Diminishing-returns epistasis among random beneficial mutations in a multicellular fungus

Abstract

Adaptive evolution ultimately is fuelled by mutations generating novel genetic variation. Non-additivity of fitness effects of mutations (called epistasis) may affect the dynamics and repeatability of adaptation. However, understanding the importance and implications of epistasis is hampered by the observation of substantial variation in patterns of epistasis across empirical studies. Interestingly, some recent studies report increasingly smaller benefits of beneficial mutations once genotypes become better adapted (called diminishing-returns epistasis) in unicellular microbes and single genes. Here, we use Fisher's geometric model (FGM) to generate analytical predictions about the relationship between the effect size of mutations and the extent of epistasis. We then test these predictions using the multicellular fungus Aspergillus nidulans by generating a collection of 108 strains in either a poor or a rich nutrient environment that each carry a beneficial mutation and constructing pairwise combinations using sexual crosses. Our results support the predictions from FGM and indicate negative epistasis among beneficial mutations in both environments, which scale with mutational effect size. Hence, our findings show the importance of diminishing-returns epistasis among beneficial mutations also for a multicellular organism, and suggest that this pattern reflects a generic constraint operating at diverse levels of biological organization.

Keywords: Aspergillus nidulans; Fisher's geometric model; adaptation; beneficial mutation; epistasis.

Figure 1.

Fisher's geometric model (FGM) and predictions of epistasis among beneficial mutations. (a) FGM in two-dimensional phenotype space. The three parameters of FGM include: the distance of the wild-type to the optimum, ρ (in terms of the average displacement of mutations, σ), the phenotypic dimensions, n (here 2), and the fitness difference between the wild-type and the fitness optimum, s₀. (b) FGM generates fitness epistasis among beneficial mutations of diverse sign and strength from the nonlinear dependence of fitness on underlying phenotypes. Both diagrams depict effects of single mutations of equal fitness effects (black arrows leading to the same fitness circle). The fitness of the constituent double mutant (red arrows) is nevertheless very different, leading to magnitude epistasis in the left and sign epistasis in the right diagram. (c) Predicted relationship between mean epistasis and effect size of beneficial mutations of the same effect-size by FGM for different values of phenotypic dimensions (n) and mutational distance to the optimum (ρ). The two solid lines are obtained from the limiting behaviours of the mean epistasis obtained by taking the small-ρ and large-ρ limits, i.e. −2 and , respectively. The straight grey lines show the relationship ɛ = −s.

Figure 2.

Beneficial mutations in the fungus Aspergillus nidulans. (a) A. nidulans colony growing under suboptimal conditions, producing mutant sectors with higher growth rates. (b) Frequency distribution of the relative selection coefficient (i.e. the difference in radial colony growth rate of isolate and ancestor normalized by the maximally fit isolate, s/s_m) of 614 isolates from the edge of colonies growing in a rich nutrient environment (left) and 824 isolates from the edge of colonies growing on a poor nutrient environment (right). The blue lines show the probability density function for fitness effects of beneficial mutations (approximately all data outside the shaded areas) predicted by FGM parametrized by the epistasis data; the green lines show this function parametrized by the distribution of single mutation effects (see electronic supplementary material and figure S4).

Figure 3.

Epistasis among beneficial mutations. (a) Histograms of the epistasis coefficients calculated for pairs of beneficial mutations of similar effect isolated in a rich (left) and poor environment (right). (b) Epistasis as a function of the mean relative selection coefficient for the two mutations used to generate the double mutant for the rich (left) and poor environment (right). The blue line in each panel is the best-fitted FGM model with parameter values (s₀/s_m = 1.41, ρ = 6.89, n = 19.3) and (s₀/s_m = 1.62, ρ = 9.81, n = 34.8), respectively. The orange shading indicates the 99% CI based on measurement error, whereas the blue shading indicates the 99% variability region resulting from the combined effect of measurement error and the intrinsic stochasticity of FGM. The orange dashed line in each panel indicates the threshold between magnitude (above the line) and sign epistasis (below the line); the green dashed line is the best-fit linear model. (c) Probability density plot of the number of instances of sign epistasis in the rich (left) and poor environment (right) predicted by FGM. Highlighted bars indicate observed numbers of sign epistatic pairs out of the total number of pairs N_total (see text).