Self-organized hyperuniformity in a minimal model of population dynamics

In this talk, I will present our recent work [1], in which we uncover self-organized hyperuniformity in a generic model of population dynamics. The model generalizes a class of models recently introduced to account for protracted transients in biological systems. In these models, competition among individuals for a shared resource generates an effective feedback mechanism that asymptotically guides the population towards a critical steady state with divergent individual lifetimes. 

Remarkably, we find that in its spatially extended form, the model exhibits hyperuniform density correlations. Through explicit coarse-graining, we derive a hydrodynamic theory that clarifies the underlying mechanism for this striking statistical behaviour. 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 asymptotic divergence of the interaction range.

These results suggest potential applications to cellular population dynamics and ecological systems. More broadly, our framework highlights how resource-mediated interactions can regulate collective behaviour in living systems, and opens new directions for exploring self-organization in non-equilibrium biological contexts.

[1] TA, N. Wiegenfeld, O. Karin, and B. D. Simons, arXiv:2509.08077 (2026).