Fig. 2.

The increase in producer fraction in all nodes of a star network is captured by a simple phenomenological model. a Experimental results showing the time evolution of the fraction of producers in one star network on average (solid blue line), each type of node within the star network (dashed dark blue line for central nodes and dashed light blue line for side nodes), an isolated population (orange), and the fully connected network on average (pale yellow). b Same as a, but for the total density of cells. c Equations the phenomenological model. N_p, N_np are the densities of producers and non-producers, respectively (in cells/μL); r is the maximum growth rate; K is the carrying capacity (common for both strains); ε corresponds to the amount of enzyme imported by producers before the rest diffuses away (expressed in units of equivalent producer cells/μL, see Methods); k_M is the amount of producers needed to produce enough enzyme to bring the growth of non-producers to half its maxiumum value; c is the cost of producing the public good. Model parameters: r = 0.5 h^-1, K = 90,000 cells/μL, c = 0.07, ε = 14 cells/μL, k_M = 26 cells/μL, growth cycle 22 h, dilution factor 650 and migration rate m = 0.6 per cycle (~0.06 per generation). d Same as a, but as predicted by the model (points show the steady state after 100 cycles). Results for isolated nodes and fully connected networks overlap exactly. e Same as b, but as predicted by the model. Results for isolated nodes and fully connected networks overlap exactly