Wright : Analysis of T.ivestock Breedino- Methods 



347 



has anything" to do with the uniformity, 

 vigor, prepotency or other character- 

 istics. 



Even if the measurement of inbreed- 

 ing is based on the ancestral connec- 

 tions Ijetween sire and dam. there re- 

 main many possible formulae which 

 could be suggested. 



Perhaps the first thought would ])e 

 to base the coefficient on the percentage 

 of common blood in sire and dam. A 

 little consideration will show, however, 

 the unreliability of such a measure. 

 Full brother and sister have 100 per 

 cent common blood, but we know that 

 much greater effects can be produced 

 by continued brother-sister mating 

 than appear in the first generation. 

 Indeed, there might be 100 per cent 

 common blood with no common ances- 

 tors of sire and dam for an indefinite 

 number of generations. Let us sup- 

 pose that the sire and dam trace to the 

 same 1,024 individuals ten generations 

 back, but have no common ancestors in 

 later generations. Common sense and 

 experiment tell us that their progeny 

 could hardly be considered to be inbred 

 at all. The coefficient of inbreeding" 

 of their progeny comes out onlv 

 1024 X (_^)-'^ = (i^)" = 0.05 per 

 cent in spite of the 100 per cent com- 

 mon blood. 



Pearl" has attempted to separate 

 from the amount of inbreeding as 

 found by his formula a portion due 

 only to relationship between the parents, 

 tlfls relationship being based on the 



number of animals common to the 

 pedigrees of sire and dam in propor- 

 tion to the greatest possible number of 

 common ancestors. This comes closer 

 to the writer's conception of inbreed- 

 ing but in practice gives very different 

 results from that given by the coeffi- 

 cient F. For example, continued mat- 

 ing of single first cousins gives results 

 rapidly approaching 100 per cent ac- 

 cording to this or any other of Pearl's 

 coefffcients, while the percentage of 

 heterozygosis is decreased only by 

 about 25 per cent in ten generations 

 (F — 25.2%). As far as the writer 

 knows there is no purely experimental 

 evidence to determine whether such a 

 system as continued mating of single 

 first cousins really approaches the ef- 

 fect of brothei--sister mating in a few 

 generations or whether it has the rela- 

 tively slight effects indicated by the 

 value of F. The writer, however, has 

 sufificient confidence in the generality 

 of Mendelian inheritance to believe 

 that it is an advantage to use a coefifi- 

 cient which measures directly the con- 

 sequences logically to be expected from 

 it as well as measuring accurately the 

 results of experiments in inbreeding 

 and crossbreeding as far as these have 

 been carried. 



Measurement of Relationship 



The measurement of relationship* is 

 naturally closely related to measure- 

 ment of inbreeding. In order to meas- 



*Following is the formula where n and n are the generations from the individuals 

 A' and F to a given common ancestor A, and F^, Fj, and Fy are the coefficients of inbreed- 

 ing of A, X and Y respectively : 



/?x^ = 





In the important case of sire and dam of the individual A' we have : 



/?sz> = 



m+w*^ 



Thus if the sire and dam are related but not themselves inbred, the coefficient of rela- 

 tionship is just twice the coefficient of inbreeding of their progeny. 



