Adam Capriola
Biology Lab Section 156
Dr. Lee
2/18/07
Plant Lab
Title: A Study in the Mendelian Inheritance Ratio of Corn and Sorghum
Abstract
This study was on the Mendelian phenotype ratio of corn and sorghum. Second
generation corn and sorghum seeds were planted, monitored, and observed for three weeks. The
phenotypes of the plants grown were recorded. Using a chi-squared test, the observed
phenotypic ratios were compared to Mendelian ratios to see if the ratios matched. The first
generation of corn agreed with a 3:1 ratio of tall plants to short plants. The second generation of
corn agreed to a 9:3:3:1 ratio of tall green plants to tall white plants to short green plants to short
white plants. The sorghum agreed with a 9:4:3 ratio of green plants to white plants to white with
green plants. In conclusion, the plants all matched Mendelian ratios, and therefore their
genotypes and their parent's genotypes were able to be determined.
Introduction
Gregor Mendel first came up with the concept of genetics in the 1860’s (Dewitt, 2003).
He discovered that parents pass genes on to their offspring coding for different physical
characteristics (phenotypes). Genes can come in different variations, called alleles. Alleles for
different phenotypes can be dominant or recessive when paired with another allele, which means
that only one allele will be expressed physically. Mendel found that when organisms with
different allele combinations (genotypes) were mated, they produced specific ratios of offspring
with specific phenotypes (Griffiths, 2000). When organisms with one dominant allele and one
recessive allele for a gene were crossed, a 3 to 1 ratio in the dominant phenotype to recessive
phenotype resulted. Depending on how many genes accounted for a phenotype and if the alleles
were completely dominant to each other or incompletely dominant among other factors, different
ratios of phenotypes resulted, including 9:3:3:1, 1:2:1, and 9:4:3. In this experiment, observed
ratios of phenotypes of plants were compared to Mendelian ratios in order to figure out the
possible genotypes of the plants.
Materials and Methods
A 1.5 inch plastic flat was obtained containing seemingly equal amounts of potting soil,
perlite, and sphagnum. These three parts were mixed evenly and the mixture was then slightly
packaged down. About 50 second generation (F2) corn seeds were obtained and inserted into the
soil. The seeds were pushed about 0.5 inches into the soil about an inch away from each other in
rows containing about 8 seeds each. Rows were about 2 inches away from each other. Once all
seeds were planted, the flat was then watered with tap water until the soil was moist. A second
and third flat were prepared in the same manner, only containing a different type of F2 corn seeds
and F2 sorghum seeds. The flats were kept in a 20º C classroom with lights on for three weeks.
The flats were watered as necessary, and plant growth was monitored and recorded during the
three weeks.
Results
For the first F2 generation of corn observed, 38 tall plants and 11 short plants were
counted (Table I). The tall plants had skinny long leaves while the short plants had shorter wider
leaves. The observed ratio was 3.45 tall plants for every 1 short plant (Table I). Comparing this
ratio to a Mendelian ratio of 3 tall plants for every 1 short plant resulted in a chi-squared value of
0.169 (Table II). This number was less than the 95% confidence value of 3.84 for 1 degree of
freedom, so this Mendelian ratio was unable to be rejected (Table II).
For the other F2 generation of corn observed, 22 green and tall plants, 9 green and short
plants, 9 white and tall plants, and 4 white and short plants were counted (Table III). The tall
phenotype meant the plants had long skinny leaves and the short phenotype meant the plants had
short wide leaves. The green phenotype meant the plant was green and the white phenotype
meant the plant was a white color. The observed ratio was 5.5 green tall plants to 2.25 green
short plants to 2.25 white tall plants to 1 white short plant (Table III). Comparing this ratio to a
Mendelian ratio of 9 green tall plants to 3 green short plants to 3 white tall plants to 1 white short
plant resulted in a chi-squared value of 1.016 (Table IV). This number was less than the 95%
confidence value of 7.82 for 3 degree of freedom, so this Mendelian ratio was unable to be
rejected (Table IV).
For the F2 generation of sorghum observed, 29 green plants, 8 white with green plants,
and 9 white plants were counted (Table V). The green plants were green in color, the white with
green plants were white in color with spots of green, and the white plants were white in color.
The observed ratio was 3.68 green plants to 1.38 white plants to 1 white with green plant (Table
V). Comparing this ratio to a Mendelian ratio of 9 green plants to 4 white plants to 3 white with
green plants resulted in a chi-squared value of 0.36 (Table VI). This number was less than the
95% confidence value of 5.99 for 2 degrees of freedom, so this Mendelian ratio was unable to be
rejected (Table VI).
Discussion
A chi-squared test takes a null hypothesis, which says that there is no difference between
observed data and predicted data, and determines whether the null hypothesis is valid (Russell,
2003). The observed data is compared to expected data using a mathematical formula to produce
a chi-squared value. That value is then compared to a probability value from a table, which is
obtained depending on the degrees of freedom. Degrees of freedom is found by taking the total
number of classes and subtracting one. The most common probability value is 95% confidence.
If the chi-squared value is greater than the probability value, the null hypothesis is rejected, but if
it is less than the probability value, the null hypothesis cannot be rejected.
