MANNER OF PRODUCTION OF MUTATIONS 499 



For these reasons the results from rings cannot yet be taken as pro- 

 viding direct evidence against an association between gene mutations and 

 breaks. However, they do mean that, if the association exists, the breaks 

 must be far more numerous than had been supposed, and it can be calcu- 

 lated that for rod chromosomes the restitutions would have to have a 

 frequency at least two orders of magnitude higher than the cases of single 

 breakage which lead to chromosome loss or to death of the zygote. This 

 conclusion again assumes importance in connection with the question of 

 how many chromosome breaks may be associated with effects like those 

 of gene mutation. For it turns out, as will be noted, that this question 

 would thereby receive an answer which was at variance with the require- 

 ments of the idea that most gene mutations are associated with breaks. 



The idea that some gene mutations may mark the sites of restituted 

 breaks, which was suggested by Muller (1941a) as a mere possibility 

 arising from the finding that the great majority of breaks restitute, has 

 more recently been revived by Lea and Catcheside (1945b), and inde- 

 pendently by Herskowitz (1946). In fact, they have been inclined to 

 regard all or most gene mutations produced by ionizing radiation as being 

 of this nature. Their argument has its root in the contrast between the 

 linear relation of the dose to the frequency of recessive lethals and its 

 ^^-power relation to the frequency of gross structural changes. As noted 

 by Timofeeff-Ressovsky (1939), the apparently quite linear relation for 

 recessive lethals as a group appears at first sight to be paradoxical, in 

 view of the fact that this group is a mixed one and that at higher doses 

 an increasingly important proportion of these lethals is associated with 

 structural changes. Although Timofeeff-Ressovsky believed that these 

 structural changes did not constitute a large enough proportion of the 

 total to be expected to influence its linear relation perceptibly, this judg- 

 ment is not shared by some of the others who have studied the observed 

 frequencies of different types of changes. 



A breakdown of recessive lethals shows them to be composed of the 

 following types: (1) gene mutations, whose frequency at lower doses is 

 known to vary Unearly with dose; (2) small structural changes (mainly 

 deletions), a part of which at least, including especially the very small 

 ones (2a), varies linearly but another part of which (2b) varies as a 

 higher power of the dose (see pp. 394-396); and (3) gross structural 

 changes, which vary approximately as the % power of the dose at ordi- 

 nary doses and, on the view proposed by Muller (Muller and Prokofyeva, 

 1934), usually owe their lethality to position effects. At low and moder- 

 ate doses from 50 r up to about 1500 or 2000 r, classes (1) and (2a) 

 together constitute a considerable majority so that in this range the over- 

 all frequency of lethals would be expected to rise practically linearly with 

 dose. However, above this dose, where class (3) and perhaps also (2b) 

 assume a considerable and ever greater relative frequency, the over-all 

 frequency of lethals would be expected to rise more and more steeply 



