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On Predation–Commensalism Processes as Models of Bi-stability and Constructive Role of Systemic Extinctions

Authors: Sanchez-Palencia, E.; Françoise, J.-P.;

On Predation–Commensalism Processes as Models of Bi-stability and Constructive Role of Systemic Extinctions

Abstract

We propose a mathematical model for a class of predator-prey systems more complex than the usual one, involving a commensalism effect consisting in an influence of the predator on the sustainability of the prey. This effect induces interesting new features, including bi-stability (two attractors with disjoint attraction basins). The question of the possibility of reaching a certain attractor starting from initial conditions with a small population of predators, which presents an interest from the vewpoint of the onset of the predator in evolution, is addressed. We propose two possibilities: the classical one involving adapted conditions in the far past and a new (up to our knowledge) one using biodiversity, specifically the presence of another predator which operates as a starter, being displaced in the sequel.

Keywords

Bi-stability, Excitability, Food Chain, “Diversity–stability debate”, Population Dynamics, [SDV.EE.IEO] Life Sciences [q-bio]/Ecology, environment/Symbiosis, [MATH] Mathematics [math], Biodiversity, Models, Theoretical, Models, Biological, Predator–prey systems, Predatory Behavior, Animals, Symbiosis

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    popularity
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    influence
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
Green
bronze
Related to Research communities
Italian National Biodiversity Future Center