No. 562] 



THE PROBLEM OF INBREEDING 



589 



Illustration II. Parent X Offspring Breeding 

 The next illustration of the application of coefficients 

 of inbreeding will be the general case of back-crossing, 

 that is, the mating of parent X offspring. Such a case is 

 illustrated in the hypothetical pedigree Table IV. . 



Pedigree Table IV. (Hypothetical) 

 To Illustrate the Breeding of Parent X Offspring 



Here it will be seen that b, the dam of y, is a daughter 

 of a, who is also the sire of y and that in each preceding 

 generation every daughter is bred back to her sire. Pro- 

 ceeding as before to calculate the coefficients of inbreed- 

 ing we have, first, 



In forming the expression for Z x we are met by the fact 

 in determining q n+1 for generation 2 that the individual a 

 has already appeared once and been counted asa" differ- 

 ent" ancestor in generation 1. Therefore it will not be 

 counted a second time in generation 2, and we have 



7 KXK* ~ 3) _ 9 . 

 Zi - | 



and by the same process, 



Z 2 = 100(8 8 - 4) = 50, 



Zs = 1 o<^ r « = 6873 



