Figure 6. Evolution of correlated traits.

The evolutionary model describes the change in phenotype relative to the founder ($\overrightarrow{\varphi }={[|{\tilde{v}}_r|,{\tilde{k}}_g]}^T$) under selection described by $\overrightarrow{\beta }$. Panels show unit vectors in the direction of observed phenotypic evolution ($\widehat{\varphi }$) and the direction of selection inferred from the reaction-diffusion model ($\widehat{\beta }$). Ellipses show quartiles for a normal distribution of phenotypes with covariance matrix $G$ that is consistent with $\overrightarrow{\varphi }$ and $\overrightarrow{\beta }$. In both panels, we set the correlation coefficient between ${\tilde{k}}_g$ and $|{\tilde{v}}_r|$ is ${\displaystyle \rho =-0.75}$ but our conclusions hold for ${\displaystyle \rho <-0.1}$. In rich medium (a) ${\sigma }_{|{\tilde{v}}_r|}/{\sigma }_{{\tilde{k}}_g}=1$ and in minimal medium ${\sigma }_{|{\tilde{v}}_r|}/{\sigma }_{{\tilde{k}}_g}=0.3$. In rich medium ${\widehat{\beta }}_{RM}=[0.78,0.61]$ and in minimal medium ${\widehat{\beta }}_{MM}=[0.87,0.49]$.

DOI: http://dx.doi.org/10.7554/eLife.24669.030

Figure 6—figure supplement 1. Determining $\overrightarrow{\beta }$ from reaction-diffusion model.

Reaction-diffusion model (main text) was used to simulate migration rates. Panels (a) and (b) plot the normalized (to the founder) predicted migration rate ($\tilde{s}$) for both rich medium (a) and minimal medium (b). (a–b) are surface plots of the heatmaps shown in Figures 2,4 of the main text. To infer the selection pressure ${\displaystyle (\overrightarrow{\beta })}$ we fit a plane (black circles) to the surfaces shown in (a) and (b). The residuals of this fit are shown in (c) and (d) respectively. The fit for rich medium is good, while the residual is large in minimal medium.

DOI: http://dx.doi.org/10.7554/eLife.24669.031

Figure 6—figure supplement 2. Direction of phenotypic evolution with ${\sigma }_{|{\tilde{v}}_r|}$ and ${\sigma }_{{\tilde{k}}_g}$.

The dot product ${\widehat{\varphi }}_{obs}\cdot {\widehat{\varphi }}_{pred}$ is plotted as a heatmap as a function of genetic variances in growth rate and run speed. Each row corresponds to a different value of the correlation coefficient ($\rho$) between run speed and growth rate as labeled. The left column is for rich medium and the right column for minimal medium. When ${\widehat{\varphi }}_{obs}\cdot {\widehat{\varphi }}_{pred}\to 1$ (dark red) this indicates regions where the predicted direction of evolution (${\widehat{\varphi }}_{pred}$) coincides with the observed direction of evolution (${\widehat{\varphi }}_{obs}$). Note our qualitative conclusions are robust to large variation in $\rho$.

DOI: http://dx.doi.org/10.7554/eLife.24669.032

Figure 6—figure supplement 3. Stochastic simulations of selection in minimal medium.

Stochastic simulations of phenotypic evolution in minimal medium. Simulations were carried out as described above. For all simulations ${\sigma }_{|{\tilde{v}}_r|}=0.1$. Each colored line represents a single simulation which initiates at $[1,1]$. Each point is the mean phenotype for a round of selection. Colors represent different values of ${\sigma }_{{\tilde{k}}_g}$ as shown in the legends. The green-yellow heatmap is the ‘fitness landscape’ interpolated from the heatmap shown in Figure 2b of the main text. Each panel shows a simulation for different, fixed, values of the trait correlation coefficient $\rho$. The red line and circles show the observed phenotypic evolution in minimal medium (Figure 4b, main text).

DOI: http://dx.doi.org/10.7554/eLife.24669.033