308 C. LEVINTHAL 



of determining the number of recombinants in a cross even when that 

 number is extremely small. Benzer has estimated that a recombinant fre- 

 quency of 10~^ (one in a hundred million) can be detected if the reverse 

 mutation rate of the parents is sufficiently low. 



More than two thousand rll mutants have been mapped with varyiug 

 degrees of precision. The results of a series of two-factor crosses can be sum- 

 marized by the construction of a one-dimensional map on which most of the 

 mutants can be arranged as a set of points. The distances between these 

 points are proportional to the recombination frequency between the mutants, 

 and the distances are roughly additive. Therefore, the first conclusion from 

 this work is that the general ideas discussed above regarding a hnear genetic 

 map apply even to these closely linked markers. 



B. Deletions 



In addition to the mutations which behave as though they occupied a 

 point on the genetic map, about 10 % of the rll mutants studied behave as 

 though they occupied an extended region. These mutants, which are called 

 "deletions," also differ from other rll's in that they show no evidence (less 

 than one in 10^ in a stock) of spontaneous reversion to wild type. In practice 

 the deletions can be selected by testing aU mutants for their reversion rate 

 and selecting those which show none. The definition of a deletion which was 

 used by Benzer is "a mutation which fails to give any wald recombinants 

 with each of three different mutations, all of which do give recombination 

 with each other." In order to apply this test, the necessary mutants must be 

 mapped and tested; this has only been done for a small number of the non- 

 reverters. However, in all cases where the nonreverters can be tested they 

 are found to be true deletions. Thus, it is reasonable to assume that all the 

 nonreverters represent deletions in the genetic map. 



The availability of the deletions makes possible an essentially new and 

 very elegant demonstration of the Unearity of the genetic map. Analytical 

 methods have been developed for treating the interactions of many deletions, 

 the principle of which can be seen in Fig. 6. If the genetic map could be 

 represented on some kind of a two-dimensional surface, there should occas- 

 ionally be found two pairs of mutants such that each pair would give recom- 

 binants when the two members of the pair were crossed with each other; but 

 no cross between members of different pairs would yield any. Such a result 

 would require a cyclic representation as shown in Fig. 6 (a). This situation 

 has never been detected, and the observed data are all consistent with a one- 

 dimensional representation such that if two mutants recombine with each 

 other and a third does not recombine with either of them, then the third 

 must lie between the two in the sense that mutant B is between A and C of 

 Fig. 6 (b). Since all mutually overlapping deletions can be unambiguously 



