The history of a lethal X-linked mutant

Much attention has recently been focused upon the role of linkage analysis in genetic counselling, and enthusiasm has led to some misleading claims. While linkage analysis will undoubtedly play an important role for traits where there are extensive pedigrees of cases, it can achieve nothing where each case is the sole appearance of a mutation. The situation for a lethal recessive X-linked trait lies, in probabilistic terms, close to this latter extreme, particularly in the current world of small families. In view of current practice and research, it seems important to have a precise quantitative assessment of the patterns of carriers and cases generated by such an X-linked lethal mutation, with particular reference to the problem of Duchenne muscular dystrophy. In this paper a branching-process analysis is used to provide such an assessment. This approach has the advantage of requiring neither possibly unrealistic equilibrium assumptions nor assumptions about mutation rates. It also allows the effects of a variety of family size distributions to be analysed. It is found that an X-linked recessive lethal mutation produces few cases (if any), and will do so within a very few generations of its occurrence. Within the usual range of modern family size distributions the mean time to appearance is remarkably constant. The mean number of carriers at the time of the first case is small, as is the expected number of future cases. Except where the family size distribution has large variance, a high proportion of cases are the first in their family.