54. The frequencies of two alleles p and q for a gene locus in a population at Hardy-Weinberg equilibrium are 0.3 and 0.7, respectively. After a few generations of inbreeding, the
    heterozygote frequency was found to be 0.28, The inbreeding coefficient will be
    (1) 0.42 (2) 0.28
    (3) 0.33 (4) 0.67

 

Problem Overview

• Allele frequencies:

  • $p=0.3$

  • $q=0.7$

• Observed heterozygote frequency after inbreeding:

  • $H=0.28$

• Population at Hardy-Weinberg equilibrium before inbreeding

Step 1: Calculate Expected Heterozygote Frequency (Hardy-Weinberg)

Under Hardy-Weinberg equilibrium, the expected frequency of heterozygotes ($2pq$) is:

$$2pq=2\times 0.3\times 0.7=0.42$$

Step 2: Use the Inbreeding Coefficient Formula

The inbreeding coefficient (F) can be calculated by comparing the observed heterozygote frequency (H) to the expected Hardy-Weinberg value:

F=2pq−H2pqF=2pq2pq−H

Where:

• $2pq$ = expected heterozygote frequency

• $H$ = observed heterozygote frequency after inbreeding

Step 3: Plug in the Values

F=0.42−0.280.42=0.140.42≈0.33F=0.420.42−0.28=0.420.14≈0.33

Step 4: Match with the Provided Options

• (1) 0.42

• (2) 0.28

• (3) 0.33

• (4) 0.67

The correct answer is (3) 0.33.

Why This Calculation Matters

• Population health: High inbreeding coefficients indicate increased risk of genetic disorders.

• Conservation: Helps manage genetic diversity in endangered populations.

• Animal and plant breeding: Guides breeders in maintaining healthy genetic pools.

In summary:
When the observed heterozygote frequency is lower than expected under Hardy-Weinberg equilibrium, the inbreeding coefficient quantifies this reduction. In this example, the inbreeding coefficient is 0.33, reflecting a significant impact of inbreeding on genetic diversity.