No. 609] 



STUDIES ON INBREEDING 



559 



^^1 = 0. In tlie second ancestral generation, on the con- 

 trary, it appears that two ancestors, b and c, in the pedi- 

 gree of X are the same individuals as appeared in the first 

 ancestral generation of a. Therefore it now appears that 

 a and x are related to the extent of 50 per cent, by the 

 existence of community of ancestry in the second an- 

 cestral generation. It would seem only logical to attach 

 the numerical measure of relationship to the generation 

 in which it is first proved to exist. A^ain, this is precisely 

 the point of view regarding the matter which has been 

 taken by the canon law and Roman civil law. 



These two points, which seem so obvious to the writer 

 as to be difl&cult to discuss, are taken up here because 

 correspondence has shown that they have been a source 

 of difficulty with some who have undertaken the study of 

 inbreeding in domestic animals by the methods set forth 

 in these studies. It is hoped that the simpler and more 

 precise definitions of both inbreeding and relationship 

 constants given in this paper may help to clear up such 

 difficulties, which must arise, it would seem, from a lack 

 of a thorough grasp of the characteristics of pedigrees. 



Summary 



In this paper the basic concepts of inbreeding are re- 

 defined in a simple and rigorous manner, and on the basis 

 of these definitions a new and more accurate method of 

 measuring and expressing numerically the degree of kin- 

 ship between any two individuals whatsoever, whose pedi- 

 grees are known, is set forth and illustrated by examples. 



A new constant, the partial inbreeding index, is de- 

 scribed. Its purpose is -to indicate numerically the part 

 of the total inbreeding exhibited in the pedigree of any 

 individual which is due to relationship between the sire 

 and the dam of that individual. 



