Hayes and Garber - Cucurbit Breeding

48 BREEDING CROP PLANTS
existence in a cross-fertilized species through heterozygosis may be
isolated by its means. Weak types appear in self-fertilized species, but
are eliminated because they must stand or fall by their own merits."
stability,
Biologists commonly believe that internal or external agencies
do occasionally modify the germ plasm. It is also commonly
accepted that somatic modifications do not impress themselves
upon the germ plasm. From the facts of segregation as explained
by the Mendelian law and the acceptance of the theory of factor
we may next consider what may be expected in selfpollinating
a naturally cross-fertilized plant, such as' corn, or
what will result in later generations after making a cross in
naturally self-fertilized plants.
Several slightly different formulae have been advanced to show
the theoretical expectation. The simplest formula for the percentage
of homozygous types in any generation following a cross
/2 n - m l\
between different forms is ( ) . In this formula n is the
number of segregating generations which has elapsed since the cross
was made and m is the number of separately inherited allelomorphic
pairs of factors involved. In self-fertilized organisms this
would not absolutely hold unless all the progeny of each genotype
were equally productive numerically.
In artificially self-fertilizing naturally cross-pollinated plants,
such as corn, it is theoretically possible to select a completely
heterozygous individual in each generation for self-fertilization
and thus obtain no reduction in heterozygosis. Jones (1919)
has worked out theoretical curves for 1, 5, 10, and 15 allelomorphic
pairs of factors for from one to 10 generations of selffertilization
following a cross.
Some facts regarding the effects of self-fertilization in generations
following a cross are apparent from a consideration of this
figure. When only a single allelomorphic pair is concerned, the
first generation of selfing reduces the percentage of heterozygous
individuals by half. When a number of factor pairs are concerned
reduction of the percentage of heterozygous individuals is
comparatively slow for the first few years of selfing. At the end
of 10 years the percentage of heterozygotes is veiy low whether
the initial cross was heterozygous for 15 allelomorphic pairs or
for a single allelomorphic pair. From the above discussion it is
apparent that after several years of self-fertilization following a