How to Calculate the Number of Individuals Carrying At Least One Dominant Allele Using Hardy-Weinberg Equilibrium

Understanding how many individuals in a population carry a specific allele is a fundamental question in genetics. The Hardy-Weinberg equilibrium provides a reliable framework for calculating genotype frequencies and, from them, the number of individuals carrying at least one copy of a given allele.

Problem Overview

• Population size: 400 individuals

• Number of homozygous for allele α (let’s call it AA): 36

• Population is in Hardy-Weinberg equilibrium

• Question: How many individuals carry at least one allele A?

Step 1: Calculate the Frequency of Homozygous AA

The frequency of AA individuals (p2p2) is:

p2=36400=0.09p2=40036=0.09

Step 2: Find the Frequency of the A Allele ($p$)

p=0.09=0.3p=0.09=0.3

Step 3: Find the Frequency of the a Allele ($q$)

$$q=1-p=1-0.3=0.7$$

Step 4: Calculate the Frequency of Heterozygotes (Aa)

The frequency of heterozygotes ($2pq$) is:

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

Step 5: Calculate the Frequency of Homozygous aa

q2=(0.7)2=0.49q2=(0.7)2=0.49

Step 6: Determine the Number of Individuals Carrying At Least One A Allele

Individuals carrying at least one A allele are those who are either AA or Aa:

Frequency=p2+2pq=0.09+0.42=0.51Frequency=p2+2pq=0.09+0.42=0.51$$\text{Number of individuals}=0.51\times 400=204$$

However, this value is not among the options. Let’s check the logic using the options and the context provided.

Alternate Approach: Exclude Homozygous aa

Individuals not carrying any A allele are only those with genotype aa (q2q2):

$$\text{Number of aa individuals}=0.49\times 400=196$$

So, the number of individuals carrying at least one A allele is:

$$400-196=204$$

Again, this matches our previous answer, but the closest provided option is 196. However, 196 is the number of individuals not carrying allele A (i.e., aa). The correct answer, based on Hardy-Weinberg calculations, is 204, but since the options do not include this, let’s review the intent:

• (1) 36 — number of AA individuals

• (2) 168 — not matching any calculation

• (3) 364 — not matching any calculation

• (4) 196 — number of aa individuals (those not carrying A)

Given the calculations, the number of individuals carrying at least one A allele should be 204, but if the question is interpreted as “those not carrying A,” then 196 is the correct figure for aa individuals. However, based on standard Hardy-Weinberg application and the intent to find those with at least one A, the calculation above is correct, but the provided options do not match.

Conclusion

The number of individuals carrying at least one allele A in this population is 204, but this value is not among the provided options. The closest interpretation from the options is (4) 196, which actually represents the number of individuals who do not carry allele A (homozygous aa). If you are asked for those carrying at least one A, the correct calculation is 204, but if you must choose from the options, none directly match the correct answer.