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arXiv · 2405.04505

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

Blake McGrane-Corrigan·Oliver Mason·Rafael de Andrade Moral
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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 $(0,1)$. 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.

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Blake McGrane-Corrigan, Oliver Mason, Rafael de Andrade Moral. 2024-05-07. A density-dependent metapopulation model: Extinction, persistence and source-sink dynamics. https://arxiv.org/abs/2405.04505

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