MATHEMATICAL CONSIDERATIONS 85 



each of the descending lines which are also represented 

 in the other line. To give an adequate mathematical esti- 

 mation of the degree of inbreeding, both constants are 

 necessary. There is, generally, some correlation between 

 them, although the Coefficient of Relationship may be 

 zero, and the Coefficient of Inbreeding still be high, as in 

 the illustration just given in which the progeny comes 

 from a pair of individuals from two distinct inbred lines. 

 The application of these methods of determining the 

 amount of inbreeding is illustrated by Pearl from the 

 pedigrees of two Jersey bulls as follows : 



Inbreeding " Z '' and Relationship " (K] ' Coefficients 



of 

 King Melia Rioter 14th and Blossom's Glorene 



(0) (0) 



A, Z,(K 2 ) 25 (0) (0) 



A 2 Z 2 (K 3 ) 25.00 (50.00) 12.50 (0) 



A 3 Z 3 (K 4 ) 37.50 (62.50) 12.50 (0) 



A 4 Z 4 (K 5 ) 50.00 (75.00) 25.00 (0) 



A s Z 5 (K 6 ) 71.88 (87.50) 29.69 (0) 



A Q Z Q (K 7 ) 81.25 (92.19) 35.94 (0) 



A, Z 7 (K 8 ) 90.63 (92.97) 40.23 (0) 



The method of making the calculations is explained 

 clearly and concisely by the originator and we shall not 

 undertake to repeat it here. What we are interested 

 in is the genetic meaning of the figures after they have 

 been obtained. 



The Coefficient of Inbreeding, Z, has to do solely with 

 total relationship, and shows the intensity of inbreeding 

 in the stockman's sense of the word by measuring pre- 

 cisely "the proportionate degree to which the actually 

 existent number of different ancestral individuals fails to 



