THE PROBLEM OF INBREEDING 151 



always under normal conditions such as are as- 

 sumed in the general treatment, we have 



«»-i = Pn-u 



fln-l = 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„_i + | p„_i + tk fn-i) AA families 

 + * (I p n -i + \ r„-i) AA + Aa families 

 + * (J r n _i) Aa families 

 + * (I Pn-i + q n -i + \ r n -i) AA 



+ 2 Aa + aa families 

 + s (u n ) Aa + aa families 

 + s (v n ) aa families. 



Or, taking coefficients alone, we have 



o„ = o„_i + \ pn-i + tV r n -i, 



Pn - I Pn-1 + \ T n -1, 



q n = f r»-i> 



r„ = | p n -\ + q n -i + J *•„_!, 



«n = | Mn-1 + i »"n-l = 2>n, 

 »n = »»-l + £ «»-l + tV r »-l = On- 

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



