Epistasis and natural selection shape the mutational architecture of complex traits

Abstract

The evolutionary trajectories of complex traits are constrained by levels of genetic variation as well as genetic correlations among traits. As the ultimate source of all genetic variation is mutation, the distribution of mutations entering populations profoundly affects standing variation and genetic correlations. Here we use an individual-based simulation model to investigate how natural selection and gene interactions (that is, epistasis) shape the evolution of mutational processes affecting complex traits. We find that the presence of epistasis allows natural selection to mould the distribution of mutations, such that mutational effects align with the selection surface. Consequently, novel mutations tend to be more compatible with the current forces of selection acting on the population. These results suggest that in many cases mutational effects should be seen as an outcome of natural selection rather than as an unbiased source of genetic variation that is independent of other evolutionary processes.

Figure 1. The additive genetic variance and the mutational variance of a trait evolve as a function of underlying levels of epistasis.

These simulation results were produced using our core set of parameters, except we imposed correlational selection, r_ω = 0.9, and varied the population size from 64 to 2048 across different runs. The top panel (a) shows the relationship between the equilibrium additive genetic variance for trait one and the population size. In a strictly additive model, larger populations maintain larger amounts of additive genetic variance (red diamonds), but with moderate to strong epistasis (green squares, open and closed circles) the pattern is reversed (with the exception of the smallest populations). The bottom panel (b) reveals the cause of this reversal. In an additive model, the mutational variance has no way to evolve, so small populations have the same equilibrium mutational variance as large populations (red diamonds). In the presence of epistasis, however, smaller populations evolve larger mutational variances than large populations (triangles, squares, circles), and these larger mutational variances in small populations contribute to a greater level of standing genetic variance, except when the effects of genetic drift are extremely strong (i.e., when N = 64). In (a) and (b), error bars show one standard error of the mean across 20 independent simulation runs; if error bars are not visible, then they are smaller than the symbol.

Figure 2. Triple alignment of natural selection, genetic variation and mutation.

Epistasis promotes alignment of the individual selection surface (the ω-matrix), the additive genetic architecture (the G-matrix) and the mutational architecture (the M-matrix) of a two-trait phenotype. The actual matrices are shown to the left, and graphical depictions of the overlapping matrices are shown to the right. These results are from simulations using our core parameter set, except that population size is 4096 and the individual selection surface (described by ω) is held at a constant shape but oriented with its long axis turned in a different direction in phenotypic space for different simulation runs (but note that within a run the individual selection surface is always constant). The ellipses are 95-percent confidence ellipses, and the angle of the long axis of each ellipse is given by the leading eigenvector of the corresponding matrix (green for M, blue for G, and orange for ω) in a plot with trait one on the x-axis and trait two on the y-axis. The ω-matrix is not drawn to scale, but its orientation and proportions are correct. As the selection surface rotates, both the G-matrix and the M-matrix evolve to align with the selection surface in phenotypic space. This alignment result is extremely general and it occurs under almost all investigated parameter combinations.

Figure 3. Epistasis allows the mutational variance to evolve as function of population size.

The average allelic effect can evolve to be correlated with the average epistatic coefficient, and the strength of this relationship varies with population size. These data are from 20 independent simulation runs using our core parameter set, except with only 10 quantitative trait loci. In addition, we allow only within-trait epistasis affecting trait one and no epistasis involving trait two, with population sizes of (a) N = 128 and (b) N = 2048. Each point represents a single quantitative trait locus. The x-axis shows the magnitude of epistasis (mean epistatic effect of a locus, averaged across all of its epistatic coefficients), and the y-axis presents the mean allelic effect (or reference effect) of alleles at the corresponding locus, averaged across all alleles segregating at the locus. In small populations, large mutational variances are maintained by the evolution of a large range in allelic effects; we see a slightly negative but non-significant relationship between epistatic coefficients and allelic effects (linear regression, N = 200, R² = 0.01, p = 0.09). In large populations (b), which evolve lower mutational variances than small populations, we see a much smaller range in allelic effects and these effects show a strong negative relationship with the mean epistatic coefficients across loci (linear regression, N = 200, R² = 0.22, p << 0.0001). Thus, the allelic effects of a particular locus tend to evolve values that are largely counteracted by the epistatic effects of the locus in question. This figure is concerned with the evolution of the mutational variance, but a similar effect explains the evolution of mutational covariances.