Universal voter model emergence in genetically labeled homeostatic tissues

Recent experiments in adult mammalian tissues have found scaling relations of the voter model in the dynamics of the genetically labeled population of stem cells. Yet, the reason for this seemingly robust appearance of the voter model remains unexplained. Here we show that the voter model kinetics is indeed a generic behavior that arises at macroscale in a linearly stable homeostatic tissue undergoing turnover. Starting from the continuum model of a multicellular system, we show that the dynamics of the labeled cell population converges to the voter model kinetics at large spatio-temporal scale of observation. We present a method to calculate the length scale and time scale of coarse-graining that is required in obtaining the effective voter model dynamics, and apply it to the growth factor competition model and the pairwise mechanical interaction model.