Evolution of dispersal in advective patchy environments

TL;DR

This paper investigates how two competing species disperse and persist in a patchy environment with directional flow, analyzing conditions for invasion and extinction based on dispersal and advection rates.

Contribution

It introduces a mathematical framework linking dispersal and advection rates to species persistence and invasion potential in flow-affected habitats.

Findings

Derived eigenvalue conditions for species persistence and extinction.

Identified thresholds for invasion success based on dispersal and advection.

Provided insights into how flow influences species competition outcomes.

Abstract

We study a two-species competition model in a patchy advective environment, where the species are subject to both directional drift and undirectional random dispersal between patches and there are losses of individuals in the downstream end (e.g., due to the flow into a lake or ocean). The two competing species are assumed to have the same growth rates but different advection and random dispersal rates. We focus our studies on the properties of an associated eigenvalue problem which characterizes the extinction/persistence dynamics of the underlying patch population model. We also derive conditions on the advection and random dispersal rates under which a mutating species can or cannot invade the resident species.