STUDIES ON OAT BREEDING. 2/ 



In order to take account of the second factor, viz. the size 

 of the deviation of the selected plant, the following points may 

 be considered. If there is an efifect of the selection the rows 

 from the plus selections will tend to deviate in the plus direction, 

 and vice versa. Owing to the regression the deviation of the 

 daughter rows will not usually be so great as that of the 

 mother plant. The amount of this regression and likewise the 

 amount and direction of the deviation of each row in relation 

 to its mother plant may be expressed as an index. If we let 

 Dm be the deviation of the mother plant from its mean and Dd 

 the deviation of the corresponding daughter row from its mean, 

 then an index, /, may be calculated in which 



Dm — Dd 



I = 



Dm 



If in this index the daughter row lies at the mean of the 

 pure line, then Dd is zero and / =^ i.o. In this case there 

 is no effect of the selection. If the deviation of the daughter 

 row Dd is in the same direction as the deviation of the mother 

 plant, then / < i.o and there is apparently an effect of the 

 selection. If, on the other hand, the daughter row deviates 

 in the opposite direction to that of its mother plant, then / 

 > I.e. 



This "Index of Selection'"^ in reality expresses the amount 

 of regression of the offspring on the parent in the individual 

 case." It also brings together considerable other information 

 into a single constant. Thus if the index is less than i we 

 know at once that the row in question deviated in the direction 

 of the selection. It likewise tells us the amount of deviation 

 relative to the selection. If the index is 0.5 the row deviated 

 half as far as the selected plant. If the index is 1.33 we know 

 that the row deviated in the opposite direction to that of the 



^''To be distinguished from a "Selection Index." Cf. Pearl R. and 

 Surface, F. 'M. — Selection Index Numbers and Their Use in Breeding. 

 Amer. Nat., Vol. XLIII, pp. 385-400, 1909. Also Pearl, R. — Further Notes 

 Regarding Selection Index Numbers, Amer. Nat., Vol. XLVI, pp. 302- 

 307, 1912. 



"It should be remem.bered, however, that these indices are not the same 

 as Pearson's coefficients of regression calculated from the correlation 

 coefficient and the standard deviations. 



