No. 511] SELECTION INDEi 



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if the breeder is deeply interested in improving the corn 

 with respect to earliness what actually will happen will 

 be this : lie will decide to take this plant on account of its 

 earliness and in spite of the defects of the ear. In selec- 

 tion work every degree of compromise of this kind is 

 made and the larger the number of characters one at- 

 tempts to deal with at the same time the more compro- 

 mises are made. Where shall the line be drawn beyond 

 which further compromise shall not he permissible! 



II. The Theory of Selection Index Numbers 

 It would seem to be highly desirable to devise, if pos- 

 sible, some method for the use of the breeder who is 

 practising selection which would get over in a greater or 

 less degree the difficulty which has been outlined in the 

 preceding section. What is needed is some method 

 whereby a selection of several characters may be made at 

 the same time in an absolutely impersonal and impartial 

 manner without throwing out absolutely those individ- 

 uals which are especially good with respect to a single 

 one of the group of characters undergoing selection and 

 mediocre or poor with respect to the other characters of 

 the group. It has occurred to us that a way of reaching 

 this desired end is found in the use of what we have 

 called "selection index numbers," borrowing the termi- 

 nology and something of the idea from the literature of 

 political economy. 



An "index number" in the sense here used means a 

 single mathematical function which combines in itself the 

 values of several independent or correlated variables. 

 In such a function each of the variables may he weighted 

 in any desired manner to meet the needs of the particular 

 problem. Having decided the relative degree to which 

 each variable shall be weighted, the index number as 

 finallv calculated gives an absolutely impartial and im- 

 personal summing up of the total combined value or effect 

 of the variables entering into it. 



The theorv of a breeding index number may be illus- 



