Fig. 5.

Example of evolutionary dynamics with a single evolving trait consisting of two phenotypes: behavior of a specific system following the outline of Fig. 4A. Phase plane diagram of the density of individuals with phenotype A and environment $\phi$ shows the possible system behavior for different values for the relative timescales of population dynamics, feedbacks, and mutation (evo). Slow feedback and mutations (${ϵ}_m=0.00005$ and ${ϵ}_e=0.0005$) lead to continual cyclic evolutionary dynamics (red lines and Top Inset), almost independent of initial conditions (two initial conditions shown). With fast feedback and mutations (${ϵ}_m=0.01$ and ${ϵ}_e=0.1$), an equilibrium is reached (gray line and Middle Inset). No mutation (${ϵ}_m=0$ and ${ϵ}_e=0.01$) leads to the extinction of one of the traits (black dashed line and Bottom Inset). See SI Appendix, section S2 for equations and parameter values. Note that Continual evo refers to continual evolution, whereas Fast evo and No evo refer to fast and no mutations, respectively.