| In this dissertation,we consider a two species Lotka-Volterra diffusion-advectioncompetition model and mainly study the role of advection on the dynamics of the system.We assume that the two species are ecologically identical except that they adopt different dispersal strategies:one disperses by random movement while the other combines random diffusion and advection upward along the resource gradient.The effects of weak and strong advection on the dynamics of this model have been studied deeply and extensively.In contrast,the role of intermediate advection and the transition of the dynamics from weak to strong advection remain largely unexplored.Therefore,Averill,Lam and Lou[1]investigated the change of the dynamics of the system as the advection increases from weak to strong.Among other results,they proposed the following conjecture:(?)assuming that the species without advection has a faster random diffusion rate than its competitor,it will always be invaded by its competitor regardless of the degree of the advection;(?)assuming that the species without advection has a slower random diffusion rate,it will exclude its competitor only when the advection is weak and lose competitive advantage when the advection rate passes some critical value.In this dissertation,we partially solved the aforementioned conjecture.In Chapter 3,by applying the principal eigenvalue theory and analyzing the linear stability properties of the semi-trivial solution of the system,we showed that Conjecture(?)holds when the domain or the distribution of resources satisfies certain conditions.In Chapter 4,we constructed a related limiting eigenvalue problem and analysed its properties.Using the principal eigenvalue theory again,we proved the following result:under certain conditions,Conjecture(?)holds when the random dispersal rate of the species without advection is sufficiently close to but lower than that of its competitor.We further showed two specific cases when such conditions do hold. |
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