Fig. 4.

Inferring the type of epistasis from synthetic data obtained from simulations on a) a diminishing-returns landscape with $\alpha (F)=20F^5$ and ${\mu }_b={\mu }_{b0}=1\times {10}^{-5}$, and b) a House-of-Cards/uncorrelated landscape with $\alpha (F)=100F$ and ${\mu }_b={\mu }_{b0}{e}^{-(F-1)}$ using different values of N. The time between successive measurements is at least a hundred (with the initial growth rate set to be 1), and each data point represents the average over 10 replicates with the error bars indicating the 95% confidence interval around the mean. The first 3 columns (from the left) are scaled trajectories obtained with different values of F_c used for estimating the initial fitness gradient. In both a) and b), how the shape of the trajectories change with N remains approximately consistent across all values of F_c, suggesting that the qualitative results are robust to how the initial fitness gradients are obtained. The last, right-most column show scaled trajectories where the initial fitness gradients are estimated from fitting the trajectories to Equation (9) assuming that the landscape takes the following form: $\alpha (F)={\alpha }_0{F}^{\varphi }$ and ${\mu }_b(F)={\mu }_{b0}{e}^{-\gamma (F-1)}$, with α₀, $\varphi ,\hspace{0.17em}{\mu }_{b0}$ and γ being free parameters used in the fitting. The solid black lines represent the fits to the data, while the inferred landscapes $\widehat{\alpha }(F)$ and $\widehat{{\mu }_b}(F)$ are shown in the insets. Based on how the shape of the scaled trajectories vary with N, one would infer that μ_b remains relatively constant in a) and decreases over time in b).