Related papers: Pattern Formation in Mesic Savannas
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…
The ecological invasion problem in which a weaker exotic species invades an ecosystem inhabited by two strongly competing native species is modelled by a three-species competition-diffusion system. It is known that for a certain range of…
Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on pattern…
The introduction of stochasticity into continuous ecological models frequently relies on phenomenological, diagonal diffusion terms that lack a rigorous microscopic basis. We demonstrate that this standard practice fundamentally…
Spontaneous pattern formation in homogeneous systems is ubiquitous in nature. Although Turing demonstrated that spatial patterns can emerge in reaction-diffusion (RD) systems when the homogeneous state becomes linearly unstable, it remains…
This article examines the dynamic phase transitions and pattern formations attributed to binary systems modeled by the Cahn-Hilliard equation. In particular, we consider a two-dimensional lattice structure and determine how different…
Atmospheric models used for weather and climate prediction are traditionally formulated in a deterministic manner. In other words, given a particular state of the resolved scale variables, the most likely forcing from the sub-grid scale…
Modelling how populations respond to habitat loss is crucial for understanding ecosystem stability, especially when positive interactions among resource species, such as plant-plant facilitation, play a key role. Habitat loss not only…
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent patterns sometimes appear as local minimisers of a…
Decisions to disperse from a habitat stand out among organismal behaviors as pivotal drivers of ecosystem dynamics across scales. Encounters with other species are an important component of adaptive decision-making in dispersal, resulting…
The theory of alternative stable states and tipping points has garnered substantial attention in the last several decades. It predicts potential critical transitions from one ecosystem state to a completely different state under increasing…
In this paper we explore the eco-evolutionary dynamics of a predator-prey model, where the prey population is structured according to a certain life history trait. The trait distribution within the prey population is the result of interplay…
Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology, among many others. The physics underlying the patterns is specific to the mechanisms, and is encoded by…
A simplified model of clonal plant growth is formulated, motivated by observations of spatial structures in Posidonia oceanica meadows in the Mediterranean Sea. Two levels of approximation are considered for the scale-dependent feedback…
We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction…
In this article we investigate the semiflow properties of a class of state-dependent delay differential equations which is motivated by some models describing the dynamics of the number of adult trees in forests. We investigate the…
Modeling environmental ecosystems is essential for effective resource management, sustainable development, and understanding complex ecological processes. However, traditional data-driven methods face challenges in capturing inherently…
We study a class of the stochastic May-Leonard models, with three species dominating each other in a cyclic nonhierarchical way, according to the rock-paper-scissors game. We introduce an unevenness in the system, by considering that one of…
Localised patterns are often observed in models for dryland vegetation, both as peaks of vegetation in a desert state and as gaps within a vegetated state, known as `fairy circles'. Recent results from radial spatial dynamics show that…