304 C. LEVINTHAL 



This is not surprising in terms of the model discussed here since no account 

 was taken of the mutations which occur very early, before the pool reaches 

 constant size; these would be expected to produce large bursts. For the events 

 which do occur during the period of the constant pool, the average number of 

 mutants observed per mutational event is equal to the burst size divided by 

 twice the number of particles in the pool. This can be seen by noting that 

 whenever a mutation occurs in the pool, on the average 1/iV of all future 

 progeny to mature will be mutants if iV is the pool size. If the mutation is 

 equally likely to occur at any time in the constant pool, then the mean 

 number of particles produced after the event is just half of the burst size. 



C. Distribution of Recombinants 



We would expect the calculations given here to be somewhat more reliable 

 for recombinants which arise in an infected cell than for mutants since the 

 probability of collision which could lead to a mating event would be expected 

 to increase as some power of the number of particles in the pool. Thus, most 

 of the mating events in a normal cross will occur after the pool has reached 

 its constant size. We will define e as being equal to the average number of 

 observed recombinants per observed recombination event; as in the case of 

 the distribution of mutants, this will be equal to the burst size divided by 

 twice the mean number of particles in the pool. The mean number of observ- 

 able recombinational events can be determined only in those systems in 

 which the recombination between two markers is rare. Under these conditions 

 a significant fraction of the single bursts will show no recombinants of a 

 particular type; from the fraction which shows none, one can calculate the 

 mean number of events under the assumption that the events are distributed 

 at random. For Tl, e is found to be approximately 2.5 and the burst size is 

 about 100 (Bresch, 1955). Thus, the mean number of particles in the pool is 

 approximately 20. This calculation for the phage T2 leads to similar results 

 (Hershey and Eotman, 1948) in rough agreement with the chemically measured 

 size of the pool; but unfortunately the data used in the calculation are not 

 as rehable as in the case of the phage Tl because of the large number of 

 mating events, whereas in Tl the chemical analysis of the pool size has not 

 yet been made. The few available experiments (Bresch, 1955) which give the 

 distribution of the number of recombinants per recombination event for 

 markers which are not extremely close do agree roughly with formula (1) 

 but the data are not adequate for a critical test of this point. 



D. The Mating Process 



The above considerations apply only to the kinetics of the pool of vegeta- 

 tive phage and do not require a specification as to the nature of the elemen- 

 tary mating event. In order to complete the model we wiU assume that the 



