Self-organized hyperuniformity in population dynamics

Living systems often operate at critical states – poised on the border between two distinct dynamical behaviours, where unique functionality emerges [1]. A striking example is the ear’s sensory hair cells, which amplify faint sounds by operating on the verge of spontaneous oscillations [2]. How such finely tuned states are maintained, and what statistical signatures characterise them, remain major questions.

In this talk, I will present a generic mechanism for critical tuning in population dynamics [3]. In our model, the consumption of a shared resource drives the population towards a critical steady state characterised by prolonged individual lifetimes. Remarkably, we find that in its spatially extended form, the model exhibits hyperuniform density correlations. In contrast to previously studied hyperuniform systems, our model lacks conservation laws even arbitrarily close to criticality. Through explicit coarse-graining, we derive a hydrodynamic theory that clarifies the underlying mechanism for this striking statistical behaviour. 

I will highlight several biological contexts in which this mechanism is expected to operate, including biomolecular complex assembly in the developing C. elegans embryo. Here, together with experimental collaborators, we identify signatures of critical tuning that may arise from resource competition.

More broadly, our framework motivates future work on how living systems harness resource-mediated interactions to regulate their dynamical states.

[1]T. Mora, W. Bialek, J Stat Phys (2011)

[2] S. Camalet, T. Duke, F. Jülicher and J. Prost, PNAS (1999)

[3].l Agranov, N. Wiegenfeld,O. Karin and B. D. Simons arXiv:2509.08077 (2025)