SELECTED TOPICS ON REACTION-DIFFUSION-ADVECTION MODELS FROM SPATIAL ECOLOGY

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. Parts of this survey are adopted from the materials in [89, 108, 109], and some very recent progress are also included.