### Description

The population frequencies for female carriers and affected males of an X-linked recessive genetic condition can be predicted from the mutation rates and reproductive fitness of affected males.

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))