BACTERIOPHAGE GENETICS 289 



where the symbols now represent the number of particles of the various types 

 in the progeny. 



If we let the ratio of the two types of parental particles in the mixedly 

 infected cell be 



p^ ah 



then it also follows from the lack of selection in the system that 



ah -\- ah'^ p^ 

 a+h+ + a+h~'f- 



And, finally, the sum of all the types in the progeny is identical with the 

 burst size (B. S.), which is the mean number of progeny liberated per infected 

 cell; in a standard cross the burst size always has the same value. Thus 



ah + a+6+ + a+h + ah+ = B. S. 



We can conclude from the foregoing that the results of any cross between 

 two markers can always be described by one number. This follows from the 

 fact that there are four numbers to be measured and three equations which 

 relate them. The measured parameter which describes the cross is usually 

 taken as the frequency of recombination. In the above cross this would be 



a+h + ah+ _ 

 B.S. ^^"^ 



D. Three-Factor Cross 



If a standard cross is made between two phage stocks which differ from 

 each other with respect to three mutations, the situation is a httle more 

 compUcated. In the cross ahc X a^b'^c'^, there wiU be in addition to the par- 

 ental types six types of recombinants produced in the progeny. However, 

 there are certain general rules which yield relationships between these eight 

 types. The total number of phages which contain the mutation a is the same 

 as the total number which contain the mutation 6 or the mutation c. Using 

 the symbol • to indicate either the mutation or the mid type, we can write 

 these relationships as a • • = • 6 . = • • c. As before, the sum of all eight 

 types is constant and equal to the burst size, and in addition the ratio of a 

 to a"^, or 6 to 6+, or c to c+ must be the same and equal to the ratio of the two 

 types of phage among the parents, that is, p^lp^. Thus, if one knows the ratio 

 of the two parental types which went into the cross, one has now four 

 equations which relate the various measured quantities in the progeny; and 

 therefore there are four independent parameters which can be determined in 

 any experiment. Three of these numbers represent the recombination 

 VOL. II — 19 



