284 Distribution of numbers of mutants in bacterial populations 

 In the final column of Table 4 we have tabulated 



1 



Ji*& 



JN. (58) 



Having determined the maximal likelihood estimate of m as just described, the value of 

 (j m ^N/m is read off from the last column of Table 4. These values of a^N/m have been 

 used in plotting the part of Fig. 3D to the left of m = 10. Between m = 3 and m= 15, the 

 values of a m ^jN/m calculated from (58) and from (53) agree satisfactorily. 



Summary 

 Statistical calculations are made of the distribution numbers of mutants in a culture of 

 bacteria in which the number of mutants increases on account both of new mutations and 

 of division of old mutants. In this way the largely qualitative conclusions of Luria and 

 Delbruck are extended and placed on a firm quantitative basis. The results of these 

 calculations, which enable the mutation rate to be inferred from experiments with parallel 

 cultures, are presented in the form of tables. Statistically efficient methods of using these 

 tables are discussed. 



REFERENCES 

 Adolph, E. F. & Bayne- Jones, S. (1932). J. Cell. Comp. Physiol. 1, 409. 

 Demerec, M. (1945). Proc. Nat. Acad. Sci., Wash., 31, 16. 



Fisher, R. A. (1938). Statistical Theory of Estimations. Calcutta University Readership lectures. 

 Fisher, R. A. & Yates, F. (1938). Statistical Tables for Biologists, Agriculturalists and Medical Research. 



Edinburgh : Oliver and Boyd. 

 Lewis, I. M. (1934). J. Bad. 28, 619. 

 Luria, S. E. & Delbruck, M. (1943). Genetics, 28, 491. 



Molina, E. C. D. (1942). Poisson's Exponential Binomial Limit Tables. New York: Van Nostrand. 

 Stewart, F. M. (1947). J. Hyg., Camb., 45, 28. 

 Witkin, E. M. (1946). Proc. Nat. Acad. Sci., Wash., 32, 59. 



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