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

On Predation–Commensalism Processes as Models of Bi-stability and Constructive Role of Systemic... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Biotheoretica Springer Journals

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

Acta Biotheoretica , Volume 69 (4) – Dec 1, 2021

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Publisher
Springer Journals
Copyright
Copyright © Springer Nature B.V. 2021
ISSN
0001-5342
eISSN
1572-8358
DOI
10.1007/s10441-021-09413-3
Publisher site
See Article on Publisher Site

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.

Journal

Acta BiotheoreticaSpringer Journals

Published: Dec 1, 2021

Keywords: Predator–prey systems; Bi-stability; Excitability; “Diversity–stability debate”; Primary 92D25 Population dynamics; 92D40 Ecology; 37G15 Bifurcations of limit cycles and periodic orbits

References