In `F_(2)` progeny of dihybrid cross, the expected genotypic proportions of individuals homozygous for both dominant character is

Options

A. `3//16`
B. `9//16`
C. `12//16`
D. `1//16`

Answer

To solve the question regarding the expected genotypic proportions of individuals homozygous for both dominant characters in the F2 progeny of a dihybrid cross, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Dihybrid Cross**:
- A dihybrid cross involves two traits, each represented by two alleles. For example, let’s consider two traits: seed color (Yellow - Y, Green - y) and seed shape (Round - R, Wrinkled - r).
- The parental generation (P) can be represented as YYRR (homozygous dominant for both traits) crossed with yyrr (homozygous recessive for both traits).

2. **Determine the F1 Generation**:
- The F1 generation from this cross will all be heterozygous (YyRr) since they inherit one allele from each parent.

3. **Perform the F2 Generation Cross**:
- The F2 generation is obtained by crossing two F1 individuals (YyRr x YyRr).
- This can be represented in a Punnett square, which will show all possible combinations of alleles.

4. **Calculate the Genotypic Ratio**:
- The genotypic ratio from the F2 generation of a dihybrid cross is typically 1:2:1 for homozygous dominant, 2:4:2 for heterozygous, and 1:2:1 for homozygous recessive.
- For two traits, this results in a total of 16 combinations (4 for each trait).

5. **Identify Homozygous Dominant Combinations**:
- The combinations that are homozygous for both dominant traits (YYRR) can be identified:
- YYRR (1)
- YYRr (2)
- YyRR (2)
- YyRr (4)
- The only combination that is homozygous for both dominant traits is YYRR.

6. **Count the Total Combinations**:
- Out of the total 16 combinations, only 1 is YYRR.

7. **Calculate the Proportion**:
- The proportion of individuals that are homozygous for both dominant traits is 1 out of 16, which simplifies to 1/16.

### Final Answer:
The expected genotypic proportion of individuals homozygous for both dominant characters in the F2 progeny of a dihybrid cross is **1/16**.