S. E. LURIA 



Let us observe the frequency distributions of the numbers of mutants (Table 

 3). The total number of mutants observed in all experiments (Table 3; total 

 clone frequency) was 766, distributed among 2874 plates containing about 

 1.8 X 10^ normal phages. The proportion of mutants is about 4 X 10"'*, and 

 their average number per plate is about 2.5 X 10~^ If the mutants were dis- 

 tributed at random, there would be about 550 plates with one mutant, about 90 

 with two or three mutants, and only four with four mutants or more. There is 

 no doubt that the distributions are not random, but clonal. 



As a test of the nature of the mutants appearing on the same plate, 11 pairs 

 of r mutants were isolated from 11 plates, which contained between 2 and 59 

 mutants. In all cases, the mutants in each pair proved allelic (probably iden- 

 tical) ; no wild-type recombinant was observed among at least 1000 plaques of the 

 yield from mixed infected bacteria. In 11 out of 12 crosses between mutants 

 isolated from different plates we observed wild-type recombinants; the twelfth 

 cross failed to show recombinants. It may have represented either a case of 

 repeated occurrence of the same mutation or a case of two mutations with 

 recombination frequency lower than 0.2 per cent, the lowest frequency detectable 

 in our rather crude tests. These results, then confirm the clonal nature of the 

 mutants produced within a given bacterium. We will now consider the clonal 

 distributions. 



Inspection of Table 3 shows that the mutant distribution, though clonal, fails 

 to fit the uniform frequency predicted for small clones of various sizes by the 

 hypothesis of independent gene replication, with mutations occurring in the 

 pattern. 



Let us turn next to the distribution predicted by the hypothesis of exponential 



duplication. 



Inspection of the data shows: (a) there are clones with two mutants; therefore, 

 if exponential reproduction occurs, the elementary process is probably one of 

 duplication (from 1 to 2) rather than triplication or quadruplication ; (b) there 

 are clones with 3, 5, 6, 7, . . . in addition to clones with 1, 2, 4, 8, . . . mutants. 

 Thus, exponential reproduction, if present, must be nonsynchronized, a conclu- 

 sion also suggested by the well-known distribution of the total burst size. 



For a quantitative test of the hypothesis of exponential reduplication we shall 

 use, instead of Equation (1), the following expression (accumulated distribution) 

 suggested by Dr. Howard Levene : 



Y. = Sy. = Sf = sf = »NS ^.^0,-"^ (forN = 2k».). (2) 



Yx is the number of clones with x or more mutants. The product Yx X x is 

 constant and a plot of log Y versus log x gives a straight Ime with slope - 1 ; the 

 vertical intercept for x = 1 is the logarithm of the total number of mutant clones. 

 This plot has the advantage that it is hardly affected by nonsynchronization. A 

 clone with three mutants can be considered either as a clone that should have had 

 two mutants and underwent one extra reduplication, or as a four-mutant clone 



144 



