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Drylands are pattern-forming systems showing self-organized vegetation patchiness, multiplicity of stable states and fronts separating domains of alternative stable states. Pattern dynamics, induced by droughts or disturbances, can result…

Pattern Formation and Solitons · Physics 2014-03-05 Yuval R. Zelnik , Shai Kinast , Hezi Yizhaq , Golan Bel , Ehud Meron

Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions…

Populations and Evolution · Quantitative Biology 2017-12-13 Simone Pigolotti , Massimo Cencini , Daniel Molina , Miguel A. Muñoz

Spatial patterning and synchronization are pervasive features of plankton communities, yet the mechanisms that allow such patterns to persist coherently under environmental noise remain unresolved. In vertically structured aquatic…

Pattern Formation and Solitons · Physics 2026-03-26 Ju Kang , Yiyuan Niu , Yuanzhi Li , Quan-Xing Liu , Chengjin Chu

Ecological networks exhibit non-random structural patterns, such as modularity and nestedness, which indicate ecosystem stability, species diversity, and connectance. Such structure-stability relationships are well known. However, another…

Populations and Evolution · Quantitative Biology 2014-06-12 Kazuhiro Takemoto , Saori Kanamaru , Wenfeng Feng

The minimal ecological requirements for formation of regular vegetation patterns in semiarid systems have been recently questioned. Against the general belief that a combination of facilitative and competitive interactions is necessary,…

Populations and Evolution · Quantitative Biology 2014-09-24 Ricardo Martinez-Garcia , Justin M. Calabrese , E. Hernandez-Garcia , C. Lopez

The scarcity of water characterising drylands forces vegetation to adopt appropriate survival strategies. Some of these generate water-vegetation feedback mechanisms that can lead to spatial self-organisation of vegetation, as it has been…

Biological Physics · Physics 2013-08-30 John Realpe-Gomez , Mara Baudena , Tobias Galla , Alan J. McKane , Max Rietkerk

Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…

Adaptation and Self-Organizing Systems · Physics 2022-08-30 Anna Zincenko , Sergei Petrovskii , Vitaly Volpert

A particular sequence of patterns, "$\text{gaps} \to \text{labyrinth} \to \text{spots}$," occurs with decreasing precipitation in previously reported numerical simulations of PDE dryland vegetation models. These observations have led to the…

Pattern Formation and Solitons · Physics 2016-03-31 Karna Gowda , Yuxin Chen , Sarah Iams , Mary Silber

In many drylands around the globe, vegetation self-organizes into regular spatial patterns in response to aridity stress. We consider the regularly-spaced vegetation bands, on gentle hill-slopes, that survive low rainfall conditions by…

Pattern Formation and Solitons · Physics 2025-05-07 Punit Gandhi , Matthew Oline , Mary Silber

Enhancement of the predictive power and robustness of nonlinear population dynamics models allows ecologists to make more reliable forecasts about species' long term survival. However, the limited availability of detailed ecological data,…

Pattern Formation and Solitons · Physics 2025-04-18 Indrajyoti Gaine , Malay Banerjee

Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance…

Understanding the causes and effects of spatial vegetation patterns is a fundamental problem in ecology, especially because these can be used as early predictors of catastrophic shifts such as desertification processes. Empirical studies of…

Statistical Mechanics · Physics 2020-06-19 Paula Villa Martín , Virginia Domínguez-García , Miguel A. Muñoz

Tree-grass coexistence is a defining feature of savanna ecosystems, which play an important role in supporting biodiversity and human populations worldwide. While recent advances have clarified many of the underlying processes, how these…

Populations and Evolution · Quantitative Biology 2026-04-21 Jelle van der Voort , Mara Baudena , Ehud Meron , Max Rietkerk , Arjen Doelman

Vegetation patterns are abundant in arid and semiarid ecosystems, but how they form remains unclear. One of the most extended theories lies in the existence of scale-dependent feedbacks (SDF) in plant-to-plant and plant-water interactions.…

Populations and Evolution · Quantitative Biology 2018-01-08 Ricardo Martinez-Garcia , Cristobal Lopez

In the past decades human activities caused global Earth system changes, e.g., climate change or biodiversity loss. Simultaneously, these associated impacts have increased environmental awareness within societies across the globe, thereby…

Physics and Society · Physics 2021-05-11 Paul Manuel Müller , Jobst Heitzig , Jürgen Kurths , Kathy Lüdge , Marc Wiedermann

We investigate how environmental flows influence spatial pattern formation and population dynamics using two nonlocal models of population dynamics, which we couple to two different stationary flows. Combining numerical simulations and…

Populations and Evolution · Quantitative Biology 2025-08-14 Nathan O. Silvano , João Valeriano , Emilio Hernández-García , Cristóbal López , Ricardo Martinez-Garcia

This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…

Analysis of PDEs · Mathematics 2026-04-14 Serena Dipierro , Enrico Valdinoci

Unstoppable feedback loops and tipping points in socio-ecological systems are the main threats to sustainability. These behaviors have been extensively studied, notably to predict, and arguably deviate, dead-end trajectories. Behind the…

Dynamical Systems · Mathematics 2023-05-11 Olivier Hamant

We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally…

Populations and Evolution · Quantitative Biology 2009-11-13 Yoshimi Yoshino , Tobias Galla , Kei Tokita

Water availability is a major environmental driver affecting riparian and wetland vegetation. The interaction between water table fluctuations and vegetation in a stochastic environment contributes to the complexity of the dynamics of these…

Populations and Evolution · Quantitative Biology 2012-05-14 Stefania Scarsoglio , Paolo D'Odorico , Francesco Laio , Luca Ridolfi