由于个体向下游漂移引起的种群数量的不断减少，从而引发的水生种群如何在河流中持续存在的问题被称为“漂移悖论”。我们研究了具有和不具有底栖阶段的种群的生长，并考虑空间非齐次的增长函数。当物种遵循logistic类型增长时，已有许多经典的结果。而具有Allee效应增长的物种则较少被注意。在本文中，个体在环境中的随机运动由被动扩散刻画，河流中的定向运动则由对流刻画。本文从严格的理论研究和数值模拟两个方面来说明具有Allee效应生长的物种的种群动态。

我们引入了一种底栖-漂移模型，该模型将漂流区和栖息区的交互行为与种群动态联系起来。在该模型中，栖息地被分成两个有交互行为的区室，漂移区和底栖区。种群也被分为居住在底栖区的个体和分散在漂移区中的个体。我们明确讨论了流速，横截面积，两个区室间的交互效率和河流异质性对种群持久性和灭绝的影响。

The question how aquatic populations persist in rivers when individuals are constantly lost due to downstream drift has been termed the ``drift paradox." Reaction-diffusion-advection models have been used to describe the spatial-temporal dynamics of stream population and they provide some qualitative explanations to the paradox. Here random undirected movement of individuals in the environment is described by passive diffusion, and an advective term is used to describe the directed movement in a river caused by the flow. In this work, the effect of spatially varying Allee effect growth rate on the dynamics of reaction-diffusion-advection models for the stream population is studied.

The dynamics of a reaction-diffusion-advection benthic-drift population model that links changes in the flow regime and habitat availability with population dynamics is studied. In the model, the stream is divided into drift zone and benthic zone, and the population is divided into two interacting compartments, individuals residing in the benthic zone and individuals dispersing in the drift zone. The benthic population growth is assumed to be of strong Allee effect type. The influence of flow speed and individual transfer rates between zones on the population persistence and extinction is considered, and the criteria of population persistence or extinction are formulated and proved.

All results are proved rigorously using the theory of partial differential equation, dynamical systems. Various mathematical tools such as bifurcation methods, variational methods, and monotone methods are applied to show the existence of multiple steady state solutions of models.