THE MUTABLE UNIT OF HEREDITY 53 



replica plating. On the streptomycin agar, whole colonies form only 

 in the spot where, on the original plate, a colony of streptomycin- 

 resistant bacteria existed. This resistant colony can be identified by 

 comparing the plates; when it is isolated and tested, it is proved to have 

 been streptomycin-resistant even though it had never encountered that 

 drug. This proves that the mutation occurred in the absence of the 

 selective agent; i.e., it was preadaptive. 



Nonetheless, certain apparently nonchromosomal mutations are spe- 

 cifically induced by chemical agents. They will be discussed in 

 Chapter 9. 



MUTATION RATES 



Good estimates can be made of the magnitude of the rates (chances) 

 of mutation. What is measured is the average frequency with which 

 the mutational event takes place per cell per division. What is estimated 

 is the frequency of mutation in an infinite number of cell divisions. 

 Since the event is random, this is the chance of its occurrence. Among 

 the units that define this chance is found the term "per division," which 

 introduces a time element and makes the chance a rate. Of course, as 

 we have already seen, the frequency of mutation is necessarily different 

 from the frequency of mutants which is often what is measured. There 

 are several methods of estimating the mutation rate from the number of 

 mutants. 



Another, simpler method does not depend on the number of mutants 

 but rather upon the frequency of clones that contain no mutants. This 

 method employs the Poisson distribution (equation 2.1) which can be 

 simplified when x = 0, for then m* and x! both equal one. We may 

 therefore write: 



P(0) = e-'" (2.2) 



which is readily solved in this form: 



In P(o) = -m (2.3) 



where the symbol In F(0) stands for the natural logarithm (to the base e) 

 of F(o). In our example of the paper exposed to the shower, we knew 

 that the average number of raindrop hits per square was one. We can 

 therefore quickly calculate that P^o) = 0.37. Thus about 37 per cent of 

 the squares would not have been hit at all. Conversely, if we knew only 

 P(0), we could easily calculate m. 



The latter is more like the case with mutation where we can measure 



