320 ILLINOIS ACADEMY OF SCIENCE 
number of parents belonging to the class (for which the frac- 
tion is supposed to indicate the amount of regression) by the 
number of parents in this class, then after adding the fractions 
divide by the total number of parents? This will not be an 
actual computation of the average for the amount of individual 
regression between each parent and each of the offspring, yet 
it will give a more accurate measure of regression according 
to class grouping method, If we do this we get the decimal 
0.943 as a measure of regression, which is only 0.057 from 
being complete. 
What then is the result of these statistical studies? We 
find that they constitute a further substantiation of my earlier 
findings in regard to the ineffectiveness of selection in Aphis 
avenae Fab. It is noted, however, if these studies are not 
carefully applied, especially in the light of a fully annotated 
pedigree, they may cause us to make very faulty conclusions. A 
brief summary of this short mathematical study of selection 
and regression in Aphis avenae Fab. is here given: 
SUMMARY 
1. This statistical study of the selection work done with 
Aphis avenae Fab., in which eighty-seven generations were 
obtained, substantiates my earlier conclusions in regard to the 
negative effects of selection. Long continued selection (in one 
case forty-four) does not produce any positive effect in re- 
gard to somatic characters in general, these remaining true 
to the genotype. 
2. By computing the regression through the parent class 
grouping method and using the mean of the line as standard 
of reference, it being reduced to 100, such figures as 1.0465 
and 0.906 are obtained (according to this method complete 
regression would be expressed by 1.) 
3. Measuring the amount of regression through the par- 
ent class grouping method facilitates the plotting (in the 
form of a graph) of the results, but does not give a very ac- 
curate measure of the amount of regression, However, this 
method is much improved from the standpoint of accuracy, if 
we multiply the results obtained for each parent class by the 
number of parents in the class, and divide the sum of such 
amounts by the total number of parents included. 
