Related papers: Gause's exclusion principle revisited: artificial …
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…
Classical understanding of the outcome of the struggle for existence results in the Darwinian survival of the fittest. Here we show that the situation may be different, more complex and arguably more interesting. Specifically, we show that…
When four species compete stochastically in a cyclic way, the formation of two teams of mutually neutral partners is observed. In this paper we study through numerical simulations the extinction processes that can take place in this system…
In this paper, we study three two competing species Lotka-Volterra competition models on finite connected graphs, with Dirichlet, Neumann or no boundary conditions. We get that when time goes to infinity, either one specie extincts while…
We consider a cyclically competing species model on a ring with global mixing at finite rate, which corresponds to the well-known Lotka-Volterra equation in the limit of infinite mixing rate. Within a perturbation analysis of the model from…
A simple mathematical homogeneous model of competition is used to describe Neanderthal extinction in Europe. It considers two interacting species, Neanderthals and Early Modern Men, in the same ecological niche. Using paleontological data…
We investigate extinction dynamics in the paradigmatic model of two competing species A and B that reproduce (A-->2A, B-->2B), self-regulate by annihilation (2A-->0, 2B-->0), and compete (A+B-->A, A+B-->B). For a finite system that is in…
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…
I introduce an axiomatic representation, called ecoset, to consider interactions between species in ecological systems. For interspecific competition, the exclusion conjecture (Gause) is put in a symbolic way and used as a basic operational…
We study a generic reaction-diffusion model for single-species population dynamics that includes reproduction, death, and competition. The population is assumed to be confined in a refuge beyond which conditions are so harsh that they lead…
The dynamics leading to extinction or coexistence of competing species is of great interest in ecology and related fields. Recently a model of intra- and interspecific competition between two species was proposed by Gabel et al. [Phys. Rev.…
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 birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra…
The competitive exclusion principle in epidemiology implies that when competing strains of a pathogen provide complete protection for each other, the strain with the largest reproduction number outcompetes the other strains and drives them…
We present properties of Lotka-Volterra equations describing ecological competition among a large number of competing species. First we extend to the case of a non-homogeneous niche space stability conditions for solutions representing…
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…
It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an…
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 paper deals with a multiple species Lotka-Volterra model with infinite distributed delays and feedback controls, for which we assume a weak form of diagonal dominance of the instantaneous negative intra-specific terms over the infinite…
In this paper we investigate two free boundary problems for a Lotka-Volterra type competition model in one space dimension. The main objective is to understand the asymptotic behavior of the two competing species spreading via a free…