When a hybrid (AaBbCcDd) is selfed then the genotypes AABbCCDd, AaBBCcDd, AaBbCcDd, aabbccdd would be in a proportion of :-

Options

A. `2 : 4 : 8 : 21`
B. `4 : 8 : 16 : 1`
C. `4 : 8 : 16 : 27`
D. `8 : 4 : 16 : 81`

Answer

To solve the problem of determining the proportions of the genotypes AABbCCDd, AaBBCcDd, AaBbCcDd, and aabbccdd when a hybrid (AaBbCcDd) is selfed, we can follow these steps:

### Step 1: Identify the Genotypes
We have the following genotypes to analyze:
1. AABbCCDd
2. AaBBCcDd
3. AaBbCcDd
4. aabbccdd

### Step 2: Determine Gamete Combinations
When we self a hybrid AaBbCcDd, we need to determine the possible gametes produced by this hybrid. Each gene can contribute two alleles (dominant or recessive), so for four genes (A, B, C, D), the possible gametes are:
- A or a
- B or b
- C or c
- D or d

The total number of gametes is \(2^4 = 16\).

### Step 3: Calculate Proportions for Each Genotype
Using the principles of Mendelian genetics, we can calculate the proportions for each genotype:

1. **AABbCCDd**:
- A: Homozygous dominant (1/4)
- B: Heterozygous (1/2)
- C: Homozygous dominant (1/4)
- D: Heterozygous (1/2)
- Proportion = \( \frac{1}{4} \times \frac{1}{2} \times \frac{1}{4} \times \frac{1}{2} = \frac{1}{64} \)

2. **AaBBCcDd**:
- A: Heterozygous (1/2)
- B: Homozygous dominant (1/4)
- C: Heterozygous (1/2)
- D: Heterozygous (1/2)
- Proportion = \( \frac{1}{2} \times \frac{1}{4} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{32} \)

3. **AaBbCcDd**:
- A: Heterozygous (1/2)
- B: Heterozygous (1/2)
- C: Heterozygous (1/2)
- D: Heterozygous (1/2)
- Proportion = \( \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{16} \)

4. **aabbccdd**:
- A: Homozygous recessive (1/4)
- B: Homozygous recessive (1/4)
- C: Homozygous recessive (1/4)
- D: Homozygous recessive (1/4)
- Proportion = \( \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} = \frac{1}{256} \)

### Step 4: Convert to Common Denominator
To express these proportions in a common ratio, we can multiply each proportion by 256 (the least common multiple of the denominators):

- AABbCCDd: \( \frac{1}{64} \times 256 = 4 \)
- AaBBCcDd: \( \frac{1}{32} \times 256 = 8 \)
- AaBbCcDd: \( \frac{1}{16} \times 256 = 16 \)
- aabbccdd: \( \frac{1}{256} \times 256 = 1 \)

### Step 5: Final Ratio
Thus, the final ratio of the genotypes AABbCCDd : AaBBCcDd : AaBbCcDd : aabbccdd is:
**4 : 8 : 16 : 1**