A monophasic feedback circuit in which cells *Z* generate an input *y* that inhibits their growth rate. The population is at steady state *Z = Z*_{ST} when *y = y*_{ST}.

A monophasic feedback circuit where cells *Z* decrease an input *y*, which increases their growth rate. The population is at steady state *Z = Z*_{ST} when *y = y*_{ST}.

Trajectories of *Z* from different initial concentrations of cells (*Z*) (i) or *y* (ii) for the circuit of (B). The healthy concentration *Z = Z*_{ST} is reached regardless of initial concentration of *Z*, as long as it is nonzero, and regardless of the initial concentration of *y*.

An arrow marks the time when a mutant with a strong activation of the sensing of *y* arises (for the circuit depicted in B). This mutant has a selective advantage and takes over the population.

A biphasic feedback circuit where *Z* generates a signal *y*, which, in turn, decreases the growth rate of *Z* at high concentrations and increases the growth rate of *Z* at low concentrations. The population is at steady state *Z = Z*_{ST} when *y = y*_{ST}, and there is also an unstable fixed point at *y*_{UST} *< y*_{ST}.

A biphasic feedback circuit where cells *Z* inhibit *y*, which, in turn, decreases the growth rate of *Z* at high concentrations and increases the growth rate of *Z* at low concentrations. The population is at steady state *Z = Z*_{ST} when *y = y*_{ST}, and there is also an unstable fixed point at *y*_{UST} *> y*_{ST}.

Trajectories of *Z* from different initial concentrations of *Z* (i) or *y* (ii) for the circuit depicted in (F). The healthy concentration *Z = Z*_{ST} is not reached for small values of *Z* (*Z << Z*_{ST}) or large values of *y* (*y >> y*_{UST}).

The arrows mark the times when a mutant with a strong activation of the sensing of *y* arises (for the biphasic circuit depicted in F). This mutant has a selective disadvantage and is thus eliminated.