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and to determine to what extent variation in phenotype is caused by
genotypic differences and to what extent it might be caused by
differences in environmental factors. We take a closer look at these
questions in the next chapter.
In this section, we present a mathematical model that explains
continuous traits by assuming there are multiple genetic loci controlling
the expression of a particular quantitative characteristic, with each
individual gene contributing to the trait's magnitude. Each of the
controlling genes can add to, or fail to add to, the magnitude of the
specific characteristic. The model explains the so-called bell-shaped
curve distribution of values exhibited by many continuous traits, such as
height, weight, or intensity of flower petal color.
This hypothesis was formulated in 1909 by Hermann Nilsson-Ehle in
relation to his study of wheat kernel colors. Similar to the experiments
Mendel performed, Nilsson-Ehle started by crossing pure lines of white
grain and red grain wheat. In the first generation, he only observed
wheat with a grain color intermediate to that of the parents. An
intercross of the first generation produced offspring with both white and
red grain color, as expected. The puzzling fact in his experiments,
however, was the presence of different shades of red among the red grain
in the F 2 , in addition to the color observed in the F 1 —a departure
from the Mendelian result. In one of the crosses, for example, a ratio
of 15/16 red to 1/16 white was observed. There were about as many
plants with grains as intensely red as in the grandparents as there
were plants with white grains. The number of plants with pure red
grains and white grains was not very large, and the largest number of
plants in the F 2 had grains of the same color as the F 1 . There were also
two intermediate shades of red that were not present in either the P or F 1
generations. The different phenotypes appeared in a ratio of 1:4:6:4:1
from the dark red through the light red grains to white. In still other
cases, Nilsson-Ehle found that 63/64 of the F 2 plants were red-kernelled
and only 1/64 had white kernels. In these experiments, the range of
intensity of the red was even wider and the variety of shades greater.
B. The Polygenic Hypothesis
To explain these experiments, Nilsson-Ehle made the conjecture, known
as the polygenic (or multiple-factor) hypothesis, that the color of the kernel is
controlled, not by one, but by several different genes. The genes are
independent and contribute cumulatively to the red pigmentation of the
wheat kernels. None of the genes is completely dominant over white,
explaining the appearance of the F 1 as a blend of the characters of the
two parents. Nilsson-Ehle conjectured that the intensity of the red
pigmentation in the wheat kernel is controlled by the number of
contributing alleles present at the loci controlling the production of red
pigmentation. In general, he conjectured that quantitative traits are
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