Figure 5.

(a) The internal equilibrium fractions ($f_{+}^i$, i ≡ s, us) of producers as a function of the levels of serum for different p₀ values. The fraction ($f_{+}^s$) at stable equilibrium is shown in red colour while blue colour indicates unstable equilibrium fractions ($f_{+}^{\mathrm{us}}$). Arrows give the critical level of serum above which only non-producers exist. Purple stars represent the lowest level of serum at which producers and non-producers coexist in a stable equilibrium state. (b,c) Phase diagrams (initial fraction f₊(0) versus % of serum) with p₀= 4.65 and p₀=4.00, respectively. Three stable phases are shown in these two figures. (i) A homogeneous phase consisting of only producers (pink colour). (ii) A heterogeneous phase consisting of both producers and non-producers (purple colour). The stable equilibrium fraction of producers is indicated by the dashed red line. (iii) A homogeneous phase with of only non-producers (blue colour). The red and blue circles represent the producer and non-producer cells, respectively. Remarkably, for both p₀ values +/+ and −/− cells coexist in a narrow range of % of serum.