The distribution of fitness effects varies phylogenetically across animals

Abstract

The distribution of fitness effects (DFE) describes the selection coefficients ( $s$ ) of newly arising mutations and fundamentally influences population genetic processes. However, the extent and mechanisms of DFE variation have not been systematically investigated across species with divergent phylogenetic histories and ecological functions. Here, we inferred the DFE in natural populations of eleven animal (sub)species, including humans, mice, fin whales, vaquitas, wolves, collared flycatchers, pied flycatchers, halictid bees, Drosophila, and mosquitoes. We find that the DFE co-varies with phylogeny, where the expected mutation effects are more similar in closely related species ( $Pagel\text{'}s\lambda =0.84,P=0.01$ ). Additionally, mammals have a higher proportion of strongly deleterious mutations (22% to 47% in mammals; 0.0% to 5.4% in insects and birds) and a lower proportion of weakly deleterious mutations than insects and birds. Population size is significantly negatively correlated with the expected impact of new deleterious mutations ( ${PGLS}_{\lambda },P=0.03$ ), and the proportion of new beneficial mutations ( $R_{\text{adj}}^2=0.73,P<0.001$ ). These findings align with Fisher's Geometric Model (FGM), which defines organismal complexity as the number of phenotypes under selection. Consistent with the FGM's predictions, we observe that mutations are more deleterious in complex organisms, while beneficial mutations occur more frequently in smaller populations to compensate for the drift load. Our study demonstrates strong phylogenetic constraints in the evolution of a fundamental population genetics parameter, and proposes that, through mechanisms of global epistasis, long-term population size and organismal complexity drive variation in the DFE across animals.

Keywords: Fisher’s geometric model; deleterious variations; distribution of selection coefficients; effective population size; organismal complexity.

Figure 1:

Mutations are more deleterious in mammals compared to insects and birds. (A) The phylogenetic relationship among the (sub)species included in this study (n = 11). (B) Assuming a gamma-distributed DFE of neutral and deleterious mutations, the expected deleterious mutation effects ($E[|s|]$) for eleven (sub)species. From top to bottom, species are increasingly divergent from humans: mice, fin whales, vaquitas, arctic wolves, gray wolves, collared flycatchers, pied flycatchers, halictid bees, Drosophila and mosquitoes. Numbers show the ranks of $E[|s|]$. (C) The shape parameter ($\alpha$) in the gamma-distributed DFE for eleven (sub)species. Numbers show the ranks of α. (D) Proportions of mutations in various categories of $|s|$. From left to right, mutations range from (nearly) neutral $\left(-{10}^{-5}<s\le 0\right)$ to very strongly deleterious $(s<-0.01)$. (E) The inferred probability point mass at $s=0(p_{\text{neu}}$) assuming a gamma-distributed DFE with a neutral point mass (neugamma DFE). In species where the Akaike Information Criterion (AIC) for the neugamma DFE is higher than that for the gamma DFE, which are mosquitoes, gray wolves and vaquitas, the bars are marked as translucent. (B-E) Gray lines represent 95% confidence intervals derived from 200 Poisson-resampled SFS.

Figure 2:

Model-averaged DFE estimates using full SFS or singleton-masked SFS. The estimates are weighted-averages of six DFE and demographic inference runs per species, combining outputs from gamma-, neugamma-, lognormal-distributed DFE given two-epoch or three-epoch demographic models by their AIC. Panels show whether full SFS or singleton-masked SFS is used in the inference. For results corresponding to singleton-masking treatments in Fig. 1, refer to Fig. S15. (A) The model-averaged expected deleterious mutation effects ($E[|s|]$) for eleven (sub)species. Numbers show the ranks of $E[|s|]$. (B) The model-averaged proportions of mutations in various categories of $|s|$. From left to right, mutations range from (nearly) neutral $\left(-{10}^{-5}<s\le 0\right)$ to very strongly deleterious $(s<-0.01)$. (A-B) Gray lines represent 95% confidence intervals.

