further data on the measurj,ment of inbreeding. 233 



Inbreeding and Relationship Coefficients. 



The pedigree of an individual consists of two halves. One 

 of these halves is made up of the sire and his ancestors ; the 

 other of the dam and her ancestors. Following the conception 

 of inbreeding set forth in detail in the earlier papers of this 

 series it is plain that the values of the coefficients of inbreeding 

 for a particular pedigree are composed of the following ele- 

 ments. 



1. The occurrence of the same individual animals more than 

 once on the sire's side of the pedigree only. 



2. The occurrence of the same individual animals more than 

 once on the dam's side of the pedigree only. 



3. The reappearance of animals which appear first on one 

 side of the pedigree (either the sire's or the dam's) on the other 

 side. 



If only I and 2 are to be found in the pedigree it means that 

 the sire and the dam are totally unrelated (within the limits 

 covered by the pedigree in the particular case). On the other 

 hand, the occurrence of 3 means that sire and dam are in some 

 degree related, and that a portion of the observed inbreeding 

 arises because of that fact. Now the coefficients of inbreeding, 

 in and of themselves, tell nothing about what proportionate 

 part has been played by these three elements in reaching the 

 final result. It is a matter of great importance to have informa- 

 tion on this point because of its genetic significance. It is the 

 purpose of the present discussion to describe a general method 

 for obtaining this desired information. 



The first step in the method, stated briefly, is to break up the 

 pedigree elimination table formed to get the successive values 

 of p — q..j^-- i^ our former notation, into four different 

 parts. One of these parts will include the primary reappear- 

 ance on the sire's side of the pedigree of such animals as appear 

 first on the same side This may be called the ''male only" table. 

 The second part will include the primary reappearance on the 

 dam's side of such animals as first appear on the same side. 

 This is the "female only" table. The third part will include the 

 primary reappearance on the dam's side of such animals as 

 first appear on the sire's side. The fourth part is the reverse 



