Native salmonid fish have been displaced worldwide by nonnatives through hybridization, competition, and predation, but the dynamics of these factors are poorly understood. We apply stochastic Lotka-Volterra models to the displacement of cutthroat trout by rainbow/hybrid trout in the Snake River, Idaho, USA. Cutthroat trout are susceptible to hybridization in the river but are reproductively isolated in tributaries via removal of migratory rainbow/hybrid spawners at weirs. Based on information-theoretic analysis, population data provide evidence that hybridization was the primary mechanism for cutthroat trout displacement in the first 17 years of the invasion. However, under some parameter values, the data provide evidence for a model in which interaction occurs among fish from both river and tributary subpopulations. This situation is likely to occur when tributary-spawned cutthroat trout out-migrate to the river as fry. The resulting competition with rainbow/hybrid trout can result in the extinction of cutthroat trout even when reproductive segregation is maintained.