Fig. 3.

Selection can only act at the host level under stringent conditions. The mean helper frequency is shown as a function of the timescale of the evolutionary dynamics at the microbe level ${\tau }_M=\frac{1}{\beta \gamma }$ relative to the host generation time ${\tau }_H=\frac{G_H}{\beta }$ and the ratio of vertical $T_{vert}=\frac{n_0}{k}$ to horizontal transmission $T_{horiz}=\frac{\theta }{\beta }$. Two different levels of sampling variance are shown: the SD of the sampling distribution $\sigma$ is 0.02 in A and 0.1 in B; A, Upper and B, Upper show the results of single simulations, and A, Lower and B, Lower show the same data but averaged within discrete bins. We varied the cost $\gamma$ and migration rate $\theta$ to obtain different values of ${\tau }_M/{\tau }_H$ and $T_{vert}/T_{horiz}$, respectively; all other parameters are as shown in SI Appendix, Table S1.