Persistence and extinction in Lotka-Volterra reaction-diffusion equations

Abstract

This paper analyzes the persistence and extinction behavior of Lotka-Volterra reaction-diffusion equations for a patch-type environment. The system of equations is the discretized version of the familiar random-diffusion model u t = f( u)+ Du xx . It is shown that diffusion can alter the persistence or extinction behavior of the Lotka-Volterra system. A competitive or predator-prey system can become extinct, whereas a mutualistic system can persist.