THE PROBLEM OF INBREEDING 113 



In the same way, 



Z. = l-M^) = 50. 



Z. = 100^ = 75. 



o 



_ 100 (16-2) _ 

 16 



These results may be expressed verbally in the 

 following way : In the last two ancestral genera- 

 tions X is 50 per cent inbred; in the last three 

 generations it is 75 per cent inbred ; and in 

 the last four generations it is 87.5 per cent 

 inbred. 



This pedigree table and the constants will 

 repay further consideration, since the case is a 

 limiting one. With the table at hand it is possible 

 to grasp a little more clearly the precise meaning 

 of the coefficients of inbreeding. Thus it is seen 

 that what the value of Z\ = 50 really signifies 

 is that because the individuals a and h were 

 brother and sister the number of different ancestors 

 which X can possibly have in any ancestral genera- 

 tion cannot be more than 50 per cent of the total 

 number theoretically possible for the generation. 

 That is, ir's sire and dam having been brother and 

 sister means that x cannot have had more than 

 2048 different great-great-great-great-great-great- 



