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Number of 

 mutants 



FIGURE 2.3. Diagrammatic representation of the numbers of mutants found in 

 independent but similar clones following a single mutation in each. 



random process. The notion of randomness has several aspects which 

 may be tested experimentally. First, there is the concept of adaptive 

 randomness. Do mutations occur without any adaptive relation to the 

 environment in which they happen? For example, do mutations from 

 str-s to str-r occur even when streptomycin is absent from the environ- 

 ment? This kind of randomness would make for an unpredictability of 

 mutation. The statistician means something else when he speaks of a 

 random process; he means that the chance of an event is constant with 

 time and the same for all units in which the event may take place. We 

 may ask whether the chance of mutation is the same for all cells in a 

 population and constant with time. Since we know that the surround- 

 ings (e.g., nitrous acid) will change the rate, we must specify the environ- 

 ment in which the mutation is occurring. We may also ask whether the 

 chance that mutation will occur in one mutable unit is independent of 

 mutation in another. Because of the rareness of mutation, we are hard 

 put to find experimental answers to these questions with higher forms, 

 but relevant experiments have been performed with microorganisms. 



The first rigorous test was performed by Luria and Delbriick in 1942. 

 Using what is called fluctuation analysis, they took advantage of the 

 fact that bacteria multiply by dividing in two, one cell thereby forming 

 a clone that may consist of billions. Let us consider a number of dif- 

 ferent clones, each originating (as the definition requires) from a similar 

 cell. For diagrammatic purpo.ses we will consider clones of only four 

 cells, but the principle to be demonstrated holds as well for the very 

 large populations usually studied. Figure 2.3 shows the numbers of 

 mutants that can be found in the various hypothetical clones. If the 

 mutation occurs in the cell that originates the clone, all four members 

 will be mutant; if it occurs in one of the first pair of cells formed, 

 only two mutants will result; mutation in the final generation will yield 



