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Self-Organized Hyperuniformity in a Minimal Model of Population Dynamics

Tal Agranov1,2,*, Natan Wiegenfeld1,3, Omer Karin4, and Benjamin D. Simons1,2

  • *Contact author: ta487@cam.ac.uk
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Phys. Rev. Lett. 137, 117401 – Published 10 September, 2026

DOI: https://doi.org/10.1103/4j35-6jxb

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 individuals over a shared resource serves as feedback that can asymptotically guide the population toward a critical steady state with a divergent individual lifetime. 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 nonequilibrium 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.

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Phys. Rev. Lett. 137, 117401– Published 10 September, 2026
  • Received 15 January 2026
  • Accepted 30 June 2026
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