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 =90 Kk, =0 
Z,=0 K, =0 
Zz = 25 K; = 50 
Z; = 37.5 Ky = 75 
Zs = 40.6 Ks = 75 
The values for K, the coefficient of relationship, were determined in the 
following fashion. In A; 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, K3; = 24 = 50 per cent. 
In A, the double primary reappearance of Champion of England in A3 
automatically determines a total of four secondary reappearances, 
and to these are added two primary reappearances of Lord Raglan. 
In Ag, therefore, K = 6g = 75 per cent. In A; 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; 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. 
Digitized by Microsoft® 
