Figure 2

The strength of epistatic interactions scales with the log growth effects of the interacting knockouts. (a) Each dot represents the variance of several thousand epistatic interactions binned according to the log growth effects of the two single knockouts, G₀₁ and G₁₀. The blue surface is the phenomenological fit:$\text{var}\left({\text{G}}_{0\text{1}},{\text{G}}_{\text{1}0}\right)=0.0\text{79}\times \text{2}\left|{\text{G}}_{0\text{1}}\right|\left|{\text{G}}_{\text{1}0}\right|/\left(\left|{\text{G}}_{0\text{1}}\right|+\left|{\text{G}}_{\text{1}0}\right|\right).$(b) Slices of the plot in (a) for G₀₁ = constant. The dots are the same as in (a), and the solid lines represent the corresponding slice of the one-parameter fitting surface. (c) Diagonal slice of the plot in (a) with finer bins (G₀₁ = G₁₀ within 20%, G = mean(G₀₁, G₁₀)). The blue shaded area is the 25 to 75% confidence interval computed by bootstrap; the red line (var(G, G) = 0.079 G) is computed from the phenomenological model, and the dashed gray line, for which var(G, G) is proportional to G², represents the lower bound to the slope predicted by the Fisher's geometric model. (c, inset) The epistatic interactions between beneficial mutations are vanishingly small, independently of the effect of the combined mutations. (d) Probability density functions p(E') for the strength of genetic interactions between two deleterious knockouts with similar log growth effects. Different colors correspond to knockouts with different effects: the growth rates effects of the single knockouts being combined are close to -38% (red), -22% (yellow), -12% (green), -6% (blue), and -3% (purple). Each curve has been rescaled so that all distributions have a standard deviation = 1. The left tail of the distributions displays a fat tail, describing the occurrence of strong negative genetic interactions (for comparison, the dashed-dotted black line is a normal distribution).