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These two workbooks model the evolution of phage resistance in a bacterial population under two alternative hypotheses. Under the hypothesis of acquired immunity, mutation produces some resistant bacteria even in the absence of phage; this resistance can be passed to their offspring. Under the mutation hypothesis, by contrast, mutation produces some resistant bacteria even in the absence of phage; again, this resistance can be passed to their offspring. Predictions of the two models can be compared to each other and to actual data.


Tony Weisstein, Truman State University
John R. Jungck, Beloit College
Doug Green, Saint Michael's Collge

Published by: BioQUEST Curriculum Consortium

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User Manuals and Curricular Materials
Popular Text Citations

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Luria, S. E. 1966. Mutations of Bacteria and of Bacteriophage. Pp. 173-179 in Cairns, J., Stent, G., and Watson, J. (Eds.) Phage and the Origins of Molecular Biology. Cold Spring Harbor Laboratory: Cold Spring Harbor, New York.

Fisher, R. A., and Yates, F. 1943. Statistical Tables for Biological, Agricultural and Medical Research, 2nd Edition. Oliver and Boyd: London.

Lenski, Richard E. 1988. Dynamics of interactions between bacteria and virulent bacteriophage. Pp. 1-44. In Marshall, K. C. (Ed.). Advances in Microbial Ecology (Vol. 10). Plenum Publishing Corporation.

Research Articles

Sniegowski, P. D., Gerrish, P. J., Johnson, T., and Shaver, A. 2000. The evolution of mutation rates: separating causes from consequences. BioEssays 22: 1057-1066.

Stewart, F. M. 1994. Fluctuation tests: How reliable are the estimates of mutation rates? Genetics 137: 1139-1146.

Stewart, F. M., Gordon, D. M., and Levin, B. R. 1990. Fluctuation analysis: the probability distribution of the number of mutants under different conditions. Genetics 124: 175-185.

Trends in Biochemical Sciences. May 1981. Obituary: Max Delbrück. Elsevier/North Holland Biomedical Press.

Villars, Felix M. H. and Benedek, G. B. Year?The Luria-Delbrück experiment: mutation as the source of bacterial immunity to virus attack. Pp. 60-84, 95-97 in Physics: Vol. 2 Statistical Physics. Addison-Wesley, Reading, Massachusetts.

Sarkar, S., Ma, W. T., and Sandri, G. vH. 1992. On fluctuation analysis: a new, simple and efficient method for computing the expected number of mutants. Genetica 85: 173-179.

Zheng, Qi. 1999. Progress of a half century in the study of the Luria-Delbrück distribution. Mathematical Biosciences 162: 1-32.

Ma, W. T., Sarkar, S., and Sandri, G. vH. 1992. Analysis of the Luria-Delbrück distribution using discrete convolution powers. J. Appl. Prob. 29: 255-267.

Luria, S. E. 1984. A Slot Machine, A Broken Test Tube. Harper & Row: New York. 228 pp.

Koch, A. L. 1982. Mutation and growth rates from Luria-Delbrück fluctuation tests. Mutation Research 95: 129-143.

Sarkar, S. 1993. Haldane's solution of the Luria-Delbrück distribution. Genetics 127: 257-261. Edited by J. F. Crow and Wm. F. Dove in Perspectives: Anecdotal, Historical and Critical Commentaries on Genetics. Boston University, Boston, MA.

Lea, D. E. and Coulson, C. A. 1949. The distribution of the numbers of mutants in bacterial populations. J. Genetics 49: 264-285.

Liebovitch, Larry S. 1998. The distribution of mutations is the same as in the St. Petersburg game. Pp. 94-95 in Fractals and Chaos: Simplified for the Life Sciences. Oxford University Press: New York.

Hovestadt T, Joachim P H, Eduard L K, 2005 Spatial patterns in species-area relationships and species distribution in a West African forest-savanna mosaic. Journal of Biogeography 32: 677-684.

Luria, S. and Delbrück, M. 1943. Mutations of bacteria from virus sensitivity to virus resistance. Genetics 28: 491-511.

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Armitage, P. 1953. Statistical concepts in the theory of bacterial mutation. J. Hygiene 51: 162-184.

Cairns, J., Overbaugh, J., and Miller, S. 1988. The origin of mutants. Nature 335: 142-145.

