Persistence/extinction scenarios in an almost periodic metapopulation with competition and habitat destruction

TL;DR

This paper analyzes an almost periodic metapopulation model with multiple competing species affected by habitat destruction, revealing how colonization and extinction rates influence persistence or extinction scenarios through exponential dichotomy theory.

Contribution

It introduces an almost periodic extension of classical metapopulation models, linking species dominance to exponential dichotomy and providing a detailed classification of persistence and extinction outcomes.

Findings

Persistence/extinction scenarios characterized by exponential dichotomy.

Colonization or extinction dominance determines species survival.

Preliminary insights into behavior when colonization and extinction are balanced.

Abstract

We study an almost periodic version of a metapopulation model developed by Tilman \textit{et.al} and Nee \textit{et.al} in the nineties, which generalizes the classical Levins approach by considering several species in competition affected by habitat destruction. The novelty is to assume that the colonization and extinction rates are positive almost periodic functions whereas our main results show that the predominance of either colonization or extinction forces of a specific species is equivalent to the property of exponential dichotomy of a scalar linear differential equation. By using well known results of exponential dichotomy theory, we carry out a recursive and exhaustive description of persistence/extinction scenarios. In addition, we start a preliminary discussion describing a more elusive behavior when the colonization and extinction forces are similar in average.