Mendel's explanation of the monohybrid cross
Mendel
hypothesized that seed colour and other phenotypes are
controlled by alternative forms of an inherited "element"
(which
we now call a gene) in the parental
plants. Each
plant receives one factor
(now
called an allele)
from each
parent. The yellow plants have two copies of the "yellow"
factor (Y) and the
green plants two copies
of the "green"
factor (y). The F1 plants
receive one Y or one y factor from either
parent, and are
thus Yy. Since the plants are
yellow like
the YY parent, the Y factor can be said to dominate the y factor in determining
the
appearance of the seeds. That is, the heterozygous Yy combination
resembles the homozygous YY combination,
rather than the homozygous yy combination.
In gamete formation, the factors segregate (separate), so that each gamete carries only one or the other. One-half (1/2) of the female gametes are Y, 1/2 are y, and the same is true for the male gametes.
The probability of two independent events occurring together is the product of their independent occurrence (the "and" rule). Then, the probability that any F2 plant will receive a Y from the female and a Y from the male is (1/2) x (1/2) = 1/4, and the probability of a y from both parents is also (1/2) x (1/2) = 1/4.
The probability of two alternative events occurring together is the sum of their separate occurrence (the "or" rule). Then, there are two ways of obtaining a Yy plant: either Y from the female and y from the male, or y from the female and Y from the male: (1/2) x (1/2) + (1/2) x (1/2) = 1/2
Finally, the probability of a plant being either YY or Yy is 1/4 + 1/2 = 3/4, and the probability of yy remains 1/4. The expected ratio of yellow ("Y-") to green ("yy") plants is 3/4 : 1/4 or 3:1, exactly as observed.
Mendel showed that these ratios were obtained for seven separate traits in peas, including seed colour and shape, pod shape, and plant form.
In gamete formation, the factors segregate (separate), so that each gamete carries only one or the other. One-half (1/2) of the female gametes are Y, 1/2 are y, and the same is true for the male gametes.
The probability of two independent events occurring together is the product of their independent occurrence (the "and" rule). Then, the probability that any F2 plant will receive a Y from the female and a Y from the male is (1/2) x (1/2) = 1/4, and the probability of a y from both parents is also (1/2) x (1/2) = 1/4.
The probability of two alternative events occurring together is the sum of their separate occurrence (the "or" rule). Then, there are two ways of obtaining a Yy plant: either Y from the female and y from the male, or y from the female and Y from the male: (1/2) x (1/2) + (1/2) x (1/2) = 1/2
Finally, the probability of a plant being either YY or Yy is 1/4 + 1/2 = 3/4, and the probability of yy remains 1/4. The expected ratio of yellow ("Y-") to green ("yy") plants is 3/4 : 1/4 or 3:1, exactly as observed.
Mendel showed that these ratios were obtained for seven separate traits in peas, including seed colour and shape, pod shape, and plant form.