No. 645] COEFFICIENTS OF INBREEDING 333 



runs from to 1, while the percentage of horoozygosis 

 is running from 50 per cent, to 100 per cent. The for- 

 mula 2h—l, where h is the proportion of complete homo- 

 zygosis, gives the required value. This can also he 

 written l—2p where p is the proportion of heterozygo- 

 sis. In the above-mentioned paper it was shown that 

 the coefficient of correlation between uniting egg and 

 sperm is expressed by this same formula, f = l—2p. 

 "We can thus obtain the coefficient of inbreeding /& for a 

 given individual B, by the use of the methods there out- 

 lined. 



The symbol nc, for the coefficient of the correlation 

 between B and C, may be used as a coefficient of relation- 

 ship. It has the value in the case of two random indi- 

 viduals, .50 for brothers in a random stock and ap- 

 proaches 1.00 for individuals belonging to a closely in- 

 bred subline of the general population. 



In the general case in which dominants and recessives 

 are not equally numerous, tlie composition of the random- 

 bred stock is of the fonn A A, 2xy Aa, aa. The per- 

 centage of homozygosis is here greater than 50 per cent. 

 The rate of increase, however, under a given system of 

 mating, is always exactly proportional to that in the 

 case of equality. The coefficient is thus of general ap- 

 plication. 



If an individual is inbred, his sire and dam are con- 

 nected in the pedigree by lines of descent from a com- 

 mon ancestor or ancestors. The coefficient of inbreeding 

 is obtained by a summation of coefficients for every line 

 by which the parents are connected, each line tracing 

 back from the sire to a common ancestor and thence for- 

 ward to the dam, and passing through no individual 

 more than once. The same ancestor may of course be 

 involved in more than one line. 



The path coefficient, for the path, sire {S) to offspring 

 (0), is given by the formula po.» = J\ ( 1 -f / ) ( 1 .A K 

 where /« and fo are the coefficients of iiibroediiig for sire 



