466 HOWARD B. NEWCOMBE 



A METHOD OF REDUCING THE DOWNWARD BIAS IN METHOD 2 DUE TO THE 

 DELAY IN PHENOTYPIC EXPRESSION (METHOD 5) 



As mentioned in the introduction, a delay between mutation and phenotypic 

 expression must be variable within a mutant clone, expression occurring in 

 some lines of descent earlier than in others. This leaves open the questions of 

 the extent of the delay, the nature of the variation, and the rate of gene muta- 



Table 7 



Increase in number of bacteria resistant to phage Tl during early growth, using strain B/r grown 

 on agar, and spraying with phage during the lag phase and early part of the first division. 



EXPERIMENT ABC 



Replicate plates 

 Bact. in inoculum, X10 8 

 Resist, bact. in inoc. r per 10* 

 Incubation, minutes 



Incr. in no. of bact. 

 New resist, bact., per 10* 

 Standard deviation 



tion, the last being to a greater or smaller degree underestimated by the meth- 

 ods dealt with so far. Method 5 is designed to obtain a less biased estimate of 

 mutation rate, and, from this, some idea of the extent of the delay. 



With a variable delay it would be expected that mutant clones arising from 

 mutations early in the growth of a culture would contain a higher proportion 

 of phenotypically resistant cells than would younger mutant clones, and that a 

 higher and less biased estimate of mutation rate would be obtained if it could 

 be calculated from these older clones alone. 



To do this the following method has been devised. In a series of similar test 

 cultures a few of the cultures contain many times the average number of re- 

 sistant cells, because of the chance occurrence in these cultures of an early 

 mutation. In such cases the precise numbers of resistant bacteria from the 

 earliest mutation and from subsequent mutations cannot be determined di- 

 rectly. The probable number from later mutations, however, is approximately 

 equal to the mean number in the whole series. This is, incidentally, a very 

 slight overestimate, and a more precise approach will be considered later. 



Using this method, the probable number of resistant bacteria descended from 

 the earliest mutation in a series of cultures is obtained by subtracting the 

 mean number of resistant bacteria per culture, r, from the highest number 

 occurring in any one of the cultures, h. At the probable time of occurrence of 

 this mutation the population in the culture would have been N/(h — r), where 

 N is the end population; and the population in the whole series of cultures 

 would have been CN/(h — r), where C is the number of cultures in the series. 

 Thus the first mutation in the series occurred when the population was 

 CN/(h — r), and since the inocula were small the number of bacterial divisions 



68 



