Selected topics on reaction-diffusion-advection models from spatial ecology

TL;DR

This paper reviews reaction-diffusion-advection models in spatial ecology, exploring how movement and heterogeneity influence population dynamics, competition, and disease spread, and discusses open problems in the field.

Contribution

It provides a comprehensive overview of recent developments and open problems in reaction-diffusion-advection models applied to spatial ecology.

Findings

Reaction-diffusion-advection models elucidate population persistence and competition.

Spatial heterogeneity significantly impacts organism movement and evolution.

Open problems highlight future research directions in spatial ecological modeling.

Abstract

We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction-diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially heterogeneous environments. Topics include Lokta-Volterra competition models, river models, evolution of biased movement, phytoplankton growth, and spatial spread of epidemic disease. Open problems and conjectures are presented.