426 RADIATION BIOLOGY 



respective chances of multiplication and elimination which are independ- 

 ent of the effects of the gene in question are equal in amount, and so they 

 tend to compensate each other exactly in the long run, when the results 

 for many mutant genes, present in a large population of stable size, are 

 added together. Thus, for a large group of hypothetical mutant genes 

 which conferred neither detriment nor benefit on their possessors, their 

 collective frequency in the population after any given number of genera- 

 tions would still be approximately equal (subject to some statistical 

 deviation) to their frequency in the first generation considered (e.g., in 

 the generation in which they originated) , even though some of the genes 

 had become multiplied and others, in compensating number, had become 

 eliminated. That is, each individual mutant gene present in the begin- 

 ning generation would on the average be represented by just one descend- 

 ant gene in the nth generation. 



However, for the vast majority of mutant genes, those which confer 

 some disadvantage, even though slight, and also for the very rare ones 

 which confer an advantage, the situation is modified by their somatic 

 effect. Considering a large group of mutant genes, all of which give rise 

 to one or another impairment of such magnitude as to reduce the average 

 chance of reproduction of an individual containing such a gene by a 

 given amount, i, which we may, for example, imagine to be 10 per cent, 

 it is evident that after one generation of breeding these genes will have a 

 frequency of approximately 1 — i in the population, after two generations 

 one of (1 - ^■)^ and after n generations one of (1 - i)". By summation 

 of these frequencies over an unlimited number of generations it is readily 

 shown that each such gene is transmitted, on the average, to a total of 

 1/i individuals. Thus, for genes whose i = 10 per cent, giving 1 chance 

 in 10 of elimination in each individual, the total number of individuals 

 which in the course of successive generations come to inherit a descendant 

 of this mutant gene before it is eliminated from the population is on the 

 average 1/0.1, or 10. The value 1/i is designated as the persistence, p, 

 i.e., l/i = p, and in our example p = 10. 



These considerations show that each mutant gene that exerts a dis- 

 advantageous over-all effect, no matter how small, is eventually elimi- 

 nated, i.e., it leads to a "genetic death" by prematurely kilUng off or 

 preventing the reproduction of, on the average, one descendant contain- 

 ing it.*^ Moreover, the number of descendants that contain and are 

 hampered by a given mutant gene is on the average exactly the reciprocal 



6 The death is to be considered as only a "half death" and the total load as only a 

 half of one unit of load for genes which are so recessive that their elimination occurs in 

 individuals homozygous for them, since in this case the cooperation of the gene from 

 the other parent is required for the effect. As pointed out in the text, however, it is 

 probable that the great majority of mutant genes, even when seemingly of a recessive 

 type, have enough dominance to be eliminated in heterozygous individuals, and there- 

 fore give rise to one death, and one unit of load. 



