A density-dependent metapopulation model: Extinction, persistence and source-sink dynamics

Fuente: arXiv
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Autori principali: McGrane-Corrigan, Blake, Mason, Oliver, Moral, Rafael de Andrade
Natura: Preprint
Pubblicazione: 2024
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author McGrane-Corrigan, Blake
Mason, Oliver
Moral, Rafael de Andrade
author_facet McGrane-Corrigan, Blake
Mason, Oliver
Moral, Rafael de Andrade
contents We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded Kolmogorov maps and coupling terms are defined by nonlinear functions taking values in $(0,1)$. These couplings describe the proportions of individuals dispersing between regions. We first give a brief survey of similar discrete-time dispersal models. We then derive sufficient conditions for the stability/instability of the extinction equilibrium, for the existence of a positive fixed point and for ensuring uniform strong persistence. Finally we numerically explore a planar version of our model in a source-sink context, to show some of the qualitative behaviour that the model we consider can capture: for example, periodic behaviour and dynamics reminiscent of chaos.
format Preprint
id arxiv_https___arxiv_org_abs_2405_04505
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A density-dependent metapopulation model: Extinction, persistence and source-sink dynamics
McGrane-Corrigan, Blake
Mason, Oliver
Moral, Rafael de Andrade
Dynamical Systems
37N25 (Primary) 39A30, 92D25 (Secondary)
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded Kolmogorov maps and coupling terms are defined by nonlinear functions taking values in $(0,1)$. These couplings describe the proportions of individuals dispersing between regions. We first give a brief survey of similar discrete-time dispersal models. We then derive sufficient conditions for the stability/instability of the extinction equilibrium, for the existence of a positive fixed point and for ensuring uniform strong persistence. Finally we numerically explore a planar version of our model in a source-sink context, to show some of the qualitative behaviour that the model we consider can capture: for example, periodic behaviour and dynamics reminiscent of chaos.
title A density-dependent metapopulation model: Extinction, persistence and source-sink dynamics
topic Dynamical Systems
37N25 (Primary) 39A30, 92D25 (Secondary)
url https://arxiv.org/abs/2405.04505