To fully understand population dynamics in river ecosystems, it is necessary to recognize that rivers are subject to major seasonal variations in environmental factors that govern population growth and dispersal. In this talk, I will introduce some recent work about the studies of population spread and persistence in varying river environments by using integro-difference equations. We consider integro-difference models for population growth and dispersal in the presence of advective flow with both periodic (alternating) and random kernel parameters. For the alternating kernel model, we obtain the principal eigenvalue of the linearization operator to determine population persistence and derive a boundary value problem to calculate it.  For the random model, we establish two persistence metrics: a generalized spectral radius and the asymptotic growth rate, which are mathematically equivalent but can be understood differently, to determine population persistence or extinction.