How do we know that threshold traits are actually polygenic even though they may have as few as two discrete phenotypic classes?
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
Traits and Variance
Problem 4a
Textbook Question
A dark-red strain and a white strain of wheat are crossed and produce an intermediate, medium-red F₁. When the F₁ plants are interbred, an F₂ generation is produced in a ratio of 1 dark-red: 4 medium-dark-red: 6 medium-red: 4 light-red: 1 white. Further crosses reveal that the dark-red and white F₂ plants are true breeding
Based on the ratios in the F₂ population, how many genes are involved in the production of color?

1
Step 1: Recognize that the problem involves inheritance of wheat color, which is quantitative and shows a range of phenotypes. This suggests polygenic inheritance, where multiple genes contribute to the trait.
Step 2: Analyze the F₂ phenotypic ratio provided: 1 dark-red : 4 medium-dark-red : 6 medium-red : 4 light-red : 1 white. This ratio resembles a binomial distribution, which is characteristic of traits controlled by multiple genes with additive effects.
Step 3: Recall that the number of phenotypic classes in a polygenic trait is determined by the formula: \( \text{Number of phenotypic classes} = \text{Number of genes} \times 2 + 1 \). Here, there are 5 phenotypic classes (dark-red, medium-dark-red, medium-red, light-red, white).
Step 4: Solve for the number of genes using the formula: \( \text{Number of genes} = \frac{\text{Number of phenotypic classes} - 1}{2} \). Substitute the number of phenotypic classes (5) into the formula.
Step 5: Conclude that the number of genes involved in the production of wheat color can be determined by solving the equation from Step 4. This will give the number of genes contributing to the trait.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Incomplete Dominance
Incomplete dominance occurs when the phenotype of heterozygotes is intermediate between the phenotypes of the two homozygotes. In this case, the dark-red and white wheat strains produce an F₁ generation with a medium-red phenotype, illustrating that neither allele is completely dominant over the other.
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Polygenic Inheritance
Polygenic inheritance involves multiple genes contributing to a single trait, resulting in a continuous range of phenotypes. The F₂ generation's diverse color ratios suggest that several genes are influencing the color of the wheat, leading to various shades from dark-red to white.
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Phenotypic Ratios
Phenotypic ratios represent the relative frequencies of different phenotypes in a population. The observed 1:4:6:4:1 ratio in the F₂ generation indicates a complex inheritance pattern, which can be analyzed to deduce the number of genes involved in color production through statistical methods.
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