Qualitative analysis for a Lotka-Volterra competition system in advective homogeneous environment

Abstract

We study a two-species Lotka-Volterracompetition model in an advective homogeneous environment.It is assumed that two species have the same population dynamicsand diffusion rates but different advection rates. We show thatif one competitor disperses by random diffusion only and the otherassumes both random and directed movements, then the one withoutadvection prevails. If two competitors are drifting along the samedirection but with different advection rates, then the one withthe smaller advection rate wins. Finally we prove thatif the two competitors are drifting along the oppositedirection, then two species will coexist.These results imply that the movement without advectionin homogeneous environment is evolutionarily stable, asadvection tends to move more individuals to theboundary of the habitat and thus cause the distribution of speciesmismatch with the resources which are evenly distributed in space.