31. A three point test cross was carried out in Drosophila melanogaster involving three adjacent genes X, Y and Z. arranged in the same order. The distance between X to Y is 32.5 map unit (mu) and that between Y to Z is 20.5 map. The coefficient of coincidence = 0.886.
What is the percentage of double recombinants in the progeny obtained from the testcross?
(1) 6%        (2) 8%
(3) 12%       (4) 16%

Introduction:

In genetics, a three point test cross is a powerful technique for mapping gene order and distances on chromosomes. This method involves analyzing three linked genes to estimate recombination frequencies and crossover events. Understanding how to calculate the percentage of double recombinants aids in elucidating genetic linkage and interference. Here we solve a problem involving genes X, Y, and Z in Drosophila melanogaster, focusing on the application of map units and coefficient of coincidence.

Detailed Explanation:

Given:

• Three genes: X, Y, Z arranged in order on a chromosome.

• Distance (map units) between X-Y = 32.5 map units (mu).

• Distance (map units) between Y-Z = 20.5 mu.

• Coefficient of coincidence (c.o.c) = 0.886.

Step 1: Understand map units and recombination frequency

• One map unit corresponds to 1% recombination frequency.

• This means, between X and Y, recombination frequency is 32.5% and between Y and Z is 20.5%.

Step 2: Calculate the expected percentage of double recombinants

• Double recombination frequency is the product of individual recombination frequencies:

  Expected double recombinants = (Recombination frequency X-Y) × (Recombination frequency Y-Z)

  = 0.325 × 0.205 = 0.066625 or 6.6625%

Step 3: Calculate the actual double recombinant frequency using coefficient of coincidence

• Coefficient of coincidence = Actual double recombinants / Expected double recombinants.

• Rearranged to find actual double recombinants:

  Actual double recombinants = c.o.c × Expected double recombinants

  = 0.886 × 6.6625% = approximately 5.9%

Step 4: Compare to given options

• (1) 6% – Closest to calculated 5.9%

• (2) 8% – Higher than calculation

• (3) 12% – Much higher

• (4) 16% – Much higher

Thus, the best answer is option (1) 6%.

Explanation of Other Options:

• Option (2) 8%: Overestimates the double recombinants, ignoring coefficient of coincidence.

• Option (3) 12% and (4) 16%: Far exceed the expected recombination rates derived from distances and coefficient of coincidence, making these incorrect.

This calculation shows how the coefficient of coincidence refines expected values by accounting for interference during crossing over, offering a more realistic estimate of double recombination frequency in progeny.

This article uses the genetic mapping concepts and formulas to solve a classical problem in Drosophila genetics with clarity for students preparing for competitive exams like CSIR NET or RPSC.

References:
The methodology is derived from standard genetics principles on three point test crosses, recombination frequencies, map units, and coefficient of coincidence calculations.