.8.2775

Stewart, 1990, Fluctuation analysis: the probability distribution of the number of mutants under different conditions, Genetics, 124, 175, 10.1093/genetics/124.1.175

Ma, 1992, Analysis of the Luria–Delbrück distribution using discrete convolution powers, J. Appl. Prob., 29, 255, 10.2307/3214564

Sarkar, 1992, On fluctuation analysis: a new, simple and efficient method for computing the expected number of mutants, Genetica, 85, 173, 10.1007/BF00120324

Kemp, 1994, Comments on the Luria–Delbrück distribution, J. Appl. Prob., 31, 822, 10.2307/3215159

Pakes, 1993, Remarks on the Luria–Delbrück distribution, J. Appl. Prob., 30, 991, 10.2307/3214530

Goldie, 1995, Asymptotics of the Luria–Delbrück distribution, J. Appl. Prob., 32, 840, 10.2307/3215135

Prodinger, 1996, Asymptotics of the Luria–Delbrück distribution via singularity analysis, J. Appl. Prob., 33, 282, 10.2307/3215284

Kendall, 1960, Birth-and-death process and the theory of carcinogenesis, Biometrika, 47, 13, 10.1093/biomet/47.1-2.13

Snyder, 1991

Chung, 1974

Zheng, 1995, On a compartmental analysis result, Math. Biosci., 130, 203, 10.1016/0025-5564(95)00008-3

Johnson, 1992

S. Wolfram, The Mathematica Book, fourth ed., Copublished by Wolfram Media, Champaign, IL and Cambridge University, Cambridge, New York, 1999

Armitage, 1953, Statistical concepts in the theory of bacterial mutation, J. Hygiene, 51, 162, 10.1017/S0022172400015606

J.J. Hunter, Mathematical Techniques of Applied Probability, Vol. 1, Discrete Time Models: Basic Theory, Academic Press, New York, 1983

N.N. Lebedev, Special Functions and Their Applications, (revised English editon, translated and edited by R.A. Silverman), Dover, New York, 1972

Puri, 1968, Interconnected birth and death processes, J. Appl. Prob., 5, 334, 10.2307/3212256

Kendall, 1953, Stochastic processes and the growth of bacterial colonies, Symposia of the Society for Experimental Biology, 7, 55

Zheng, 1997, A unified approach to a class of stochastic carcinogenesis models, Risk Anal., 17, 617, 10.1111/j.1539-6924.1997.tb00902.x

Tan, 1982, On distribution theories for the number of mutants in cell populations, SIAM J. Appl. Math., 42, 719, 10.1137/0142050

Tlsty, 1989, Differences in the rates of gene amplification in nontumorigenic and tumorigenic cell lines as measured by Luria–Delbrück fluctuation analysis, Proc. Nat. Acad. Sci. USA, 86, 9441, 10.1073/pnas.86.23.9441

Kimmel, 1994, Fluctuation test for two-stage mutations: application to gene amplification, Mutation Res., 306, 45, 10.1016/0027-5107(94)90166-X