CONDUCTING BREEDING INVESTIGATIONS 601 



and dam are totally unrelated lags only one generation behind the value 

 for continued brother-sister matings. Pearl, therefore, proposes to de- 

 termine not only the coefficient of inbreeding, but also a coefficient of 

 relationship which shall express mathematically the degree of kinship 

 existing between an individual's parents. We again take the pedigree of 

 Roan Gauntlet as an illustration of the method of calculation employed. 

 We obtain the following series of values: 



Z = K, = o 



Z l = K t = 



Z t = 25 K t = 50 



Z 3 =37.5 K 4 =75 



Z 4 = 40.6 K t = 75 



The values for K, the coefficient of relationship, were determined in the 

 following fashion. In A 3 on the sire's side, Champion of England which 

 has already appeared on the dam's side reappears twice. The maximum 

 possible number of animals different from those on the dam's side in this 

 generation is four. Since two of these are identical with an individual 

 which has already appeared on the dam's side, K 3 = % = 50 per cent. 

 In At the double primary reappearance of Champion of England in A 

 automatically determines a total of four secondary reappearances, 

 and to these are added two primary reappearances of Lord Raglan. 

 In A^, therefore, K = % = 75 per cent. In A 5 there are no additional 

 primary reappearances involving both sides of the pedigree, consequently 

 the value of K remains at 75 per cent. It seems wise for breeders to use 

 these coefficients in order to gain precision in the use of terms, if for no 

 other purpose. 



Of course the use of inbreeding coefficients does not alter the prob- 

 lem of inbreeding from a biological standpoint. That problem is 

 concerned with the effect of mating closely related animals. It has 

 already been pointed out that the coefficient of inbreeding may be high 

 when there is no relationship between sire and dam as, for example, when 

 a closely inbred Jersey cow is bred to a closely inbred Holstein-Friesian 

 bull. Such matings are of course not a part of the problem of inbreeding 

 as it is understood in practice. For a precise expression of this problem 

 we must look to the coefficient of relationship. A coefficient of relation- 

 ship of 50 per cent, for A 3 would probably be a fair mathematical require- 

 ment for inbreeding as conceived in practice. A coefficient of relation- 

 ship of this magnitude includes double cousin matings as well as those 

 of brothers with sisters and parents with offspring, but this appears to be 

 a fair inclusion, if reference be made to the curves of inbreeding given 

 in Fig. 233. For further details of the applications of these coefficients 

 reference must be made directly to Pearl's work. 



