126 MAINE AGRICULTURAI, EXPERIMENT STATION. I913. 



and by specifying the location in the series of the generation 

 under discussion. 



This statement is ampHfied and made more precise in the 

 following propositions. 



1. The production of the individual must be the point of 

 departure in any analytical consideration of inbreeding, leading 

 towards its measurement. That is, the question to which one 

 wants an answer is : What degree of inbreeding was involved 

 in the production of this particular animal? 



2. It is therefore necessary practically to start with the indi- 

 vidual and work backwards into the ancestry in measuring in- 

 breeding, rather than to start back in the ancestry and work 

 down towards the individual. 



3. In the genetic passage from the n-j-i'th generation to the 

 w'th, or in other words the contribution of the matings of the 

 w-j-i'th generation to the total amount of inbreeding involved 

 in the production of an individual, the degree of inbreeding 

 involved will be measured by the expression 



100 (p , — a , ,) 



where Vn+i denotes the maximum possible number of different 

 individuals involved in the matings of the n-\-i generation, 

 q , , the actual number of different individuals involved in 

 these matings. Zn may be called a coefficient of inbreeding. If 

 the value of Z for successive generations in the ancestral series 

 be plotted to the generation number as a base, the points so 

 obtained will form a curve which may be designated as the 

 curve of inbreeding. 



It will be noted that the coefficient of inbreeding Z is the 

 percentage of the difference between the maximum possible 

 number of ancestors in a given generation and the actual num- 

 ber realized in the former. The coefficient may have any value 

 between o and 100. When there is no breeding of relatives 

 whatever (that is, in the entire absence of inbreeding) its 

 value for each generation is o. As the intensity of the inbreed- 

 ing increases the value of the coefficient rises. 



4. The above measure of inbreeding has to do solely with 

 the relationship aspect of the problem. It has nothing whatever 



