Management of riparian plant invasions across the landscape requires understanding the combined influence of climate, hydrology, geologic constraints and patterns of introduction. We measured abundance of nine riparian woody taxa at 456 stream gages across the western USA. We constructed conditional inference recursive binary partitioning models to discriminate the influence of eleven environmental variables on plant occurrence and abundance, focusing on the two most abundant non-native taxa, Tamarix spp. and Elaeagnus angustifolia, and their native competitor Populus deltoides. River reaches in this study were distributed along a composite gradient from cooler, wetter higher-elevation reaches with higher stream power and earlier snowmelt flood peaks to warmer, drier lower-elevation reaches with lower power and later peaks. Plant distributions were strongly related to climate, hydrologic and geomorphic factors, and introduction history. The strongest associations were with temperature and then precipitation. Among hydrologic and geomorphic variables, stream power, peak flow timing and 10-yr flood magnitude had stronger associations than did peak flow predictability, low-flow magnitude, mean annual flow and channel confinement. Nearby intentional planting of Elaeagnus was the best predictor of its occurrence, but planting of Tamarix was rare. Higher temperatures were associated with greater abundance of Tamarix relative to P. deltoides, and greater abundance of P. deltoides relative to Elaeagnus. Populus deltoides abundance was more strongly related to peak flow timing than was that of Elaeagnus or Tamarix. Higher stream power and larger 10-yr floods were associated with greater abundance of P. deltoides and Tamarix relative to Elaeagnus. Therefore, increases in temperature could increase abundance of Tamarix and decrease that of Elaeagnus relative to P. deltoides, changes in peak flow timing caused by climate change or dam operations could increase abundance of both invasive taxa, and dam-induced reductions in flood peaks could increase abundance of Elaeagnus relative to Tamarix and P. deltoides.