For the first generation of corn observed, the observed proportion of 3.45 tall plants to
every 1 short plant was compared to the Mendelian ratio of 3 tall plants to every 1 short plant
(Table I). This resulted in a chi-squared value of 0.169, which is less than the 95% confidence
value of 3.84 for 1 degree of freedom (Table II). This means the proposed ratio could not be
rejected and that it is a possibility for the actual proportion of tall plants to short plants. The
genotypes would have to be ¼ TT, ½ Tt, and ¼ tt, with the tall allele (T) being completely
dominant to the short allele (t). Both plants with TT and Tt genotype would be tall, resulting in
¾ tall plants and ¼ short plants, matching the 3:1 Mendelian ratio. This means that the parents
of this generation must have been both heterozygous in order to produce the 1:2:1 genotype ratio.
For the second generation of corn observed, the observed proportion of 5.5 green tall
plants to 2.25 green short plants to 2.25 white tall plants to 1 white short plant was compared to
the Mendelian ratio of 9 green tall plants to 3 green short plants to 3 white tall plants to 1 white
short plant (Table III). This resulted in a chi-squared value of 1.016, which is less than the 95%
confidence value of 7.82 for 3 degrees of freedom (Table IV). This means the proposed ratio
could not be rejected and that it is a possibility for the actual proportion. The genotypes would
have to be 9/16 G- T-, 3/16 G- tt, 3/16 gg T-, and 1/16 gg tt, with the green allele (G) being
completely dominant to the white allele (g), and the tall allele (T) being completely dominant to
the short allele (t). The parents for this generation must have been both heterozygous for both
traits in order to produce a 9:3:3:1 phenotype ratio.
Lastly, for the generation of sorghum observed, the observed proportion of 3.68 green
plants to 1.38 white plants to 1 white with green plant was compared to the Mendelian ratio of 9
green plants to 4 white plants to 3 white with green plants (Table V). This resulted in a chisquared value of 0.36, which is less than the 95% confidence value of 5.99 for 2 degrees of
freedom (Table VI). This means the proposed ration could not be rejected and that it is a
possibility for the actual proportion. The genotype for this plant is dependent on two genes,
green (G) being completely dominant to white (g), and normal pigmentation (N) is completely
dominant to a variation in pigmentation (n). The recessive allele for variation in pigmentation
causes a plant with a dominant green allele to have white patches (a lack of pigmentation). A
white plant with the recessive pigmentation genotype will have no visible effect in its phenotype
because it does not have any pigmentation. This is an example of epitasis, in which one gene is
dependent on another (Griffiths, 2000).
The green plants consists of the genotype G- N-, which adds up to 9/16 of the proportion
(1/16 GG NN, 1/8 GG Nn, 1/8 Gg NN, and 1/4 Gg Nn). The white phenotype consists of the
genotypes gg NN, gg Nn, and gg nn, which adds up to 4/16 of the proportion (1/16 gg NN, 1/8
gg Nn, and 1/16 gg nn). Finally, the white with green phenotype includes the genotypes Gg nn
and GG nn, which adds up to 3/16 of the proportion (1/8 Gg nn and 1/16 GG nn). The parents
for this generation had to have been heterozygous for both genes in order to produce a 9:4:3
phenotypic ratio.
Literature Cited
DeWitt, Stetten Jr. 2003. The Genetic Basics: What Are Genes and What Do They Do?.
(National Institute of Health). http://www.history.nih.gov/exhibits/genetics/sect1f.htm.
Griffiths, Anthony J.F., Miller, Jeffrey H., Suzuki, David T., Lewontin, Richard C., and William
M. Gelbart. 2000. An Introduction to Genetic Analysis. W.H. Freeman and Company.
Russell, Peter J. 2003. Essential iGenetics. Benjamin Cummings, San Francisco.
Tables
Table I:
Phenotype
Tall
Short
Number
Observed
38
11
Table II:
Degrees of Freedom
1
Number
Observed
Green/Tall 22
Green/Short 9
White/Tall 9
White/Short 4
Table V:
Phenotype
Green
White with
Green
Mendelian
Ratio
3
1
95% Confidence Value
3.84
Table III:
Phenotype
Table IV:
Degrees of Freedom
3
Observed
Ratio
3.45
1
Observed
Ratio
5.5
2.25
2.25
1
Mendelian
Ratio
9
3
3
1
95% Confidence Value
7.82
Number
Observed
29
8
Observed
Ratio
3.63
1
Mendelian
Ratio
9
3
Expected
Number
36.75
12.25
Exp. –
Obs.
-1.25
1.25
(Exp. –
Obs.)2
1.56
1.56
Total:
(Exp. –
Obs.)2/Exp.
0.042
0.127
0.169
(Exp. –
Obs.)2
7.56
0.56
0.56
1.56
Total:
(Exp. –
Obs.)2/Exp.
0.31
0.068
0.068
0.57
1.016
(Exp. –
Obs.)2
4
1
(Exp. –
Obs.)2/Exp.
0.15
0.11
Chi-squared value
0.169
Expected
Number
24.75
8.25
8.25
2.75
Exp. –
Obs.
2.75
-0.75
-0.75
-1.25
Chi-squared value
1.016
Expected
Number
27
9
Exp. –
Obs.
-2
1
White
11
Table VI:
Degrees of Freedom
2
1.38
4
95% Confidence Value
5.99
12
1
Chi-squared value
0.36
1
Total:
0.08
0.36