Mathematical models reveal a 'hidden order' in dryland vegetation worldwide

Sadie Harley
scientific editor

Robert Egan
associate editor

If you've ever traveled through drylands, you may have noticed striking vegetation patterns—stripes, spots, or rings—scattered across otherwise barren landscapes. From "tiger bush" in West Africa to the enigmatic "fairy circles" of Namibia, these patterns have long inspired wonder and scientific curiosity.
Decades of research show that such patterns emerge spontaneously through a process called spatial self-organization. These self-organized patterns are more than aesthetics—they can help the organisms cope with stress such as prolonged droughts, allowing the ecosystems to persist and function well even in extreme environments.
Recently, a study in Proceedings of the National Academy of Sciences discovered a new self-organized vegetation state, known as "disordered hyperuniformity," across global drylands.
"'Disorder' means that if you're standing in the field and looking around at plants within a few meters, their positions seem completely random—there's no obvious order. But if you zoom out—say, with a drone capturing hundreds of meters of landscape—you'll find that plant density is surprisingly uniform across the entire area. That's hyperuniformity," explained Wensi Hu of Nanjing University, China, the study's lead author.
"Disordered hyperuniformity is a kind of 'hidden order,' because it is invisible to the naked eye," added Professor Lijuan Cui of the Chinese Academy of Forestry, the study's co-lead author.
"It's fundamentally different from the regular, spatially periodic patterns we've studied before." So far, this phenomenon had been found mostly in microscopic systems, such as the arrangement of light-sensitive cells in bird eyes.
Using mathematical models, the researchers explored how such a hidden order could emerge in drylands. They found that it arises from simple, local interactions between plants and their environment. For example, in arid conditions, plants typically compete fiercely for water and nutrients (a negative interaction). Yet, established plants also improve local soil conditions—enhancing water retention and nutrient availability—a positive effect that can persist even for years after the plants die.
This "ecological legacy" makes it easier for new seedlings to establish near the remains of their predecessors. Over time, as this cycle of death and rebirth repeats, the vegetation gradually organizes into a disordered hyperuniform state.
"This legacy effect mimics a kind of random reorganization," said Professor Ricard Solé of Universitat Pompeu Fabra, Spain. "In physics, we know that similar particle movements can produce robust disordered hyperuniform material structures as an emergent property at the 'critical absorbing state.'"
"Disordered hyperuniformity may arise from various combinations of positive and negative ecological interactions, but these interactions boil down to a few fundamental physical principles, such as the Turing principle and phase separation principle," said Professor Quan-Xing Liu of Shanghai Jiao Tong University.
Critically, ecosystems in a hyperuniform state use limited rainfall far more efficiently. "This collective organization allows dryland vegetation to support higher plant densities and persist under harsh conditions," said Dr. Miguel Berdugo of Universidad Complutense de Madrid, Spain.
But there's a catch. "Forming this hidden order takes time," said Professor Sonia Kéfi at Université de Montpellier, France. "Once disrupted—say, by overgrazing or land degradation—it's difficult to recover. There's no free lunch in nature."
To test how widespread this phenomenon is, the team analyzed high-resolution satellite imagery from over 400 dryland sites around the globe.
"Roughly one in 10 of the sites we studied showed clear signs of disordered hyperuniformity," said Professor Manuel Delgado-Baquerizo at Instituto de Recursos Naturales y AgrobiologÃa de Sevilla (IRNAS) and Consejo Superior de Investigaciones CientÃficas (CSIC). "This isn't a rare oddity—it's a global feature of dryland ecosystems."
The discovery bridges scales and disciplines. "What's most fascinating," said Professor Chi Xu of Nanjing University, "is that the same physical principles governing the arrangement of particles or cells also shape entire ecosystems. Elegant design in nature can hide in plain sight–even in something as seemingly simple as dryland vegetation."
More information: Wensi Hu et al, Causes and consequences of disordered hyperuniformity in global drylands, Proceedings of the National Academy of Sciences (2025).
Journal information: Proceedings of the National Academy of Sciences
Provided by Nanjing University