542 



THE AMERICAN NATURALIST [Vol. LIV 



In this paper I wish to give a modification and some extensions 

 to the method worked out hy Pearl with the purpose of bringing 

 all the measurements of inbreeding and relationship on the same 

 scale and using total coefficients based on calculations of areas 

 as. the fundamental method in expressing degrees of kinship 

 numerically. 



I. Definition of the Coefficient of Relationship 



If we plot the values of the coefficient of relationship obtained 

 in accordance with the above indicated method together with 

 the values of the corresponding coefficients of inbreeding for a 

 given pedigree, we shall find that these corresponding values 

 are not directly comparable as they are not worked out in rela- 

 tion to the same scale. To obtain this we need to change slightly 

 the definition and formula of the coefficient of relationship. 



Pearl's definition is the following: The coefficient of relation- 

 ship indicates the number of ancestors common to both pedigrees 

 of the two individuals whose relationship is being measured in 

 proportion to the greatest possible number of common ancestors 

 in this generation. 



The proposed definition is this : The coefficient of relationship 

 indicates the number of ancestors common to both pedigrees of 

 the two individuals whose relationship is being measured in 

 proportion to the total maximum number of different ancestors in 

 the two pedigress taken together in the generation in question. 



The formulae are now the following : 



_ 100(pn fl — qnu) — (sZn.,- S p, + dZn_i • dp n ) . 



(2) (If any two different individuals are concerned) 

 P°+i 



The difference between these formula? and the first mentioned 

 is only that the denominator in the fractions is multiplied by 

 two. The total values, therefore, are exactly one half of Pearl's. 



The maximum value of the coefficient of relationship will in 

 every generation be 50, as no more than 50 per cent, of the indi- 

 viduals in a generation of a pedigree can appear in both halves 

 of the pedigree. 



