82 INBEEEDINa AND OUTBREEDING 



ancestors compared with the possible nimiber. It is 

 derived from the formula: 



lOO/p -q \ 

 \ n + 1 n + 1/ 



Z ^ 



n p 



« + l 



where pn^^ denotes the maximum possible number of 

 different individuals involved in the matings of the n + 1 

 generation, and gn+i the actual number of different indi- 

 viduals involved in these matings. As an illustration, any 

 individual in bisexual matings has two parents in the first 

 ancestral generation, four grandparents in the second 

 ancestral generation, and so on, according to the following 

 symbolical representation 



X -^-> (1) 2<-> (2) 4-^— > (3) 8<— >(4) 16-<— > (5) 32<-^ (»)2'» . . ., 



in which the enclosed numbers represent the ancestral 

 generations (1 = parents, 2 = grandparents, 3 = great- 

 grandparents, etc.), and the other figures the number of 

 ancestors. In the second or earlier generations the an- 

 cestors may not all be different individuals, so that in any 

 generation previous to the parental the actual number of 

 ancestors may be less than the possible number. For ex- 

 ample, in brother and sister mating, any individual in- 

 stead of having four different grandparents, has only two. 

 Expressed symbolically, as above, the representation for 

 this type of mating would be 



X <-^ (1)2 -^-> (2)4-2/1 -^-> (3)8-7/2 <-> (4) 16-1/3 <-> (5)32-2/4. . . , 



where 2/1 = 2, 1/0 = 6, y.^ = 14, 2/4 = 30. 



In this case y has the value of 2" - 2, and this is the highest 



value it can have in any system of mating where two indi- 



