D. E. Lea and C. A. Coulson 265 



being either bacteria which had recently undergone mutation, or bacteria derived from 

 the division of mutants which arose earlier in the growth of the culture. When the culture 

 was divided into ten equal portions the phage-resistant organisms were distributed 

 at random between the ten portions. We may expect, therefore, the numbers in the 

 different portions to fall in a multinomial distribution with variance nearly equal to the 

 mean. 



On the adaptation or induced mutation theory, it is supposed that no phage-resistant 

 bacteria arose during the growth of the culture. The ten portions, at the time of plating 

 out, each contained 10 8 normal bacteria and no resistant bacteria. On being brought into 

 contact with the phage most were lysed, but a few were able to adapt themselves to the 

 phage (or the phage-induced mutations in them). The probability of this process is very 

 small, but was presumably the same for all the bacteria. On this theory, therefore, we 

 expect the number of resistant colonies on the ten parallel plates to be distributed in a 

 Poisson distribution with variance equal to the mean. Either theory is thus capable of 

 accounting for the experimental variance, and this experiment alone does not make 

 possible a decision between the two theories. 



A second experiment is now made in which (say) ten cultures, of (say) 10 8 bacteria are 

 tested for phage-resistant organisms. On the adaptation or induced-mutation theory this 

 experiment is not essentially different from the preceding one, and we again expect the 

 numbers of phage-resistant colonies on the ten test plates to be distributed in a Poisson 

 distribution with variance equal to the mean. For, on this theory, the phage-resistant 

 mutants do not appear until the bacteria are plated out on the phage-impregnated medium, 

 and there can be no relevant difference between a culture of 10 9 bacteria divided into ten 

 equal portions, and ten separately grown cultures of 10 8 bacteria. 



In practice a very different result is obtained : the distribution obtained is much wider 

 than in the former experiment, and has a variance many times — perhaps fifty times — 

 the mean. 



On the spontaneous mutation hypothesis a very wide distribution of the number of 

 phage-resistant bacteria in parallel cultures is to be expected. The reason is that not only 

 do the parallel cultures differ in the numbers of mutations which have occurred, but also, 

 and much more importantly, they differ in the stages at which the mutations occurred. 

 If a mutation occurs towards the end of the growth of a culture, it will give rise to one 

 phage-resistant organism, but if it occurs early in the growth, say when the culture is only 

 one-hundredth of its final size, it will give rise to a large number of phage-resistant 

 organisms. Thus even in cultures in which equal numbers of mutations have occurred, the 

 numbers of phage-resistant organisms will usually be widely different. 



It is evident, therefore, that the hypothesis that spontaneous mutation to phage 

 resistance occurs during the growth of the culture before it is brought into contact with 

 the phage is in qualitative agreement with the experimental result, while the alternative 

 hypothesis of mutation induced by the phage, or adaptation of the bacterium to the phage, 

 is not. Luria and Delbruck's method thus provides, for the first time, a clear means of 

 distinguishing between the two hypotheses. 



As left by Luria and Delbruck, the method is a qualitative one, since they do not derive 

 the shape of the distribution to be expected on the spontaneous mutation theory. They do 

 derive expressions for the mean and variance of the distribution, but as they point out, on 

 account of the extreme skewness of the distribution, the mean and variance are very 



25 



