Castle doubts the utility of such a co-efficient, inas- 

 much as vigor and fecundity have no necessary relation to 

 the amount of in-breeding in the ancestry, and as uniform- 

 ity is not necessarily increased when a heterozygote is used 

 as an ancestor. Moreover, Galton's Law is not now con- 

 sidered a safe guide in biological reasoning (Castle, Genetics 

 and Eugenics). 



Co-efficient of Relationship. — ^It is quite possible, how- 

 ever, for two animals with the same Co-efficient of Inbreed- 

 ing to differ greatly in germinal constitution, for example 

 when a closely inbred animal of one breed is mated to an- 

 other closely inbred animal of another breed. To give 

 some measure of the inter-relation of the lines of descent , 

 Pearl has devised the term Co-efficient of Relationship, which 

 is the per cent of the individuals in each line which are also 

 represented in the other line, and is a measure of the com- 

 munity of ancestry of the dam and the sire (Pearl, In- 

 breeding and Relationship Co-efficients. Am. Nat. 1914). 



King Melio Rioter 14th, the Jersey Bull, has a co- 

 efficient of Inbreeding of 90% at the seventh ancestral gen- 

 eration, but a co-efficient of Relationship of 40%; while 

 Blossom's Glorena had co-efficients of 93% and 0% re- 

 spectively. 



"These two co-efficients taken together, give us the 

 first quantitative measure of inbreeding as a system of mat- 

 ing, but obviously they do not tell anything concerning the 

 actual germinal constitution of any individual resulting 

 from a given system of inbreeding. The germinal composi- 

 tion of any individual can be determined only by actually 

 testing its breeding qualities, its transmissive powers. But 

 an indication of the germinal constitution of an individual 

 produced by any long-continued system of inbreeding, as 

 far as the degree of heterozygosity or homozygosity is con- 

 cerned, can be obtained by the laws of probability to Men- 

 delian formulae" (East and Jones). 



We have already seen (page 96) that the probable char- 

 acter of the segregating generation when inbred, when n 

 character pairs are concerned, may be expressed by the ex- 

 pansion of the binomial (3:1)". For any generation it 

 may be expressed by the expansion of the binomial 

 [(2r — 1)" + 1], where the exponent of the first term gives 

 homozygous characters and that of the second term the 

 number of heterozygous characters. 



151 



