82 INBEEEDING AND OUTBREEDING 



ancestors compared with, the possible mnnber. It is 

 derived from the formula: 



lOO/p -q ) 

 V n + l n+1/ 



n p 



n + l 



where p»+i denotes the maximum possible number of 

 different individuals involved in the matings of the n + l 

 generation, and g'n+i the actual number of different indi- 

 viduals involved in these matiugs. As an illustration, any- 

 individual in bisexual matings has two parents in the first 

 ajacestral generation, four grandparents in the second 

 ancestral generation, and so on, according to the following 

 symbolical representation 



x-^-^d) 2-«— ?- (2) 4-t-> (3) 8^— ^(4) 16<— > (5) 32-«— > (re)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, ia 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 



*-^-^ (1)2 -«-^ (2)4-2/1 <-^ (3)8-2/2 -t-* (4)16-2/3<-^ (5)32-2/4. . ., 



where «/i = 2, y.^ 6, y^ = 14, /y^ = 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- 



