Figure 5.

Quorum sensing parameters optimized for different ecological scenarios and different types of public goods. (A–C) Left side panels: Green curves shows optimal production rate, ${\sigma }_E^{opt}$, as a function of population size N. Black full line and dashed line show the production rate as a function of population size, N, when production is regulated by (A): a QS system with parameters such that cumulative fitness, w is optimized for a public good with the concave benefit function shown in Figure 1 (α = 1.1, K_S = 2200, ${\sigma }_E^{max}=0.33$), (B): a system with QS parameters for a public good with a convex benefit function maximizing cumulative fitness w in only “turn on” scenarios, (α = 2, K_S = 980, and ${\sigma }_E^{max}=0.43$), and (C): a QS system with parameters that maximize cumulative fitness w for a public good with a concave benefit function in both “turn on” and “turn off” scenarios, (α = 1.4, K_S = 2600, and ${\sigma }_E^{max}=0.6$). (A–C) Right side panels: Green lines show Δg^opt, the increase in growth rate achieved, as a function of N when producing public good using the optimal production curve ${\sigma }_E^{opt}$. Full black line shows Δg as a function of N for the QS regulated production curve marked “Turn on” in the plot to the right. Dashed black line shows Δg as a function of N for the QS regulated production curve marked “Turn off” in the plot to the left. The colored area underneath the Δg curves in the range N = [1, N_max], (N_max = 70) is proportional to the cumulative fitness, w (defined in Equations 7 and 8).