Wright: Analysis of IJvestock Breeding- Methods 



345 



The Pedigree of Favourite 



As an example of such an irregular 

 case, let us take the pedigree of the 

 bull Favourite (Figure 3). None of the 

 ancestors of the sire and dam (Boling- 

 broke and Phoenix) are shown as in- 

 bred, so that we merely need to count 

 the generations in each path connect- 

 ing sire and dam, add one and use as 

 an exponent of Vz to obtain the contri- 

 bution of each path to the coefficient. 



We find that Foljambe was the sire 

 of both Bolingbroke and Phoenix. The 

 contribution due to this connection is 

 thus {YzY or 12.5 per cent. Foljambe 

 as Bolingbroke's sire is not connected 

 with the dam of Phoenix. This disposes 

 of all possible connections through 

 Foljambe as the sire's sire. The sire's 

 dam. Young; Strawberry, is connected 



twice with Foljambe as the dam's sire 

 through common descent from the 

 Studley Bull (626). The latter is 

 four generations back of Bolingbroke 

 and seven back of Phoenix in each of 

 two lines through her sire. These con- 

 tributions are thus (K')" + (/^)" oi' 

 0.05 per cent, an almost negligible 

 quantity. We have finally to consider 

 the connections between sire's dam 

 (Young Strawberry) and dam's dam 

 (Favourite Cow). First we note that 

 Favourite Cow was herself the dam 

 of Young Strawberry. We have here 

 a contribution of (^)' or 6.25 per 

 cent. The sire of Young Strawberry 

 is connected with Favourite Cow 

 through descent from Smith's Bull. 

 The contribution is (J/^)" or 0.39 per 

 cent. This disposes of all connections. 

 The work may be arranged as follows : 



Inbreeding of Favourite (252) 



Common Ancestor Generation from 



Name Inbreeding Bolingbroke Phoenix Contribution 



Foljambe 1 1 12.50 



Studley BuH 4 7.7 0.05 



Favourite Cow 2 1 6.25 



Smith's Bull 4 3 0.39 



~ Total 19.19 



The total percentage of inbreeding 

 is 19.2. It will be noticed that this 

 would not be appreciably modified by 

 omission of the remote connections 

 through descent from Studley Bull and 

 Smith's Bull. This coefficient means 

 that Favourite departs 19.2 per cent 

 from the genetic heterogeneity of the 

 foundation Shorthorn stock in the di- 

 rection of complete genetic homogenei- 

 ty in other words has 19.2 per cent less 

 heterozygosis. 



Comparison with Other Measurements 

 of Inbreeding 



As the coefficient of inbreeding is 

 derived from theoretical considerations, 

 it will be well to consider for a moment 

 how it is related to the degree of in- 



breeding in the popular sense. This 

 is a somewhat difficult question to an- 

 swer since inbreeding in the popular 

 sense is a rather vague term. Pearl" 

 has defined inbreeding on the basis of 

 the ratio of the number of ancestors in 

 each ancestral generation to the maxi- 

 mum possible number. The smaller 

 the ratio the greater the inbreeding. 

 This is a very different conception 

 from the writer's, which is based on 

 the reduction of genetic heterogeneity 

 present in the foundation stock and is 

 hence in the main a function of the 

 ancestral connections between the par- 

 ents. The contrast in the two concep- 

 tions can be seen very clearly by com- 

 paring the two pedigrees of Figure 4. 

 The upper represents a mating be- 



