FIELD CROPS, 39 



"The characters studied are subject to rather wide fluctuations, due to en- 

 vironment. For this reason it is not possible to compare the absolute values 

 of these characters from year to year. Instead the deviations of the plants 

 and rows from the mean of their pure line in the given year have been used. 

 As a first approach to the problem in hand we have determined the number of 

 rows, grown from plus selections, which deviated in the plus direction and like- 

 wise the number deviating in the minus direction. The same thing has 

 been done for rows grown from minus selected plants. Thus for each selection 

 there are four classes of rows. Also the sum of the deviations of the rows in 

 each class has been determined and likewise the average deviation in each class. 



" From these data for the yield of grain it is pointed out that usually in the 

 next year following a given selection there is an excess deviation in the direc- 

 tion of the selection. This apparent effect of a given selection is very much 

 less noticeable or not at all in the later years. It is probable that the effect 

 in the first year is due to physiological rather than genetic causes. Considering 

 the effect of two and of three successive selections in the plus direction it is 

 seen that there is an excess deviation in the direction opposite to the selection. 

 However, with two and three selections in the minus direction there is an excess 

 in the direction of the selection. These results balance each other so that it 

 appears safe to conclude that neither were due to the effect of the selection, 



" The methods of analysis described above leave out of account two factors, 

 viz, the difference in the variability of the different pure lines, and, second, the 

 size of the deviation of the selected plant. The first of these factors can be 

 partially taken into account by expressing each deviation as a percentage of its 

 mean. *The second factor can be accounted for by expressing the deviation of 

 each plant as an index : 



Dm—Dd 

 ^~ Dm 



where Dm is the deviation of the mother plant from its meaji and Dd is the 

 deviation of the daughter row from its mean. If there is no effect of the selec- 

 tion, as Johannsen claims, then this index should on the average equal 1. If 

 regression takes place within these pure lines, as claimed by the Galton- 

 Pearson theory of ancestral heredity, the index would on the average approach 

 0.33. In general if the index is significantly less than 1 it indicates some effect 

 of the selection. 



> " For the yield of grain, these indexes have been calculated for the effect of each 

 selection upon the rows grown in each of the following years. The average index 

 for each class of selection and for all the selections are given in [tabular form]. 

 As shown in their probable errors these mean indexes are not significantly 

 different from 1. This indicates that there is no effect of the selections within 

 these pure lines. The mean indexes showing the effect of two or three succes- 

 sive selections in the same or in different directions are shown in [tabular 

 form]. These indexes are also significantly equal to 1, with the possible ex- 

 ception of the successive minus selections. These latter indexes are con- 

 sistently less than 1. Whether they really indicate an effect of the selections 

 or not can not be determined from the present data. The values are not very 

 far below 1, and in view of the other evidence we are inclined to regard them 

 as random fluctuations. 



" It is pointed out that where selections are made which are only slightly 

 above or below the mean of their pure line, spurious values of this index are 

 sometimes obtained. This is especially true if a relatively small number of rows 

 are grown from such a selection. The reason for this is that the means of 



96619° 



