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Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability,…

Populations and Evolution · Quantitative Biology 2026-02-02 Ton Viet Ta

We introduce the concept of 'dynamical phase coexistence' to provide a simple solution for a long-standing problem in theoretical ecology, the so-called "savanna problem". The challenge is to understand why in savanna ecosystems trees and…

Biological Physics · Physics 2010-03-09 F. Vazquez , C. Lopez , J. M. Calabrese , M. A. Munoz

Local coexistence of species in large ecosystems is traditionally explained within the broad framework of niche theory. However, its rationale hardly justifies rich biodiversity observed in nearly homogeneous environments. Here we consider…

Populations and Evolution · Quantitative Biology 2021-11-17 Deepak Gupta , Stefano Garlaschi , Samir Suweis , Sandro Azaele , Amos Maritan

Vegetation patterns are a ubiquitous feature of water-deprived ecosystems. Despite the competition for the same limiting resource, coexistence of several plant species is commonly observed. We propose a two-species reaction-diffusion model…

Populations and Evolution · Quantitative Biology 2019-11-26 Lukas Eigentler , Jonathan A. Sherratt

Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…

Cell Behavior · Quantitative Biology 2016-11-23 Adriano Bonforti , Salva Duran-Nebreda , Raul Montañez , Ricard Solé

Metapopulation models have been instrumental in demonstrating the ecological impact of landscape structure on the survival of a focal species in complex environments. However, extensions to multiple species with arbitrary dispersal networks…

Populations and Evolution · Quantitative Biology 2024-11-06 Prajwal Padmanabha , Giorgio Nicoletti , Davide Bernardi , Samir Suweis , Sandro Azaele , Andrea Rinaldo , Amos Maritan

In order to understand the role of space in ecological communities where each species produces a certain type of resource and has varying abilities to exploit the resources produced by its own species and by the other species, we carry out…

Dynamical Systems · Mathematics 2011-02-14 Yun Kang , Nicolas Lanchier

This paper investigates the dynamics of vegetation patterns in water-limited ecosystems using a generalized Klausmeier model that incorporates non-local plant dispersal within a finite habitat. We establish the well-posedness of the system…

Analysis of PDEs · Mathematics 2026-01-27 Maciej Tadej , Ricardo Martinez-Garcia , Michael Hecht

Patterned vegetation is a characteristic feature of many dryland ecosystems. While plant densities on the ecosystem-wide scale are typically low, a spatial self-organisation principle leads to the occurrence of alternating patches of high…

Populations and Evolution · Quantitative Biology 2020-05-05 Lukas Eigentler

Soil is a complex, dynamic material, with physical properties that depend on its biological content. We propose a cellular automaton model for self-organizing soil structure, where soil aggregates and serves as food for microbial species.…

Biological Physics · Physics 2025-10-10 Riz Fernando Noronha , Kim Sneppen , Kunihiko Kaneko

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

Mutualisms are key for structuring ecological communities, but they are sensitive to environmental change and fluctuations in population size. Consequently, how mutualisms achieve stability remains an open question in ecological theory.…

Populations and Evolution · Quantitative Biology 2026-05-08 Matheus Bongestab , David Pinto-Ramos , Ricardo Martinez-Garcia

Forest-savanna bistability - the hypothesis that forests and savannas exist as alternative stable states in the tropics - and its implications are key challenges for mathematical modelers and ecologists in the context of ongoing climate…

Populations and Evolution · Quantitative Biology 2025-05-05 Kimberly Shen , Simon Levin , Denis D. Patterson

We analyze a spatially extended version of a well-known model of forest-savanna dynamics, which presents as a system of nonlinear partial integro-differential equations, and study necessary conditions for pattern-forming bifurcations.…

Pattern Formation and Solitons · Physics 2023-08-28 Denis D. Patterson , Simon A. Levin , A. Carla Staver , Jonathan D. Touboul

Vegetation in semi-arid ecosystems frequently organizes into spatially heterogeneous mosaics that regulate ecosystem functioning, productivity, and resilience. These patterns arise from local biological interactions, including facilitation…

Populations and Evolution · Quantitative Biology 2026-02-06 Àlex Giménez-Romero , Bernard A. Afful , Priscilla E. Greenwood , Manuel A. Matías , Luis F. Gordillo

Ecological systems comprise an astonishing diversity of species that cooperate or compete with each other forming complex mutual dependencies. The minimum requirements to maintain a large species diversity on long time scales are in general…

Populations and Evolution · Quantitative Biology 2012-09-10 Joachim Mathiesen , Namiko Mitarai , Kim Sneppen , Ala Trusina

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

In work with a variety of co-authors, Staver and Levin have argued that savanna and forest coexist as alternative stable states with discontinuous changes in density of trees at the boundary. Here we formulate a nonhomogeneous spatial model…

Probability · Mathematics 2024-11-26 Rick Durrett , Ruibo Ma

Regular vegetation patterns in semiarid ecosystems are believed to arise from the interplay between long-range competition and facilitation processes acting at smaller distances. We show that, under rather general conditions, long-range…

Populations and Evolution · Quantitative Biology 2014-07-24 Ricardo Martinez-Garcia , Justin M. Calabrese , Emilio Hernandez-Garcia , Cristobal Lopez
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