16 BULLETIN 1396, U. S. DEPARTMENT OF AGRICULTURE 
that this requirement is not always fulfilled. In a careful and com- 
prehensive comparison of the value of 10 selfed lines as the parents. 
of F, hybrids the most desirable selfed line was one of the weakest. 
If the selfed lines must be tested in combination before selection 
is practicable the problem is greatly complicated, and it may not be 
out of place to discuss briefly what is to be expected under these 
circumstances. The object is to obtain the maximum number of 
dominant characters. 
An F, cross between two varieties or two individuals of the same 
variety falls short of producing the minimum number of homozy- 
gous recessive characters to be derived from the cross only to the 
extent that factors heterozygous in both parents have united to 
produce one in four homozygous recessive individuals. 
If the number of common heterozygous characters is small in 
comparison with the number of homozygous characters which are 
dominant in one parent and recessive in the other, any combination 
of selfed lines from the original cross will almost certainly have a 
larger number of homozygous recessive characters than the original 
cross, because of the characters which were DD in one parent and RR 
in the other that will reappear as RR. Thus, if the parental plants 
are distantly related 1t would be hopeless to attempt an increase 
over the vigor of the F,. 
The other extreme in which the parents have a maximum number | 
of heterozygous characters in common would be represented by two 
F, plants in a hybrid between two unrelated stocks. The question 
then would be to decide whether it is possible to obtain a stock by 
combining selfed lines that would exceed the F, in the number of 
dominant characters. This should be possible, for even a random 
combination of selfed lines would equal a random F; population in | 
dominant factors. The conditions imposed, however, are not likely 
to be met with in practical breeding. The nearest approach that 
would occur isin the attempt to improve a commercial variety without. | 
introducing foreign blood, as in the experiment here reported. The | 
marked decline in vigor that follows the first generation of selfing | 
indicates that commercial varieties are far from representing the 
extreme condition assumed above and that very different sets of | 
characters are heterozygous in different individuals. 
The most practicable method of obtaining a large Sahin ee of 
simple dominant characters would seem to be to make a series of 
hybrids between plants of unrelated strains and compare their vigor, 
retaining remnants with which to continue either selfed or crossbred 
stocks of the most desirable parents. 
SEGREGATION OF MULTIPLE-FACTOR CHARACTERS 
If the deleterious characters that are to be eliminated from maize. 
varieties are largely multiple-factor characters, the problem takes 
on a very different aspect. 
Most of the conspicuous abnormalities that have been observed 
in maize require for their expression more than one homozygous. 
recessive factor. Many of these characters appear in one-quarter 
of the individuals of a progeny, indicating a single factor difference; 
but when the abnormal individuals are cutcrossed to unrelated 
strains it develops that the mutation or segregation bringing the 
