Fig. 2.

Global and local scaling under phenotypic interference. Average population data are plotted against the number of genes, g, for the minimal biophysical model at steady-state asexual evolution. Simulation data (circles) for different average gene selection coefficients f₀ (indicated by color) show a crossover from the regime of independently evolving genes (brown dashed lines) to phenotypic interference (red dashed lines). The error bars (SD) are smaller than or equal the diameter of the symbols. The crossover point $g_0~10^2$ is marked. a, b Global observables. Average total fitness variance, σ², and coalescence rate, $\tilde{\sigma }$; phenotypic interference scaling ${\sigma }^2~g^2∕c$ and $\tilde{\sigma }~g∕c$ (red dashed lines) as given by Eqs. 5, 7 with a fit parameter $c_0\approx 80$. c, d Local observables. Average scaled trait diversity ${\delta }_G={\mathrm{\Delta }}_G∕{ϵ}_G^2$ and mean square selection coefficient at sequence sites s²; phenotypic interference scaling ${\delta }_G~c∕g$ and $s^2=4{\tilde{\sigma }}^2~g^2∕c^2$ (red dashed lines) as given by Eqs. 6, 7. Values ${\delta }_G<1$ indicate that individual proteins are in the low-mutation regime. The scaling $s^2~{\tilde{\sigma }}^2$ is independent of f₀, signaling that site selection coefficients emerge from a feedback between global and local selection (see text). Other simulation parameters: $N=1000$, $u=1.25\times 10^{-3}$, ${ϵ}_G∕k_{\mathrm{B}}T=1$; see Methods section for simulation details. Supplementary Fig. 2 shows global and local observables as functions of $\tilde{\sigma }$