A three-gene system of additive genes (A, B, and C) controls plant height. Each gene has two alleles (A and a, B and b, and C and c). There is dominance among the alleles of each gene, with alleles A, B, and C dominant over a, b, and c. Under this scheme, the dominant genotype for a gene contributes 10 cm to height potential, and the recessive genotype contributes 4 cm. What is the height potential of a plant that is homozygous for all three dominant alleles?
Table of contents
- 1. Introduction to Genetics51m
- 2. Mendel's Laws of Inheritance3h 37m
- 3. Extensions to Mendelian Inheritance2h 41m
- 4. Genetic Mapping and Linkage2h 28m
- 5. Genetics of Bacteria and Viruses1h 21m
- 6. Chromosomal Variation1h 48m
- 7. DNA and Chromosome Structure56m
- 8. DNA Replication1h 10m
- 9. Mitosis and Meiosis1h 34m
- 10. Transcription1h 0m
- 11. Translation58m
- 12. Gene Regulation in Prokaryotes1h 19m
- 13. Gene Regulation in Eukaryotes44m
- 14. Genetic Control of Development44m
- 15. Genomes and Genomics1h 50m
- 16. Transposable Elements47m
- 17. Mutation, Repair, and Recombination1h 6m
- 18. Molecular Genetic Tools19m
- 19. Cancer Genetics29m
- 20. Quantitative Genetics1h 26m
- 21. Population Genetics50m
- 22. Evolutionary Genetics29m
20. Quantitative Genetics
Analyzing Trait Variance
Problem 29d
Textbook Question
A three-gene system of additive genes (A, B, and C) controls plant height. Each gene has two alleles (A and a, B and b, and C and c). There is dominance among the alleles of each gene, with alleles A, B, and C dominant over a, b, and c. Under this scheme, the dominant genotype for a gene contributes 10 cm to height potential, and the recessive genotype contributes 4 cm. What are the phenotypes and proportions of each phenotype among the F₂?

1
Step 1: Understand the genetic system described in the problem. Each gene (A, B, and C) has two alleles: a dominant allele (A, B, C) and a recessive allele (a, b, c). Dominant alleles contribute 10 cm to plant height, while recessive alleles contribute 4 cm. The phenotype is determined by the sum of contributions from all three genes.
Step 2: Determine the possible genotypes for each gene in the F₂ generation. Since the F₂ generation results from a dihybrid cross (AaBbCc × AaBbCc), each gene can have the following genotypes: AA, Aa, or aa; BB, Bb, or bb; CC, Cc, or cc. Use a Punnett square to calculate the proportions of each genotype for each gene.
Step 3: Calculate the height contribution for each genotype. For example, AA contributes 10 cm, Aa contributes 10 cm (due to dominance), and aa contributes 4 cm. Repeat this for BB, Bb, bb and CC, Cc, cc. Combine the contributions from all three genes to determine the total height for each genotype combination.
Step 4: Determine the phenotypes based on the total height contributions. For example, a plant with genotype AA BB CC will have a height of 10 cm + 10 cm + 10 cm = 30 cm, while a plant with genotype aa bb cc will have a height of 4 cm + 4 cm + 4 cm = 12 cm. List all possible phenotypes and their corresponding heights.
Step 5: Calculate the proportions of each phenotype among the F₂ generation. Multiply the probabilities of each genotype for the three genes (from the Punnett square) to find the overall proportion of each phenotype. For example, the proportion of AA BB CC is the product of the probabilities of AA, BB, and CC occurring independently.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Additive Gene Interaction
Additive gene interaction occurs when multiple genes contribute to a single trait, with each gene's alleles having a cumulative effect on the phenotype. In this case, the three genes (A, B, and C) each contribute a specific amount to the plant height, leading to a range of possible heights based on the combination of dominant and recessive alleles.
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Dominance and Alleles
Dominance refers to the relationship between alleles, where a dominant allele masks the effect of a recessive allele in a heterozygous genotype. In this scenario, alleles A, B, and C are dominant over their respective recessive alleles (a, b, and c), influencing the phenotype of the plants based on which alleles are present.
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Phenotypic Ratios in F₂ Generation
The F₂ generation results from crossing two F₁ individuals, leading to a variety of genotypes and phenotypes. The phenotypic ratios can be predicted using a Punnett square or by applying the principles of Mendelian inheritance, which helps determine the proportions of each phenotype based on the combinations of dominant and recessive alleles from the parental generation.
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