Discreteness inducing coexistence

https://doi.org/10.1016/j.physa.2013.07.058Get rights and content
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Highlights

  • We proposed a simple model that seems to violate the competitive exclusion principle.

  • Demographic noise favors less dense populations at the expanse of the denser ones.

  • The discontinuous character of interactions can induce coexistence.

  • The slower species suffers deleterious effects of noise in a homogeneous medium.

Abstract

Consider two species that diffuse through space. Consider further that they differ only in initial densities and, possibly, in diffusion constants. Otherwise they are identical. What happens if they compete with each other in the same environment? What is the influence of the discrete nature of the interactions on the final destination? And what are the influence of diffusion and additive fluctuations corresponding to random migration and immigration of individuals? This paper aims to answer these questions for a particular competition model that incorporates intra and interspecific competition between the species. Based on mean field theory, the model has a stationary state dependent on the initial density conditions. We investigate how this initial density dependence is affected by the presence of demographic multiplicative noise and additive noise in space and time. There are three main conclusions: (1) Additive noise favors denser populations at the expense of the less dense, ratifying the competitive exclusion principle. (2) Demographic noise, on the other hand, favors less dense populations at the expense of the denser ones, inducing equal densities at the quasi-stationary state, violating the aforementioned principle. (3) The slower species always suffers the more deleterious effects of statistical fluctuations in a homogeneous medium.

Keywords

Additive noise and demographic stochasticity
Diffusion
Competition model
Monte Carlo simulation

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