Inferring Parameters of the Distribution of Fitness Effects of New Mutations When Beneficial Mutations Are Strongly Advantageous and Rare

Abstract

Characterizing the distribution of fitness effects (DFE) for new mutations is central in evolutionary genetics. Analysis of molecular data under the McDonald-Kreitman test has suggested that adaptive substitutions make a substantial contribution to between-species divergence. Methods have been proposed to estimate the parameters of the distribution of fitness effects for positively selected mutations from the unfolded site frequency spectrum (uSFS). Such methods perform well when beneficial mutations are mildly selected and frequent. However, when beneficial mutations are strongly selected and rare, they may make little contribution to standing variation and will thus be difficult to detect from the uSFS. In this study, I analyze uSFS data from simulated populations subject to advantageous mutations with effects on fitness ranging from mildly to strongly beneficial. As expected, frequent, mildly beneficial mutations contribute substantially to standing genetic variation and parameters are accurately recovered from the uSFS. However, when advantageous mutations are strongly selected and rare, there are very few segregating in populations at any one time. Fitting the uSFS in such cases leads to underestimates of the strength of positive selection and may lead researchers to false conclusions regarding the relative contribution adaptive mutations make to molecular evolution. Fortunately, the parameters for the distribution of fitness effects for harmful mutations are estimated with high accuracy and precision. The results from this study suggest that the parameters of positively selected mutations obtained by analysis of the uSFS should be treated with caution and that variability at linked sites should be used in conjunction with standing variability to estimate parameters of the distribution of fitness effects in the future.

Keywords: adaptation; beneficial mutations; distribution of fitness effects; population genetics.

Figure 1

Population genetic summary statistics collated across all simulated genes. α_Obs is the observed proportion of substitutions fixed by positive selection. π_s/π₀ is genetic diversity relative to neutral expectation (π₀ = 0.01). S_Adv./S is the proportion of segregating nonsynonymous sites that are advantageous in the simulated datasets.

Figure 2

The uSFS for advantageous mutations under different combinations of positive selection parameters. The three bar charts show observed uSFS from simulations that model positive selection parameters that yield similar α. The lines in each panel show the expected frequency spectra for different strengths of beneficial mutations and were obtained using Equation 2 from Tataru et al., (2017).

Figure 3

Estimates of the parameters of advantageous mutations and the proportion of adaptive substitutions they imply from simulated datasets. A) γ_a is the inferred selective effect of a new advantageous mutation; B) p_a is the proportion of new mutations that are beneficial, the horizontal dashed gray lines indicate the simulated values in each case; C) α_DFE is the proportion of adaptive substitutions expected under the inferred DFE, the dashed lines indicate α_Obs, the proportion of adaptive substitutions observed in the simulated datasets. Error bars indicate the 95% range of 100 bootstrap replicates.

Figure 4

The likelihood surface for the γ_a and p_a parameters for three simulated datasets. Hue indicates differences in log likelihood between a particular parameter combination and the best-fitting model. Best fitting models are indicated by red points and the true parameters are given above the plots and indicated by the white plus signs on the likelihood surface. The relation γ_ap_a = 0.1 is shown as a turquoise line and is constant across the three datasets shown.