AN APPROXIMATE METHOD OF CALCULATING COEFFI¬ 
CIENTS OF INBREEDING AND RELATIONSHIP FROM 
LIVESTOCK PEDIGREES 1 
By Sewall Weight, Animal Husbandman in Genetics , and Hugh C. McPhee, 
Associate Animal Husbandman in Genetics , Bureau of Animal Industry , United 
States Department of Agriculture 
INTRODUCTION 
In previous papers 2 one of the writers has described coefficients of 
inbreeding ana relationship designed to make possible the inter¬ 
pretation of livestock breed histories in terms of the Mendelian 
theory of inbreeding and crossbreeding. The formula for the 
coefficient of inbreeding may be repeated here for convenience: 
In this formula, F x is the required coefficient, and F a is the similar 
coefficient for Any common ancestor that makes the closest connect¬ 
ing link between a line of ancestry tracing back from the sire and one 
tracing back from the dam. The generations from sire and dam to 
such a common ancestor are designated n and n 1 , respectively. The 
contribution of a particular tie between the pedigrees of sire and 
dam is (%) n+nl+1 (l + F a ). There is a factor £ for every generation in 
the tie between the germ cells which unite to form the individual, 
reckoning the germ cells as each half a generation from sire and dam. 
The factor (1 + FJ measures the effect of prepotency of a common 
ancestor that is himself inbred. The total coefficient is simply the 
sum of all such contributions. It is to be noted that the same animal 
may form the tie between many different pairs of ancestral lines of 
the sire and dam. 
This coefficient was shown theoretically to give the coefficient of 
correlation between the egg and sperm which unite to produce the 
individual in question. As far as Mendelian factors are involved, 
its use implies the definition of inbreeding as the bringing together 
of similar germ cells. It was also shown that this coefficient measures 
the percentage reduction from the average degree of heterozygosis 
in the foundation stock. As experiments with different kinds of 
animals and plants have indicated that the effects of inbreeding, 
such as decline in vigor, fixation of type, prepotency in crosses, vary 
directly with the increase in homozygosis, the coefficient appears to 
be the proper one to use from the physiological standpoint. 
It may be well to call attention to the point that the coefficient is not 
an absolute, but a relative, measure of a quality of an animal. It 
measures the probable similarity of the germ cells which united to 
{ >roduce him, relative to the similarity of random germ cells from the 
oundation stock. Random-bred descendants of the foundation 
stock would have a coefficient of zero, even though the. foundation 
stock itself might be highly inbred relative to more remote ancestors. 
i Received for publication Oct. 7, 1924; issued September, 1925. 
* Wright, S. coefficients of inbreeding and relationship. Amer. Nat. 56: 330-338. 1922. 
-. MENDELIAN ANALYSIS OF THE PURE BREEDS OF LIVESTOCK. I. THE MEASUREMENT OF INBREED 
ING AND RELATIONSHIP. Jour. Heredity 14:339-348, illuS. 1923. 
Journal of Agricultural Research, 
Washington, D. C. 
( 377 ) 
Vol. XXXI, No. 4 
Aug. 15,1925 
Key No. A-95 
