40 APPLICATION OF PRINCIPLES OF HEREDITY TO BREEDING. 



Table B. — Method of determining the relative 'proportion of the various types of progeny 

 produced by generations Fo and of a hybrid, with seJf -fertilization. 



T3T)es and their relative frequency. 





DD 



DR 



RR 



Types in F2: 



\DD...a2 



2 

 1 







2DR 4 



2 



1 



2 



\RR 2 



Frequency of types in F3 







3 



2 



3 



Types in F3: 



3Z>Z)... 06 



6 

 1 







2DR 4 : 



2 



1 



6 



ZRR 6 



Frequency of types in F4 







7 



2 



7 





Types of progeny pro- 

 duced by each F3 

 type, and their rela- 

 tive frequency. 



a These numbers are taken instead of 1, 2, 1 (3, 2, 3 in F3) to avoid fractions in the next three columns. 



Here we see that the proportion of the types changes from gen- 

 eration to generation, the homozygote types increasing while the 

 heterozygotes decrease in relative frequency. 



It will be noticed that the sum of the relative frequencies in 

 is 4 ; in F3, 8 ; and in F4, 1 6 ; and so on ; that is, in Fg it is 2^ ; in Fg, 2^ ; in 

 F4, 2*; etc. In general, in Fn it is 2^. Similarly, the frequency of each 

 of the types DD and RR is, in 



F. 



F3 F3 



F, Fe--. 



1 3 7 15 31 

 Or, 21-1 22-1 2^-1 2^-1 2^-1 



The frequencies of all the types in Fn are — 



DD, 2^-1 - 1 

 DR, 2 

 RR, 2^-1-1 



Fn 



1. 



2x2^-l = 2^ 



The above calculations have been made for a single character pair 

 for convenience. Exactly the same method may be pursued when two 

 or more Mendelian pairs are concerned, except that where two pairs 

 are involved we must deal with nine types instead of three, and where 

 three pairs are involved we must deal with twenty-seven types, and 

 so on. In general, the number of types appearing in Fg and later gen- 

 erations is 3"^, where the n is the number of character pairs involved. 



To illustrate the effect of selection to a dominant type, let us con- 

 sider the case of two character pairs, which we may denominate Aa 

 and Bh, where A and B are dominant and a and h recessive. Gener- 

 ation Fi produces nine types of progeny, which, with their relative 

 frequencies, are shown in Table C. Here the selected types are those 

 that have the appearance of the type AABB, namely, AABB, AABh, 

 AaBB, and AaBh. It is seen that while type AABB is only one- 

 sixteenth of generation F2, it constitutes one-fourth of the selection 

 made in F3. By continuing Table C to ten generations, the data from 

 which figure 3 was constructed may be obtained. 



165 



