Analytically considered a selection index is an expres- 

 sion of the general form 



h = Hx,y,p,q, ■ ■ ,iv) (1) 

 where l x denotes the selection index and x, y, p, q, etc., 

 are the variables upon which it desired to carry out 

 selection. The practical question which has to be solved 



shall be the form of the function <£. The formula for an 

 index should fulfill the following requirements: 



1. It should be simple and easily calculated. 



2. The value of the index should increase as the desira- 

 bility of the individual as a breeder increases. 



3. The index should be relatively more sensitive to 

 small changes in important characters than to those in 

 unimportant characters ; that is, the variables should be 

 differentially weighted. 



4. The value of the index should decrease as undesir- 

 able characters become relatively marked. 



It has seemed to the writers that to a first approxima- 

 tion the following general form of expression will be 

 found to be well suited for a selection index: 



In this expression x, y, z, • ••, w are variables which be- 

 come more desirable (*. e., from the breeder's standpoint) 

 as their values increase; whereas p, q, r, t are vari- 

 ables which become more desirable as their values de- 

 crease. 2 The quantities a, b, c, n, and a', b', c' n' 

 are constants to be given arbitrary values in the pro- 

 portions that the different variables are to be weighted. 



It will be seen that a selection index number as de- 

 scribed above is in a sense an adjunct or supplement to 

 a score card. The index affords a means of condensing 

 the entire information which the score card gives into 

 one unit which can be then dealt with individually. 



