66 A. D. HERSHEY AND RAQUEL ROTMAN 



influenced by burst size unless the latter has an effect on the fraction m. 

 According to the data it does not, and m is a parameter having the average 

 value 37/50. This interpretation requires that 26 percent of either kind of 

 parental virus in the cell should multiply in effective isolation from the other 

 parent. 



It will be noticed that the expressions (4) and (5) reduce to mk if one makes 

 the approximations mentioned in connection with equation (3). This provides 

 a theoretical basis for the correction we have applied to yields of recombinants 

 in crosses between unlinked factors. An analogous justification for its use in 

 crosses between linked factors will appear in the discussion to follow. 



The predictions for the cross hXr7 are different from the preceding case, be- 

 cause here the markers are situated on homologous linkage structures, so that 

 recombination requires something like crossing over, whiqh in turn requires 

 something like synapsis. The expected fractional yields of recombinants are 



p(h+r+) = p(Ar) = § msc, (6) 



in which m has been defined previously, s is a fraction independent of m ex- 

 pressing frequency of pairing, and c is a crossover frequency. In order to make 

 c independent of m and s it is evidently sufficient to define the product ms as 

 the fraction of the viral yield made up of particles in which the marked unit 

 has descended from an unlike synapsed pair. The application of (6) leads to 

 ambiguity if exchanges can occur between descendants of unlike synapsed 

 pairs (Hershey and Rotman 1948). In what follows this difficulty does not 

 appear to be very serious, but no rigorous analysis has yet been attempted. 



For the cross hXr7, if exchanges are reciprocal, one expects the correlation 

 between proportions of the two recombinants to be disturbed only by fluctua- 

 tions in relative growth of the two exchange products, in contrast to the cross 

 hXrl, where the correlation is subject to fluctuations in the growth of four 

 independent units. That these fluctuations are individually considerable is 

 shown by the variations in relative and total viral yields in mixedly infected 

 bacteria. A weak but probably significant correlation between proportions of 

 the two recombinants is nevertheless visible in the cross hXr7. No such cor- 

 relation can be seen in the cross hXrl. If the mechanism of exchange for these 

 two crosses were the same, the greater correlation would be expected in the 

 cross hXrl, which gives the larger yield of recombinants. 



The predictions for the cross hXrl3 are the same as for hXr7 except as 

 modified by the much smaller yield of recombinants, presumably owing to a 

 smaller frequency of crossing over. We have shown that in this cross the re- 

 combinants come from two or three individual exchanges per bacterium, and 

 that there is little growth of recombinants subsequent to exchange. These cir- 

 cumstances ought to be favorable for testing the hypothesis of reciprocal ex- 

 change. The data are nevertheless inconclusive of this point. 



The experiments provide information about the sequence of events in the 

 cell. A mechanism of exchange limited to an initial phase of multiplication is 

 ruled out by the following consideration. If exchange occurred at a time when 

 there were few replicas in the cell, any cross yielding a small average number of 



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