A woman may become a carrier of an X-linked condition in genetic equilibrium for the population by inheritance of the condition:
(1) from her mother who is a carrier (risk = (female population frequency) / 2)
(2) as a new mutation from a normal mother (risk = female mutation rate)
(3) from her father who is an affected (risk = (male population frequency) * (fitness))
(4) as a new mutation from a normal father (risk = male mutation rate)
where:
• fitness = ability of affected individual to pass on their genotype to offspring
• fitness ranges from 0 to 1
• a fitness = 0 indicates that the patient is sterile, incapable of reproducing or dies before being able to reproduce
• a fitness = 1 indicates that the patient is able to reproduce the same as unaffected brothers
population frequency of female carriers =
= N * (female mutation rate) =
= ((2 * (female mutation rate)) + (2 * (fitness) * (female mutation rate)) + (2 * (male mutation rate))) / (1 - (fitness))
N =
= ((2 * (female mutation rate)) + (2 * (fitness) * (female mutation rate)) + (2 * (male mutation rate))) / ((female mutation rate) * (1 - (fitness)))
population frequency of affected males =
= M * (male mutation rate) =
= (((female mutation rate) + ((fitness) * (female mutation rate)) + (male mutation rate)) / (1 - (fitness)))+ (female mutation rate)
M =
= (((female mutation rate) + ((fitness) * (female mutation rate)) + (male mutation rate)) / ((male mutation rate) * (1 - (fitness)))) + ((female mutation rate) / (male mutation rate))
If the male mutation rate is the same as the female mutation rate, then
N =
= (4 + (2* fitness)) / (1 - (fitness))
M =
= 3 / (1 - (fitness))
