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THE AMERICAN NATURALIST [Vol. XL VII 



Z 7 =6,900/256 = 26.95, 

 Z % =14,800/512 = 28.91, 

 Z 9 =30,000/1,024 = 29.30, 

 Z 10 = 29.30, 

 Z n = 29.30. 



From these values it is seen that, so far as the ancestry 

 is known the bull Saxton is 29.3 per cent, inbred. The 

 curve of inbreeding, Fig. 2, shows that this intensity was 

 gradually and steadily attained, by slight additional in- 

 breeding in each generation. In the end (always within 

 the limitation of the hnoivn ancestry) Saxton is some 4 

 per cent, more closely inbred than he would have been 

 had his dam been his sire's daughter, without other in- 

 breeding in the ancestry. In the first five ancestral gen- 

 erations Saxton is less intensely inbred than Postumus. 



Coefficients of Inbreeding and the Gametic Const 

 tion of the Individual 

 Up to this point the whole discussion has looked at i 

 problem of inbreeding solely from the standpoint of the 

 kinship of mated individuals. Nothing whatever has 

 been said about the germinal make-up of the individuals. 

 This method of treatment was not accidental, or due to 

 any oversight of so important a phase of the problem, but 

 was deliberately planned to bring out clearly that the 

 development of the coefficient of inbreeding was quite 

 independent of any theory of the mechanism of the hered- 

 itary process. These coefficients measure a real and 

 definite attribute of a pedigree. 



