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

TL;DR

This paper introduces a nonlinear discrete-time population model that captures dispersal, extinction, and persistence dynamics across heterogeneous landscapes, revealing complex behaviors like chaos and periodicity.

Contribution

It develops a novel density-dependent metapopulation model with nonlinear coupling, providing new conditions for stability, persistence, and extinction, and explores complex dynamics numerically.

Findings

Conditions for extinction and persistence are derived.

Model exhibits periodic and chaotic behaviors.

Numerical simulations illustrate 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 $(0,1)$. 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.