Calculating Genotype Numbers in a Hardy-Weinberg Population: Red, Pink, and White Flowered Plants

The Hardy-Weinberg equilibrium allows us to predict genotype frequencies in a population if allele frequencies remain constant and the population is not affected by evolutionary forces. Here’s how you can use this principle to determine the number of homozygous dominant (red flowered, RF) and heterozygous (pink flowered, PF) plants when given the percentage of recessive homozygotes (white flowered, WF).

Problem Overview

• Total population: 14,000 plants

• Recessive homozygotes (white flowers, WF): 40% of the population

We are to find:

• Number of homozygous dominant red flowered (RF) plants

• Number of heterozygous pink flowered (PF) plants

Step 1: Assign Alleles and Genotypes

• Let R = allele for red flowers (dominant)

• Let r = allele for white flowers (recessive)

• RR = Homozygous dominant (red flowers, RF)

• Rr = Heterozygous (pink flowers, PF)

• rr = Homozygous recessive (white flowers, WF)

Step 2: Calculate Recessive Allele Frequency

• Frequency of rr = q2=0.40q2=0.40

• q=0.40≈0.6325q=0.40≈0.6325

• $p=1-q=1-0.6325=0.3675$

Step 3: Find Genotype Frequencies

• RR (homozygous dominant): p2=(0.3675)2≈0.135p2=(0.3675)2≈0.135

• Rr (heterozygous): $2pq=2\times 0.3675\times 0.6325\approx 0.465$

• rr (homozygous recessive): q2=0.40q2=0.40

Step 4: Calculate Number of Individuals

• Number of RR (RF): $0.135\times 14,000=1,890$

• Number of Rr (PF): $0.465\times 14,000=6,510$

• Number of rr (WF): $0.40\times 14,000=5,600$

Step 5: Match to Provided Options

• (1) RF-5600 PF-1891

• (2) RF-1891 PF-6508

• (3) RF-5600 PF-6508

• (4) RF-5145 PF-8855

The closest match to the calculated values is (2) RF-1891 PF-6508.

Conclusion

In a Hardy-Weinberg population of 14,000 plants where 40% are white-flowered recessive homozygotes, the number of homozygous dominant red-flowered plants is approximately 1,891, and the number of heterozygous pink-flowered plants is approximately 6,508.

Correct answer: (2) RF-1891 PF-6508