Fig. 1.

Multiple signals allow greater environmental resolution. (A) With one auto-inducing signal molecule, populations can discriminate two environmental states in density/mass-transfer space (0,1). (B) With two signals, populations can, in principle, discriminate four states [(0,0),(0,1),(1,0), and (1,1)], if one signal (red) is more fragile than the other (blue). Signal-molecule concentration dynamics are given by by dS_k/dt = (p + a_kS_k)N − (m + u_k)S_k, where N is cell density, is baseline production, is the increased production due to autoinduction, is mass-transfer rate, and is decay rate. We define a signal to be “ON” (autoinduced) when is above an unstable equilibrium = Np/(m − a_kN + u_k), which occurs when is negative: that is, when Na_k > m + u_k. See SI Text for details.