THE PROBLEM OF INBREEDING 111 



to accept it as such, and hold fast to it, because 

 it will help him over some apparent paradoxes 

 later. 



The method of calculating coefficients of in- 

 breeding, and their real significance, will be made 

 much clearer by the consideration of illustrative 

 examples of their application. To these we may 

 therefore turn. 



THE CALCULATION OF COEFFICIENTS OF IN- 

 BREEDING 



We may first consider some simple hypothetical 

 pedigrees, before attacking the more complicated 

 ones actually realized in stock-breeding. 



ILLUSTRATION I. CONTINUED BROTHER X SISTER 

 BREEDING 



Let us begin with the most extreme type of 

 inbreeding possible ; namely, the mating of brother 

 with sister for a series of generations. Pedigree 

 Table III gives the pedigree of an individual so 

 bred. 



Let us now proceed to the calculation of the 

 coefficients of inbreeding, Z , Zi, Z 2 , and Z 3 . 

 For Z we have 



2, 



