Related papers: Extinction behaviour for competing continuous-stat…
Classical models for competition between two species usually predict exclusion or divergent evolution of resource exploitation. However, recent experimental data show that coexistence is possible for very similar species competing for the…
We study an almost periodic version of a metapopulation model developed by Tilman \textit{et.al} and Nee \textit{et.al} in the nineties, which generalizes the classical Levins approach by considering several species in competition affected…
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…
In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. "Adaptive dynamics" is the standard mathematical framework to describe…
Established populations often exhibit oscillations in their sizes. If a population is isolated, intrinsic stochasticity of elemental processes can ultimately bring it to extinction. Here we study extinction of oscillating populations in a…
Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short-term transition from imminent doom to evolutionary rescue. But…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with Allee effect, to account for the role of demographic stochasticity. In the mean-field deterministic limit we recover…
Community ecology has traditionally relied on the competitive exclusion principle, a piece of common wisdom in conceptual frameworks developed to describe species assemblages. Key concepts in community ecology, such as limiting similarity…
For autonomous Lotka-Volterra systems of differential equations modelling the dynamics of n competing species, new criteria are established for the existence of a single point global attractor. Under the conditions of these criteria, some…
We study the combined impact of a colored environmental noise and demographic noise on the extinction risk of a long-lived and well-mixed isolated stochastic population which exhibits the Allee effect. The environmental noise modulates the…
This work deals with two problems arising in mathematical ecology. The first problem is concerned with diploid branching particle models and its behavior when rapid stirring is added to the interaction. The particle models involve two types…
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…
We study a generalized system of ODE's modeling a finite number of biological populations in a competitive interaction. We adapt the techniques in two previous articles to prove the convergence to a unique stable equilibrium.
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
The study of interactions between multiple species in an ecosystem is an active and impactful direction of inquiry. This is true in particular for fragile systems in which even small perturbations of their functional parameters can produce…
May and Leonard (SIAM J. Appl. Math 1975) introduced a three-species Lotka-Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete…
Species populations often modify their environment as they grow. When environmental feedback operates more slowly than population growth, the system can undergo boom-bust dynamics, where the population overshoots its carrying capacity and…
This paper deals with extinction of an isolated population caused by intrinsic noise. We model the population dynamics in a "refuge" as a Markov process which involves births and deaths on discrete lattice sites and random migrations…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…