THE MEASUREMENT OF THE INTENSITY OF INBREEDING. I29 



sible 4096. He may have had fewer than 2049, but Zi:=5o tells 

 us that he could not have had more. Similarly Zi-=^'jz^ indicates 

 that since c and d, the grand-sire and grand-dam of x were 

 brother and sister, x cannot have in any ancestral generation 

 more than 25 percent of the theoretically possible number of 

 ancestors for that generation. And so on for the other values 

 of Z. 



In the limiting case of the closest inbreeding possible the suc- 

 cessive Z's will have the values given in the following table. 



TabeE I. 



Values of the Successive Coefficients of Inbreeding (Zo to Zisj 

 in the Case of the Most Intense Inbreeding Possible (Brother 

 X Sister Out of Brother X Sister Continued). 



Coefficient of 



Ancestral Generations 



Numerical Value of 



Inbreeding. 



Included. 



Coefficient. 



Zo 



1 







Zi 



2 



50 



Z2 



3 



75 



Z3 



4 



87.5 



Z4 



5 



93.8 



Zd 



6 



96.9 



Z6 



, 7 



98.4 



Z7 



8 



99.2 



Z8 ■ 



9 



99.6 



Z9 



10 



99.8 



Zio 



11 



99.9 



Zn 



12 



99.95 



Z12 



13 



99.98 



Z13 



14 



99.99 



Zl4 



15 



99.994 



Z15 



16 



99.997 



From this table it is apparent that while the narrowing or 

 exclusion of the possible different source lines of descent pro- 

 ceeds very rapidly in the first few generations of brother X 

 sister breeding, only relatively little change is made by further 

 generations of this sort of breeding. Thus in seven generations 

 of brother X sister breeding all but about i 1-2 percent of the 

 potentially different ancestral "blood-lines" will have been 

 eliminated. 



The -values of the Z's in Table i are maxima : No particular 

 coefficient of inbreeding can have a higher value than that given 

 in the table. It is not possible, for example, so to breed any 

 domestic animal that its pedigree on analysis will give Zi > 



