HEREDITY 543 



~ 



. 



which shows that i of the desired character will be present 



2" 



in any generation. Hence the stock will always breed true to 

 the per cent of the character established. 



It may be remembered in the above that mediocrity has been 

 assumed in the ancestry back of the n selected generations of 

 offspring ; but if this were not assumed, we have seen that after 

 a few generations we obtain approximately Galton's coefficients. 

 Hence, without assuming mediocrity back of n generations, we 

 may safely say that the offspring will breed true to the amount 

 of the character established by selection. 



The following table presents the amount of a character estab- 

 lished by selection of i, 2, 3, 4, 5, and 6 generations of ancestry. 

 To illustrate how these breed true we may take the simplest 

 case where 0.6 of the character is established by selecting one 

 generation. Suppose, then, that a generation is produced with- 

 out selection. The amount of the character present will be 

 given by 



(0.6) (0.5 122) + 0.2927 = 0.6, 



which illustrates that stability is established. 



