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12 BULLETIN 1396, U. S. DEPARTMENT OF AGRICULTURE 
stricting the pollinations to the 10 best-appearing rows narrows the 
foundation stock to 10 ears the first season. In succeeding years 
the rejecting of 10 of the 20 rows before making pollinations will 
eliminate the blood of still other foundation ears. Eventually, how- 
ever, the intermingling of blood through cross-pollination will bring 
about a condition in which at least a trace of the blood of all the 
remaining foundation ears will be present in each of the progenies. 
When this condition is reached no further eliminations can take 
place. 
An analysis of the pedigrees shows that in this experiment seven 
of the foundation ears were represented in the selections of 1924. 
The total contribution by the individual ears varied from 1.6 to 21.8 
per cent. 
In the selfed method as planned in this experiment a maximum 
of 15 foundation ears might be retained the first season, but as self- 
ing continues additional ears would be dropped. In this experiment 
but two foundation ears were represented in the 1923 plantings, and 
in 1924 all progenies were descended from a single foundation ear. 
The number of foundation ears retained in a pedigree is a very 
imperfect indication of the degree of inbreeding. For the maize 
breeder the most valuable measure of inbreeding would be one that 
expressed the degree of heterosis. Fortunately, such a measure is 
now available in the coefficient of inbreeding of Wright (6, 7, 8)?. 
Beginning at any generation in the ancestry of an individual or 
strain, this coefficient gives the percentage of the characters or factors 
heterozygous at the beginning of the pedigree that have become homo- 
zygous through consanguineous matings. The generally accepted 
theory of heterosis, or hybrid vigor, assumes this increased vigor to be 
due to the increased number of dominant factors. The larger 
number of dominant factors in a hybrid as compared with the mean 
of the inbred lines of which it is composed is due entirely to the 
increase of heterozygous factors and the phenomenon of dominance. 
Since the coefficient. of inbreeding determines the degree of heter- 
ozygosity, it should be a direct measure of heterosis. 
Any method of breeding except the continued use of F, hybrids 
involves some reduction in heterosis, and it is therefore of impor- 
tance to know to what extent selection may overcome or offset the 
ill effects of inbreeding. 
The theory of the coefficient of inbreeding assumes a relatively 
large number of factors heterozygous in the foundation stock. As 
a result of consanguineous matings a portion of this number will 
become homozygous. The coefficient expresses this portion as a 
yercentage of the total number of factors heterozygous in the 
foandation stock. It represents an average condition and is only 
applicable to any particular individual within the limits of random 
sampling. It further assumes the absence of selection. In the 
absence of selection the homozygous factors would be dominant and 
recessive in equal numbers. Where the selection of vigorous lines 
and individuals is practiced there would be a tendency to retain 
lines and individuals with an excess of dominant factors and also 
those with a larger number of heterozygous factors. If selection 
were without effect we should expect a close negative correlation 
2 The serial numbers (italic) in parentheses refer to ‘“‘Literature cited,’”’ at the end of this bulletin. 
