USA Biology Olympiad (USABO) Practice Exam

In a population affected by an autosomally recessive inherited disorder frequency of 1 in 4, what is the proportion of carrier individuals assuming Hardy-Weinberg equilibrium?

1. 25%

2. 50%

3. 75%

4. 100%

The correct answer is: 50%

In a population where an autosomally recessive disorder has a frequency of 1 in 4, we can use the Hardy-Weinberg principle to determine the proportion of carrier individuals. In this case, the frequency of affected individuals (those expressing the disorder) is represented by "q²." Given that the frequency is 1 in 4, we can say that q² = 0.25. Taking the square root of both sides, we find that q = 0.5. This represents the frequency of the recessive allele in the population. To find the frequency of the dominant allele (p), we can use the equation p + q = 1. Substituting the value of q, we have: p + 0.5 = 1, which gives us p = 0.5. Next, we are interested in the frequency of carriers, which are heterozygous individuals (genotype Aa). The frequency of carriers can be calculated using the formula 2pq, where p is the frequency of the dominant allele and q is the frequency of the recessive allele: 2pq = 2(0.5)(0.5) = 0.5. Therefore, the proportion