The fraction of double homozygous recombinants in the `F_(2)` of a Mendelian dihybrid cross is

Options

A. `6//16`
B. `2//16`
C. `4//16`
D. `3//16`

Answer

To find the fraction of double homozygous recombinants in the F2 generation of a Mendelian dihybrid cross, follow these steps:

### Step 1: Understand the Dihybrid Cross
A dihybrid cross involves two traits, each controlled by different genes. For example, consider two traits: seed shape (round vs. wrinkled) and seed color (yellow vs. green). Each trait has two alleles:
- Round (R) is dominant over wrinkled (r)
- Yellow (Y) is dominant over green (y)

### Step 2: Determine the Parental Generation
In a typical dihybrid cross, the parental generation (P) is usually homozygous for both traits. For example:
- Parent 1: RRYY (homozygous round yellow)
- Parent 2: rryy (homozygous wrinkled green)

### Step 3: F1 Generation
The F1 generation will all be heterozygous for both traits:
- F1: RrYy (all offspring will have round yellow seeds)

### Step 4: F2 Generation
To obtain the F2 generation, we cross two F1 individuals:
- RrYy × RrYy

### Step 5: Create a Punnett Square
Construct a Punnett square for the F2 generation. Each parent can produce four types of gametes (RY, Ry, rY, ry). The resulting Punnett square will have 16 squares (4x4).

### Step 6: Identify Double Homozygous Recombinants
Double homozygous recombinants are individuals that are homozygous for both traits, meaning they have two dominant alleles or two recessive alleles. In this case, the double homozygous recombinants are:
- Round Yellow (RRYY)
- Wrinkled Green (rryy)

### Step 7: Count the Outcomes
From the Punnett square, count the occurrences of the double homozygous recombinants:
- RRYY (1 occurrence)
- rryy (1 occurrence)

### Step 8: Calculate the Fraction
There are 2 double homozygous recombinant outcomes out of a total of 16 outcomes in the F2 generation. Therefore, the fraction is:
\[ \text{Fraction of double homozygous recombinants} = \frac{2}{16} = \frac{1}{8} \]

### Step 9: Simplify the Fraction
The fraction can be simplified to:
\[ \frac{2}{16} = \frac{1}{8} \]

### Final Answer
The fraction of double homozygous recombinants in the F2 generation of a Mendelian dihybrid cross is \( \frac{2}{16} \).

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