How can we ascertain the number of polygenes involved in the inheritance of a quantitative trait?
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 4b
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
How many additive alleles are needed to produce each possible phenotype?

1
Step 1: Understand the concept of additive alleles. Additive alleles are genes that contribute incrementally to a trait, such as color intensity in wheat. Each additive allele increases the trait's expression, while non-additive alleles do not contribute to the trait.
Step 2: Analyze the phenotypic ratio in the F₂ generation. The ratio provided is 1 dark-red: 4 medium-dark-red: 6 medium-red: 4 light-red: 1 white. This suggests a polygenic inheritance pattern, where multiple genes contribute to the phenotype.
Step 3: Determine the number of additive alleles involved. The phenotypic categories (dark-red, medium-dark-red, medium-red, light-red, white) correspond to different levels of color intensity. The extremes (dark-red and white) are true breeding, indicating they have either all additive alleles or none. Count the phenotypic categories to infer the number of additive alleles.
Step 4: Assign additive alleles to each phenotype. For example, dark-red likely has the maximum number of additive alleles, while white has none. Intermediate phenotypes (medium-dark-red, medium-red, light-red) have varying combinations of additive and non-additive alleles.
Step 5: Use the phenotypic ratio to confirm the number of additive alleles. The ratio 1:4:6:4:1 corresponds to a binomial distribution, which is characteristic of traits controlled by two additive alleles. Each phenotype represents a specific combination of these alleles.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Additive Alleles
Additive alleles are multiple alleles that contribute to a quantitative trait in a cumulative manner. In this context, each allele adds a specific amount to the phenotype, resulting in a range of phenotypic expressions. The more additive alleles present, the more intense or varied the phenotype, which is crucial for understanding the intermediate phenotypes observed in the F₁ and F₂ generations.
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Phenotypic Ratio
The phenotypic ratio describes the relative frequencies of different phenotypes in a given generation. In this case, the F₂ generation exhibits a specific ratio of dark-red, medium-dark-red, medium-red, light-red, and white phenotypes. Analyzing these ratios helps determine the number of alleles involved and their interactions, which is essential for predicting the outcomes of genetic crosses.
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True Breeding
True breeding refers to organisms that consistently produce offspring with a specific phenotype when self-fertilized or crossed with similar organisms. In this scenario, the dark-red and white F₂ plants are true breeding, indicating that they possess homozygous alleles for their respective traits. This concept is important for understanding the genetic stability of certain phenotypes and how they contribute to the overall inheritance patterns observed in the experiment.
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