The narrow-sense heritability of the number of seeds per flower is 0.9. The mean of the population is 6.0 seeds per flower. A flower breeder crosses one flower with 7 seeds to another plant with 9 seeds. What is the expected number of seeds per flower in the offspring of this cross?
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
Heritability
Problem 7b
Textbook Question
Erma and Harvey were a compatible barnyard pair, but a curious sight. Harvey's tail was only 6 cm long, while Erma's was 30 cm. Their F₁ piglet offspring all grew tails that were 18 cm. When inbred, an F₂ generation resulted in many piglets (Erma and Harvey's grandpigs), whose tails ranged in 4-cm intervals from 6 to 30 cm (6, 10, 14, 18, 22, 26, and 30). Most had 18-cm tails, while 1/64 had 6-cm tails and 1/64 had 30-cm tails.
If one of the 18-cm-tail F₁ pigs is mated with one of the 6-cm-tail F₂ pigs, what phenotypic ratio will be predicted if many offspring resulted? Diagram the cross.

1
Step 1: Recognize that the problem involves quantitative traits, which are typically controlled by multiple genes (polygenic inheritance). The range of tail lengths (6 cm to 30 cm) and the intermediate phenotype (18 cm) in the F₁ generation suggest that tail length is influenced by additive alleles at multiple loci.
Step 2: Determine the genetic basis of the trait. Since the F₂ generation shows a phenotypic ratio where 1/64 of the offspring have the extreme phenotypes (6 cm or 30 cm), this indicates that the trait is controlled by 6 additive alleles (3 loci, each with 2 alleles). Each dominant allele contributes to an increase in tail length, while each recessive allele does not.
Step 3: Analyze the genotypes of the parents. The F₁ generation (18 cm tails) is heterozygous at all loci (AaBbCc), as they are intermediate between the two parental phenotypes (6 cm and 30 cm). The F₂ generation includes a range of genotypes, including the homozygous recessive genotype (aabbcc, 6 cm tails) and the homozygous dominant genotype (AABBCC, 30 cm tails).
Step 4: Set up the cross between the F₁ pig (18 cm tail, genotype AaBbCc) and the F₂ pig with a 6 cm tail (genotype aabbcc). For each locus, the F₁ pig can contribute either a dominant or recessive allele, while the F₂ pig can only contribute recessive alleles. This simplifies the inheritance pattern for the offspring.
Step 5: Predict the phenotypic ratio of the offspring. Since the F₂ pig can only contribute recessive alleles (a, b, c), the offspring's phenotype will depend entirely on the alleles contributed by the F₁ pig. For each locus, there is a 50% chance of inheriting a dominant allele and a 50% chance of inheriting a recessive allele. Use a Punnett square or probability rules to calculate the distribution of phenotypes based on the number of dominant alleles inherited (0 to 3), and convert this into the corresponding tail lengths (6 cm, 10 cm, 14 cm, etc.).

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Phenotype and Genotype
Phenotype refers to the observable traits of an organism, such as tail length in pigs, while genotype refers to the genetic makeup that determines these traits. In this scenario, the phenotypes of the F₁ and F₂ generations illustrate how traits can vary based on genetic combinations. Understanding the relationship between genotype and phenotype is crucial for predicting the traits of offspring.
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Mendelian Inheritance
Mendelian inheritance describes the patterns of inheritance first outlined by Gregor Mendel, which include concepts like dominant and recessive alleles. In this case, the tail length trait appears to follow Mendelian ratios, where the F₁ generation shows an intermediate phenotype, and the F₂ generation exhibits a range of phenotypes. This framework helps in predicting the outcomes of genetic crosses.
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Punnett Square
A Punnett square is a diagram used to predict the genetic outcomes of a cross between two organisms. It allows for the visualization of how alleles from each parent combine to produce offspring genotypes and phenotypes. In this question, constructing a Punnett square for the mating of an 18-cm-tail F₁ pig with a 6-cm-tail F₂ pig will help determine the expected phenotypic ratio of their offspring.
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