Lethal mutations with fluctuating heterozygous effect: the lethal force of effective dominance

Abstract

The theory of population genetics leads to the expectation that in very large populations the frequencies of recessive lethal mutations are close to the square root of the mutation rate, corresponding to mutation-selection balance. There are numerous examples where the frequencies of such alleles are orders of magnitude larger than this result. In this work we theoretically investigate the role of temporal fluctuations in the heterozygous effect (h) for lethal mutations in very large populations. For fluctuations of h, around a mean value of $\bar{h}$, we find a biased outcome that is described by an effective dominance coefficient, h_eff, that is generally less than the mean dominance coefficient, i.e., ${h}_{{\rm{eff}}}\, < \, \bar{h}$. In the case where the mean dominance coefficient is zero, the effective dominance coefficient is negative: h_eff < 0, corresponding to the lethal allele behaving as though overdominant and having an elevated mean frequency. This case plausibly explains mean allele frequencies that are an order of magnitude larger than the equilibrium frequency of a recessive allele with a constant dominance coefficient. Our analysis may be relevant to explaining lethal disorders with anomalously high frequencies, such as cystic fibrosis and Tay-Sachs, and may open the door to further investigations into the statistics of fluctuations of the heterozygous effect.