Models of human genetic disease: how biased are the standard formulae?

Abstract

Standard theory provides a simple prediction for the frequency of a recessive lethal allele conferring heterozygous protection against an infectious disease (the best-known example being sickle cell protection against malaria). This relationship allows historic disease mortality rates to be estimated. There are, however, hidden biases in this approach. Reproductively active human females in archaic societies normally produce children at intervals of around 4 years. If death of the fetus or young infant (less than around 3 years of age) occurs, then the mother re-enters oestrus and produces another child. This ‘reproductive compensation’ reduces selection against the agent causing early mortality (the recessive allele or infective agent) and biases our estimates of historic mortality rates. The magnitude of these biases is investigated. Re-conception also constitutes a demographic selective pressure acting alongside natural selection: lethal genetic diseases (or tightly linked loci) will be selected to become ever more virulent, killing at ever decreasing ages, to allow the mother to re-enter oestrus and re-conceive a (hopefully unaffected) sibling; this effect also invalidates statistical tests using the number of alleles to distinguish overdominance from drift as explanations for high allele frequency. The same bias affects calculations of mutation/selection balance: for any given mutation rate, syndromes which kill early in life will reach much higher frequencies than those killing at later ages. An intriguing consequence is that lethal recessive disorders in humans will increase in frequency by up to 45% as a consequence of the recent demographic transition to planned family size.