D. E. Lea and C. A. Coulson 277 



large values of m (e.g. when the fraction of cultures without mutants exceeds 0-9 or is less 



than 0-01), the value of (ar m /m) is much increased. Fig. 2>A shows graphically — sjN as 



m 



a function of m. 



The low precision at small values of m is to be attributed simply to the fact that an 



experiment in which the great majority of the cultures have no mutants does not provide 



much precise information about the mutation rate. The reduced precision at high values 



of m is, however, to be ascribed to the fact that this method of determining m does not 



1000 



Fig. 3. The precision of the estimate of m derived by various methods: A, the method of the proportion of 

 cultures without mutants; B, the method of the median; C, the method of S[x]-0; D, the method of 

 maximal likelihood. 



make full use of the experimental data, and in these cases more suitable methods, which 

 we shall describe, enable a more precise estimate of m to be made from the same data. 



mfrom the median 

 When the mutation rate is to be deduced from an experiment in which all, or nearly all, 

 the cultures had mutants, so that the method just discussed is inapplicable, a very 

 convenient method is to deduce m from the median of the distribution. The counts of the 

 numbers of mutants in N parallel cultures are arranged in ascending order, and the middle 

 one selected. The count in this culture is an estimate of r , the median of the distribution 

 of r . Since we know that (approximately) the derived variate 



4 



Jm — log m + b 



with a = 11-6, 6 = 4-5, c = 2-02 



(36) 



37 



