THE PROBLEM OF INBREEDING 139 



From this we have, for the inbreeding coeffi- 



cients ' Z = 



Zi = 25.00 

 Z 2 = 25.00 

 Z 3 = 37.50 

 Z 4 = 50.00 

 Z 5 = 71.88 

 Z 6 = 81.25 

 Z 7 = 90.63 

 Z 8 = 92.77 

 Z 9 = 93.65 

 Z 10 = 93.85 

 Zu = 93.85 



These facts will possibly be made clearer to 

 those not actually working much with pedigrees 

 by Table VII, which gives the first four ancestral 

 generations * of the pedigree of King Melia Rioter 

 14th. 



Generalizing the above reasoning we get the 

 following result : 



In, A 3 , and higher ancestral generations, f = 

 50.00 per cent of the dam's ancestors are animals 

 which are also ancestors of the sire. 



1 In the study of pedigrees stress is naturally laid on the ancestral 

 generations, rather than on the filial, as in breeding experiments. 

 It becomes very convenient to have a brief designation for ancestral 

 generations, in the same way that F u Fi, etc., are used to denote 

 filial generations. I would suggest the use of the letter A with sub- 

 numbers for this purpose. We then have A\ denoting the parental 

 generation, Az the grandparental, Az the great-grand-parental, etc. 



