Population growth and persistence in a heterogeneous environment: the role of diffusion and advection

TL;DR

This paper reviews mathematical models based on reaction-diffusion-advection equations to understand how diffusion and advection influence population persistence in heterogeneous environments, highlighting critical conditions for survival.

Contribution

It introduces and analyzes simple and complex reaction-diffusion-advection models to elucidate the roles of advection and diffusion in population persistence.

Findings

Advection can either promote or hinder population survival depending on conditions.

Critical thresholds for population persistence are derived mathematically.

Models applied to phytoplankton dynamics in water columns.

Abstract

The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional reaction-diffusion-advection equations, for the growth of a population on a heterogeneous habitat. Considering a number of models of increasing complexity we investigate the often contrary roles of advection and diffusion for the persistence of the population. When it is possible we demonstrate basic mathematical techniques and give the critical conditions providing the survival of a population, in simple systems and in more complex resource-consumer models which describe the dynamics of phytoplankton in a water column.