106 MODES OF RESEARCH IN GENETICS 



2 = grandparents, 3 = great-grandparents, and so 

 on), and the free figures denote the maximum 

 possible number of different ancestors to the 

 indicated generation. If in any generation in the 

 series relatives are bred together, the same indi- 

 vidual will appear more than once in the ancestral 

 series, and the number of different individual 

 ancestors in the higher terms will be accordingly 

 diminished below the maximum number as given 

 in (i). The series will then become 



x -e-> (1)2 <-► (2)4 -yi**+ (3)8 - y 2 <-+ (ii) 



(4)16 -y,** (5)82 -y«. . ., 



where y\,y 2 ,y%, . . . may, in the nth generation, 

 have any value not greater than 2" — 2, in the 

 case of organisms in which two individuals must 

 cooperate in the process of reproduction. The 

 final limiting case is, of course, self-fertilization, 

 where the number of ancestors reduces to 1 in each 

 generation. 



The Measurement of the Degree of In- 

 breeding 



This brings us to a consideration of a practical 

 and general measure of the degree of inbreeding 

 exhibited in a particular pedigree. This problem 

 has been attacked by a number of investigators, 

 but so far as I have been able to learn all previous 

 measures have been modifications in one form or 



