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, phytoplanktongrowth, and spatial spread of epidemic disease. Open problems and conjectures are presented.P arts of this survey are adopted from the materials in [89,108,109], and some very recent progress are also included.
Highlights
Recent years have witnessed unprecedented progress of experimental technologies in the life sciences
We consider some issues in spatial ecology via reaction-diffusion models, focusing upon the effect of movement of species on population dynamics in spatially heterogeneous environments
One basic question in spatial ecology is: How does the spatial heterogeneity of environment affect the invasion of exotic species and the competition outcome of native and exotic species? The term heterogeneity refers to the non-uniform distribution of various environmental conditions
Summary
Recent years have witnessed unprecedented progress of experimental technologies in the life sciences. As an important mathematical area, nonlinear partial differential equations have been one of the most active research fields in the 21st century. It has found new opportunities in mathematical biology in recent years. The importance of space is hardly a question, and a practical question is to quantify the effect of space in different biological scenarios In this survey, we consider some issues in spatial ecology via reaction-diffusion models, focusing upon the effect of movement of species on population dynamics in spatially heterogeneous environments.
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