If the frequency of hemophilia, an X-linked recessive disease, is 10% in males, what is the frequency of females with hemophilia?
From Google
Females can also have hemophilia, but this is much rarer. In such cases both X chromosomes are affected or one is affected and the other is missing or inactive. In these females, bleeding symptoms may be similar to males with hemophilia. A female with one affected X chromosome is a “carrier” of hemophilia.
I could not find the exact incidence of hemophilia in women.
To determine the frequency of females with hemophilia, we need to consider that hemophilia is an X-linked recessive disease. In humans, females have two X chromosomes (XX), while males have one X and one Y chromosome (XY). Since hemophilia is recessive and located on the X chromosome, females need to have two copies of the affected gene to express the disease, whereas males only need one copy.
Given that the frequency of hemophilia in males is 10%, we can infer that 10 out of every 100 males will have hemophilia. To find the frequency in females, we need to consider that these affected males receive their X chromosome from their carrier mothers.
Assuming that the population follows a Hardy-Weinberg equilibrium (no mutations, no migration, no natural selection, random mating), we can calculate the frequency of female carriers using the formula:
q = √(2 × p × q)
Where:
- p is the frequency of males with hemophilia (10% or 0.10)
- q is the frequency of carriers in females
By substituting the given value into the equation, we have:
q = √(2 × 0.10 × q)
To solve for q, we need to isolate it. Squaring both sides of the equation, we get:
q^2 = 0.20q
Rearranging the equation:
q^2 - 0.20q = 0
Factoring:
q(q - 0.20) = 0
This equation has two solutions: q = 0 and q = 0.20. However, q cannot be zero since there are affected males in the population. Therefore, the frequency of carriers in females is 0.20 or 20%.
To find the frequency of females with hemophilia, we multiply the carrier frequency by the probability that a female carrier will pass on the affected gene to her son. Since the affected gene is on the X chromosome, there is a 50% chance that a carrier mother will pass on the affected X chromosome to her son. Thus, the frequency of females with hemophilia is:
Frequency of females with hemophilia = Carrier frequency × Probability of passing on the affected gene
= 0.20 × 0.50
= 0.10 or 10%
Therefore, the frequency of females with hemophilia is 10%.