THE PROBLEM OF INBREEDING 105 



erations than the maximum possible number for 

 that generation or generations. This appears to be 

 the most general form in which the concept of 

 inbreeding may be expressed.^ In whatever way 

 the mating of relatives is accomplished, or what- 

 ever the degree of relationship of the individuals 

 mated together, the case in last analysis comes back 

 to the above statement ; namely, that there are ac- 

 tually in the pedigree of the inbred individual fewer 

 different ancestors in some particular generation or 

 generations than the maximum possible number.^ 

 The idea suggested in the foregoing paragraph 

 may be expressed symbolically as follows. If 

 there is absolutely no collateral relationship 

 between any of the individuals in a pedigree, the 

 number of different individuals in succeeding 

 ancestral generations will be given by the series 



X <--> (1) 2 <->(2) 4 <-^ (3) 8 <r^ (4) 16 <r^ 



(5) 32 <~> (n) 2 % (i) 



where the numbers in parenthesis denote the 

 numbers of the ancestral generations (1 = parents, 



^ This, of course, looks at the matter primarily from the standpoint 

 of kinship. This is all that is intended here. 



2 This generalized concept of inbreeding seems to me to be in 

 essential (though not entirely in verbal) agreement with that of O. F. 

 Cook, whose interesting general discussions of this and related prob- 

 lems are summarized in a recent paper ("The Superiority of Line 

 Breeding over Narrow Breeding," U.S. Dept. Agr., Bur. Plant Ind. 

 Bui. 146, 1909). I use "inbreeding" as a generic term, while Cook 

 regards it as a species of "line breeding." This seems to me to be a 

 purely terminological difference, and not of great consequence. 



