If a polygenic trait is controlled by 3 polygenes, what will be `F_(2)` phenotypic ratio?

Options

A. `1:6:15:20:15:6:1`
B. `1:4:6:4:1`
C. `1:6:10:30:10:6:1`
D. `1:4:15:20:15:4:1`

Answer

To determine the F2 phenotypic ratio for a polygenic trait controlled by three polygenes, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Polygenic Traits**:
- Polygenic traits are influenced by multiple genes. In this case, we have three polygenes (let's denote them as A, B, and C). Each gene can have two alleles: a dominant allele and a recessive allele.

2. **Genotype Combinations**:
- For three polygenes, the possible combinations of alleles can be represented as follows:
- Each gene can contribute either a dominant (A, B, C) or a recessive (a, b, c) allele.
- The combinations of these alleles will lead to different phenotypes.

3. **F1 Generation**:
- If we cross a homozygous dominant individual (AABBCC) with a homozygous recessive individual (aabbcc), the F1 generation will all be heterozygous (AaBbCc).

4. **F2 Generation**:
- When we self-cross the F1 generation (AaBbCc x AaBbCc), we can use a Punnett square or combinatorial methods to determine the phenotypic ratios.

5. **Calculating Phenotypic Ratios**:
- The phenotypic ratio for a trait controlled by three polygenes can be derived from the number of ways the dominant and recessive alleles can combine.
- The resulting phenotypic ratio for three polygenes is typically 1:6:15:20:15:6:1.

6. **Conclusion**:
- Therefore, the F2 phenotypic ratio for a polygenic trait controlled by three polygenes is **1:6:15:20:15:6:1**.

### Final Answer:
The F2 phenotypic ratio for a polygenic trait controlled by three polygenes is **1:6:15:20:15:6:1**.