SHOETEE AETICLES AND DISCUSSION 



STUDIES ON INBREEDING. VIIL A SINGLE NUMER- 

 ICAL MEASURE OF THE TOTAL AMOUNT OF 

 INBREEDING^ 



1. In the earlier numbers of these Studies, and particularly in 

 VII,2 methods have been given for measuring the amount or de- 

 gree of inbreeding exhibited in a particular pedigree by a series 

 of inbreeding coefficients, Z^, Z^, Z^, . . Zn, one for each an- 

 cestral generation. The inbreeding for the whole pedigree is 

 indicated by an inbreeding curve, formed by plotting and con- 

 necting by a line the several coefficients. 



2. From the earliest stages of this investigation the writer has 

 been aware of the desirability of a single numerical measure, to 

 supplemejit or replace the inbreeding curve as a designation of 

 the total inbreeding exhibited. Such a designation has now been 

 found, which, it is believedj uniquely and rigorously meets the 

 requirements. It is the purpose of the present paper to describe 

 this new constant. 



Consider Fig. 1. This gives, in the heavy line and solid circles, 

 the inbreeding curve for 9 ancestral generations of the Brown 

 Swiss bull, Saxton (2668).3 The values of the inbreeding co- 

 efficients are: 



0, .^, = 12.50, Z,== 26.95, 



0, ^5 = 17.19, = 28.91, 



Z^=^ 6.25, = 21.09, = 29.30. 



The smooth curve of Fig. 1 is the inbreeding curve for con- 

 tinued brother X sister mating. This represents the closest or 

 maximum degree of inbreeding possible in sexually reproducing 



It is clear from inspection of this diagram, that Saxton is 

 much less intensely inbred in fact than he would be if in all his 

 ancestry the matings had been of brother X sister out of brother 



periment Station. No. 118. 



2 Pearl, E., Amer. Nat., 1917, in press. 



3 Cf . Pearl, R., these Studies, I. Amer. Nat., Vol. XLVII., p. 603, 1913. 



636 



