  To maintain renewing epithelial tissues in a healthy, homeostatic state,
(stem) cell divisions and differentiation need to be tightly regulated.
Mechanisms of homeostatic control often rely on crowding control: cells are
able to sense the cell density in their environment (via various molecular and
mechanosensing pathways) and respond by adjusting division, differentiation,
and cell state transitions appropriately. Here we determine, via a
mathematically rigorous framework, which general conditions for the crowding
feedback regulation (i) must be minimally met, and (ii) are sufficient, to
allow the maintenance of homeostasis in renewing tissues. We show that those
conditions naturally allow for a degree of robustness toward disruption of
regulation. Furthermore, intrinsic to this feedback regulation is that stem
cell identity is established collectively by the cell population, not by
individual cells, which implies the possibility of `quasi-dedifferentiation',
in which cells committed to differentiation may reacquire stem cell properties
upon depletion of the stem cell pool. These findings can guide future
experimental campaigns to identify specific crowding feedback mechanisms.
