In quantitative inheritance, when a character is controlled by two pair of genes, the ratio obtained in `F_(2)` generation is …………

Options

A. `1:2:1`
B. `1:4:6:4:1`
C. `9:3:3:1`
D. `1:6:15:20:15:6:1`

Answer

To determine the ratio obtained in the F2 generation when a character is controlled by two pairs of genes in quantitative inheritance, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Quantitative Inheritance**:
- Quantitative inheritance, also known as polygenic inheritance, involves multiple genes (more than one pair) influencing a single trait. This results in a continuous range of phenotypes.

2. **Identify the Number of Genes**:
- In this case, we are looking at a character controlled by two pairs of genes. Let's denote these genes as A and a (first pair) and B and b (second pair).

3. **Determine the Possible Combinations**:
- Each gene can have two alleles. Therefore, for two pairs of genes, the possible combinations of alleles in the F2 generation can be calculated using the binomial expansion.
- The combinations can be represented as:
- AABB (homozygous dominant for both traits)
- AABb, AaBB, AaBb (various combinations of dominant and recessive alleles)
- AAbb, Aabb, aaBB, aaBb, aabb (homozygous recessive for both traits)

4. **Calculate the F2 Generation Ratio**:
- When two pairs of genes are involved, the phenotypic ratio in the F2 generation typically follows the pattern of 1:4:6:4:1. This ratio arises from the distribution of phenotypes based on the combinations of dominant and recessive alleles.

5. **Select the Correct Option**:
- Among the given options, the ratio 1:4:6:4:1 corresponds to the F2 generation of a trait controlled by two pairs of genes.
- Other options represent ratios from different types of crosses (monohybrid or trihybrid) and are therefore incorrect.

### Final Answer:
The ratio obtained in the F2 generation when a character is controlled by two pairs of genes in quantitative inheritance is **1:4:6:4:1**.

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