Invasions in heterogeneous habitats in the presence of advection

TL;DR

This study analyzes how advection influences biological invasions in heterogeneous habitats with periodic favorable and unfavorable patches, revealing that advection can both hinder and facilitate invasion depending on its strength and the population dynamics.

Contribution

It provides a combined analytical and numerical investigation of invasion conditions and speeds in heterogeneous habitats with advection, including effects of Allee dynamics and patch size.

Findings

Advection generally increases invasion speed downstream.

Advection reduces overall population size of invaders.

Strong advection can enable invasions in cases with Allee effects.

Abstract

We investigate invasions from a biological reservoir to an initially empty, heterogeneous habitat in the presence of advection. The habitat consists of a periodic alternation of favorable and unfavorable patches. In the latter the population dies at fixed rate. In the former it grows either with the logistic or with an Allee effect type dynamics, where the population has to overcome a threshold to grow. We study the conditions for successful invasions and the speed of the invasion process, which is numerically and analytically investigated in several limits. Generically advection enhances the downstream invasion speed but decreases the population size of the invading species, and can even inhibit the invasion process. Remarkably, however, the rate of population increase, which quantifies the invasion efficiency, is maximized by an optimal advection velocity. In models with Allee effect, differently from the logistic case, above a critical unfavorable patch size the population localizes in a favorable patch, being unable to invade the habitat. However, we show that advection, when intense enough, may activate the invasion process.