Self-organized hyperuniformity in a minimal model of population dynamics

Abstract

By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the population towards a critical steady state with prolonged individual life time. We show that, in its spatially extended form, this many-particle model exhibits hyperuniform density fluctuations. Through explicit coarse-graining, we develop a hydrodynamic theory that conforms closely with the results of stochastic simulations. Unlike previous models for non-equilibrium hyperuniform states, our model does not exhibit conservation laws, even when approaching criticality. Instead, hyperuniformity arises from the divergence of the interaction range as the system approaches the critical point. These findings may find applications in engineering, cellular population dynamics, and ecology.