Figure 3:

Grid-search-based likelihood-ratio tests confirm the phylogenetic signal in DFE evolution. (A-C) The log-likelihood surfaces for the shape ($\alpha$) and scale (${\beta }^{\prime }$) parameters (A) under the null model where all species are constrained to the same parameters or under the alternative model allowing species’ parameters to vary in representative (B) fin whales and (C) Drosophila datasets (other species’ log-likelihood surfaces shown in Fig. S17). Background colors from yellow to red indicate the differences in log-likelihood for given parameters to data. On each log-likelihood surface, the maximum likelihood estimate (MLE) derived for (A) the null model or (B-C) the alternative model in respective species is overlaid as the asterisk. In (A), the colored points showing MLEs for each species derived from the alternative model are overlaid for comparison. The two wolves datasets’ MLEs derived from parameter optimization procedures (Fig. 1) exceed the grid-search derived MLE plotted here. For all other species, the MLEs from the grid search and parameter optimization are the same. (D) Pairwise LRT statistics ($\mathrm{\Lambda }$) for each species pair is colored on a log10 scale and hierarchically clustered. Darker cells represent more similar DFE estimates in the species compared, such as the human-mouse pair, whereas lighter cells represent more distinct DFEs, such as the human-Drosophila pair. The dendrogram derived from hierarchical clustering is annotated. (E) The boxplot of pairwise LRT statistics in (D), categorized by whether species pair belong to the same Class. The y-axis is in log10 scale.

Figure 4:

Long-term population size ($N_a$) and body mass are correlated with the expected mutation effects ($E[|s|]$), but $N_a$ does not explain all the variations in the DFE across species. The phylogenetic generalized least square model with simultaneously inferred phylogenetic signal (${\mathrm{P}\mathrm{G}\mathrm{L}\mathrm{S}}_{\lambda }$) was fitted for $E[|s|]$ with (A-C) long-term population size, (D-F) body mass, and other life history traits (Figs. S19, S20). $E[|s|]$ were computed from (A,D) gamma DFE, (B,E) model-averaged DFE using full SFS or (C,F) model-average DFE using singleton-masked SFS. The ${\mathrm{P}\mathrm{G}\mathrm{L}\mathrm{S}}_{\lambda }$ results are overlaid as a dashed black line, with equations, inferred phylogenetic signal ($\lambda$), and likelihood-ratio derived p-value annotated at the bottom. The linear regression results are overlaid as dotted gray line, with equations and p-values annotated at the bottom. (G) Assuming a gamma-distributed DFE, the expected population-scaled deleterious mutation effects ($E\left[\left|2N_{a}s\right|\right]$) are not conserved across eleven species. Numbers show the ranks of $E\left[\left|2N_{a}s\right|\right]$. (A-G) Each point represents one species, with gray vertical lines representing confidence intervals. All axes are in log10 scale. (H) Proportions of mutations with various ranges of $\left|2N_{a}s\right|$. From left to right, mutations ranged from (nearly) neutral ($-1<2N_{a}s\le 0$) to very strongly deleterious ($2N_{a}s\le -1000$). Gray lines represent 95% confidence intervals.

Figure 5:

Fitting a Fisher’s Geometric Model (FGM) derived DFE. (A) The inferred long-term effective population size ($N_a$) from the FGM-derived DFE (y-axis) is correlated with the effective size inferred from genetic variation data using $\partial a\partial i$ (x-axis). Axes are on a log10 scale. (B) The estimated scale of mutation effects ($\sigma$) and mutation pleiotropy ($m$) parameters for eleven (sub)species, grouped by the Class of each species. Note that $\sigma$ is higher in mammals compared to insects. The y-axis is on a log10 scale. (C) The estimated proportion of beneficial mutations ($s>0$) is negatively correlated with long-term population size inferred from $\partial a\partial i$. The x-axis is on a log10 scale. (D) Proportions of mutations in various categories of $s$ estimated from the FGM-derived DFE for each species. From left to right, mutations range from beneficial $(s>0)$, (nearly) neutral $\left(-{10}^{-5}<s\le 0\right)$ to very strongly deleterious $(s\le -0.01)$. Dashed line marks $s=0$. Gray lines represent 95% confidence intervals.

Figure 6:

The drift-barrier of DFE evolution. (A) In large populations, efficient natural selection results in robust proteins. Because proteins are robust, subsequent deleterious mutations, whose effects we measured in our study, are only weakly deleterious. The inferred DFE becomes more neutral. (B) In smaller populations, natural selection is less effective at optimizing proteins. Thus, subsequent deleterious mutations, whose effects we measured in our study, are more strongly deleterious. The inferred DFE becomes more deleterious. Proportions of mutations in various categories of $|s|$ is generated assuming a gamma-distributed DFE, with the same population-scaled shape and scale parameters of $\alpha =0.2$, $\beta =5000$, but different $N_a$ of 10⁶ in (A) and 10000 in (B).