Figure 4.

Simulation results for the growth of a metapopulation. The time course of the global producer fraction $\overline{x}$ (a) is computed by numerically solving equations (4) for a given distribution of stochastic initial compositions (b) (parameter values: $\alpha$ = 200, $s$ = 0.05, initial size $n_0={10}^{-3}$). The producer fraction initially increases as populations with more producers begin to expand earlier (see also Supplementary Movie S1). After reaching a maximum value ${\overline{x}}_{\max }$, the global producer fraction decreases. (c) The maximal magnitude of the increase $\mathrm{\Delta }\overline{x}={\overline{x}}_{\max }-\overline{x}\left(0\right)$ decreases with stronger growth reduction $s$ ($s$ between 0.01 and 0.9, other parameters identical to panel (a): for low $s$ it is comparable to the initial producer fraction, while very low producer growth precludes any increase at all.