CONDUCTING BREEDING INVESTIGATIONS 



vidual might have in a given generation, and the amount of repetition 

 which has occurred in its ancestry. 



In the above formula for Z, the coefficient of inbreeding, P w +, 

 denotes the maximum possible number of different ancestors which an 

 individual might have in matings of the (n + l)th generation and 

 Q n + i, the actual number of different ancestors which he has. For an 

 application of this coefficient we take the pedigree of Roan Gauntlet as 

 given in Fig. 232. It gives the following series of values for Z: 



7 100 (2 - 2) 



^o = 2 ~ per cent. 



100 (4 - 4) 

 &\ - 7 = per cent. 



100 (8 - 6) 

 At = g = 25 per cent. 



100 (16 - 10) 

 ^3= jg = 37.5 per cent. 



100'(32 - 19) 

 &\ = oo = 40.625 per cent. 



To determine these values we have started with the A i generation in 

 which pi = 2 and of necessity gi = 2 also. The value of Z , therefore, 

 must be in all cases. In the A z generation p 2 = 4 and </ 2 = 4, also, 

 because all these four animals are different and have not previously 

 appeared in the pedigree. The value for Zi, therefore, is 0. In genera- 

 tion A s , p 3 = 8. Champion of England appears twice in this genera- 

 tion, and since he has appeared already in A 2 , the two reappearances 

 in A 3 are crossed out. Counting the remaining individuals in this genera- 

 tion, we find q 3 = 6, and consequently Z 2 = 25 per cent. Now this Z 2 = 

 25 signifies not only that Roan Gauntlet in the third ancestral generation 

 has 25 per cent, less than the maximum possible number of different 

 ancestors, but also that in any generation further removed he must of 

 necessity have at least 25 per cent, less than the maximum possible 

 number of ancestors. In the next following generation, A\, p* = 16. 

 In determining q n +i we strike out Lancaster Comet and Virtue, sire 

 and dam respectively, of Champion of England. It is worth while noting 

 here that these two animals are automatically eliminated in this genera- 

 tion because of the reappearance of an animal in a lower generation in this 

 same line of descent. Reappearances at the apex of a line of descent are 

 called primary reappearances and are marked in this pedigree, whereas 

 reappearances which are determined by the primary reappearance of 

 an individual in a lower generation are called secondary reappearances 

 and they are marked with the sign X . It is only necessary to determine 

 primary reappearances in calculating the coefficient of inbreeding, for 

 secondary reappearances may be accounted for by simply doubling the 

 total number of reappearances in the next lower generation. Continuing 



