A framework for studying transients in marine metapopulations

TL;DR

This paper develops a comprehensive framework for analyzing transient dynamics in marine metapopulations, emphasizing the biological relevance of norms and incorporating stage structure to better understand population responses.

Contribution

It introduces a unifying approach for studying transient behaviors in marine metapopulations, including new metrics and methods for stage-structured systems.

Findings

The $ ext{l}_1$ norm provides a biologically meaningful way to measure transient dynamics.

Reactivity and attenuation are linked to habitat source-sink distributions.

Stage structure significantly influences transient response measurements.

Abstract

Transient dynamics can often differ drastically from the asymptotic dynamics of systems. In this paper we provide a unifying framework for analysing transient dynamics in marine metapopulations, from the choice of norms to the addition of stage structure. We use the $\ell_1$ norm, because of its biological interpretation, to extend the transient metrics of reactivity and attenuation to marine metapopulations, and use examples to compare these metrics under the more commonly used $\ell_2$ norm. We then connect the reactivity and attenuation of marine metapopulations to the source-sink distribution of habitat patches and demonstrate how to meaningfully measure reactivity when metapopulations are stage-structured.