Self-organized hyperuniformity in a minimal model of population dynamics

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 individuals over a shared resource serves as feedback that can asymptotically guide the population towards a critical steady state with divergent individual life time.

We show that, in its spatially extended form, this many-body 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 in the asymptotic regime.

Instead, hyperuniformity arises from the divergence of the range of the resource-mediated interactions.

These findings may find applications in engineering, cellular population dynamics, and ecology.