Risk of Recurrence and Carrier Frequency for X-Linked Lethal Recessives

It is generally supposed that one third of cases of a genetically lethal, fully penetrant, completely recessive X-linked trait are fresh mutations. This principle is explored here in detail. First, it is shown that the probability of a reproducing female being a carrier is roughly four times the mutation rate. A similar but not exactly equal result is found under the assumption that, ignoring all other information, the posterior probability of being a carrier for a woman with one affected son is two thirds. The closeness of the results under differing starting assumptions lends weight to the principle of Morton and Chung as an excellent approximation. In genetic counseling, the expected value of the quoted posterior probability when there is only one affected son is a function of the distribution of family size in the population: numerical tables illustrate the effects of different distributions on the values of quoted posterior probability and the insensitivity of this posterior probability to changes in the mutation rate.