Self-balancing of cell populations via martingale turnover with amplification

Adaptive control in biological systems, such as intestinal immunity, remains poorly understood despite detailed knowledge of underlying regulatory networks. We propose an alternative framework based on stochastic martingale turnover, in which cells proliferate through mutual competition and decay without cell-type-specific regulation. Through stochastic simulations and mathematical analysis, we show that this process autonomously generates balanced population compositions associated with low-decay probabilities. The compositional dynamics can be described as a random walk whose step lengths decrease in low-decay regions. Reduced decay leads to larger total population sizes and an increase in the number of compatible microscopic states, which in turn shapes the distribution of compositions under fluctuating conditions. More generally, the dynamics follow a modified Langevin equation, in which constant mass is replaced by a fitness-dependent effective mass proportional to the total population size. Thus, biological systems regulate resistance to change, not merely direction, in shaping their macroscopic behavior.