In this talk, we consider two-species competition patch models in advective heterogeneous environments, where the two species are ecologically identical except for their dispersal rates. Treating one species as a resident species and the other one as a mutant species. For the case with better resources in downstream locations, we show that there exist two critical values such that the species with slower dispersal rate wins the competition if the drift rate is smaller than one critical value, whereas the species with faster dispersal rate is selected if the drift rate is larger than the other critical value. Moreover, the dispersal rate of the resident species can be an evolutionarily stable strategy for some intermediate drift rate between the above two critical values. For the case with better resources in upstream locations, some different phenomenons may occur.