150 MODES OF RESEARCH IN GENETICS 



will be in the next generation one family of the 

 A A -\- Aa -\- aA + aa type. In all succeeding 

 generations there will be six types of families, 

 viz. : 



(1) AA families. 



(2) AA + Aa families. 



(3) Aa families. 



(4) A A + 2 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 On-i denote the number of A A families in the 

 71 — 1th generation, and 



Pn-i denote the number of A A + Aa families 

 in the n — 1th generation, and 



g„_i denote the number of ^a families in the 

 n — 1th generation, and 



Tn-i denote the number of A A -j- 2 Aa -\- aa 

 families in the n — 1th generation, and 



Un-i denote the number of ^ a + aa families, 

 and 



Vn-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 



