378 
Journal of Agricultural Research 
Vol. XXXI, No. 4 
Similarly, from the viewpoint of decrease in heterozygosis, the 
coefficient ineasures merely the change from the situation in the 
foundation stock toward perfect homozygosis, whether the founda¬ 
tion stock showed 50 per cent heterozygosis or 1 per cent or the 
infinitesimal amount which would doubtless be found with complete 
knowledge of the genetic constitution. In analyzing breed history, 
it is as legitimate to trace all pedigrees back to some arbitrary date 
as to trace them to the beginning of the herdbook. It is merely 
necessary to exercise due care in interpreting the results as relative 
to whatever foundation stock is used. 
Closely related to the coefficient of inbreeding is the coefficient of 
relationship, which gives the degree of correlation to be expected 
between two individuals (X and Y) in characteristics which are 
entirely genetic and without dominance, conditions under which 
the correlation between parent and offspring or between brothers in a 
random-bred stock is +0.50. The interpretation, of course, depends 
on the choice of foundation stock. 
V(1 + F X ) (1 + F y ) 
In this formula F ? and F y are the coefficients of inbreeding of the 
two individuals, F a is that of the closest common ancestor connecting 
a pair of ancestral lines in their pedigrees, and n and n 1 are the number 
of generations from X and Y to this common ancestor along the lines 
in question. 
APPLICATION TO BREED HISTORY 
These coefficients have been applied, in a. recent paper, 3 to the 
analysis of Thomas Bates’ methods of breeding in developing his famous 
Duchess family of Shorthorns. The coefficient of inbreeding of each of 
the 64 Duchesses, and of their sires and dams, was calculated from the 
pedigrees carried back to the foundation stock of the breed as com¬ 
pletely as the pedigrees are recorded in the herdbook. The degrees 
of relationship of Si of the Duchesses, and of their sires and dams, 
to the bull Favourite (252), the most important foundation animal of 
the breed, were also found from the complete pedigrees. 
' The Duchesses, however, came fairly early in Shorthorn history. 
The longest straight female line in the pedigrees was only 13 genera¬ 
tions. Even here it was a rather tedious process to work out the 
coefficients for the later animals. It is obvious that the amount 
of work would become practically prohibitive in dealing with the 
breeds as they are to-day. The complete pedigree of a modem 
Shorthorn would require the tabulation of several million names. 
Fortunately, there is a very simple approximate method, the results 
of which can be brought as close as desired to the complete method. 
This approximate method, which it is the purpose of the present 
paper to describe, rests on the tabulation of random samples of the 
pedigrees of sire and dam. The reliability of the results can be 
tested by the ordinary theory of sampling. 
8 Weight, S.- mendelian analysis of the pure breeds of livestock, n. the duchess family of 
shorthorns AS bred by thomas bates. Jour. Heredity 14: 405-422, illus. 1923. 
