Related papers: Patterns robust to Disorder in spatially-interacti…
The eigenvalue spectrum of a random matrix often only depends on the first and second moments of its elements, but not on the specific distribution from which they are drawn. The validity of this universality principle is often assumed…
Stochastic, spatially extended models for predator-prey interaction display spatio-temporal structures that are not captured by the Lotka-Volterra mean-field rate equations. These spreading activity fronts reflect persistent correlations…
We study communities emerging from generalised random Lotka--Volterra dynamics with a large number of species with interactions determined by the degree of niche overlap. Each species is endowed with a number of traits, and competition…
Random matrix theory successfully connects the structure of interactions of large ecological communities to their ability to respond to perturbations. One of the most debated aspects of this approach is the missing role of population…
A diffusive Lotka-Volterra competition model is considered for the combined effect of spatial dispersal and spatial variations of resource on the population persistence and exclusion. First it is shown that in a two-species system in which…
We compute the typical number of equilibria of the Generalized Lotka-Volterra equations describing species-rich ecosystems with random, non-reciprocal interactions using the replicated Kac-Rice method. We characterize the…
The composition of ecological communities varies not only between different locations but also in time. Understanding the fundamental processes that drive species towards rarity or abundance is crucial to assessing ecosystem resilience and…
We use generating functionals to derive a dynamic mean-field description for generalised Lotka-Volterra systems with higher-order quenched random interactions. We use the resulting single effective species process to determine the stability…
Understanding the conditions of feasibility and stability in ecological systems is a major challenge in theoretical ecology. The seminal work of May in 1972 and recent developments based on the theory of random matrices have shown the…
Ecological communities are composed of species interactions that respond to environmental fluctuations. Despite increasing evidence of temporal variation in these interactions, most theoretical frameworks remain rooted in static…
We analyze purely competitive many-species Lotka-Volterra systems with random interaction matrices, focusing the attention on statistical properties of their asymptotic states. Generic features of the evolution are outlined from a…
Multispecies ecosystems modelled by generalized Lotka-Volterra equations exhibit stationary population abundances, where large number of species often coexist. Understanding the precise conditions under which this is at all feasible and…
We introduce an individual-based model of a complex ecological community with random interactions. The model contains a large number of species, each with a finite population of individuals, subject to discrete reproduction and death…
We investigate the global dynamics of a special case of the classical Lotka-Volterra competition-diffusion system in spatially heterogeneous environment. This model indicates that the evolution of the density of the predator is independent…
In this work we study the stability of the equilibria reached by ecosystems formed by a large number of species. The model we focus on are Lotka-Volterra equations with symmetric random interactions. Our theoretical analysis, confirmed by…
The state space is a fundamental concept for describing the trajectory of a dynamic system. Depending on its form, it can highlight certain changes over time while ignoring others. This is particularly the case for the spaces associated…
Disordered systems theory provides powerful tools to analyze the generic behaviors of highdimensional systems, such as species-rich ecological communities or neural networks. By assuming randomness in their interactions, universality…
Species coexistence is a complex, multifaceted problem. At an equilibrium, coexistence requires two conditions: stability under small perturbations; and feasibility, meaning all species abundances are positive. Which of these two conditions…
The assembly and persistence of ecological communities can be understood as the result of the interaction and migration of species. Here we study a single community subject to migration from a species pool in which inter-specific…
We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a…