Inferring the distribution of selective effects from a time inhomogeneous model

Abstract

We have developed a Poisson random field model for estimating the distribution of selective effects of newly arisen nonsynonymous mutations that could be observed as polymorphism or divergence in samples of two related species under the assumption that the two species populations are not at mutation-selection-drift equilibrium. The model is applied to 91Drosophila genes by comparing levels of polymorphism in an African population of D. melanogaster with divergence to a reference strain of D. simulans. Based on the difference of gene expression level between testes and ovaries, the 91 genes were classified as 33 male-biased, 28 female-biased, and 30 sex-unbiased genes. Under a Bayesian framework, Markov chain Monte Carlo simulations are implemented to the model in which the distribution of selective effects is assumed to be Gaussian with a mean that may differ from one gene to the other to sample key parameters. Based on our estimates, the majority of newly-arisen nonsynonymous mutations that could contribute to polymorphism or divergence in Drosophila species are mildly deleterious with a mean scaled selection coefficient of -2.81, while almost 86% of the fixed differences between species are driven by positive selection. There are only 16.6% of the nonsynonymous mutations observed in sex-unbiased genes that are under positive selection in comparison to 30% of male-biased and 46% of female-biased genes that are beneficial. We also estimated that D. melanogaster and D. simulans may have diverged 1.72 million years ago.

Fig 1. True vs. estimated values of the four model parameters.

The true values (x-axes) of the four parameters (μ_γ, σ_b, σ_w, t_div) and their corresponding model estimates (y-axes) (${\widehat{\mu }}_{\gamma },{\widehat{\sigma }}_b,{\widehat{\sigma }}_w,{\widehat{t}}_{\text{div}}$) for the two simulated data sets. Straight lines represent y = x.

Fig 2. Distribution of selective effects.

Estimated distribution of scaled selection coefficients γ of newly arisen nonsynonymous mutations that have been observed as polymorphism or divergence within Drosophila species. The distributions infer only for those mutations whose selective effects are not so severe such that there is a reasonable chance for these mutations to accumulate high frequencies in a population and hence to be included in a relatively small sample. Three distributions are based on the estimates of the 33 male-biased genes (yellow), 28 female-biased genes (gray), and 30 sex-unbiased genes (red).

Fig 3. Estimated selection coefficients for the three gene classes.

Median estimates of the scaled selection coefficient γ for the male-biased, female-biased, and sex-unbiased genes with the loci sorted by the values of the estimates. Error bars represent 95% credible intervals.

Fig 4. Estimates of the expected population proportions.

Median estimates of the expected population proportions of positively selected nonsynonymous mutations among newly arisen new mutations (N), sample polymorphisms (S), and sample fixed differences (F) with error bars representing 95% credible intervals. Proportions are calculated based on the 33 male-biased genes (yellow), 28 female-biased genes (gray), 30 sex-unbiased genes (red), and the 91 genes together (purple).