Question

6. Suppose that the X-linked recessive condition Duchenne muscular dystrophy affects 1 in 3600 males in the United States. Assume that the only two alleles present are normal and disease-causing and that the population is in Hardy-Weinberg equilibrium. If the population of females in the United States is 160 million, how many females in the country do you expect to have the disease? HINT: Begin by calculating the allele frequencies from the hemizygous males of the U.S. population.

Answer 1

To calculate the number of females with Duchenne muscular dystrophy in the United States, we need to determine the allele frequencies from hemizygous males. Using a frequency of 1 in 3600 for affected males, we can calculate the allele frequencies and then estimate the number of affected females based on the female population.

Step-by-step explanation:

To calculate the number of females expected to have Duchenne muscular dystrophy in the United States, we need to calculate the allele frequencies from the hemizygous males in the population.

Given that 1 in 3600 males are affected by the condition, the allele frequency for the disease-causing allele (a) can be calculated as 1/3600 = 0.0002778. Since this is a recessive condition, the frequency of the normal allele (A) can be calculated as 1 - 0.0002778 = 0.9997222.

Now we can calculate the expected number of females with the disease. Since the population of females in the United States is 160 million, we can multiply this by the recessive allele frequency to get the expected number of affected females: 160,000,000 * 0.0002778 = 44,448. Therefore, we expect approximately 44,448 females in the United States to have Duchenne muscular dystrophy.

Answer 2

In a U.S. population of 160 million females, and given the frequency of the dystrophy-causing allele, about 44,444 females are expected to have Duchenne muscular dystrophy.

If the disease affects 1 in 3,600 males, this means the frequency of the disease-causing allele (q) is 1/60. The normal allele frequency (p) then is 1-q, which is 59/60.

In the Hardy-Weinberg equilibrium, the genotypic frequency of homozygous recessive females is q².

Therefore, we can expect (1/60)² * 160,000,000

= 44,444 females to have Duchenne muscular dystrophy.