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THE AMERICAN NATURALIST [Vol. XLVHI 



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 1 and 2 are to be found in the pedigree it menus 

 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 arc in some degree related, and that a portion of the 

 observed inbreeding arises because of that fact. Now 

 tlic (•(»(■ t'ficients 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 information on this 

 point, because of its genetic significance. It is the pur- 

 pose of this paper to describe a general method for ob- 

 taining this desired information. 



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

 up the pedigree elimination table formed to get the suc- 

 cessive values of p n+1 — q n+u in our former notation, into 

 four different parts. One of these parts will include the 

 primary reappearance 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 of the third. These last two may be called the 

 "cross tables." The sums of the totals of these partial 

 tables will give the total p» +1 - r/„ +1 values for the succes- 



The formation of the tables on this plan may be illus- 

 trated with some examples. These examples will also 

 show the skeleton method of writing pedigree elimination 

 tables, which saves much labor. This was referred to, 

 but not significantly illustrated, in the earlier papers. It 

 consists simply in doubling the total of the column for 

 each generation rather than the separate items. 



