430 RADIATION BIOLOGY 



through heterozygotes to compensate for the mutations arising, twice as 

 high a frequency of them must be eUminated as the frequency n that 

 would be necessary if the ehmination could be carried out in the germ 

 cell stage. 



The term "overlapping" as applied to genetic deaths refers to two 

 types of cases. In the first, which may be called the cases of "independ- 

 ent overlapping," an individual who meets genetic extinction through the 

 effect of a given gene would have met extinction anyway through the 

 effect of one or more other independently acting genes which he also 

 happened to carry, so that the one death accomplished more than one 

 effective gene-elimination. In the second, which may be called the cases 

 of "dependent overlapping," the individual's genetic survival is prevented 

 by a synergistic (i.e., more than factorially cumulative) action of two or 

 more mutant genes, which thereby exercise a kind of economy in causing 

 extinctions. The frequency of independent overlapping can readily be 

 calculated from the mutation frequency and turns out to be relatively 

 unimportant unless /x exceeds 0.1. Where, however, (as might be the 

 case in man) /i is as high as 0.5, independent overlapping would reduce 

 the frequency of genetic deaths of individuals from 1.0 (= 2fx) to about 

 0.63. Dependent overlapping seems hitherto to have been ignored in 

 calculations of elimination rate. Although probably important, its 

 amount of influence cannot at present, in the absence of empirical data 

 on the subject, be estimated. It seems very unlikely, however, from 

 calculations based on plausible assumptions as to the frequencies of 

 genes having various grades and multiplicities of synergistic interaction, 

 that it would reduce the elimination rate of individuals by a factor of 

 more than 2 or 3, and there is more latitude than this anyway in present 

 estimates of the human spontaneous mutation rate. For the present, 

 then, the extent of this influence will have to be left doubtful.'^ 



There are reasons to conclude (Muller, 1950b) that 0.1 (i.e., 1 germ 

 cell in 10) represents a low minimum for the per-generation frequency of 

 new spontaneous mutations among human germ cells; 0.2 or even 0.4 

 appear much more probable figures, and some competent students of the 

 subject believe the rate to be considerably higher yet. Taking 0.3 as a 

 probable value not on the excessive side, 2ju becomes 0.6, and, if the 

 seemingly high allowance of a factor of 3 is made for overlapping, of both 

 the types just discussed, we obtain 0.2, or an average of one person in 

 every five, as the frequency, probably minimal, of individuals being 

 genetically eliminated. This would apply in a human population that 

 was maintaining a constant frequency of mutant genes. 



The condition of constant or equilibrium frequency of mutant genes can 



^ The possible importance of what we have termed "dependent overlapping" was 

 recently pointed out by Neel and Falls (1951), and also in a personal communication 

 received from Altenburg. 



