Question

The number of recombinants in the 1280 progeny obtained through a dihybrid cross of Mendel in the F₂ generation.

• A. 240
• B. 360
• C. 720
• D. 480

Hint:

In a dihybrid cross, recombinants appear with a probability of \( \frac{6}{16} \) (or \( \frac{3}{8} \)) of the total progeny.

Answer 1

The Correct Option is D

Step 1: Understanding Recombinants in a Dihybrid Cross In a Mendelian dihybrid cross, the recombinant frequency follows a \(9:3:3:1\) phenotypic ratio. Recombinants are those that do not resemble the parental types. 
Step 2: Calculating the Expected Recombinants The fraction of recombinants is given by: \[ \frac{3+3}{16} = \frac{6}{16} = \frac{3}{8} \] Multiplying by the total progeny: \[ \frac{3}{8} \times 1280 = 480. \]

Answer 2

1. Understand Mendel's Dihybrid Cross F₂ Ratio:

In a typical Mendelian dihybrid cross (e.g., RrYy x RrYy), assuming independent assortment, the F₂ generation exhibits a phenotypic ratio of 9:3:3:1.

• 9/16: Dominant for both traits (Parental Type 1, e.g., Round Yellow if parents were RRYY x rryy)
• 3/16: Dominant for trait 1, Recessive for trait 2 (Recombinant Type 1, e.g., Round Green)
• 3/16: Recessive for trait 1, Dominant for trait 2 (Recombinant Type 2, e.g., Wrinkled Yellow)
• 1/16: Recessive for both traits (Parental Type 2, e.g., Wrinkled Green)

2. Identify Recombinant Phenotypes:

Recombinants are the progeny showing new combinations of traits compared to the original P generation parents. In the F₂ generation, these correspond to the middle two categories of the 9:3:3:1 ratio.

3. Calculate the Proportion of Recombinants:

The proportion of recombinant phenotypes in the F₂ generation is the sum of the proportions of the two recombinant classes:

Proportion of Recombinants = 3/16 (Recombinant Type 1) + 3/16 (Recombinant Type 2) = 6/16

This fraction can be simplified to 3/8.

4. Calculate the Number of Recombinants in the Given Progeny:

The total number of progeny obtained is given as 1280.

Number of Recombinants = (Proportion of Recombinants) × (Total Number of Progeny)

Number of Recombinants = (6/16) × 1280

Alternatively, using the simplified fraction:

Number of Recombinants = (3/8) × 1280

Number of Recombinants = 3 × (1280 / 8)

Number of Recombinants = 3 × 160

Number of Recombinants = 480

Conclusion: The expected number of recombinants in the 1280 progeny is 480.

This corresponds to Option D.