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 to red- flowered plants, all \(\mathrm{F}_{1}\) plants have yellow flowers. When these produced an \(\mathrm{F}_{2}\) 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 \(\mathrm{F}_{1}\) plants had yellow flowers and the \(\mathrm{F}_{2}\) showed a 9: 3: 3: 1 ratio, as just shown. (a) Describe the inheritance of flower color by defining gene symbols and designating which genotypes give rise to cach of the four phenotypes. (b) Determine the \(F_{1}\) and \(F_{2}\) results of a cross between truebreeding red and true-breeding mauve-flowered plants.

Short answer

- F1 generation: __________ - F2 generation: __________

Step-by-step solution

Analyze the given information

We are given the following information: - When blue-flowered plants are crossed with red-flowered plants, all F1 plants have yellow flowers. - In the F2 generation, the ratio is 9/16 yellow, 3/16 blue, 3/16 red, 1/16 mauve. - When yellow-flowered plants are crossed with mauve-flowered plants, all F1 plants have yellow flowers. - In the F2 generation, the ratio is 9:3:3:1 (yellow:blue:red:mauve). From this information, we can infer that the inheritance of flower color follows a dihybrid inheritance pattern since we observe a 9:3:3:1 ratio in the F2 generation.

Define gene symbols

We will use the capital letter Y for the dominant yellow allele and y for the recessive mauve allele. Similarly, we will use the capital letter R for the dominant-red allele and r for the recessive blue allele.

Determine genotypes of the four phenotypes

Based on the information given and the gene symbols we have defined, the genotypes for each flower color are as follows: - Yellow: \(YYRR, YYRr, YyRR,\) or \(YyRr\) - Blue: \(YYrr\) - Red: \(Yyrr\) - Mauve: \(Yyrr\)

Predict the F1 and F2 generation results for a cross between true-breeding red and true-breeding mauve-flowered plants

True-breeding red plants have the genotype \(Yyrr\) and true-breeding mauve plants have the genotype \(yyrr\). We will now cross these plants and evaluate the F1 and F2 generation results. (a) F1 generation: Parents: \(Yyrr \times yyrr\) Offspring: All the F1 offspring will have the genotype \(Yyrr\). Therefore, all the F1 generation plants will have red flowers. (b) F2 generation: To predict the F2 generation, we will perform a self-cross between two F1 generation plants. So, the cross will be: Parents: \(Yyrr \times Yyrr\) We can use a Punnett square to determine the resulting F2 genotypes and phenotypes: 1. \(YYRR\) (yellow) - \(1/16\) 2. \(YYRr\) (yellow) - \(2/16\) 3. \(YyRR\) (yellow) - \(2/16\) 4. \(YyRr\) (yellow) - \(4/16\) 5. \(YYrr\) (blue) - \(1/16\) 6. \(Yyrr\) (red) - \(4/16\) 7. \(yyrr\) (mauve) - \(1/16\) As a result, in the F2 generation, we observe a 9:1:4:1 ratio (yellow:blue:red:mauve).

Key concepts

Dihybrid Inheritance

Dihybrid inheritance is a fascinating concept in genetics that explains how two different traits are inherited through generations. In this concept, we are not just looking at a single trait, like flower color, but rather at two, which can be different alleles influencing a characteristic in organisms.
This type of inheritance was first described by Gregor Mendel during his pea plant experiments. When examining dihybrid inheritance, you typically observe a 9:3:3:1 ratio among the phenotypes in the \( F_2 \) generation.
This ratio suggests a combination of dominant and recessive allele pairs being inherited separately yet simultaneously, showing the law of independent assortment.
In our exercise, where flower colors are crossed, the resulting yellow, red, blue, and mauve flowers represent different combinations of these gene alleles.

Punnett Square

The Punnett Square is an extremely useful tool in genetics that aids in predicting the possible genotypes of offspring from a particular cross. It is structured like a grid that helps visualize how alleles from each parent might combine.
For a dihybrid cross, you use a four-by-four square because there are two genes moving independently. So, sixteen possible combinations can occur.
Each cell in the grid shows a potential genotype of the offspring.

• By determining genotype probabilities, the Punnett Square guides students in understanding how traits are likely to appear in subsequent generations.
• In our flower color example, it allows us to see how the offspring get their mix of alleles, leading to the various phenotypic expressions.

Though it looks a bit complex at first, once understood, it provides clear insight into genetic inheritance.

Phenotypic Ratios

Phenotypic ratios refer to the relative numbers of offspring manifesting different phenotypes, or observable traits, after a genetic cross. With dihybrid inheritance, like the plant color example, these ratios often spell out the story of genetic inheritance.
When two traits are examined at once through a dihybrid cross, we often see a 9:3:3:1 ratio, showing:

• 9 showing both dominant traits,
• 3 showing one dominant and one recessive trait,
• 3 showing the opposite dominant and recessive trait, and
• 1 showing both recessive traits.

This ratio illuminates how different alleles interact to create diverse phenotypic results in offspring.
Understanding these ratios helps in grasping the underlying principles of Mendelian genetics, as they highlight the predictability and mathematical nature of genetic inheritance.