CHAPTER V 



MATHEMATICAL CONSIDEEATIONS OF 



INBREEDING 



The term inbreeding can be used in a relative sense 

 only, except when dealing with hermaphroditic organ- 

 isms. To say that one individual of a bisexual species is 

 inbred and another not is as indefinite as saying one is 

 short, the other tall. Strictly speaking, inbreeding refers 

 only to the way in which individuals are mated together. 

 This fact is well expressed by Pearl,^^^ who says: '' It is 

 clear that underlying all definitions of inbreeding is to be 

 found the concept of a narrowing of the network of 

 descent as a result of mating together at some point in 

 the network of individuals genetically related to one an- 

 other in some degree. Let us take this as our basic 

 concept of inbreeding. It means that the number of po- 

 tentially different germ-to-germ lines or *^ blood-lines" 

 concentrated in a given individual is fewer if the individ- 

 ual is inbred than if he is not. In other words, the inbred 

 individual possesses fewer different ancestors in some 

 particular generation or generations than the maximum 

 possible number for that generation or generations.^* 

 Thus, according to the evolutionist's conception of the 

 origin of species by natural selection, not only are all 

 members of a species related in some degree, however 

 remote, but all members of all species from any one 

 original life-sparh presumably are members of one inbred 

 liyie. This wholly ridiculous conclusion follows, because 

 the lines of descent terminating in any one individual, 

 though they radiate back in widening angles for a time, 



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