In polygenic inheritance, a trait is controlled by two pairs of genes. Two individuals which are heterozygous for both genes, crossed each other, such type of cross produces what phenotypic ratio ?

Options

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

Answer

To solve the question regarding the phenotypic ratio produced by a cross between two individuals that are heterozygous for two pairs of genes in polygenic inheritance, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Polygenic Inheritance**:
- Polygenic inheritance involves multiple genes (more than one) contributing to a single trait. In this case, we are dealing with two pairs of genes.

2. **Identifying the Genotypes**:
- Let's denote the two genes as A and B. Since both individuals are heterozygous for both genes, their genotypes can be represented as AaBb.

3. **Setting Up the Punnett Square**:
- To determine the offspring's genotypes, we can set up a Punnett square. Each parent can produce four types of gametes: AB, Ab, aB, and ab.
- The gametes from both parents can be combined in a 4x4 Punnett square.

4. **Filling in the Punnett Square**:
- The combinations from the Punnett square will yield the following genotypes:
- AABB
- AABb
- AaBB
- AaBb
- Aabb
- AAbb
- aaBB
- aaBb
- aabb

5. **Counting the Phenotypes**:
- The phenotypes can be categorized based on the presence of dominant alleles:
- **Phenotype 1**: A_B_ (at least one dominant A and one dominant B) - 9 occurrences
- **Phenotype 2**: A_bb (at least one dominant A and two recessive b) - 3 occurrences
- **Phenotype 3**: aaB_ (two recessive a and at least one dominant B) - 3 occurrences
- **Phenotype 4**: aabb (two recessive a and two recessive b) - 1 occurrence

6. **Determining the Phenotypic Ratio**:
- The resulting phenotypic ratio from the cross is 9:3:3:1.

7. **Final Answer**:
- Therefore, the phenotypic ratio produced by the cross of two individuals that are heterozygous for two pairs of genes is **9:3:3:1**.