Fig. 1.

Phase diagram and flows for a two-phenotype model of a biofilm. (Upper) Phase diagram showing two distinct phases. One phase consists only of a single genotype, either 00 or 11, and thus only one phenotype. The other phase is characterized by the stable coexistence of both phenotypes and called the coexistent phase. The solid lines represent phase boundaries while the dashed line denotes the separatrix between the phenotypes in the single-phenotype phase. The separatrix is a point of unstable equilibrium, where coexistence of phenotypes is in principle possible but practically impossible, being unstable to any perturbations or fluctuations in the dynamics. (Lower) Schematic flow diagram in both the single phenotype regime (Left) and the coexistent regime (Right) projected onto the ψ₀₀–ψ₁₁ plane. Note that in the single phenotype regime, the system dynamics tends to flow toward either all 00-genotypes (ψ₀₀ = 1) or all 11-genotypes (ψ₁₁ = 1). In the coexistent phenotype phase, the phase flows toward genotype fractions given by Eq. 4 and away from unstable fixed points at ψ₀₀ = 1 and ψ₁₁ = 1.