The Theory of Population Genetics ; 107 



The reason for this change in rate of removal is that the propor- 

 tion of recessive genes in the heterozygotes increases rapidly as the 

 gene frequency decreases. Where q = gene frequency of a, the 

 percentage of a genes in the heterozygotes is as follows: 



The recessive genes in the heterozygotes are "hidden" from selec- 

 tion, since only the homozygous recessives are lethal. The lower the 

 gene frequency, the smaller the proportion of recessive genes ex- 

 posed in homozygotes becomes, and the progress toward removal 

 of the gene from the population slows down accordingly. This result 

 is of particular interest to students in eugenics. If a particular unde- 

 sirable gene (a) had a gene frequency q = .01 in the human popu- 

 lation, so that q- (aa) individuals made up .0001 of the individuals 

 (one defect per 10,000 "normals"), it would take 100 generations 

 (roughly 2,500 years) of a program of sterilization of defective 



and similarly 



2q 



2pq 



2q 



p^ + 2pq 1 



p-p— + J-— =1 q = gene frequency of a = - X - 



2q 



+ q 1 + q 



p=l-q=l 



q _ 



I + q I + q 



f The genotype frequencies before selection are obtained by iwing the new p 

 and q values and expanding the following: 



\ l+q l + q) 



For example, the zygotic frequency of 



AA= (new p)^-= /^_V= ^—— 



^' \l + q/ (l+qV- 



t Frequencies after selection are calculated as in the first footnote, e.g., 



1/(1 + qr- 1 



1/(1 + 9)^ + 2(//(l + g)= l+2q 



