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 F2sorghum 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 F2generation 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 chi-squared 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).
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 / Number Observed / Observed Ratio / Mendelian Ratio / Expected Number / Exp. – Obs. / (Exp. – Obs.)2 / (Exp. – Obs.)2/Exp.Tall / 38 / 3.45 / 3 / 36.75 / -1.25 / 1.56 / 0.042
Short / 11 / 1 / 1 / 12.25 / 1.25 / 1.56 / 0.127
Total: / 0.169
Table II:
Degrees of Freedom / 95% Confidence Value / Chi-squared value1 / 3.84 / 0.169
Table III:
Phenotype / Number Observed / Observed Ratio / Mendelian Ratio / Expected Number / Exp. – Obs. / (Exp. – Obs.)2 / (Exp. – Obs.)2/Exp.Green/Tall / 22 / 5.5 / 9 / 24.75 / 2.75 / 7.56 / 0.31
Green/Short / 9 / 2.25 / 3 / 8.25 / -0.75 / 0.56 / 0.068
White/Tall / 9 / 2.25 / 3 / 8.25 / -0.75 / 0.56 / 0.068
White/Short / 4 / 1 / 1 / 2.75 / -1.25 / 1.56 / 0.57
Total: / 1.016
Table IV:
Degrees of Freedom / 95% Confidence Value / Chi-squared value3 / 7.82 / 1.016
Table V:
Phenotype / Number Observed / Observed Ratio / Mendelian Ratio / Expected Number / Exp. – Obs. / (Exp. – Obs.)2 / (Exp. – Obs.)2/Exp.Green / 29 / 3.63 / 9 / 27 / -2 / 4 / 0.15
White with Green / 8 / 1 / 3 / 9 / 1 / 1 / 0.11
White / 11 / 1.38 / 4 / 12 / 1 / 1 / 0.08
Total: / 0.36
Table VI:
Degrees of Freedom / 95% Confidence Value / Chi-squared value2 / 5.99 / 0.36