128 MAINE AGRICULTURAL EXPERIMENT STATION. I913. 



before attacking the more complicated ones actually realized in 

 stock-breeding. 



Illustration I. Continued Brother X Sister Breeding. 



Let us begin with the most extreme type of inbreeding pos- 

 sible, namely the mating of brother with sister for a series of 

 generations. Pedigree Table I gives the pedigree of an indi- 

 vidual so bred. 



Let us now proceed to calculation of the coefficients of in- 

 breeding Zo, Zi, Z"., and Z^. For Zo we have 



100 (o) 



whence Zo = ^ o 



2 



100 (4 — 2) 



In the same way Zi = — = 50 



2 

 100 (8 — 2) 



Z^- = = 75 



8 



100 (16 — 2) 



Za = = 87.5 



16 



These results may be expressed verbally in the following 

 way : In the last two ancestral generations x is 50 per cent 

 inbred ; in the last three generations it is 75 percent inbred ; and 

 in the last four generations it is 87.5 per cent inbred. 



This pedigree table and the constants will repay further con- 

 sideration, since the case is a limiting one. With the table at 

 hand it is possible to grasp a little more clearly the precise bio- 

 logical meaning of the coefficients of inbreeding. Thus it is 

 seen that what the value of Zi^5o really signifies is that 

 because the individual a and b were brother and sister the num- 

 ber of different ancestors which x can possibly have in any 

 ancestral generation cannot be more than 50 percent of the 

 total number theoretically possible for the generation. That is, 

 .r's sire and dam having been brother and sister means that x 

 cannot have more than 2049 different great-great-great-great- 

 great-great-great-great-great-grandparents, instead of the pos- 



