Date on Master's Thesis/Doctoral Dissertation

12-2016

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Mathematics

Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Bingtuan, Li

Committee Co-Chair (if applicable)

Bradley, Mary Elizabeth

Committee Member

Bradley, Mary Elizabeth

Committee Member

Gill, Ryan

Committee Member

Hu, Changbing

Committee Member

Remold, Susanna

Author's Keywords

reaction-diffusion model; lotka-volterra competition model; lattice differential equations; spreading speed; traveling wave; upper and lower solutions

Abstract

A reaction-diffusion model and a lattice differential equation are introduced to describe the persistence and spread of a species along a shifting habitat gradient. The species is assumed to grow everywhere in space and its growth rate is assumed to be monotone and positive along the habitat region. We show that the persistence and spreading dynamics of a species are dependent on the speed of the shifting edge of the favorable habitat, c, as well as c*(∞) and c*(−∞), which are formulated in terms of the dispersal kernel and species growth rates in both directions. When the favorable habitat edge shifts towards the right, c>0, we demonstrate that the rightward spreading speed is c*(∞) when c is relatively small and is c*(−∞) when c is relatively large, and the leftward spreading speed is c*(−∞). When the favorable habitat edge shifts towards the left, c*(∞), and the leftward spreading speed is one of |c|, c*(−∞) or c*(∞). We also show the persistence and spreading dynamics of two competing species along shifting habitats in the simplest situations. Their spreading behavior will be affected by the resource distribution and habitat shifting speed.