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Vast landscapes extending from southern Angola, Namibia, and South Africa exhibit localised barren patches of vegetation called fairy circles. They consist of isolated or randomly distributed circular areas devoid of any vegetation. They…

Smooth cordgrass Spartina alterniflora is a grass species commonly found in tidal marshes. It is an ecosystem engineer, capable of modifying the structure of its surrounding environment through various feedbacks. The scale-dependent…

A number of mechanisms that lead to the confinement of patterns to a small part of a translationally symmetric pattern-forming system are reviewed: nonadiabatic locking of fronts, global coupling and conservation laws, dispersion, and…

Spatial structure and species interactions jointly shape the dynamics and biodiversity of ecological systems, yet most theoretical models either neglect spatial heterogeneity or sacrifice analytical tractability. Here, we provide a unified…

Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous…

Motivated by theoretical analyses of spatially localized structures with arbitrarily long periodic plateaus, we provide a framework of assumptions that simplifies their analysis and leads to a topological criterion for when localized…

We propose a general population dynamics model for two seagrass species growing and interacting in two spatial dimensions. The model includes spatial terms accounting for the clonal growth characteristics of seagrasses, and coupling between…

Comparative and evolutive ecologists are interested in the distribution of quantitative traits among related species. The classical framework for these distributions consists of a random process running along the branches of a phylogenetic…

Regular patterns of vegetation are considered widespread landscapes, although their global extent has never been estimated. Among them, spotted landscapes are of particular interest in the context of climate change. Indeed, regularly spaced…

We propose a general framework for solving inverse self-assembly problems, i.e. designing interactions between elementary units such that they assemble spontaneously into a predetermined structure. Our approach uses patchy particles as…

Within the statistical literature, a significant gap exists in methods capable of modeling asymmetric multivariate spatial effects that elucidate the relationships underlying complex spatial phenomena. For such a phenomenon, observations at…

Plants frequently contain numerous organs, organized in 3D branching systems defining the plant's architecture. Reconstructing the architecture of plants from unstructured observations is challenging because of self-occlusion and spatial…

We study the self-assembly behaviour of patchy particles with `protein-like' interactions that can be considered as a minimal model for the assembly of viral capsids and other shell-like protein complexes. We thoroughly explore the…

Resource competition is a fundamental interaction in natural communities.However little is known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyze the competition of two…

Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R.…

Many ecological and spatial processes are complex in nature and are not accurately modeled by linear models. Regression trees promise to handle the high-order interactions that are present in ecological and spatial datasets, but fail to…

We study analytically and numerically a model metabolic cycle composed of an arbitrary number of species of catalytically active particles. Each species converts a substrate into a product, the latter being used as the substrate by the next…

We propose dynamical collapse models in which the stochastic collapse terms affect only photons and/or gravitons. In principle, isolated systems comprising only massive particles could evolve unitarily indefinitely in such models. In…

Large responses of ecosystems to small changes in the conditions--regime shifts--are of great interest and importance. In spatially extended ecosystems, these shifts may be local or global. Using empirical data and mathematical modeling, we…

In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories,…