THE PROBLEM OF INBREEDING 151 



always under normal conditions such as are as- 

 sumed in the general treatment, we have 



Un-l = Pn-U 

 Vn-1 = On-U 



t/71 t-^n* 



It is necessary, therefore, to consider only the 

 coeflBcients 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{On-i + i Pn-i + tV ^n-i) AA families 

 + 5 (J pn-i + i Tn-i) AA + Aa families 

 + s (I Tn-i) Aa families 



+ 5 (i Pn-l + Qn-l + i Tn-l) AA 



•^ ^ Aa -\- aa families 

 ■^ s {uy^ Aa -\- aa families 

 •\- s {Vr) aa families. 



Or, taking coeflScients alone, we have 



On = On-l + J Pn-l + iV ^n-1, 

 Pn = h Pn-l + i Tn-U 



r„ = i Pn-l + Qn-l + i Tn-l, 



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



