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THE AMERICAN NATURALIST [Vol. LI 



The degree or amount of relationship, in accordance 

 with the above definition, is numerically measured by 

 relatioiiship coefficients, one for each ancestral genera- 

 tion. The coefficients are calculated in two slightly differ- 

 ent ways according to whether they are being evaluated 

 in connection with inbreeding coefficients, which will 

 usually be the case, or independently. 



A. When calculated in connection with inbreeding 

 coefficients, a relationship coefficient is calculated, by 

 methods presently to be shown by example, in accordance 

 with the followiug equation: 



100 ipn,, ' ^ ^ 



where the letters have the same significance as in (i) 

 with the additions that K denotes a relationship coeffi- 

 cient, a prefixed subscript s means that letters following 

 it refer to the pedigree of the sire only, and a prefixed 

 subscript d means that the letters following refer to the 

 pedigree of the dam only. 



B. When calculated independently of inbreeding coeffi- 

 cients, as, for example, to measure the relationship be- 

 tween two male animals, the relationship coefficient 

 becomes 



Kn _ ^r,,., 



100" , ' 



where — r„,i denotes the iiunibei- of ancestors in the 

 n + 1-th generation (each individual and its ancestry being 

 counted once only) which occur, in the n -f 1-th or some 

 earlier ancestral generation, in the pedigrees of both ani- 

 mals, or in other words which are common ancestors ; 

 pn^i denotes the total number of ancestors in the same 

 generation of both pedigrees taken together. 



III. Inbreeding, defined in I, may exist in respect of 

 any individual, as a result of any one or a combination of 

 the following circumstances: (a) the sire of the individual 

 has fewer than the maximum possible number of different 

 ancestors, and no ancestors in common with the dam ; 



(iii) 



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