THE PROBLEM OF INBREEDING 151 



always under normal conditions such as are as- 

 sumed in the general treatment, we have 



Un-l = Pn-l> 



V n -i = O n _i, 



U n = p n , 



V n = O n . 



It is necessary, therefore, to consider only the 

 coefficients for the first four types of family. In 

 the nth generation the constitution of the popula- 

 tion in respect of families (not individuals) will 

 be as follows : 



Families in the nth generation 



= s(o n -i + \ p n -i + T V r n _i) AA families 

 + s (J p n -i + i r n _i) AA + Aa families 

 + s (| r n _i) A a families 

 + s (J p n -i + q n -i + i r-i 



+ % Aa + aa families 

 + s (u n ) Aa + aa families 

 + s (v n ) aa families. 



Or, taking coefficients alone, we have 



o n = o n _i + J p n _i + T V r n _i, 

 Pn = I p-i + J r n _i, 



^n = \ U n - 



V n = fl-l 



Let us see how this formula works out in a con- 



-1 + V f-l = O n . 



