DELAYED EXPRESSION OF MUTATIONS 449 



in the experiments under consideration. To determine this proportion it is of 

 course necessary to test whole cultures, as distinct from samples. 



This method will be known as method 1 throughout the present paper. It 

 should be noted that it is based upon an estimate of the number of resistant 

 clones developing in the series (this estimate being obtained from the propor- 

 tion of cultures in which no resistant mutants have developed), and that 

 it takes no account of the numbers of individuals in these clones at the end of 

 the growth. For the purpose of this paper, the term "mutant clone" will 

 refer to those individuals carrying genetic factors for phage resistance which 

 have a common origin in a single mutation. Within a mutant clone individuals 

 which are phenotypically resistant to phage will be collectively termed a 

 "resistant clone." A culture may contain one or more mutant clones of varying 

 age. 



The second method of Luria and Delbruck uses the average number of 

 resistant bacteria in a series of similar cultures and calculates mutation rate 

 from this value, the average population, and the number of cultures. The 

 number of mutants arising during the growth of a culture is of course, on the 

 average, a function of the mutation rate. But there are very large variations in 

 the number of mutants present in different cultures grown under identical 

 conditions, these being due to chance variations in the time of occurrence of 

 the mutations. Thus the occasional occurrence of a mutation early in the 

 growth of a culture, at a time when the population is small, willjesult in a 

 much higher than average number of mutants in that culture. Because of 

 these statistical fluctuations, mutation rate cannot be calculated from the 

 number of mutants in a single culture started from a small inoculum. It can, 

 however, be estimated from the average number of mutants in a series of 

 similar cultures; and the mathematical details of the method have been 

 worked out by Luria and Delbruck (1943). This method will be known as 

 method 2 throughout the present paper. It differs from method 1, which utilizes 

 the number of resistant clones occurring in liquid cultures, in that it takes into 

 consideration the number of resistant individuals. Furthermore, in the event 

 of any change in the mutation rate during growth, method 2 would give an 

 average of the mutation rates obtaining in each of the generations during which 

 mutations had occurred — equal weight being given to the early generations 

 when the population and the number of mutations occurring were small, and 

 to the later generations when both these values had increased. In contrast to 

 this, in method 1 changes in the mutation rate during growth would give an 

 estimate strongly biased in favor of the rate obtaining during the later period 

 when the population and the absolute number of mutations occurring was 

 large. Moreover, a delay in the phenotypic appearance of a mutation would re- 

 duce the rate as estimated by method 1, because recent mutations would not 

 be detectable. The rate as estimated by method 2 would be affected less, 

 since early mutations, which have a greater number of generations in which to 

 become phenotypically resistant, are represented by larger numbers of de- 

 scendants than are the later mutations. The possibility that mutation rate is 



