A density-dependent metapopulation model: Extinction, persistence and source-sink dynamics
Abstract
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 . 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.
Cite
@article{arxiv.2405.04505,
title = {A density-dependent metapopulation model: Extinction, persistence and source-sink dynamics},
author = {Blake McGrane-Corrigan and Oliver Mason and Rafael de Andrade Moral},
journal= {arXiv preprint arXiv:2405.04505},
year = {2024}
}