124 MAINE AGRICULTURAL EXPERIMENT STATION. I913. 



In order that progress may be made in the analysis of this 

 important problem of inbreeding there is a fundamental need 

 which must first be met. This is the need for an appropriate 

 and valid method of pedigree analysis, which possesses general- 

 ity, and can on that account be depended on to give comparable 

 results when applied to two (or more) different pedigrees. 

 Specifically, there seems not to have been worked out any ade- 

 quate general method of measuring quantitatively the degree of 

 inbreeding zvhich is exhibited in a 'particular pedigree. Without 

 such a measure it is clearly impossible to proceed far in the 

 analysis of inbreeding. 



It is the purpose of the paper of which this is an abstract to 

 present a method for measuring, and expressing numerically in 

 the form of a coefficient, the degree of inbreeding which exists 

 in any particular case, and to show by illustrations the manner 

 in which these coefficients may be computed. It is shown that 

 the method is (a) unique, in the sense that the value obtained 

 in any particular instance can only be affected by the degree or 

 amount of inbreeding which has been practiced in the line of 

 descent under consideration, and (b) general, in the sense that 

 it is equally applicable to all pedigrees and to all degrees and 

 types of inbreeding. 



Preliminary Definitions. 



In attempting any general analysis of the problem of inbreed- 

 ing from the theoretical standpoint one is confronted with the 

 necessity for a definition of inbreeding, which shall be at once 

 precise and general, that is, such as to include all of the most 

 diverse ways in which this sort of breeding may be practised. 



Leaving aside for the moment all consideration of details as 

 to how a particular piece of inbreeding may be brought about is 

 to be found the concept of a narrowing of the network of 

 descent as a result of mating together individuals genetically 

 related to one another in some degree. Let us take this as our 

 basic concept of inbreeding. It means that the number of 

 potentially different germ-to-germ lines, or "blood-lines" con- 

 centrated in a given individual animal is fezver if the individual 

 is inbred than if it is not. In other words, the inbred individual 

 liossesses fezver different ancestors in some particular genera- 

 tion or generations than the maximum possible number for that 



