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.

Verified step by step guidance

1. Step 1: Recognize that the problem involves a dihybrid cross, as evidenced by the 9:3:3:1 ratio in the F₂ generation. This ratio suggests that two genes are involved, each with two alleles, and that these genes assort independently according to Mendel's laws.
2. Step 2: Assign alleles to the genes controlling flower color. For example, let 'A' and 'a' represent the alleles for one gene, and 'B' and 'b' represent the alleles for the second gene. The specific combinations of these alleles determine the flower color (e.g., yellow, blue, red, or mauve).
3. Step 3: Analyze the given information about the F₁ and F₂ generations from the previous crosses. For the blue × red cross, the F₁ generation (all yellow) indicates that yellow is dominant over both blue and red. The F₂ generation ratio (9 yellow: 3 blue: 3 red: 1 mauve) suggests that the mauve phenotype occurs when both genes are homozygous recessive (aabb).
4. Step 4: For the cross between true-breeding red (aaBB) and true-breeding mauve (aabb), determine the F₁ genotype. Since the red parent contributes 'aaBB' and the mauve parent contributes 'aabb', the F₁ offspring will all have the genotype 'aaBb'. Based on the dominance relationships, this genotype will express the blue phenotype.
5. Step 5: To determine the F₂ results, perform a Punnett square for the F₁ cross (aaBb × aaBb). This involves considering all possible combinations of alleles for the two genes. The expected phenotypic ratio in the F₂ generation will depend on the dominance relationships and the genotypes produced. Use the information from the previous crosses to predict the phenotypes and their proportions.

Key Concepts

Mendelian Genetics

Mendelian genetics is the study of how traits are inherited through generations based on the principles established by Gregor Mendel. It involves understanding dominant and recessive alleles, where dominant traits mask the expression of recessive ones. This framework helps explain the inheritance patterns observed in the F₁ and F₂ generations of the plant crosses described in the question.

Phenotypic Ratios

Phenotypic ratios represent the relative frequencies of different observable traits in the offspring resulting from a genetic cross. In the given question, the 9:3:3:1 ratio in the F₂ generation indicates a dihybrid cross involving two traits, where the dominant traits appear more frequently. Understanding these ratios is crucial for predicting the outcomes of genetic crosses.

True Breeding

True breeding refers to organisms that consistently produce offspring with a specific phenotype when self-fertilized or crossed with another true-breeding organism of the same phenotype. In the context of the question, true-breeding red and mauve-flowered plants will produce offspring that exhibit predictable traits, which is essential for determining the F₁ and F₂ results of the cross.