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How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and…
The competitive exclusion principle asserts that coexisting species must occupy distinct ecological niches (i.e. the number of surviving species can not exceed the number of resources). An open question is to understand if and how different…
Species interactions through cross-feeding via leakage and uptake of chemicals are important in microbial communities, and play an essential role in the coexistence of diverse species. Here, we study a simple dynamical model of a microbial…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
The entanglement of population dynamics, evolution, and adaptive radiation for species competing for resources is studied. For resource harvesting, we modify the model used in Ref. Phys. Rev. Lett. 118 048103 and introduce new resource…
We consider a Nicholson's equation with multiple pairs of time-varying delays and nonlinear terms given by mixed monotone functions. Sufficient conditions for the permanence, local stability and global attractivity of its positive…
In this paper we study the well-known Khasminskii-Type Theorem, i.e. the existence and uniqueness of solutions of stochastic evolution delay equations, under local Lipschitz condition, but without linear growth condition. We then establish…
We investigate a model of interacting clusters which compete for growth. For a finite assembly of coupled clusters, the largest one always wins, so that all but this one die out in a finite time. This scenario of `survival of the biggest'…
We consider a mutation-selection model of a population structured by the spatial variables and a trait variable which is the diffusion rate. Competition for resource is local in spatial variables, but nonlocal in the trait variable. We…
We study the role of the noise in the dynamics of two competing species. We consider generalized Lotka-Volterra equations in the presence of a multiplicative noise, which models the interaction between the species and the environment. The…
A chemostat enables long-term, continuous, exponential-phase growth in an environment limited as prescribed by the researcher. It is thus a potent tool for laboratory evolution - selecting for strains with desired phenotypes. However,…
The Crump-Young model consists of two fully coupled stochastic processes modeling the substrate and microorganisms dynamics in a chemostat. Substrate evolves following an ordinary differential equation whose coefficients depend of…
In this paper, we investigate a two-species Lotka-Volterra competition patch model in a Y-shaped river network, where the two species are assumed to be identical except for their random and directed movements. We show that competition…
The storage effect is a general explanation for coexistence in a variable environment. The generality of the storage effect is both a strength - it can be quantified in many systems - and a challenge - there is not a clear relationship…
We investigate the competition dynamics of two microbial or viral strains that live in an environment that switches periodically between two states. One of the strains is adapted to the long-term environment, but pays a short-term cost,…
A fundamental problem in evolutionary ecology research is to explain how different species coexist in natural ecosystems. This question is directly related with species trophic competition. However, competition theory, based on the…
We present a Lyapunov type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature most results concerning existence and uniqueness are obtained under…
We study the stability of $\mathcal{M}_0$, an invariant subset of a Markov process $(X_t)_{t\geq 0}$ on a metric space $\mathcal{M}$. By building the theory of average Lyapunov functions, we formulate general criteria based on the signs of…
In this paper, we investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in \textit{vivo}. The model has two distributed time delays describing time needed for infection of cell…
In this paper, we investigate a class of non-monotone reaction-diffusion equations with distributed delay and a homogenous boundary Neumann condition, which have a positive steady state. The main concern is the global attractivity of the…