Gene Frequencies 539 



offspring from this population would again be in the ratio of 

 '^%^AA : %^Aa : ^oso^a. 



Obviously, the frequencies of the two original types might be 

 any value. The general case, the Hardy- Weinberg law, can be 

 stated by assuming that the original frequency of AA organisms 

 is q and of aa organisms (1 — g). If these values are substi- 

 tuted in the checkerboard, the offspring will fall into the ratio of 

 q- AA : 2q{l — q) Aa : (1 — q)- aa. If the gametes are ob- 

 tained from all the organisms of this generation, they will be 

 found with the following frequencies: 



A=q^^\' 2g(l - q) = q 

 a = i • 2g(l - g) + (1 - q? =(!-?) 



Thus the frequencies of A and a are exactly the same as they 

 had been for the preceding generation so that the offspring of 

 this generation will be in the same proportion as this generation 

 itself. This proportion is repeated indefinitely so that the gene 

 frequencies of both the dominant and the recessive genes will 

 be the same generation after generation unless conditions change. 

 To state this generally, the two types of gametes in any genera- 

 tion will be proportional to the gene frequencies. Such a popu- 

 lation is said to be in equilibrium for it will continue to have 

 the same structure unless some change occurs in the given con- 

 ditions. Some of the factors that change the gene frequencies 

 and thus upset the equilibrium are mutation, selection, nonran- 

 dom mating, and inbreeding. If, suddenly, one of these factors, 

 such as mutation of one allele to the other, would arise, the 

 previous equilibrium would be upset and, provided there were 

 random mating, a new equilibrium would be established after 

 one generation. This new equilibrium would then be maintained 

 unless another change upset it and a still different equilibrium 

 became established. Equilibrium will be reached when the pro- 

 portion of heterozygotes is twice the square root of the product 

 of the two homozygous classes. When there is equilibrium, there 

 is no evolution; but a change in gene frequencies will lead to 

 evolution. 



The use of gene frequencies has become an important method 

 in an analysis of human traits. This method is especially use- 



