No. 609] 



STUDIES ON INBREEDING 



547 



the dam of the individual has fewer than the maximum 

 possible number of different ancestors, and no ancestors 

 in common with the sire; or, (c) the sire and dam have a 

 certain number of common ancestors, and hence are, in 

 the common sense of the word, related to each other in 

 some degree. 



IV. We may separate conceptually that portion of the 

 total inbreeding due to a or b or any combination of a and 

 b, from that portion of the total inbreeding due to c, and 

 define as due to relationship between the sire and dam 

 that amount or degree of inbreeding (in the sense of I) 

 which remains after the amount due to a or b (of III) 

 or any combination of a and b has been subtracted from 

 the total inbreeding. 



A numerical expression of the portion of the inbreeding 

 in the nth. generation due to relationship is obtained by a 

 partial inbreeding index of the following form: 



i.Z„ = ^^. (iv) 



Expressed in words this means that we take as an index 

 of the part of the inbreeding due to relationship the per- 

 centage which one half of the relationship coefficient is of 

 the inbreeding coefficient, both referred of course to the 

 same ancestral generation. 



2. The above paragraphs define a relationship coeffi- 

 cient much more rigorously and generally than was done 

 in my earlier paper on the subject,' or in "Modes of Re- 

 search in Genetics.'" Not only is this a gain in itself, 

 but also it makes possible a great simplification in the 

 actual work of calculating coefficients of relationship 

 from pedigrees. Extensive experience has shown that 

 the method of making these determinations given in my 

 earlier paper left much to be desired in the direction of 

 simplicity, ease of application, and even of accuracy in 

 case the pedigree dealt with was at all coinpli.'ntod in 



2 Pearl, R., Amer. Nat., Vol. XLVTIT, pp. 5LV.')2a, IDK. 



3 Pearl, R., "Modes of Research in Genetics," Now York, 1915 (Mac- 

 millan & Co.). Cf. pp. 101-156. 



