Joint Prediction of the Effective Population Size and the Rate of Fixation of Deleterious Mutations

Abstract Mutation, genetic drift, and selection are considered the main factors shaping genetic variation in nature. There is a lack, however, of general predictions accounting for the mutual interrelation between these factors. In the context of the background selection model, we provide a set of equations for the joint prediction of the effective population size and the rate of fixation of deleterious mutations, which are applicable both to sexual and asexual species. For a population of N haploid individuals and a model of deleterious mutations with effect s appearing with rate U in a genome L Morgans long, the asymptotic effective population size (Ne) and the average number of generations (T) between consecutive fixations can be approximated by Ne≈N exp [−2U/(2s +L) (1−1/UT)3] and T≈[exp(2sNe) −1]/[2UsNe]. The solution is applicable to Muller’s ratchet, providing satisfactory approximations to the rate of accumulation of mutations for a wide range of parameters. We also obtain predictions of the effective size accounting for the expected nucleotide diversity. Predictions for sexual populations allow for outlining the general conditions where mutational meltdown occurs. The equations can be extended to any distribution of mutational effects and the consideration of hotspots of recombination, showing that Ne is rather insensitive and not proportional to changes in N for many combinations of parameters. This could contribute to explain the observed small differences in levels of polymorphism between species with very different census sizes.