2. Mendel's Laws of Inheritance

Probability and Genetics

2. Mendel's Laws of Inheritance

Probability and Genetics

2:28 minutes

Problem 21a

Textbook Question

In a unique species of plants, flowers may be yellow, blue, red, or mauve. All colors may be true breeding. If plants with blue flowers are crossed with red-flowered plants, all F₁ plants have yellow flowers. When these produced an F₂ generation, the following ratio was observed:
9/16 yellow: 3/16 blue: 3/16 red: 1/16 mauve
In still another cross using true-breeding parents, yellow-flowered plants are crossed with mauve-flowered plants. Again, all F₁ plants had yellow flowers, and the F₂ showed a 9:3:3:1 ratio, as just shown.
Describe the inheritance of flower color by defining gene symbols and designating which genotypes give rise to each of the four phenotypes.

Verified step by step guidance

Define the gene symbols: Assign two genes, A and B, to control flower color. Each gene has two alleles: A (dominant) and a (recessive), and B (dominant) and b (recessive).

Determine the phenotypes based on genotypes: From the F₂ ratio (9:3:3:1), this is a classic dihybrid cross pattern. Assign phenotypes to genotypes as follows: A-B- (yellow), A-bb (blue), aaB- (red), and aabb (mauve).

Explain the F₁ generation: When blue (A-bb) is crossed with red (aaB-), the F₁ generation is heterozygous for both genes (AaBb), resulting in yellow flowers due to the dominance of A and B alleles.

Analyze the F₂ generation: The F₂ generation results from a dihybrid cross (AaBb x AaBb), producing a 9:3:3:1 phenotypic ratio. This confirms the inheritance pattern and the genotypic assignments for each phenotype.

Describe the second cross: When yellow (A-B-) is crossed with mauve (aabb), the F₁ generation is again heterozygous (AaBb) and yellow due to dominance. The F₂ generation from this cross also shows the 9:3:3:1 ratio, further supporting the genetic model.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mendelian Inheritance

Mendelian inheritance refers to the principles of heredity established by Gregor Mendel, which describe how traits are passed from parents to offspring through discrete units called genes. In this context, traits such as flower color are determined by alleles, which can be dominant or recessive. Understanding these principles is crucial for predicting the outcomes of genetic crosses, such as the F₁ and F₂ generations mentioned in the question.

Phenotypic Ratios

Phenotypic ratios represent the relative frequencies of different observable traits in the offspring resulting from a genetic cross. The 9:3:3:1 ratio observed in the F₂ generation indicates a dihybrid cross involving two traits, where the dominant traits mask the recessive ones. This ratio helps in understanding the inheritance patterns and the expected distribution of phenotypes based on the genotypes of the parents.

Genotype and Alleles

Genotype refers to the genetic constitution of an organism, specifically the alleles it possesses for a given trait. In this case, flower color is influenced by different alleles, which can be represented by symbols (e.g., Y for yellow, B for blue, R for red, and M for mauve). Identifying the genotypes that correspond to each phenotype is essential for accurately describing the inheritance patterns and predicting the outcomes of future crosses.

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Textbook Question

In a species of the cat family, eye color can be gray, blue, green, or brown, and each trait is true breeding. In separate crosses involving homozygous parents, the following data were obtained:

How many genes are involved? Define gene symbols and indicate which genotypes yield each phenotype.

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Textbook Question

In a plant, a tall variety was crossed with a dwarf variety. All F₁ plants were tall. When F₁xF₁ plants were interbred, 9/16 of the F₂ were tall and 7/16 were dwarf. What proportion of the F₂ plants will be true breeding if self-fertilized? List these genotypes.

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Textbook Question

In a plant, a tall variety was crossed with a dwarf variety. All F₁ plants were tall. When F₁xF₁ plants were interbred, 9/16 of the F₂ were tall and 7/16 were dwarf. Explain the inheritance of height by indicating the number of gene pairs involved and by designating which genotypes yield tall and which yield dwarf. (Use dashes where appropriate.)

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Textbook Question

In a unique species of plants, flowers may be yellow, blue, red, or mauve. All colors may be true breeding. If plants with blue flowers are crossed with red-flowered plants, all F₁ plants have yellow flowers. When these produced an F₂ generation, the following ratio was observed:

9/16 yellow: 3/16 blue: 3/16 red: 1/16 mauve

In still another cross using true-breeding parents, yellow-flowered plants are crossed with mauve-flowered plants. Again, all F₁ plants had yellow flowers, and the F₂ showed a 9:3:3:1 ratio, as just shown. Determine the F₁ and F₂ results of a cross between true-breeding red and true-breeding mauve-flowered plants.

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Textbook Question

A 'wrongful birth' case was recently brought before a court in which a child with Smith–Lemli–Opitz syndrome was born to apparently healthy parents. This syndrome is characterized by a cluster of birth defects including cleft palate, and an array of problems with the reproductive and urinary organs. Originally considered by their physician as having a nongenetic basis, the parents decided to have another child, who was also born with Smith–Lemli–Opitz syndrome. In the role of a genetic counselor, instruct the court about what occurred, including the probability of the parents having two affected offspring, knowing that the disorder is inherited as a recessive trait. What is the probability that one of them is a carrier and the other is not? [Hint: The p values in (b), (c), and (d) should equal 1.]

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Textbook Question

A 'wrongful birth' case was recently brought before a court in which a child with Smith–Lemli–Opitz syndrome was born to apparently healthy parents. This syndrome is characterized by a cluster of birth defects, including cleft palate, and an array of problems with the reproductive and urinary organs. Originally considered by their physician as having a nongenetic basis, the parents decided to have another child, who was also born with Smith–Lemli–Opitz syndrome. In the role of a genetic counselor, instruct the court about what occurred, including the probability of the parents having two affected offspring, knowing that the disorder is inherited as a recessive trait. What is the probability that neither of them is a carrier?

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Textbook Question

A 'wrongful birth' case was recently brought before a court in which a child with Smith–Lemli–Opitz syndrome was born to apparently healthy parents. This syndrome is characterized by a cluster of birth defects including cleft palate, and an array of problems with the reproductive and urinary organs. Originally considered by their physician as having a nongenetic basis, the parents decided to have another child, who was also born with Smith–Lemli–Opitz syndrome. In the role of a genetic counselor, instruct the court about what occurred, including the probability of the parents having two affected offspring, knowing that the disorder is inherited as a recessive trait. Calculate the probability that both the male and female are carriers for TSD.

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Textbook Question

Datura stramonium (the Jimsonweed) expresses flower colors of purple and white and pod textures of smooth and spiny. The results of two crosses in which the parents were not necessarily true breeding are shown below. Assuming that true-breeding strains of all combinations of traits are available, what single cross could you execute and carry to an F₂ generation that will prove or disprove your hypothesis? Assuming your hypothesis is correct, what results of this cross will support it?

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