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THE AMERICAN NATURALIST [Vol. XLVII 



1. The production of the individual must be the point 

 of departure in any analytical consideration of inbreed- 

 ing, leading towards its measurement. That is, the ques- 

 tion to which one wants an answer is : What degree of in- 

 breeding was involved in the production of this particular 

 animal ? 



2. It is therefore necessary practically to start with the 

 individual and work backwards into the ancestry in meas- 

 uring inbreeding, rather than to start back in the ancestry 

 and work down towards the individual. 



3. In the genetic passage from the n -f 1th generation 

 to the wth, or in other words the contribution of the 

 matings of the n + 1th 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 



z _ ioo(p» +1 - gwQ 



Pn+1 



where p n+1 denotes the maximum possible number of dif- 

 ferent individuals involved in the matings of the n -f 1 

 generation, p n+1 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 genera- 

 tions in the ancestral series be plotted to the generation 

 numbers 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 number realized, in the former. The coefficient 

 may have any value between and 100. When there is no 

 breeding of relatives whatever (that is, in the entire 

 absence of inbreeding) its value for each generation is 0. 

 As the intensity of the inbreeding increases the value of 

 the coefficient rises. 



4. The above measure of inbreeding has to do primarily 

 with the relationship aspect of the problem. The theo- 

 retical bearings of this fact will be discussed in a later 

 section. 



