Some reaction diffusion models in spatial ecology

Abstract

The goal of this survey is to introduce applications of reaction diffusion equations in biology, focusing on the effect of environmental spatial heterogeneity on population dynamics, evolution, and disease spread. On one hand we develop and analyze a series of reaction diffusion models which integrate spatial ecology, evolution and disease spread, hoping to understand the underlying biological processes and mechanisms. On the other hand we propose new mathematical models, raise new mathematical questions, develop some new mathematical techniques, and hope to stimulate further research in theories of reaction diffusion equations. The topics covered include total biomass of a single population in heterogeneous habitat, effect of spatial heterogeneity on competing species, role of diffusion and advection in persistence and competition of populations, evolution of population in heterogeneous environment, persistence and competition of single or multiple phytoplankton species, transport of organisms in rivers, and spatial spread and evolution of disease in heterogeneous environment.