Source–sink models are a promising empirical tool for the sustainable management of animal populations across landscapes. Recent work has demonstrated a theoretical link between the demographic processes addressed in both source–sink and metapopulation models and the formation of species’ range limits. In the face of large-scale anthropogenic disturbances (e.g., increasing temperature and sea level with global climate change), conceptual range-limit models that are functionally linked to these demographic mechanisms may help predict range shifts and provide insights for the management of vulnerable populations. However, the value of such models is limited by their ability to offer precise and testable predications about how demographic parameters might respond to environmental change and thus influence population dynamics. Here, we illustrate the gulf between the promise of conceptual demographic models and the difficulty of their empirical application by developing a model of range limits for a narrowly distributed tidal-marsh songbird, the coastal plain swamp sparrow (Melospiza georgiana nigrescens, CPSS). We first modeled a gradient in CPSS fecundity that depends on environmental factors varying with latitude. To predict the species’ range limits we embed this fecundity gradient in Pulliam’s (1988) source–sink model. Our resulting model predicts current CPSS range limits reasonably well. However, its predictions are also subject to substantial uncertainty. Our model framework generally conforms to the conceptual unification of source–sink theory, Hutchinson’s (1957) fundamental niche, and species’ range limits recently expounded by Pulliam (2000).