Problem 12 - Campbell Biology Concepts & Connections

Question

Sickle-cell disease is caused by a recessive allele. Roughly one out of every 400 African Americans \((0.25 \%)\) is afflicted with sickle-cell disease. Use the Hardy-Weinberg equation to calculate the percentage of African Americans who are carriers of the sickle-cell allele. (Hint: \(\left.q^{2}=0.0025 .\right)\)

Step-by-Step Solution

Answer

Approximately 9.5% of African Americans are carriers of the sickle-cell allele.

Step 1: Understand the Given Information

We are given that the frequency of individuals with sickle-cell disease \((q^2)\) is 0.0025. This is a key piece of information because it represents the frequency of the homozygous recessive genotype in the population.

Step 2: Calculate the Recessive Allele Frequency (q)

To find the frequency of the recessive allele (q), take the square root of \(q^2\). So, \( q = \sqrt{0.0025} = 0.05 \).

Step 3: Determine the Frequency of the Dominant Allele (p)

Using the Hardy-Weinberg principle, the frequency of the dominant allele (p) can be found using the equation \( p + q = 1 \). Therefore, \( p = 1 - q = 1 - 0.05 = 0.95 \).

Step 4: Calculate the Carrier Frequency (2pq)

Carriers of the sickle-cell allele have the heterozygous genotype (2pq). To find this frequency, use the equation \( 2pq = 2 \times p \times q \). Substituting the values, we get \( 2pq = 2 \times 0.95 \times 0.05 = 0.095 \).

Step 5: Convert Frequency to Percentage

To express the carrier frequency as a percentage, multiply by 100. So, \( 0.095 \times 100 = 9.5\text{\textpercent} \).

Key Concepts

Sickle-Cell Disease

Sickle-cell disease is a genetic condition that affects red blood cells. People who have this disease produce abnormal hemoglobin, which causes red blood cells to become sickle-shaped. These abnormal cells can block blood flow, leading to pain and other health problems. Sickle-cell disease is inherited in an autosomal recessive manner. This means a person needs to inherit two copies of the sickle-cell allele (one from each parent) to have the disease. If only one copy is inherited, a person will be a carrier but typically won't show symptoms.

Allele Frequency

Allele frequency, often represented by 'p' and 'q' in population genetics, refers to how often an allele appears in a population. For example, in the case of sickle-cell disease, 'q' is the frequency of the sickle-cell allele and 'p' is the frequency of the normal allele. These frequencies are part of the Hardy-Weinberg equation, where the sum of the frequencies of all alleles must equal 1 \(p + q = 1\). By knowing the frequency of the homozygous recessive genotype \(q^2\), we can calculate 'q' and then 'p'. This helps us understand the distribution of genetic traits in a population.

Carrier Frequency

Carrier frequency refers to the proportion of individuals in a population that carry one copy of a recessive allele for a trait or disorder. In the case of sickle-cell disease, carriers (heterozygotes) possess one sickle-cell allele and one normal allele. They are represented by the genotype '2pq' in the Hardy-Weinberg equation. By calculating '2pq', we can estimate how many people in the population are carriers. Using the given figures: \( q = 0.05\) and \( p = 0.95\), we find that \( 2pq = 2 \times 0.95 \times 0.05 = 0.095\), or 9.5% of the population. This is important for understanding the risk of passing the allele to offspring.