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From tumour invasion to cell sorting and animal territoriality, many biological systems rely on nonlocal interactions that drive complex spatial organisation. Partial differential equations (PDEs) with nonlocal advection are increasingly…
Self-cycling fermentation is an automated process used for culturing microorganisms. We consider a model of $n$ distinct species competing for a single non-reproducing nutrient in a self-cycling fermentor in which the nutrient level is used…
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…
In this paper we consider the 2-component reaction-diffusion model that was recently obtained by a systematic reduction of the 3-component Gilad et al. model for dryland ecosystem dynamics. The nonlinear structure of this model is more…
Systems composed of distinct complex networks are present in many real-world environments, from society to ecological systems. In the present paper, we propose a network model obtained as a consequence of interactions between two species…
The architecture of bipartite networks linking two classes of constituents is affected by the interactions within each class. For the bipartite networks representing the mutualistic relationship between pollinating animals and plants, it…
This thesis focuses on the applications of mathematical tools and concepts brought from nonequilibrium statistical physics to the modeling of ecological problems. The first part provides a short introduction where the theoretical concepts…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
We describe pattern formation in ecological systems using a version of the classical Lotka-Volterra model characterized by a spatial scale which controls the predator-prey interaction range. Analytical and simulational results show that…
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 study the statistics of ecosystems with a variable number of co-evolving species. The species interact in two ways: by prey-predator relationships and by direct competition with similar kinds. The interaction coefficients change slowly…
Evolutionary and ecosystem dynamics are often treated as different processes --operating at separate timescales-- even if evidence reveals that rapid evolutionary changes can feed back into ecological interactions. A recent long-term field…
From critical infrastructure, to physiology and the human brain, complex systems rarely occur in isolation. Instead, the functioning of nodes in one system often promotes or suppresses the functioning of nodes in another. Despite advances…
Living organisms produce metabolites of many types via their metabolisms. Especially, flavonoids, a kind of secondary metabolites, of plant species are interesting examples. Since plant species are believed to have specific flavonoids with…
Environmental variation can play an important role in ecological competition by influencing the relative advantage between competing species. Here, we consider such effects by extending a classical, competitive Moran model to incorporate an…
Motivated by a potential application in economics, we investigate a simple dynamical scheme to produce planted solutions in optimization problems with continuous variables. We consider the perceptron model as a prototypical model. Starting…
Previous work indicates that tropical forest can exist as an alternative stable state to savanna. Therefore, perturbation by climate change or human impact may lead to crossing of a tipping point beyond which there is rapid forest dieback…
The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…
Coexistence of individuals with different species or phenotypes is often found in nature in spite of competition between them. Stable coexistence of multiple types of individuals have implications for maintenance of ecological biodiversity…
We consider a population organised hierarchically with respect to size in such a way that the growth rate of each individual depends only on the presence of larger individuals. As a concrete example one might think of a forest, in which the…