292 C. LEVINTHAL 



each other. And, finaUy, they showed that if the mating act is similar to the 

 crossing-over process which occurs in higher organisms, five rounds of mating 

 are, on the average, necessary to account for the results of a standard cross. 

 In T2, if lysis is inhibited, the mean number of rounds of mating will increase 

 by a factor of six or seven before aU the mature phage has been formed; during 

 this increased period of phage production, the burst size rises by roughly the 

 same factor. 



The same type of population analysis has been used to interpret the data 

 obtained with the phages Tl (Bresch and Menningmann, 1954; Bresch and 

 Trautner, 1955) and A (Kaiser, 1955; Jacob and WoUman, 1954, 1955; 

 Wollman and Jacob, 1954) and the same basic assumptions give a good fit 

 with the experimental results if the assumed number of rounds of mating is 

 about one-tenth that in T2. Thus, in these other phages, only about one-half 

 of the particles in the progeny have themselves or their ancestors arisen in a 

 mating act. 



The most important result of these analyses is that after aU the corrections 

 have been made for multiple matiiigs, the results of all crosses between any 

 markers, except those which are extremely closely linked (see Section VII, 

 D) can be summarized in terms of a single linkage map. The genetic markers 

 can be represented as points along this one-dimensional map, with the 

 distances between markers made proportional to the recombination fre- 

 quencies corrected for multiple switching events (or cross-overs). ^ Thus, for 

 any three markers, the map distances are strictly additive once all corrections 

 have been made. 



In 1958 several groups independently re-analyzed, in more general terms, 

 the problem of multiple matings in order to determine whether the basic 

 assumption of pair-wise mating could be justified by experiment, Stahl and 

 Steinberg, using an essentially new and very powerful, analytical method, were 

 able to show that none of the experiments previously reported could be used 

 to determine the number of particles which enter the mating event, and that 

 no information as to the mechanism of the mating event could, in principle, 

 be obtained from any standard mass culture crosses. Thus a smgle particle 

 which is produced in a mating could contain genetic information from three 

 or more parental structures. This phenomenon they caUed group mating. 

 Hershey (1958) carried out an extensive study of recombuiation stimulated 

 by ultraviolet light and concluded that in this case, at least, the results 

 were more easily understood in terms of group than of pair-wise mating, 



^ This correction allows for the fact that if two, four, or any even number of switches 

 (or cross-overs) occur between two markers, there will be no observable recombination. 

 This results in the following expression, giving recombmation probabilities ^ as a function 

 of map distances d (Haldane, 1917): 



p = 1/2(1 - e-2<^) 



