150 MODES OF RESEARCH IN GENETICS 



will be in the next generation one family of the 

 A A + Aa + a A + aa type. In all succeeding 

 generations there will be six types of families, 

 viz. : 



(1) AA families. 



(2) A A + Aa families. 



(3) Aa families. 



(4) A A + % Aa + aa families. 



(5) Aa + aa families. 



(6) aa families. 



The proportionate number of each of these 

 types of families will change in successive genera- 

 tions according to the following system : 



Let o_i denote the number of A A families in the 

 n 1th generation, and 



p n -i denote the number of A A + Aa families 

 in the n 1th generation, and 



q n -\ denote the number of A a families in the 

 n 1th generation, and 



r n _i denote the number of A A + % Aa + aa 

 families in the n 1th generation, and 



u n -i denote the number of Aa + aa families, 

 and 



# n _i denote the number of aa families. 



It will be possible to write down u and v in any 

 case without calculation because of the symmetri- 

 cal relations of a Mendelian population, since 



