306 C. LEVINTHAL 



parents, and growth after formation of the heterozygous particles is assumed 

 to segregate it into pure types. The number of heterozygotes expected in the 

 progeny can be calculated by considering that if such a particle is formed in 

 a pool of constant size it has a probability of one-half of being extracted as 

 such and a probability of one-half of being segregated as it duplicates. Thus, 

 there will be one mature heterozygous particle which arises directly from a 

 mating for every two mating events that occur in the pool. In Tl, with a 

 maximum of 13 % recombinants between distant markers, about 25 % of the 

 particles in the output mvist have either mated or been the descendents of 

 particles which mated nonincestuously. Each mating event produces on the 

 average about 2.5 recombinant particles (e — 2.5) and the burst size is about 

 100, so we can conclude that there must have been on the average 

 100 X .25/2.5 = 10 recombinant producing events in each infected cell. But 

 only in half of these events would the immediate product of the mating have 

 been extracted by maturation without further division, so that only in five 

 particles in a burst of one hundred would it be possible to find heterozygosis. 

 In T2, when one selects for particles which came only from a mating by 

 selecting those which are heterozygous for one m.arker, one finds 6 % are 

 heterozygous for another marker. If the same frequency obtained in Tl, one 

 would expect 6 % of the five particles per burst to be heterozygous for any 

 one marker. Thus one would expect to find of the order of three heterozygous 

 particles per thousand progeny. This expectation is to be compared with 

 about one per thousand found by Trautner (1957). The same type of analysis 

 for the phage A yields similar results. It is not yet clear whether this difference 

 between the observed and the expected values is significant or is due to the 

 various uncertainties in the measurements. 



E. Distribution of Recombinants for Close Markers 



There is one additional prediction which comes out of this model. If two 

 markers are closer together than the length of the heterozygous overlap 

 region, the distribution in the number of recombinants produced per recom- 

 bination event is changed significantly. The exact nature of the new distribu- 

 tion will depend on whether the heterozygous particle which yields one 

 parental type and one recombinant is scored as a recombinant or not. In an 

 experiment reported by Stahl (1956), using two rll mutants, heterozygous 

 particles of this type would have been scored as recombinants; in this case 

 one expects a very different distribution in the number of recombinant par- 

 ticles. For now, instead of the heterozygous particle segregating to produce 

 two recombinants, it segregates to produce one recombinant particle and one 

 parental, so that the probability of getting a clone of size one, instead of 

 being 50 % as in the case of distantly linked markers, becomes 75 % (50 % 

 being the probability of extracting the heterozygote and an additional 25 % 



