Related papers: A modified chemostat exhibiting competitive exclus…
We give an new proof of the well-known competitive exclusion principle in the chemostat model with $n$ species competing for a single resource, for any set of increasing growth functions. The proof is constructed by induction on the number…
In this paper, we consider a competition model between $n$ species in a chemostat including both monotone and non-monotone response functions, distinct removal rates and variable yields. We show that only the species with the lowest…
This paper studies a two microbial species model in competition for a single resource in the chemostat including general interspecific density-dependent growth rates with distinct removal rates for each species. We give the necessary and…
We study a model of competition for resource through a chemostat-type model where species consume the common resource that is constantly supplied. We assume that the species and resources are characterized by a continuous trait. As already…
In this paper, we study the global dynamics of a chemostat model with a single nutrient and several competing species. Growth rates are not required to be proportional to food uptakes. The model was studied by Fiedler and Hsu [J. Math.…
We are interested in modeling the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions, in the specific scales of the biological framework of adaptive dynamics.…
We study the chemostat model for one species competing for one nutrient using a Lyapunov-type analysis. We design the dilution rate function so that all solutions of the chemostat converge to a prescribed periodic solution. In terms of…
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…
Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…
This article is dedicated to the study and comparison of two chemostat-like competition models in a heterogeneous environment. The first model is a probabilistic model where we build a PDMP simulating the effect of the temporal…
Explaining biodiversity in nature is a fundamental problem in ecology. An outstanding challenge is embodied in the so-called Competitive Exclusion Principle: two species competing for one limiting resource cannot coexist at constant…
The processes and mechanisms underlying the origin and maintenance of biological diversity have long been of central importance in ecology and evolution. The competitive exclusion principle states that the number of coexisting species is…
Biodiversity conservation becoming increasingly urgent. It is important to find mechanisms of competitive coexistence of species with different fitness in especially difficult circumstances - on one limiting resource, in isolated stable…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
We study a spatially homogeneous model of a market where several agents or companies compete for a wealth resource. In analogy with ecological systems the simplest case of such models shows a kind of "competitive exclusion" principle.…
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…
Competitive exclusion, a key principle of ecology, can be generalized to understand many other complex systems. Individuals under surviving pressure tend to be different from others, and correlations among them change correspondingly to the…
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…
Cyclic dominance is frequently believed to be a mechanism that maintains diversity of competing species. But this delicate balance could also be fragile if some of the members is weakened because an extinction of a species will involve the…