Streams and rivers are examples of vital ecosystems that frequently undergo various environmental and anthropogenic stresses. A core question in population ecology is whether a given population will persist under changing ecological conditions. This thesis consists of three papers and is devoted to the mathematical analysis of responses of river-dwelling species to population persistence threats. The first paper presents a stochastic approach to the 'drift paradox' problem, where the classical reaction-advection-diffusion model is replaced by a birth-death-emigration process. We explore the effects of temporally varying flow on the persistence probability and highlight the importance of the benthic stage for the persistence of stream organisms. The second paper addresses the problem of river network fragmentation through disconnecting structures such as dams. We construct a population matrix model that incorporates the spatial structure of the studied river network and compare structural connectivity to an indicator of population persistence. The third paper adapts the same basic matrix model to examine fish response to disturbances travelling downstream from upstream sites. The study of these three aspects of persistence challenges for river populations contributes to the cumulative effects assessment on river networks.