In a polygenic inheritance of skin colours controlled by two gene pairs, how many phenotypes, mulattoes and total progenies are formed in `F_(2)`

Options

A. 3, 3, 16 respectively
B. 5, 6, 16 respectively
C. 7, 20, 64 respectively
D. 7, 6, 16 respectively

Answer

To solve the question regarding the polygenic inheritance of skin color controlled by two gene pairs, we need to follow these steps:

### Step 1: Understand the Genes Involved
In polygenic inheritance, multiple genes contribute to a single trait. Here, we have two gene pairs (let's denote them as A/a and B/b) that control skin color.

### Step 2: Determine the Possible Alleles
Each gene can have two alleles:
- Gene A: A (dominant) and a (recessive)
- Gene B: B (dominant) and b (recessive)

### Step 3: Determine the Genotypes of the Parents
Assuming we are crossing two individuals that are both heterozygous for both traits, the parental genotypes would be:
- Parent 1: AABB
- Parent 2: aabb

### Step 4: Create a Punnett Square
To find the F2 generation, we first need to determine the gametes produced by each parent. The gametes from the heterozygous parents (AaBb) would be:
- AB, Ab, aB, ab

We can set up a Punnett square to visualize the combinations of these gametes.

### Step 5: Calculate the Total Progeny
When we cross AaBb with AaBb, we will get a 4x4 Punnett square, leading to a total of 16 possible combinations (progeny).

### Step 6: Determine the Phenotypes
In this case, the phenotypes can be categorized based on the combinations of dominant and recessive alleles:
1. **AABB** - Darkest skin color
2. **AABb** - Dark skin color
3. **AaBB** - Dark skin color
4. **AABb** - Dark skin color
5. **Aabb** - Medium skin color
6. **Aabb** - Medium skin color
7. **aaBB** - Light skin color
8. **Aabb** - Medium skin color
9. **aabb** - Lightest skin color

### Step 7: Count the Unique Phenotypes
From the combinations, we can categorize the phenotypes:
- Dark skin (3 combinations)
- Medium skin (3 combinations)
- Light skin (2 combinations)
- Lightest skin (1 combination)

Thus, we have a total of **5 unique phenotypes**.

### Step 8: Identify the Number of Mulattoes
Mulattoes typically refer to individuals with a mixed phenotype, often associated with medium skin color. In our case, we have identified **3 combinations** that can be classified as mulattoes.

### Final Summary
- Total progeny in F2 = 16
- Total phenotypes = 5
- Total mulattoes = 3