68 A. D. HERSHEY AND RAQUEL ROTMAN 



understood in terms of random pairing between homologous structures. In the 

 simplest case one visualizes unrepeated pairing, that is, pairing limited to a 

 phase in which there is no multiplication, and during which no structure finds 

 more than one partner. For this case, the frequency of synapsis in equation 

 (6) is simply the ratio of the number of unlike homologous pairs to the total 

 number of homologous pairs. This ratio can be written 



2ab 



(a + b)(a + b- 1) 



(8) 



where a and b are the respective numbers of the two unlike homologous 

 structures. Inspection of (8) shows that this ratio is essentially 2k as given by 

 equation (3) when a-f-b is large compared to unity. Instead of equation (6) we 

 have, therefore, 



p (wild type) = mkc, 



(9) 



from which the proportion of either recombinant expected in crosses between 

 distant linked factors can be computed as follows. 



The parameter m, taken to be the average fraction of virus randomly mixed 

 in the cells at the time of reconstitution of virus from subunits, was found to 



Table 9 



Three Point Linkage Tests of Linear Structure 



The symbol r2,3 refers to the double mutant containing r alleles at the loci r2 and r3, etc. 

 Ci is the crossover frequency for the region between r2 and r 3 . 

 C2 is the crossover frequency for the region between r3 and r6. 

 The locus r3 is assumed to lie between r2 and r6. 

 The factor 0.14 is explained in the discussion. 



be 37/50 in crosses between unlinked factors. In (9) we require the corre- 

 sponding fraction at the time of pairing, and assume this to be the same. The 

 average of k for bacteria giving mixed viral yields (table 4) is 0.21, or 0.19 if 

 one includes the ten percent of bacteria yielding only one type of virus. If k 

 and m vary independently, their mean product is the same as the product of 

 means, or 0.14 averaged over all bacteria. The average yield of either recom- 

 binant from equation (9), for factors sufficiently far apart so that c = 0.5, 

 is accordingly seven percent, computed solely from the data for crosses 

 between unlinked factors. This is the maximum actually found in crosses 



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