Delbrück, Max. 1986. Mind From Matter? An Essay on Evolutionary Epistemology. G. Stent, et al. (Eds.). Blackwell Scientific Publications. Palo Alto, California. 290 pp.

Kimmel, M., Axelrod, D. E. 1994. Fluctuation test for two-stage mutations: application to gene amplification. Mutation Research 306: 45.

Russell J C, Clout M N, McArdle B H, 2004 Island biogeography and the species richness of introduced mammals on New Zealand offshore islands. Journal of Biogeography 31: 653-664.

Richardson, Sarah. 1994. Survival of the mutable: in which the ghost of that oft-reviled ancestor, Jean-Baptiste Lamarck, returns to trouble the sleep of neo-Darwinian evolutionists. Discover 15 (9): 27-28.

Jones, M. E., Thomas, S. M., and Rogers, A. 1994. Luria-Delbrück fluctuation experiments: Design and analysis. Genetics 136: 1209-1216.

Hall, Barry G. 1992. Selection-induced mutations. Current Opinion in Genetics and Development. 2: 943-946.

Lenski, Richard E., Slatkin, M., and Ayala, F. J. 1989. Mutation and selection in bacterial populations: alternatives to the hypothesis of directed mutation. Proc. Natl. Acad. Sci. USA. 86: 2775-2778.

Sniegowski, P. D., and Lenski, R. E. 1995. Mutation and adaptation: the directed mutation controversy in evolutionary perspective. Annu. Rev. Ecol. Syst. 26: 553-78.

Stewart, F. M. 1991. Fluctuation analysis: the effect of plating efficiency. Genetica 82: Pages

Lenski, Richard E. 1988. Experimental studies of pleiotropy and epistasis in escherichia coli. II. Compensation for maladaptive effects associated with resistance to virus T4. Evolution 42 (3): 433-440.

Sniegowski, P. D., Gerrish, P. J., and Lenski, R. E. 1997. Evolution of high mutation rates in experimental populations of E. coli. Nature 387: 703-705.

Holl K D, Crone E E, 2004 Applicability of landscape and island biogeography theory to restoration of riparian understorey plants. Journal of Applied Ecology 41: 922-933.

Cairns, John, and Foster, P. 1991. Adaptive reversion of a frameshift mutation in escherichia coli. Genetics 128: 695-701.

Aggarwal, A. and Sarkar, S. 1992. On the evolution of complex genomes: adaptive graph computations with a CM-2 connection machine. Boston University. Association for Computing Machinery: 798-807.

Liebovitch, Larry S. 1998. Example where the variance does not exist: evolution. Pp. 92-93 in Fractals and Chaos: Simplified for the Life Sciences. Oxford University Press: New York.

Keller, Evelyn F. 1992. Between language and science: the question of directed mutation in molecular genetics. Perspectives in Biology and Medicine 35 (2): 293-306.

Lenski, Richard E. and Levin, B. R. 1985. Constraints on the coevolution of bacteria and virulent phage: a model, some experiments, and predictions for natural communities. The American Naturalist 125 (4): 585-602.

Lenski, Richard E. 1988. Experimental studies of pleiotropy and epistasis in escherichia coli. I. Variation in competitive fitness among mutants resistant to virus T4. Evolution 42 (3): 425-432.

Education Research & Pedagogical Materials

Hornbach, D. 1996. Biometrics. The BioQUEST Library IV:(Candidate Collection): University of Maryland – College Park.

Calley, J. N.; Jungck, J. R. 1996. Microbial Genetics Construction Kit. The BioQUEST Library IV:(Candidate Collection): University of Maryland – College Park

Green, Douglas S., and Bozzone, Donna M. 2001. A test of hypotheses about random mutation: using classic experiments to teach experimental design. The American Biology Teacher 63 (1): 54-58.

Access Excellence: Evers, Chris. (Accessed 01/07/06) Bacterial Mutations: Luria and Delbruck Hit the Jackpot (1943)

Stewart, F. M., 1992. DataFit (Macintosh software for analyzing Luria-Delbrück fluctuation tests). Department of Mathematics, Brown University, Providence, Rhode Island.

Weisstein Tony , Jungck John R., Green Doug () Luria-Delbruck. A module of the Biological ESTEEM Collection, published by the BioQUEST Curriculum Consortium. URL: